2001 N.3 VOL.4 CASJ

8/17/2019 2001 N.3 VOL.4 CASJ

http://slidepdf.com/reader/full/2001-n3-vol4-casj 1/76

A

Retrospective

on

Air

and

Wood

Modes

Catgut

Acoustical

Society

To

increase

and

diffuse

the

knowledge

of

musical

acoustics

and

to

promote

construction

of

fine

stringed

instruments

Vol.

4,

No. 3

(Series II)

May

2001

8/17/2019 2001 N.3 VOL.4 CASJ


My

first

action as new

CAS

J ournal

Editor

was

to read

through

37

years

ofCAS

newsletters

and

journals,begin-

ning

with

Newsletter

No.

1,

published

in

May

1964. It

occurred

to

me

that

the

most

striking thing

about

the

early

newsletters,

in

contrasttomodern scientific

journals,

is

thatthe

pages

are

infused

with

congeniality,

enthusiasm,

and

(in

today's lingo) "synergy."

The

early

CAS

newsletters are

just

as

much

about

people

asabout

stringed

instruments

or

acoustics. This

is

appropriate

because

people develop ideas,

conduct

experiments,

formulate

results,

and

perhaps

most

importantly, play

and

enjoy

music.

I

hope

the

CAS

J ournal

will

continue

to

play

a

key

role in

fostering

this con-

genial

spirit

among

our

members.

One

of

the

most

important

of

the

early

acoustical

researchers

inthe

CAS

was

J ohn

Schelleng.

This

retrospective

issueon airandwood

modes focuses

on

two articles

by

Mr.

Schelleng,

along

with

eleven

otherbenchmark

papers.

We

thank

Carleen Hutchins

for

writing

a short

biography

of

J ohn

Schelleng, selecting

the

articles,

and

providing

anintro-

ductionto the

retrospective.

A

collection of

articles such as this has

many

advantages

for readers.

Firstly,

thework

of

selecting

and

organizing

articles

revolving

around

thecentral

theme has been

done

by

a

highly

respected

authority

on

the

subject.

Secondly,

these

articles allow readers

to follow the

development

of

ideas

over a

period

of

many years.

Finally,

thecollection

presents

a

range

of

perspectives,

from theoretical

to

highly

practical.

We

thank

Paul

Ostergaard

and

J ay

VandeKopple

for

scanning

and

digitallyprocessing

these articles.

In addition

to

our

retrospective,

we

also

lookforward in time

in

this

issue.

GeorgeBissinger

gives

an

update

on

the

VIOCADEAS

project

and

Ephraim

Segerman

presents

information

aboutwood structure

andfunction.

We

also

include

bookreviews on

varnish andviolin

making,

a

summary

of

activities

of the

NewViolin

Family

Association,

a

description

of

workshops

and

titles

of

preliminary

abstracts

for

talks

planned

for

ISM

A

2001,

and

other

features.

Thank

you

for

subscribing,

and,

as

always,

we are

open

to

your

suggestions

and

comments.

J effrey

S. Loen

Additional

copies

of

this

Special

Issue can

be

ordered

from theCAS

office at a costof

$50

plus

postage.

The CAS

Journal

is

published

twice a year

by

the

Catgut

Acoustical Society

Inc.,

a

non-profit

organization

which

aims to

increase

and diffuse

knowledge

of

musical

acoustics

and to

promote

the

construction

of

fine

stringed

instruments.

The annualfee for

membership

in the

Catgut

Acoustical

Society is:

Individuals US

$50

Students US

$25

Institution

tudents US

$25

Institutions

US

$75

An

additional

postage&

handling

charge

of

US

$10

applies

to

memberships

outside the

USA.

For

membership,

back-issues

and

reprints

contact

the

CAS

Office,

55

Park

Street,

Montclair,

New

J ersey

07042,

USA.

Tel:

973.744.0371 Fax:

973.744.0375

Website:

www.marymt.edu/ cas

E-mail:

[email protected]

8/17/2019 2001 N.3 VOL.4 CASJ


C AS J O U R N A

May

2001

The

Catgut

Acoustical

Society

is known for

fostering

pioneer

research

in

musical

acoustics

and the

application

of

these

principles

tothe

making

of

fine

stringed

instruments. To

fulfill

its

mission,

the

Society

supports

publications,

meetings

forresearchers and

makers,

musical

compositions,

lectures, and concerts.

effrey

S.

Loen

casj

[email protected]

Editors

Gregg

Alf

[email protected]

Virginia

Benade

[email protected]

Evan

Davis

[email protected]

Bob Schumacher

[email protected]

Editors

Charles

Besnainou

George Bissinger

Xavier

Boutillon

J oseph

Curtin

Knut

Guettler

Martin Schleske

J im

Woodhouse

Manager

Deana

Campion

catgutas@msn.

com

Advisory

DanielW. Haines

Carleen

M.

Hutchins

A.

Thomas

King

J ohn

T.

Randerson

Oliver

E.

Rodgers

The

Violin

Octet

5

Some

Aspects

of

Wood Structure

J

A

Tribute

to

■*■

W

J ohn

C.

Schelleng

by

Carleen

Hutchins

1

y

A

Retrospective

on

A^

Air

and

Wood

Modes

Introduction

by

Carleen Hutchins

AS

J ournal

(ISSN 0882-2212)

is

published semi-annuallyby

the

Catgut

Acoustical

Society,

Inc.,

55

Park

Street,

New

J ersey

07042.

Neitherthe

Society

nor

the

J ournal's

editorial

staff is

responsible

for

facts

and

expressed

in

articles

or

other

materials

contained

in

the

J ournal.

Copyright

2001

Vol.

4,

No.

3

(Series

II)

3

From the

Contributing

Editors

=

V I O C A D E A S

—

Revisited

by

George Bissinger

and

Function

by

Ephraim

Segerman

Page

71

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

A,

No.

3

(Series

II),

May

2001

George Bissinger

is

Professorof

Physics

at

East

Carolina

University

and

Director of the Acoustics

Laboratory.

His

princ

research

efforts

are

concentrating

on

normal

mode

frequencies, dampings,

shapes

and

densities of

assembled

violins,

and

inv

tigating cavity

modes and their interaction

with

the

corpus.

Mary

Lee

Esty

obtained

a

PhD in Health

Psychology

from Union Institute

in

1995. She

hasconducted

research in

the

fields

biofeedback and

neurotherapy

and

in

her

private practice

specializes

in

treating

traumaticbrain

injuries,

ADD,

and chronic

life-threatening

medical

problems

using

methods such

as

biofeedback,

hypnosis,

andvisualization.

Carolyn

W.Field is a

graduate

ofSwarthmore

College

(BA, 1948) and

the

University

ofHouston (MA, 1973). She worked

studentand then

colleague

ofCarleen

Hutchins

between 1977

and

1989.

Since 1989

she

has made

stringed

instruments in

her

s

in Oak

Ridge,

and

she

is

currently

in

the

process of

completing

instrument

number

36.

Carleen

M.

Hutchins

is one

of

the

founders of

theCatgut

Acoustical

Society

(1963)

and founderof

the

New

Violin

Family

As

ciation

(1999). She

has

made

more

than

350

violins, violas,cellos,

and

basses

and has infused

the artof

stringed

instrumentm

ing

with relevant

acoustical

science

through

extensive

testing

of

these and other

instruments.

For

this

lifetime achievement

was

honored

in 1997

with

the

Honorary

Fellowship

ofthe

Acoustical

Society

of

America,

its

highest

honor

(first

awarded

Thomas

A. Edison).

Hutchins

is

well

known

for

the

developmentof

two

test

methods,

Free

Plate

Tuning

ofviolins

before

ass

bly,

andMode

Tuning

of

assembled

instruments,

and is

the

originator

of

the Violin

Octet,

an

acoustically

matched consortwh

projects

the

clarity

ofbalanced

violin-type

sound

into

all

octaves of

written music

(a

concept

thathad been

unsuccessfully

p

sued

since

the 160Q's). A

graduate

of

Cornell

University

(BA,

Biology)

and

New

York

University

(MA,

Education),

she

ho

honorary

Doctorates

from Concordia

University,

Hamilton

College,

St. Andrews

College,

and Stevens

Institute.

Erik V.

J ansson

is Associate

Professor

ofMusical

Acoustics at

the

Royal

Institute of

Technology

(KTH),

Stockholm,

Swed

He

spent

a

year

as

research assistant

at

CaseWesternReserve

University,

where

he

workedwithArthur

Benade,

and

after

retu

ing

to

Swedenhefinished his PhD

atKTH. In

cooperation

with

N.E.

Molin,

J ansson

has recorded

vibration

modes of the

v

lin

body

and

developed

practical

material

tests

with

wooden

blanks. In

cooperation

with

BenedyktNiewczyk,

Posnan

Pola

J ansson

has

investigated

properties

of

experimental

violins

and

assembled violins

also

of

soloist

quality.

A

specially

develop

method

was

used torecord

bridgemobility.Majorpapers

can

befound in

thebooks

Benchmark

Papers

(1975,1976

and

1977)

a

Research

Papers

in

Violin

Acoustics

(1993).

J ohn

Schelleng

was an

electrical

engineer

with

Bell

Telephone

Laboratories,

retiring

in

1967

as

Director ofRadio

Resear

He

was

influential

in

developing

the

theoretical

aspects

ofviolin

research

of

Dr.

F.

A. Saunders. A fine

professional

cellist

and

g

ed

experimenter,

Schelleng

became

interested inviolin

research

through

the

analysis

of

the

wolf

tone,

and

joined

Saunders'

sm

research

group

in

the

mid

19505,

studying

allfacets oftheviolin

from

the

resonancecharacteristics and the

bowed

string

to

wo

and varnish.

His

application

of

scaling

theory

helped

to make

possible

the

development

ofthe

violin octet.

His

seminal

pa

"The Violin as a

Circuit,"

(1963)

represents

thefirst

time

that

anyone

hadconsidered the

interactive

processes

ofthe violin a

whole,

and is still

used

by

contemporary

researchers

as a

basis for

much

of

their

thinking

in terms of the

application

ofmod

technology

to theviolin. In

addition

to some20

other

papers,

Schelleng's

"The

Acoustical

Effects

of Violin

Varnish,"

(1968),

a

"Physics

of the

Bowed String," (1974)

are

still considered definitive.

Ephraim

Segerman

was

born

in

The

Bronx,N.Y.

in

1929,

and

relocated

to

Northern

England

in

1963,

where

he

raised

a

fam

and set

up

Northern Renaissance

Instruments,

which makes historical

stringed

instruments,

strings

and

varnish

materials.

8/17/2019 2001 N.3 VOL.4 CASJ

http://slidepdf.com/reader/full/2001-n3-vol4-casj 5/76CASJ

Vol.

A,

No.

3

(Series

II),

May

2001

3

VIOCADEAS

—

THE

V I O L I N

OCTET

REVISITED

George

Bissinger

Physics

Department

East

Carolina

University

Greenville,

NC

27858

[email protected]

Introduction

In the

November

1998

issue

oftheCAS

J ournal

I

outlined the

VIOCADEAS

Project

[1]

—

undertakenfor

making

normal

mod

measurements

on

the

violin

—

and

updated

it

with

a

progress

report

the

following

year

[2].

Since

then

more

good things

hav

happened,

so

this

is

an

apt

time

to

bring

Catgut-ers

up

to

date.

Let

meoutline our

progress

since thelast

report:

We

now

perform

500+

point

modal

analyses

onviolin

top

and back

plate,

ribs,

bridge,

tailpiece,

and

neck-fingerboard

(the

latter

three

from

two

orthogonal

directions).

Our

hammer-impact

excitation

routinely

is done in

two

perpendicular

striking

directions

on

the

G-side

cornerofthe

bridge

All

scanning

laser

response

measurements on violins are

performed

in

our

anechoic

chamber,

using

a

low-damping

holding

fixture.

We

have added

a

modest

facility

to

do

cavity

mode

analysis.

Modal

analyses

at

100+

points

on

top

or

back

plates

can be

ARCHPLATE

experiment

weremeasured.

done

in

-30

minutes.

Last

summer

10

matched

plates

in the

CT

scans

of

violins

are

now

done three

at

a

time.

Our CT

scan

slices have

been

analyzed

to extract

detailed

density

information

on

the

violins

and free

plates.

We

havebeen

successful in

doing

finite

element

analysis

on

a

CT-scan-generated

solidmodel of

a

back

plate

"density-stripped

off

theviolin

in

the

computer.

Room-averaged

acoustic

output

for

the

violin,

excited

exactly

as

in the

modal

analyses,

is nowused

to

provide

information

on

how

strongly

each

normal

moderadiates.

We

expect

our automated

microphone

array

measurements in

the anechoic chamber to

come

onlinethis summer.

These

cove

a

sphere

around

the violin

in

15-degree

increments

to

give mode-by-mode

radiation

patterns,

as

well

as

averaged-over-all-

directions

acoustic

output.

The

first trial of

our

data

acquisition

system

was

the

—

delightfully

apropos

—

modal

analysis

of

a

complete

violin

octet,

the

string

instruments to

use

physical scaling

laws

in

their

design.

HUTCHINS-SCHELLENG Violin

Octet

Revisited

was

really

a stroke

of

luck

when Carleen Hutchins

shipped

us a

complete

violin octet

(the

St.

Petersburg

octet)

in

J uly

1999

and

their

shipping

crates filled

ourAcoustics

Lab for

a

year

androde out

Hurricane

Floyd,

which

shut

down

the Univer-

for

two weeks

in the Fall

of

1999,

with

nary

a

problem.

When

a

software

module

we

planned

on

using

to

help

create

solid

from

CT scans

was

withdrawn

from

the

market

last

year

it left

a

gaping

hole in

ourresearch

schedule

that

was

filled

quite

by

the

octet.

We

performed

modal,

cavity

mode,

and

room-averaged

acoustic

analysis

on

this octet

over

last

summer,

and

a

chance tomarvel at

the

audacitydisplayedby

Carleen and

J ohn

Schelleng

when

they

took

on

not

just

a

trial

scaling

of

one

from

theviolin but

eight

instruments Itwould behard to conceive

of

practical

instruments

much

smaller than

the

or

larger

than the

large

bass.

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3

(Series

II),

May

200

Bissinger

-

Viocadeas

—

The Violin

Octet

Revisited

It took mostof the fall to

analyze

all the octet

data,

including

categorizing

modes,

so that

Schelleng's

octet

scaling

coul

checked. In his classic 1963

article

"Theviolin as a circuit"

Schelleng

[3]

described

how

to

use

flat

plate

scaling

theory

to

p

the "main

wood"

resonance

(now

identified as

the

first

corpus

bending

modes

Bl-

and

B1+) 14semitones

above

the

freque

of

the lowest

string

[4].

This would

normally

place

itunder

the

upper

of

the middle

two

strings

of

the octet

(although

not fo

basses). Our normal

mode

analysis

easily

isolated Bl-

and

Bl+for each

instrument,

as well as the

C-boutvertical transla

modes (CBV), some

of which

surprisingly

showed

"doublets";

in

fact

the

tenor

showed

fourfirst

corpus

bending

modes

du

various

couplings.

Generally

Schelleng's

flat

plate

scaling

successfully

positioned

the

averaged

first

corpus

modes

frequency

c

to

the

desired

scaling

placement.

For

the "mainair AO

resonance

Schelleng

employed

theHelmholtz

relationship

to scale

from

theviolin.

This

theory

h

real

"hole"

in

it

as

Schelleng

realized

evenback in

1963.

Shaw's 1990

2-degree-of

-freedom

(2DOF )model

[5]

made

this

clear

w

it

exposed

coupling

between

AO and Al

[6].

Al has

really

beenon

aroll

lately

it

seems,

whatwithits

coupling

to

AO which

m

itcrucial to understand the "main

air

resonance,

as

well

as

being retroactively

placed

by

Hutchins

[4]

in the "mainwood"

onance

The

octethas

such

an

enormous

range

of

cavity

size

parameters

-

-4.5

in

length,

-10 in f-hole

area,

-

7 in

rib

height,

-128

in

volume

-

thatit

was

possible

to

develop

a

much

improved

understanding

of

how

and

why

theHelmholtz

relations

failed

evenwhen

applied

to situations where one

might

reasonably

expect

it to work

best,

such

as

in the La

Empierre

alumin

violin

cavity

[7].

Ouroctet

analysis

indicates

that

AO-A1

coupling

conspires

with

cavity

compliance

to

disguise

the

problem.

W

a

new

semi-empirical

compliance

correction

the 2DOF

model

nowis

capable

of

placing

both

the AO and Al mode

frequen

within

-10%

ofthe desired

placement

for any

member

of the

octet.

Lots

of

octet

details

and

results

have

been

collected

into

two

papers

and

submitted

for

publication.

One

deals

with

AO

Al,

(plus

A2nd

A

4)

cavity

modes

including

ways

to

compute

the

frequencies

of

all these

modes

and

how

well

they

satisfied

desired

scaling

placement

(Al

should

fall in

with the

Bl modes).

The other

presents

the modal

analysis

check

on

the succes

Schelleng's

flat

plate

scaling

theory

for

Bl

modes

that

also

talks about substructures and their

coupling.

And

the

room-avera

radiation

results

—

bet

you

won't look at Al the same

anymore

—

have more

than

a

few

surprises.

Hopefully, by

the

time

read this

report

some

of

the

results

will

beavailable

on

the

web,

including

modeanimations

with

a

special

reader

program.

Fufure

REFERENCES

While

good

things

are

happening

we have

barely

scratched thesurfaceofVIO-

1 G

Bissingei

.

Toward

a

normal

m

CADEAS.

Analyzing

theoctet

has

alreadygiven

us

some

idea of

its

organizing

understanding

of the

violin:

CAS

J our

and

comparative

capabilities.

Actual

databasing

of

quality-rated

violins

should

vi

3-^ feer

j

es

m

D

21-22

('199

commence in

Fall

2001

—

that

is

really

exciting

Of course a normal mode

2 G

3^

Moda

l

analysis

of assem

database

is

no

better than its

data. We

must

measure

poor

violins

—

after

all

strine

instruments-

the VIOCADE

how

do

you recognize

peaks

ifthere are

no

valleys?

—

but the

value

ofaviolin

p

pro

ect

_

a

progress

report:

CAS

J our

database

grows enormously

when

we

can getsome

fine

instruments for

com-

y

Q

j

3

j

s

t

q

g

(Series

II)

p

19-23(199

parison.

In

the

sense

of

building

fine

violins,

it

seems

equally

valuable for the

3j

Q

Scne

n

eng The

yio

iin

as a

circuit

1

1

__

j

11

1

__

j

J ©'

maker

toknow

what NOT

to

do,

aswellas what

to do.

Acoust.

Soc.

Am.,

v.

35,

p.

326-338

(19

also

see

erratum

on

p.

1291.

Beating

theBushes

4.

C.M.

Hutchins,

A

30-year

experimen

Our measurement

capabilities

here

in

the

Acoustics

Laboratory

are

muchbet-

ter

than would be

possible

in the

field,

especially

in

terms

of

measuring

the

acoustic

output. But,

how

do we

get

the

fine

violins to

measure?

This

puts

a

the acoustical

and

musical

developmen

violin-family

instruments:

/.

Acoust.

Am.

v.

92,

p.

639-650

(1992).

premium

on

finding

folks who

own

fine violins who

are

willing

to

bring

them

5. E.A.G.

Shaw,

Cavity

resonance in the

here

for

measurement.These instruments

should

be in excellent

form,

proper-

ly

setup,

and

recentlyplayed. They

will

be tested

exactly

as

played,

except

for

removal

of

any

chin

or

shoulder

rest

(which

c an

be

simulated

later

in

the

com-

lin:

network

representation

and the e

of

damped

and

undamped

rib

hole

Acoust. Soc.

Am.,

v.

87,

p.

398-410

(19

puter).

I

encourage

anyone

who has a

fine

violin

they

would like to have

6.

G.

Bissinger,

A

0

nd

Al

coupling, arch

included

in

the database

to

please

contactme.

rib

height,

and f-hole

geometry

depe

ence in

the

2-degree-of-freedom

netw

model of violin

cavity

modes:

/.

Aco

We

are

grateful

to

theNational

Science

Foundation

for

its

essential support

of

the

VIOCADEAS

Project

(DMR-9802656).

■

CASJ

Soc. Am. v.

104,

p.

3608-3615

(1998).

7. G.

Bissinger,

The

effect of

cavity

volu

(height) changes

on

the

cavity

mo

below

2

kHz: CAS

J ournal,

vol.

2,

n

(Series

II), p.

18-21(1992).

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

A,

No.

3

(Series II),

May

2001 5

SOME

ASPECTS

OF WOOD

STRUCTURE

AND

F U N C T I O N

By

Ephraim

Segerman

Northern Renaissance Instruments

Manchester M2l

BAA,

U.K.

[email protected]

Introduction

A

scientific

theory

is

an

assumed

picture

of

what

is

happening

that

can

reasonably

explain

all

of the relevant

evidence. That

evidence canbe

just

simple

observations

of

phenomena.

Careful

measurements

undercontrolledconditions

are

good

to

make.

They

create

more evidence

that

challenges

a

theory

to

try

to

explain,

and

if it

fails,

the

theory

is

discarded.Only

a

failure

to

adequately

explain

evidence

c an

invalidate

a

theory,

not

(as

some

assume)

a

lack

of

supporting

careful

measurements.

A

series

of

theories

are

presented

here thatoffer

explanations

of

observed

phenomena

in terms of the wood

struc-

ture,

either

physical

orchemical

(includ-

ing

adsorbed

water).

They

include

explanations

of

permanent

and

recover-

able inelastic

bending,

sound

absorption

during playing-in

and

reduced sound

absorption

in

stewedand

aged

wood.

Basic

Wood Chemistry

Wood

is

a

remarkably

simple

material,

both

chemically

and

physically.

Chemi-

cally,

if we

ignore

the

adsorbed

water,

99%

of wood

is

comprised

of

three

types

of chemicals:

about

half

is

cellu-

lose,

and abouta

quarter

each is

ofhemi-

cellulose

and

lignin.

Cellulosemolecules

are

long

linear

(unbranched)

polysac-

charide

polymers,

hemicellulose

mole-

cules

are

shorter

branched mixed

poly-

saccharide

and

polyuronide polymers,

and

lignin

molecules

are

phenolic

poly-

mers. Cellulose

is

largely crystalline,

organized

into

microfibrils,

and is stable

in

normal

environments.

Hemicellulose

and

lignin

are

not

crystalline,

with

hemi-

cellulose

being

rather

unstable and

lignin

very stable.

Hemicellulose

is the

only

compo-

nent

that

absorbs

water to

any

extent.

All of

the

changes

in the

dimensions of

wood

with

changing

weather

are

due

to

how

much the

hemicellulose

is

swollen

with

adsorbed

water. Small

ions

like

lithium

and sodium

can

join

with and

stabilize

more

adsorbed

water

molecules

(sodium

ions c an raise

the

equilibrium

moisture

content

by

up

to 2%

—

signif-

icant

at

low

moisture

contents). When

dry,

hemicellulose

breaks down

into

car-

bon

dioxide

and

water. At

20

degrees

C,

this

would

reduce wood

weight by

1%

per

century.

When

there

is

water

pres-

ent,

acid

breaks

down

the

hemicellulose

somewhat

faster

by 'hydrolysis',

mostly

into

sugar

molecules. Addedacid

speeds

this

up,

but this

happens

normally

because of the natural

acidity

of

wood.

These

processes

ofhemicellulose break-

down

are

called

'degradation',

and

they

get

very

much

faster

with

higher

tem-

peratures

[I].

The Basic

Physical

Structure

of

Wood

Physically,

wood

is a

collection

of

lo

thin

pointed

cells

made

up

ofcell

wa

on

the

outside

andair

in

the inside.

Ea

cell wall

has four

layers,

with the

'p

mary'

layer

on

the

outside

and

thr

'secondary'layers

inside.

The

amount

hemicellulose

is

about

the

same in

ea

layer

because

the

layers

need

to sw

and contract

together

without stre

between them

when

moisture

conte

changes. The

cellulose

content

of

ea

layer

increases

steadily

from

the

out

'primary' layer

to

the

innermost

'se

ondary'layer.

The

lignin

content

cons

quently

decreases

in

that

sequence.

Th

cellulose

microfibrils lie

parallel

to

ea

other

within each

layer,

and

spir

around the

cell's

long

direction.

Diffe

ent

layers

have different

angles

of

spira

ing.

The

hemicellulose combined

wi

the

lignin

acts

as

glue

that

holds

toget

er

the

layers

and

the cellulose

microfi

rils

within each

layer.

Most

cells

have

their

long

direction

parallel

in

the

direction

of

tree

grow

(some

bundles of

cells

lie

perpendicul

to this

majority, forming

the

'rays'

se

in a

radial

section).

The

wall

ofeachce

has

a

cross-sectional

shape

that

is recta

gular

with

slightly

rounded

corner

Adjacent

cells have their

walls

glued

one-another

by

a

mixture of abo

three-quarters

lignin

and

a

quarter

hem

6

Needham

Avenue,

Chorlton-cum-Hardy

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3

(Series II),

May

2001

Segerman

-

Some

Aspects

ofWood

Structure

and Function

cellulose. The

gluelayer

is about

as

thick

as

anindividual cell-wall

layer

except

at

the

rounded

corners,

where it fills

the

space.

Pairs

of

glued-together

adjacent

cell walls

act

as structural units.

There

are

evenly

spaced

holes in

the cell walls

called

'pits'

which

are

usually

lined

up

with

similar

holes

in

adjacent

cell walls.

These

holes

allow

the

passage

of

water

or air between

cells,

and

ultimately

between

the insideand outside

of

a

piece

of

wood.

Bending

and

Taking

a

Set

Whenwood

is

bent

at normal

tempera-

tures,

the

cells

on

the convex

side ofthe

bend tend

to

be

stretched,

and

those

cells on

the concave

side

tend to

be

com-

pressed.

The

cell

walls

c an

hardly

be

stretched.

They

lie

along

the

grain

(long

direction);

the

sides of

the

cross-section-

al

rectangles

line

up

along

the

radial

direction,

and lie

along

but

are

staggered

in

the

tangential

direction.

There

is thus

little

scope

for

deforming

cell

shapes

to

respond

to a

stretching

force

along

the

grain

and radial

directions,

a

bit more

scope

along

the

tangential

direction,

and

a

lot

more

scope

in

other

directions

in-

between these. There

are

no directional

constraints

in

changing

the

shapes

of

the

cell

walls

in

response

to

a

compressing

force. If the

bending

force is

released,

the cell

walls

spring

back

to their

previ-

ous

shapes,

but

if

theforce is

applied

for

a

period

of

time,

thewood takes

a

'set',

and

only

some

ofthe

bend would

spring

back

if

the

force

is released.

That

time

can

be shortened

by higher

temperature

and

moisture

content

and

by

internal

mechanical

stresses such

asvibration

and

moisture

gradients

due

to

changes

in

humidity.

It is

very

short

if the

tempera-

ture is

over

90

degrees

C,

with

enough

moisture to avoid

drying,

when

the

glue

between

cell

walls becomes

plastic

and

flows

readily.

In

taking

a

set,

the

individual cell

walls in the

pairs

slip

past

oneanother in

the

direction that

tends

to relieve

the

stress caused

by

the

bending

force.

The

glue

between cell walls

'gives', allowing

sliding.

This is called

'creep.

In

the

grain

direction,

the

long

thin

pointed

cells can

slide

along

their

long

directions

relative

to

one-another.

In

directions

perpendi-

cular

to the

grain

direction,

the

slips

between

adjacent

cell

walls

are

towards

making

new

rectangular

cell

shapes

that

are

shorter

in

the

direction

of

compres-

sion

and

longer

in

the direction

of

stretching.

After

creep,

if the

bending

force

is

released

at

normal

temperature,

the

cell-

wall

glue

holds. When the

creep sliding

is

along

the

grain

direction,

there

are

no

residual

internal

stresses in the wood

structure caused

by

the

movement,

and

so

the bend

is

permanent,

with

no

'memory'

of the

original

relationships

between

cells. This

happens

when

bows

are

bent

to

shape.

If

the

creep

sliding

changed

the

shapes

ofthe

cells,

there

are

internal

stresses

that were

not

there

before,

as a

'memory'

of the

original

shapes,

and

under the

right

conditions,

the

original

shapes

c an

be

recovered.

These

internal stresses

could

well be in

the

originally-grown

corners of the cell

walls

having

to

open

out in

straight

regions,

andthe

regions

that

were

origi-

nally straighthaving

to

bend at

corners.

After

the

original bending

force

is

removed,

with

time

(which

can

be

short-

ened

dramaticallyby high

temperature

and

moisture content),

the

original

shapes

will

largely

be

restored. Thus

a

'warped'

bridge

(which

has

creep

due to

stresses

only

in

the

radial

direction

of

the

tree)

will

spontaneously

straighten

with heat

and

moisture.

Figure

1

illustrates

how elastic

bending

of a

straight

piece

of

wood

stretches

the

convex

side

and

compress-

es

the concaveside

and,

if

the

bending

involves

the

grain

direction,

how stress

relief

by

creep

(where

cells

slide

with

respect

to

oneanother

in the

grain

direc-

tion)

unrecoverably

fixes the bent

shape.

Figure

2

shows

a

typical

cross-sectional

structureofa

group

of

spruce

cells.

Fig-

ure 3

gives

models

of how a

typical

one

of

thesecells distorts

under

deformation

forces

strong

(or

persistent) enough

to

lead to

creep,

but not

strong

enough

to

damage

thecell walls.

The

creep

involves

slip

ofthe walls ofonecell

with

respe

to its

neighbors.

In

the extension

mod

els,

the cell

changes

shape

(in

a

wa

tending

towards

relieving

the

stretchin

force) by moving

the

original

cell

wa

corners,

creating

new corners.

In

th

compression

models,

pairs of

adjace

walls form

zigzags

of

opposite

bend

At each

bend,

there is more cell wall

o

theconvex

side than on

theconcave sid

In

the

pair

of

bends,

eachcell wall

is

o

the concave

side

at

one bendand

on

th

convex

side at the

other.

That

shape

stabilized

by

shear movement

along

th

glue

between

the

two

cell

walls

in

th

region

between the

twobends.

More

Destructive

Aspects

of

Wood

Bending

When

wood is

dented,

it

can often

b

swelled

back

by

moisture and

heat,

bu

only

if the

dent

is

fresh.

The

intern

Figure 1

■

Cross section

of

wood

deformation,

showing

grain

direction.

-^

direction

—

_►

unbent

elastically

bent

stress

relieved

by

creep

(unrecoverable)

Figure

2

■

Cross

section

of

wood

cell

structure.

radial direction

tangentia

direction

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3

(Series

II),

May

2001

Segerman

-

Some

Aspects

ofWood

Structure

and

Functio

Figure

3 ■Models

for

recoverable creep deformationof

a

typical

cell

(cross-section

view).

A. Radial

extension;

B. Radial

compression;

C.

Tangential

extension;

D.

Tangential

compression]

Radial

Compression

adial Extension

A

original

cell

comers

c

stresses

are

in

thebends

incell

walls that

originally grew straight.

The

compres-

sion

models

of figure

3

should

be rele-

vant

here.

The

residual

stresses can

drive

a

swelling-out

of the dentif

the

surfaces

between cell

walls are

made

mobile

by

heat

and

moisture.

If the dent

is

not

swelled

out

quickly,

the

bends

c an

migrate,

either

to

each other or

to

the

cell

corners. In

either

case,

the walls

straighten

out,

but at

the

expense

of

the

cell

corners

no

more

being

at

right

angles.

Possibly

because

of

cleavage

of

the

primary layer

of

cell

walls

at

the

acute-angle

bends, the

original

cell

shapes

cannot be restored

by

heat and

moisture.

Curvature

of wood

perpendicular

to

the

grain

direction can

be made

per-

manent

by

high

heat.

The

side on

which

it is

applied

becomes

concave. The

scorching

or

near-scorching

heat

breaks

down

much

of

the

hemicellulose in the

cell

walls,

thus

contracting

thewood

on

that side. This makes

the

heated wood

#4

V*

original

j

cell

J

_

comers

Tangential

Extension

Tangential Compression

lose

most

ofits

capacity

to absorb

water,

so

the

contraction is

permanent.

Staves

of

bent-stave

English

17th

century

viol

bellies were

bent this

way

with scorch-

ing

irons,

with

the bends

forming

parts

of the

arching

curve.

Sound

Absorption

by

Creep

When

one first

tightensup

the

strings

of

a

new bowed

instrument,

there are

new

bending

forces

on

the structure.

The

string

tensions

tend

to

compress

the

length

of

the

top

plate,

increasing

the

longitudinal arching

curvature

and

rais-

ing

the

archingheight.

This

is

complicat-

ed

by

the

downward

pressure

from

the

bridge,

which tends to

straighten

out

both the

longitudinal

and

sideways

arching

curvatures in the

bridge

region.

So the

longitudinal arching

curvature

away

from

the

bridge region

tends

to

become

greater.

Figure

4 illustrates this.

These

changes

cause

other

distortions

and

changes

ofcurvature

over

the

body.

Each

change

of curvature is

subject

to

creep,

and

while

creep

occurs,

it m

probably

absorbs

vibrational

ener

whenever

the

instrument is

vibrate

This is

suggested

because

creep

in

str

stretching

absorbs vibrational

ener

dulling

the

sound[2].

The

material

u

that

energy

to

speed

up

the

creep.

Cre

is

greatest

at the

beginning

(most

dur

the

firstweek)

[3],

and it slows contin

ously, eventually

settling

down

to a

n

ligible

rate.

Vibrating

the instrument

well

as

heat,

moisture and thestresses

moisture

gradients

during

humid

cycling[4])

will

shorten

the

time

it

tak

to settle down.The

speeding-up

of

cre

by

vibration

appears

to

be the

mech

nism

by

which

playing-in

helps

[s].

If

an

instrument is leftwith

reduc

string

tension

for

some

time,

the

chang

of

curvature

along

the

grain

cannotrec

er,

but

those

perpendicular

to the

gr

directioncan to the extent

allowed

by

constraints

(recovery would

be

help

particularly

by

the

moisture

gradients

humidity

cycling).

Then,

when

tuned

again,

some

creep

could occur

again,

some

playing

in

may

be

appropriate.

Changes

of moisture content in

equilibrium

with a

particular

relative

humidity

We

should

not confuse the

above

eff

of

vibrating

the

wood

during

playing

with

any

improvement

of

sound

that

c

result

from

warming-up

playing.

Th

Figure

4 ■

Diagrammatic

cross

section

of

longitudinal

arching

of

a bowed

instrument.

A.

Before

stringing;

B.

After

stringing.

Longitudinal

arching

before

stringin

A

1

O yj

v

curvature

meek

tail

Deformed

arching

after

stringing

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3

(Series

II),

May

2001

Segerman

-

Some

Aspects

of Wood Structure and

Function

is

evidence

suggesting

that

vibrating

wood

has

lower

equilibrium

moisture

content than

wood

under

the

same

con-

ditions

but not

vibrating[6].

The

more

moisture

there

is in

the

wood,

the

more

absorption

of

vibrational

energy

there

is. So,

according

to

this

theory,

during

warming

up

by

playing,

some of

the

moisture that

was

in the

wood

before

is

freed,

and

so

less

sound is

absorbed.

It

is

unlikely

that this

physical

effect

is

large

enough

to be

noticed.

Sincevibration

affects

the

equilibri-

um moisture

content

ofwood

at con-

stant

temperature

and

relative

humidity,

we

would

expect

static

stresses

todo the

same.

This

seems

to

apply

when two

pieces

of

wood

with

different

grain

ori-

entations

are

gluedtogether

at

one

rela-

tive

humidity,

and then

the

humidity

changes.

The

glue

joint

holds,

so one

piece

is under

compression

and

theother

under extension in the

glued

area. The

wood

region

in

compression

can

hold

less water

than

it

normally

could

at

the

new

humidity,

and

that

in extension

more.

It

seems

likely

that

wood under

static stresses

takes

the

equilibrium

water

content

appropriate

for

its

con-

strained

dimensions

rather

than

that

appropriate

for

unstressed

wood

at

the

ambient

relative

humidity.

Thus

the

weight

of

plywood

varies

much

less

with

changes

in relative

humidity

than

normal

woods.

Another

example

of

this

principle

is

the

observation

that

the cracks

on cen-

old

lute

soundboards

tend

to ter-

at the

cross-bars (with the

grain

to

that

in

the

soundboard)

lued underneath.

The

grain

directionof

cross

bar

is

along

the

long

dimen-

and

its

length

would

have

varied

little with variation in

humidity.

kept

the

soundboard

wood

glued

o the

cross

bars

from

expanding

or

con-

perpendicular

to the

grain,

and

it was

kept

at

a

relatively

constant

content.

The

soundboard

that was not

next to

the bars

and

contracted

with

humidity

and

the

stresses

resulting

from

gradients

associatedwith

these

changes

enhanced

the

normal

ageing

effects

of

degrading

the

hemicellulose

that

contracted the wood. Thus the

soundboard

cracks

between the

bars

result from

contraction

there

that

did

not occur at

the bars.

Sound

Absorption

by

Water

The

adsorbed water

is

a

major

contribu-

tor

to the sound

absorbed

by

the

wood

of

musical

instruments.

Adsorbed

water

converts some

of the

energy

of sound

vibration into heat

energy[7].

There

is

typically

a

3.5%

decrease

in

damping

coefficient

for

each

1% decrease

in

moisture

content[BJ .

Since

hemicellulose

is the

component

of

wood that

adsorbs

water,

and

its

capacity

to

adsorb

water

depend

on

how

much

hemicellulose

remains in

the

wood,

the

hemicellulose

content is

directly

related

to the amount

of sound

absorption.

Thus

instrument

response,

which

depends

on

the sound

vibration

that

is

not

absorbed,

would

improve

as the

hemicellulose

degrades.

This is

probably

the

main

reason

why

instruments made of

matured

wood

have

more

response

than

thosemade of

freshly

dried

wood,

and

why

old

instru-

ments

seem

to

have

more

response

than

newly

made instruments. Since

hemicel-

lulose

itself

most

probably

absorbs

sound

energy,

its loss increases

response

more

than

just

that due

to the

reduced

moisture content.

The closeness

of

the label date

and

dendrochronological

date of

some

Guarneri instruments

suggests

that

wood

maturation was sometimes

con-

siderably

shortened,

probablyby

stew-

ing,

which

greatly

accelerates

hemicellu-

lose

degradation.

It

was

traditional

then

to

'salt'

wood

to

stabilize

and

preserve

it[9],

and

impregnated

salts

have been

found

in

Guarneri

wood[lo].

The salt

helps

dimensional

stability

by

raising

moisture content at

low

humidity,

but

the main

effect on

stability

and

sound is

due to the

hemicellulose

degradation

of

stewing.

Some

makers

today

are

stewing

the wood

used in

their

instruments

to

give

the

effect

of

aged

wood.

There is

additional sound

absor

tion

by

moisture

gradients

in th

wood[ll].

It

appears

that

the soun

energy

absorbed is

used

to

speed

up

th

movement

of water from

regions

o

higher

to

lower

moisture

content.

there has

been

anychange

intherelativ

humidity

around an

instrument,

this

probably

a

more

important

reason fo

warming up

an

instrument

before

pe

forming

on

it

than

the

small

lowering

o

the

equilibrium

moisture content.

Conclusion

These

theories

explain

all

of the

relevan

evidence

the author is

aware

of. Suc

theories

are not

for

believing

in,

bu

should

be respected

unless

and

unt

theories that better

explain

the evidenc

emerge.

In

principle,

these

are

all tes

able.

They

could

be

considered

rathe

speculative

since

most

have not bee

challenged by

careful

experiments.

I

such

experiments

were

easy

to

perform

they

would

have

been

performed lon

ago,

and

appropriate

theories formulat

ed.

Theories can

result from

or

preced

experiments.

It

is

hoped

that

these

theo

ries

will

stimulate

appropriate

exper

mentation. ■

CAS

REFERENCES

AND COMMENTS

1

.

A.J .

Stamm,

Forest

Products

J ourna

Vol.

6 (5) (1956),

p.

210.

Cited

in A

J .

Stamm,

Preprints

of

the

Contribu

tions

to the 1970

New

York

Confer

ence on

Conservation

of

Stone an

Wooden

Objects,

Second cd. (1971)

Vol.

2,

pp.

1-11.

Almost

all

of th

statements

made

here about

th

chemistry

of

wood

are

derived

from

this source.

2.

Players

can

often

tell that a

gut

string

is

going

to

break

soon

by

its

nee

for

more

regular

tuning

(some

fibers

are

already

broken

and

the

remaining

fibers

stretch

more

because

their

share of the

tension

is

increased)

and

the sound

gets

dul

(the

fibers

stretching

absorb

vibra

tion energy).

Also,

it is

well

known

8/17/2019 2001 N.3 VOL.4 CASJ


3

4

5

CASJ

Vol.

4,

No.

3

(Series

II),

May

2001

Segerman

-

Some

Aspects

of

Wood Structure and

Functi

in

harpsichord

circles that

newly

Comm.

1472,

p.

55. When

new

in-

8. D. G. HuntandE.

Balsan,

op.

cit.

mounted

brass

strings

don't sound

struments are

strung

up,

the

wood

9.

R.

Gug,

'Salted

soundboards

a

fully

when first

mounted,

and

only

deforms

in

response

to

the

forces.

sweet

FoMRHI

Quarte

soundfullywhen

they

have

stopped

The creep

in this

deformation

_._,

T

.

*

nnn

.

i

i

i

I v v a -v

■

a

■

No.

52,

J uly,

1988),

Comm.

881

theirinitial

stretching.

<J 1

relevance absorbs

sound

vibrations,

reducing

>

j

. />

here,

engineers

have

measured

response.

In

'playing

in',

sound

44-dd. tie

reported

that in

lis

sound

produced

by

materials vibration accelerates the

creep,

mak-

Palissy

wrote

'Salt improves

undergoing

creep.

ing

the instrumentsettle in

faster.

voice of all sorts

of

musical

inst

A.

Beavitt,

'Taking

tone

from

the

air',

6. D. G. Hunt andE.

Balsan,

'Why

old

ments'. The

impregnation

ofwo

The

Strad,

(Nov. 1996), p.

916-920.

fiddles sound

sweeter',Nature,

Vol.

,

.

.

,

.

i

n

r i 1

~

/ .

r. i

by

salts

was common

practi

Beavitt

claimed that

all

of

the sound

379,

(22

Feb,

1996),

p.

681.

Sound

.

j-i.i

improvement

in

the lifeof

a

violin is

absorption

increases

considerably

in

Stewm

8

the

wood

m the

salt so

associated

with

creep,

which

is

facil- the

non-equilibrium

situation

of

ris-

tlon did

it. The

purposes

usua

itated

by

humiditycycling.

ing

moisture

content. I

interpret

stated for

salting

wood

were

R. Hearmon

and

J .

Paton,

Forest

their

experiment

(Segerman,

1996)

a void rot, to

repel

woodworm a

Products J ournal,

Vol.

14(8) (1964),

as

showing

that when wood is

tQ

stabilize

it

dimensionally

(so

p. 357-359. Cited

by

Beavitt.

They

vibrated,

the moisture content

in

.

. .

.

i

, ,

i

_,.

.

i

-ii

reacts less to weather

changes).

showed

that

humidity

cycling equilibrium

with

a

given

outside

rel-

...

increases

the

rate

of

creep

in

stressed

ative

humidity

decreases.

The

effect

m

y

interpretation,

it

is

likely

t

wood.

is

small and

has

only

been observed

mostofthe

sound

improvement

a

E. Segerman, 'Wood structure

and

at

veryhigh

humidity.

stabilization was due

to

hemice

what

happened

inthe

Hunt

& Bal- 7. D.

Noak

and H.

Becker,

Wood

Sci-

j

ose

degradationby

the

stewing

san

experiment',

FoM ß H l

Quarter-

ence&

Technology,

Vol.

2 (1968), p.

1n T>T

(T

,

.

_

.

i

>_

~.„

~~~

_^

ii

-^

rr.i

10-

I-

Nagyvary,

lhe

Chemistry o

ly,

No.

84,

(J uly,

1996),

Comm.

213-230.

Cited

by

Beavitt.

They

J

,

.

'

.

.

.

1471,

p.

53-55. See also the follow-

showed

that the

damping

of

sound

Stradivarms',

Chemical &

Engine

ing

paper:

E. Segerman,

'Modelsfor

is

strongly

increased

by

increased

ing

News,

(May

23,

1988),

p.

24-

sound

improvement

on

playing

in',

moisture content. 11. D. G.

Hunt

and

E.

Balsan,

op.

cit

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No. 3

(Series

II),

May

2001

■

* S BK

:-

'3B_f .__B_H____i

:

-

■

T

4k'

l%f

,

.

_■_____■_______________■

*

Carleen

M.

Hutchins

There

is

no

doubt

that

without

the

research

and

amazing

work

of

J ohn

Schelleng,

the

Catgut Acoustical

Society

would

never

have

developed.

It is

with

great

pleasure

that

we

dedicate

this

issue

to

the

memory

of

J ohn

Schelleng.

J ohn's

career

spanned

two scientific

disciplines.

During

his

first

forty years,

he

specialized

in the

principles

of

radio

trans-

mitters,

radio

antennas and radio wave

propagation

over the

earth

—

a career thatwitnessed the

extensionof the

radio

spec-

trum

from

wavelengths

of

kilometers to

wavelengths

of

millime-

ters.

His second

career

in "retirement"

was

in

research

on

the

acoustics ofthe

violin

family,

an

interest which

combined

his love

or

the cello

with

his

wonderfully

keen

analytical

approach

to

complex

vibrational

systems

based

on

electrical

circuit

theory. In

an interview

shortly

before his

death,

J ohn

said his

first

idea

was

to

try

to

analyze

the

wolf

note in the

cello,

which

seemed

feasi-

ble

because

all

he

neededwas

"a

large

supply

of

paper,

pencils,

his

ello

and

a

quantity

of

chewing

gum."

This

effort

resulted

in his

monumental

paper

"The Violin

as a Circuit

(J ASA

Vol.

35, 3,

326-338

March, 1963, republished

here),

in

which he

not

only

thewolf-note to rest,

but

provided

the

firstmodel for

analy-

and

functioning

of the

violin

as a

whole.

As recounted in

Newsletter

No.

29,

the

small

group

work-

g

with

Frederick

A.

Saunders in violin

acoustics

during

the

1950s

jokingly

called itself

the Catgut Acoustical Society,

an

which

as

we

know

has grown

to

be

respected

in

string

instrument

research and

development.

In

on

the

work

of Saunders and

others,

Schelleng

per-

a

pivotal

role

in the

maturation

of

stringed

instrument

to

a

high

current

level

of

sophistication

—

asevidenced

the

frequent

references to his

publications

in the

writings

of

he new

generation

of

researchers.

His classical studies

in

the

area

the

bowed

string

and the

effect

ofvarnish

on

wood

vibrations

e

based on

simple

experimental

models

that

have

led

to

signifi-

analytical

developments.

It

was his

scaling

theory

thatmade

the

theoretical

development

of

the

eight

new instru-

of theviolin family.

J ohn

C. Schelleng(1892-1980)

On

the

personal

level,

J ohn's

forceful

and

lucid

expression

of

sparked

many

a

fruitful

discussion

and

produced

writings

of

deep

significance

that

his

wonderful

senseof

humor

often

gave

light

and

engaging

touch at

just

the

right

time.

Working closely

with

J ohn

Schelleng

was a

continual

joy

and

challenge

of

the

level.

He was

a never

failing

source of

helpful

criticism and

encouragement,patient

and

understanding,

with a

no-non

reaction

to

sloppy thinking,

anda

strong

moral

senseof

right

and

wrong.

J ohn

Schelleng

provided

the

center

around

which

he

early

development

of both

theoretical

and

practical

work

of

others

flourished.

His work was

quoted

widely, especially

his

paper

"The

Violin

as a Circuit.

Michael

Mclntyre,

a

highly

respected

theoretical

physicist

and

member

of the

Roya

in

England,

oncetold

Hutchins thatwhen

he

retired,

he

'wanted to

go

back

and

start

where

Schelleng

left

off.' The

foot-

ofa

giant

leave

deep

marks

in the

earth,

marks of

a

tremendous

all-around

person

whose

likes we

shall

notsee

again

soon

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No.

3

(Series II),

May

2001

11

Hutchins

-

A

Tribute

to

John

C.

Schel

len

Here

are

a

few

quotes

—

J ohn's

legacy

lies

in

his

writings,

which

are

available

to

everyone,

andhis

personal

influence

on

the

formation

and

growth

ofthe

Society"

—

George

Bissinger

J ohn's

experimental

ability

was

phenomenal. In

the

tradition

of

Faraday

and

Raleigh

(and

fostered

by

the

budgetary

limitations

of

a man

doing

research

without foundation

support),

J ohn's

measurements

weredone

with the

simplest equipment.

Nevertheless,

the

set-up

was

always

such as to

give

unequivocal

results of

high

precision.

Much

of

his

work

on

the action ofbows

was

done

with

a

"driver"

consisting

of

a

heavy

box

of

stones hung

pendulum-like

in his closet door.With

the

bow

moving

back

and

forth

with

precisely

measurable

amplitude

and

frequency,

J ohn

had

his choice

ofbow

speeds

under

precise

control,

always

under

more or less

live

conditions where the

speed

is

varying.

It is

an

arrangement

like this

that

makes surethatno

anomalies

of

speed

and

pressure

"slip

in between

the data

points"

and

guarantees

(via

repeated

traversals ofeach data

point)

that the

observed behavior

is well

defined.

"The

way

inwhich

J ohn

Schelleng

carried

on

his

mathematical

operations was

of

a

piece

with

his

experimental

work.

Straightforward

technique

of

bare-bones

simplicity,

sophisticated

insight

into

questions

of

relevance

and

great

synthesizingability

across the

fields

of

engineeringphysics

and

practical

music

were

his

trademark.

He

was

a

master

at

scraping

up

bits

of

data

from

the

most

unexpected

sources,

and at

putting

them

together

into

a

cohesive

whole.

"Possibly

the

greatest

of

J ohn's

abilities,

whichcontributed

mightily

to

the

explosive

growth

ofmusical

acoustics

in the

last 25

years,

was

his

ability

to formulate his

questions

and

his

results

in

a

way

thathad

immediately

testable

implications

in the

practical

world

of

music.

Because he was

a

pretty

good

fiddle

player

he

could

notice,

appreciate

and

think about subtleties ofwhat

goes

on,

without

everything running

on

automatic" as

is

the

necessity

for

a

professional

player.

It

was

the

essential,

butoften

tangible

input

ofideasfrom this

source that

fed the

springs

of

J ohn's

creative

life in theCatgut

Society."

—

Arthur

H. Benade

J ohn

Schelleng'swritings

on

the

violin

circuit

analogy,

varnish,

and bowed

string,

will

endure

as

focal

points

for

serious students

ofmusical

acoustics.

His

experiments

were

always simple

and

elegant.

One

of

his

last,

a

study

of

pitch

distortion

in his

own

hearing,

is a tribute to

J ohn's

ability

to find

scientific

signif-

icance in the

most

unlikely

places.

J ohn

was

a

great

teacher,

persuasive, patient

and

always

striving

for

clarity.

He

would

not

tolerate

humbug

and

rejected

it

with

his

delightful

sense

of

humor.

Best of

all,

we

could

always

count on

J ohn

to listen

and

offer

thoughtful suggestions.

J ohn

was warmand kind.

We

have

lost

a

marvelous

friend."

—

Daniel W

Haines

■CASJ

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3 (Series

May

2001

Carleen

M. Hutchins

The

collected

papers

in

this

J ournal

begin

with

two

technical

ones

by

J ohn

Schelleng,

followed

by

the

first

full

description

of

some

of

the

higher

airmodes

oftheviolin

cavity

written

by

Erik

J ansson.

As

a

student of

Arthur

Benade,

J ansson

learned

to measure

many

of the

higher

air

modes within

a

cavity.

Until

the

publication

of this

paper,

violinmakers

and

scientists alike

thought

that

theviolin

contained

only

oneair

mode,

namely,

the

Helmholtz

resonance,

or

breathing

mode,

which

moves in and

outof the

f-holes

as

the box

expands

and

contracts.

Frederick A. Saunders was sure

that

there

were other

air

modes

in the

cavity

and

spent

long

hours

looking

for

evidence of

these

with a

ten-power

microscope

and

a feather

barbule

mounted

on

the

edge

of anf-hole. He was unable to

find

any

motion,

largely

because

the

modes hewas

looking

for

had their

nodal

areas

around

the

f-holes

and

did

not

radiate

through

the

f-holes.

The

next

question

was

—

do

any

of

the

higher

air

modes affect

the

body

modes

of thevio-

lin

corpus?

Mostresearchers

thought

thatsince the

cavity

modes

were

longitudinal

they

could

not

have

much

effect

on

the vibration

of the

top

andback

plates.

The

five

papersby Bissinger

and

Hutchins

represent

a

long-term

series

of

studies

showing

that

there

is

indeed

much

important

coupling

between

theair and

body

modes that have

a

marked

affect

on the

sound

and

playing

qualities

of

aninstrument.

This is followed

by

thefirst

paper describing

the

physical

mechanisms involved

in the

AO-

BO mode

coupling,

that

well-trained

violinmakers have worked

with

intuitively

forcenturies.

This

paper

illustrates

some

of

the

affects

of

bringing

the

AO-BO mode

frequencies

to

the

same

pitch.

Note: For those

interested

in

an

excellent

theoretical

discussion

of

this,

J im

Woodhouse

has

written

a scientific

paper

"The

Acoustics

of

AO-BO

Mode

Matching

in the

Violin,"

Acustica,

Vol.

84,

1998,

Acta

Acustica.

Thefinal

paper

here

written

by

Caroline

Field

explains

how

to

achieve

AO-BO

matching

for the violinmaker.

Forthose interested in

bringing

their information

up

to

date at

this

point,

see

"The

Air

and

Wood

Modes

ofthe

Violin,"

by

C. M.

Hutchins,

(J .

Audio

Eng.

Soc,

Vol.

46,

No.

9,

Septem-

ber,

1998).

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No.

3

(Series

II),

May

2001

1

The

Violin

as

a

Circuit

J ohn

C.

Schelleng

310

Bender

mere

Avenue,

Asbury

Park,

New

J ersey

(Received

6

August 1962)

The

paper

applies

elementary

circuit

ideas

to

bowed-string

instruments

and their

component

parts.

Parametersaredefined

and calculations

based

on

simple

circuit

diagrams

for

the

main

resonanceand

the

air

resonance;

curvesdescribe

theircombined

performance.

Th erelative

importance

of circuit

resistances-

wood

loss,radiation,

andwall-surface

loss—

is

discussed.

Wall-surface

loss

is

an

important

component

ofair

decrement.

Nomaterialimprovement

is

to

be

expected

from

change

in

decrementor

enclosure

volume.

A

theory

for

the

wolfnote

is

given

in

terms of the

beating

of two

equally

forced

oscillations,

together

with

a

criterion

for

its occurrence

and

a

method for its

elimination.

Thepaper

analyzes

principles of dimensional

scaling

between

members

of

the

violin

family

and shows

why

the

cello

and

viola

are

more

susceptible

to

wolftone

than

th e

violin.

A

study

of

impedance

requirements

in

wood shows thatflexural similarity

depends

on the

parameter c/p

(compression^

velocityover

density);

high

values are

in

general

favorable

in

the

top

plate.

In the

violin,

cross-grain

losses

probablyexceed

those

along the

grain.

INTRODUCTION

THOUGH

the

use

of

circuit

concepts is a

standard

practice

in

acoustics,

ip

the

specific

field of the

bowed-string

instrument

they

have

hardly

been em-

phasized

to

the

degree

which their

usefulness

justifies.

The violin family

presents

many

unsolvable

problems

;

its

shape

and

the

peculiarities

of its materials

were

certainly

not

selected

with

regard

to convenience in

analysis.

This, however,

only

emphasizes

the

need

for

understanding

the

simplicities

that do exist and

may

even condonea certain

amountof

oversimplification.

It

is,

therefore,

with

no

thought

of

novelty

that

this

paper

applies

elementary

circuit

ideas

to

bowed-string

instru-

ments,

but

rather with thebelief

that

something

can

be

gained through

representation

by

circuit

concepts

and

diagrams

even

though

some

of

the

results

are

only

roughly

quantitative.

These relations

lead

naturally

to

such

related topics

as

the relation^

between

different

instruments of the family

from

point

of

view

of

di-

mensional

scaling

and the

physical

requirements

of the

wood.

LIST OF SYMBOLS

A

equivalent

piston

area

E

Young's

modulus

F force

H

thickness

X characteristic

impedance

of

string,

(7»

}

L

maximum

safe load

M mass

Po

barometric

pressure,

10

6

dyn/cm

2

Q

quality factor of

a

resonance,

ir/8

R resistance

5

stiffness

«S

area

of surface of

cavity

T

string

tension

U

volume

velocity

V volume of

enclosure

W

potential energy

per

unitarea

Z

impedance

(Appendix

II)

a,b

subscripts

for

air,

body;

dimensions

of

a

rectangular

plate

d

diameter of

port

/

frequency;

subscript

denotes

resonance

i (-I)*

I

length

of

string

or

plate

h

length

of

string

from bow

to

bridge

li I

—

l\

lb,

length

of

string

having

frequency

that

of

body

resonance

m

mass

loading

on

bridge

r

subscript

for

radiation;

also

radius of

curvature

of

a

plate

c

speed

of

compressional

waves

in

air,

c=3.45X10*

cm/sec

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

A,

No.

3

(Series II),

May

2001

Schelleng

-

The Violin

as

a

Circuit

s

amplitude

of

vibration

i

time

v

particle

velocity

A

frequency of

separation

of fundamental

pair

a

(AppendixH)

acoustical absorption

coefficient

7

ratio

specific

heats

J

log

decrement

tobase e

t

=t/@-2.305_

0

c

low-note

scaling

ratio

(Sec

V I I )

V

resonance

scaling

ratio (Sec. VH)

X

air

wavelength

X,

wavelength

on

string

n mass

of

string per

cm

p

density

;

for

air

p

0

=

1.2

X

0~*

gm/cc

<r

length

(breadth)

scaling

ratio (Sec. V I I )

«

2t/;

a

subscript

denotes

resonance

L GENERAL

CHARACTERISTICS

In

contrast

withmoe* of the

wide-band radiation

systems of

today,

such

as.

the

horns of acoustics and

microwaves

and hi-fi

loudspeaking

systems, the 17th-

centurycreators

of

theviolin

of

necessityaccomplished

their

"broadbanding"by

distributing

through

its wide

frequency range

many

relatively

narrow

resonances,

rather than

using

one

or two bands

of

nearly

aperiodic

response.

The

frequencies

desired extend

from

about

200 to 6000

eps,

a

span

of

five

octaves. In the

upper

octaves thewood

provides

body

resonances

in

number

sufficientto

give

a

quasiuhifonnity

of

response.

In the

lower

octaves

this

series

comes

to

an

end,

and

the

lowest

o^

next-to-lowestresonance

—

in

the

vicinity

of

460

cps

—

s

commonly

called

the

"main

body

resonance"

because

ofjts

pronounced

effects. Without

reinforcement

below

this

point,

response

would fall

off

at

a

rateof 12

dB

per

octave

ormore.

Air

resonance similar

to that in

loud-

speakers

is

employed

tosustain

the

Volume

for

thebetter

jiart

of another

octave,

that

is,

resonance of the air

chamber

breathing through

th

6/

holes.

It is

common

knowledge

that

even a

fine violin

has

strong and

weak

regions

hi

its

frequencyrange,

but the

effect

is

byno

means

as

extremeas

the

measured char-

acteristics

suggest

F.

A.

Saunderp

and

co-workers

1

point

out that the

subjective

feeling of

uniform

strength,

which

a

good

violin

evokes;

depends

markedly

on the

well-known effect

in

which

the

ear

credits

the

funda-

mental with

an

increase of volume

actually brought

about

by

a

strengthened

nanubnic

This

subjective

re-

duction

of

depressions

occurring

in

an

objective

response

curve

contributes

not

only

to uniformity

of

loudness,

but

gives

subtle

and

interesting

differences

in

tone color.

In

Fig.

1(a)

is

shown

a.

violin with

names

of

various

parts.

Figure

1

(b)

represents

its circuits in

terms of

elec-

trical

symbols

in accord

with standard conventions

of

I

C.

M.

Hutchins,

A.

S.

Honping,

and

F. A.

Saunders,

J .

Acoust.

Soc

Am.

32,

1443-1449

(I960).

acoustics

for

the

direct

or

impedance

type of

analogy.

Letters on the

circuit

correspond

to

those in

Fig.

1(a).

H.

THE CIRCUIT IN

BRIEF

The

circuit

begins

at

point

B where the

bow rubs

across

the

string

giving

rise

to

a

negative

resistance.

In

the

simplest

Helmholtz

mode*-

1

for

the

bowed

string,

the

string

at

every

moment

comprises

two

straight

sec-

tions

either

sideof a

discontinuity

which

shuttles

from

end

to

end

of the

string

around

a

narrow

lenticular

path.

Ideally

the

string clings

to

the

bow

except

for

brief

recovery periods

in which

short,

negative pulses

occur. From

the

circuit

point

of

view,

the

important

result is that the

bow-string

contact

B

is

a

constant-

velocity

generator.The

weight

applied

to the

string

by

thehand

provides

a condition

necessary

for

vibration,

but

is

unimportant

in

its

effect

on

amplitude

and

velocity.

It is

inherent

in

the

Helmholtz concept that

capture

and

release

of

the

string

are timed

by

the

shuttling

dis-

continuity

that

provides

the

trigger

by

which

the

pulse

is

regenerated.

Since

sharpness

of

discontinuity

de-

pends

on

properly

phased

harmonics

more

than

fun-

damental,

it

is

necessary

to

bear them in mind in

any

question

concerning

frequency

produced.

One

naturally

expects the

occurrence

of a

frequency

for

which

re-

actance

seen

by

the

bow at

thefundamental

is

zero;

if

this were

so,

however,

the frequency

near

the main

resonance (to be discussed)

would

depart

intolerably

from

the natural

frequency

of

the

string.

Thanks

to

harmonics,

whose

impedance

is

independent

of themain

resonance,

this

effect

is small.

The motion

ofthe contact is

in series

with the two

parts

into

which

it

divides

the

string.

Except

for

high

harmonics,

Sec.

AB

is

essentially

positive

mechanical

from

Plates

distributed

compliance

nSfflS

/HOLE

(b_

Fig.

1.

Violin and

an

equivalent

circuit.

A,

B,

andX

appear

on

both

diagrams.

I

H.

Helmholtz,

On the Sensations

of

Tone

(Dover

Publica-

tions,

Inc.,

New

York,

1954),

pp.80-68 and

384^387.

*C. V.

Raman,

Indian Assoc.

Cultivation of

Science.

Bull.

No.

16,

11

(1918).

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3

(Series

II),

May

2001

1

Schelleng

-

TheViolin as a

Cir

reactance,

and.

Sea

BCi

except

as

modified

by bridge

impedance;

is

negative;

together

they

form

a series

resonant

circuit.

For

our

purposes,

the

string

may

be

treated

as

a

lossless

transmission

line.

Bridge

pi

is

.the

transducer:

that

accepts

power

from

the

string:

and;

transfers

it

to;

the

body,

which

in

turn

excites

the

air

within

and

surrounding

it.

Since

themo-

tion

of

the

bridge

in

its

own

plane

may

be

regarded

es-

sentially

as;

that

of

:a;

rigid

body,

it acts in

the

lower

oc-

taves

primarily.as

a

transformer/

Presumably

its com-

pliance

.is

-important

to

normal transmission

at

higher

frequendes,>ithough Minnaert

and

I

Vlam

consider

that

its

main

function

is.

to;

permit

yielding

to extraneous

(e.g.ji

torsional)

motions.

Foil present

purposes,

it is simplest

to

regard

the

sound

post

as

an

important

part of the

body.

It shares

with the

ribs

the

function

of

connecting

theback to the

source

of

vibration,

and is

necessary

for

strength;

it is

extremely

important

as

a

means

for

providing

the dis-

symmetryneeded

for

effective

radiation,

and

playsacru-

cial

role in

determining

the

frequency-

and

geometric

form of

the

natural

modes

of the

box.

The

use

of

anenclosure—

a

boxwith

vibrating

walls-

isan ancient

device

in instrument

making.

Even

though

the/

holes

of a violin

were

narrowed to the

point

of

eliminating

them

as

emitters of

sound,

the enclosure

would still

be

essential

since

it

is

the variations of its

volume which

give

the character

of

a

simple

source,

these

changes

in

volume

being

a

difference effect be-

tween

oppositely

phased

parts of

its

surface.

The

bridge

stands

with

one

foot

near

the

soundpost

and theother

over

the

bassbar.

With

no losses and no

radiation,

the

bridge

would see

the top

plate

with

its

many

vibrational

modes

as

a

complicated reactive

cir-

cuit.'J n

terms

3

of

Foster's reactance

theorem,

there

would be

a series

of

frequencies

with zero

reactance,

each)

separated

from its

neighbor by

a frequencyof in-

finite reactance.

Losses

in

material

and

by

radiation

modify the

reactance

curve

and

add

a curve of

finite

re-

sistance.

The

curve, however,

remains

a

very bumpy

one.

For

each

frequency the

motional

response

of

the

body

to theforce

exerted

by

the

bridge

is

thesummation

of

responses

of

the

various

modes.

The low resistance

of a

resonant

mode

tends

to

"short-circuit" the others.

The

body

thus

acts

like

a

number

of

seriesresonant cir-

cuits

in

parallel,

as

shown in

Fig.

1(b),

but

even

at

resonance

resistance

must

ba several times

the

charac-

teristic

impedance

of

the

string.

It.

does

not

follow

that

acoustical

peaks

must be

associatedwith

points

of

lowest

impedance.

There

is

at

least

one

important

exception—

theairmode that

inter-

poses

an

impedance

maximum

tending

torestrict

bridge

motion.

This part

of the

circuit

j~HG in

Fig.

1

(b)

j,

being

described

in,

terms

of

volume

velocity,

is

shown

con-

nected

with

the

mechanical circuits

by

a

mechanical-

*

M. Mmnaertand

C. C.

Vlam,

Physica

4,

361-372

(1937).

"The mass. of thebridge

added to

the

body leads

to

natural

modes

somewhat

different

fronj

those

ofthe

body

alone.

to-acoustical

transformer

at

T,

with

transformer

ratio

A

to

1.SinceA is

differentfor

each

mode,

separate

trans-

formers are

shown;

all

these

feed

into the

same

circuit

MHG.

6

m. THE MAIN BODY

RESONANCE

Meinel

7

has

traced the nodal lines

appearing

on

top

andback of

one

good

violin

for the

seven

lowest

modes

of

vibration.

(See

also

reference

8.)

The

surface

is

di-

vided

withmore or less

clearness

into

many

small areas

at

the

higher

frequencies,

but

a

certain

simplicity

marks

the lower

three octaves.

It is of

ten

necessary

in

tracing

a

nodal

line

to

follow

it

along

a

plate

to

the

edge,

to cross

theribs

directly

or

peripherally,

thence

along

the other

plate,

andsoforth. For eachof the

following

resonances,

366 eps

(the

lowest),

690, 977,

and

1380,

but

not

at its

"main"

resonance

at

488,

the

entire

body

was

divided

into

only

two

areas

separatedby

one

endless nodal line.

At the

"main"

resonance there were three

areas.

The

number of

areas

equals

the number of lines

plus

one.

He

and

others

have found a definite

tendency

for

large

areas

to

be

oriented

lengthwise

so

as

to

include

the

bass

bar.

In the low

octaves

the

restraining

effect

of

thesound

post

near

the

right

foot

of the

bridge

leads to

a

greater

motion

at the

left

than

at

the

right

foot.

Bridge

bassbar

and

top

plate

thusrock about

a

nodalpointnearthepost.

Instrumentmakers have

commonly

located themain

resonance about 15 semitones

above

the

lowest

tone in

the

violin,

17 in the viola and cello.

The

following

method

has

been used

to

determine

equivalent

series stiffness and

mass,

S andM

.

The

fre-

quency

of resonance was

measured

with

different

small

loads

m

clamped

to

thebridge

with

mass

centered

at

the

string

notch. The

wolftone,

if there

is

one,

can

be

used as relative indicator

of

resonance.

Since

<a=

[5/

(M

+*»)]]*,

itfollows

by

differentiation

that

at

«=0:

In

this

manner,

data

from Raman* and Saunders

10

have

been used to calculate

M

and

5

for

one cello

and

one

violin

:

/(cps)

S(dyri/cm)

3f(g)]

(SM)*,

cgs

ohms

Cello 176 1.13X10

1

92.

1.02X10*

Violin 500

1.76X10*

17.8

0.56X10*.

It

is

interesting

that

the

stiffnesses

for

tnese

two

instru-

ments

of

widely

different size

are not

very

different.

Such

relations

will be

examined

in

Sec. VH

on

scaling.

This

resonantcircuit

has

been characterized

by

5 and

M,

but

any

two

of

the four

quantities

above

can be

used.

Violin

makers,

in

particular

thosewho use

elec-

tronic

techniques,

1

explicitly

consider

one

of these

the

'

Strictlyspeaking,

theradiations

from

plates

and

/holes

should

be shownas

from

a

single simple

source.

7

H.

Meinel,

Elekt. Nach. Tech.

4,

119-134(1937).

'

F.

Eggers,

Acustica

9,

453-465

(1959).

C. V.

Raman,

Phil.Mag.

32,

391-395

(1916).

10

F. A.

J .

Acoust.Soc Am.

25,

491-498

(1953).

M=-y/(df/dm)

and

S*=-2**ZP/(df/dm)J

(1)

8/17/2019 2001 N.3 VOL.4 CASJ


16

CASJ

Vol.

4,

No.

3

(Series

II),

May

2001

Schelleng

-

The

Violin

as a Circuit

location of

the

resonance in

the

range

of the instrument.

A

second

is not used

exceptas

it

is

implicit

in rules for

dimensioning

and in

particular

in

the selection of

wood.

The

foregoing

estimation

of

M and 5

is

useful in

dealing

with

a

narrow

band

about

resonance,

as

later

in

connectionwith

thewolfnote. The

stiffness measured

is predominately

that

of the body,

strings being

ac-

countable

for less

than

10%.

The air circuit (see

follow-

ing

section)

also

contributes

significantly

to

both

mass

and stiffness.

The

third

circuit

constant is resistance. It

can

be ob-

tained

by dividing

(SM)*

by

Q,

the

quality

factor of the

resonance.

Q

may

be found

from

measurements of

logarithmic

decrement

8,

such

as

those

by

Saunders

11

(s io=t/2.30 Q). His

values of

8

1(s

range

between

0.062

and0.14. Clearly the

measurement

should be made

for

the

particular

instrument

studied.

For the

principal

mode,

Meinel

maps

the

amplitude

ofmotion

over

the

two

plates

of a

violin.

7

This

provides

data

for

estimating theequivalent

simple

source

and

re-

sulting

radiation,

Net

change

in

volume

is

equated

to

volume

displacedby

piston

area

A

conceived

as

moving

with the

bridge-string

contact

;

in this way

one

can esti-

mate

series

radiation

resistance

referred

to the

same

point

for which

equivalent

mass

and

stiffness have been

measured. Themotion

at

the

string

is

greater

than

that

at the

left foot

of the

bridge by

a

factor

of

about

1.5.

From

Meinel's data

:

Amplitude

left

foot 28

n

Amplitude

bridge

slot

(lever

ratio

1.5)

42

Average

amplitude

over

plates

7 /_

Area,

two

plates

(ribs

neglected)

1000

sq

cm

Since

424

-

7X

A

-

1

70

sq

cm

Considering

the body

as

a

small

source,

radiation re-

sistance

»po/M

2

/<_

turns

out

at

470

eps

in this

example

to

be

700

cgs

mechanical

ohms.

This

is

a

component

of

the

total resistance to

bridge

motion,

viz.,

(SM)*/Q.

With the value

previously

mentioned

for

a

particular

violin

as

the

numerator,

and

as

denominator

Saunders'

smallest

value

of

Q,

thetotalresistance

is 5900

cgs

ohms.

Radiation resistance is therefore

12%

of the

total.

Lacking

measurementson

the

same

instrument,

we

have

chosen

data

so

as

not to

overestimate

radiation. Us-

ually

it

will

be

considerably higher

than

12%.

Radia-

tion

efficiency,

however,

is not

to

be confused with

over-all efficiency, which is much lower

owing

to

in-

efficiency

of

conversion

at

the

bow.

Similar

study

at

other

body

resonances

might

prove

interesting.

IV.

AIR

RESONANCE

The

plate

motions that

produce

the

simple

source

of

the

previous

section

cause

changes

in the

opposite

sense

in the airwithin the

body.

The

equivalent piston

area

is the same. If frequency is

very

low,

the air

passes

through

the

/holes

without

change

of

pressure;

if

high,

the air

is

trapped

and

compression

occurs;

the

cavity

11

F. A.

Saunders,

J .

Acoust. Soc. Am.

17,

169-186

(1945).

with its

ports

in this

oversimplified

concept

is thus

a

parallel-tuned

circuit

[HK

in

Fig.

(lb)],

8

and

has

an

obvious

similarity

to reflex-bass

enclosures

in

loud-

speakers.

(To avoid

anachronism the

comparison

should

be reversed.) Of the

many

modes

possible, only

the

lowest in frequency is

important.

Similarity

to

a

Helm-

holtz

resonator

is

obvious.

However,

with

as

peculiar

a

shape

as that

of

the

/

hole and with

nonrigid

walls,

one

hardly

expects to use

Rayleigh's w=c(<f/F)*,

even

though

he showed

12

'

that

with

elliptical

ports of small

eccentricity

the

same

fre-

quency

occurs

as

with

a

circular

one

of

equal

area.

As

a

matter

of

fact,

the

expression yields

rough

estimates

with

/

holes,

the

area

of one

being

considered

with

half

the

volume.

13

The frequency

thus

calculated will

be

a

semitone

or so too

low.

Along

with the

measurements of

logarithmic

decre-

ments of

body

resonance,

Saunders

11

measured decre-

ments associated with

the

decay

of transient oscilla-

tions

at

air

resonance

for

many

violins,

old

and

new.

The total decrement

comprises

components

from several

causes: useful

radiation,

surface

absorption,

viscosity

in the

air,

and

wall motion (loss

in

the

wood).

It

would

beuseful toknow

their

relative

importance.

Radiation decrement.

It can

readily

beshown

that

the

logarithmic

decrement to base

10

caused

by

radiation is

which

applies

onlyto

the

lowest

mode,

forwhich volume

is

very

small

compared

with

a

cubic

wavelength.

Wall

motion

is

assumed blocked.

Wall-surface

loss.

This is the component ascribed

to

the surface

regarded

as

stationary. Absorption

coeffi-

cients

derived

from

architectural

acoustics

may

be

used.

By

contrast,

the

violin is much smaller

than

a

wave-

length

at

resonance,

and

pressure

and

phase

are sub-

stantially

the

same

throughout

the volume.

For

small

absorption

coefficients

a

w

,

the

logarithmic

decrement

to

base

10

of

a

large

enclosure

(all

boundaries

of same

ma-

terial) is

l4a

5

w

=0.543c5o

w

/7/.

It

can

be

shown

that

equal

energy

densities

produce

mean

squares

of

sound

pressure

on

the walls of

violin and

room which

are

in

theratio

1/2

to 1

;

decrements are

in

the

same ratio.

18

v

Lord

Rayleigh,

Theory

of

Sound

(Dover

Publications, Inc.,

New

York,

1945)

:

(a)

Article

306,

p.

179;

(b)

Article

225;

(c)

Arti-

cle

214,

Eg. (2).

v

If the

cavity

werebisected

by

a thin

longitudinal

wall,

there

would

be

no

effect

on frequency

of

air

resonance.

Calculationin-

dicates that

frequency

is lowered

about

one-fifthtone

by

the

air

mass

added

by

plate

thickness.

"

L.

L.

Beranek,

Acoustics

(McGraw-Hill

Book

Company,

Inc.,

1954):

(a)

p.

305;

(b)

p.

300.

11

The

reason

becomes

apparent

onconsiderationof

a ny

oblique

mode

in a

rectangularspace

in

comparison

with the

(0,0,0)

mode,

an

approximation

to

which can

be

realized

by adding

a

port,

as

in

the

Helmholtz

resonator.

In

the

zero

mode,

p?

averaged

along

an

edge

exceeds

thatfor

an

oblique

mode

by

one

factor of

2,

over

the walls

by

two

factors

of

2,

and

overthe volume by threesuch

since the

average

valueof cosine

squared

is

\.

Decrement

isproportional

to

p

averaged

overthewalls

(rate

of

dissipation),

divided

by

ft

averaged

over the

volume

(energy

storage). This

adds

a factorof

4/8,

or

to

theratio ofthedecrement

for

the

zero

order

divided

by

that

for

the

oblique

mode.

8r

=

(2t

B

F /X

8

)/2.30=

27F/X

8

, (2a)

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No.

3

(Series

II),

May

2001

1

Schelleng

-

The Violin

as a Circ

Fig.

2.

Simplification

of

Fig. 1(b), showing

air

resonance

and

one

body

resonance.

Hence

wall-loss

logarithmic

decrement in theviolin

is

Viscosity

in

the

air. It

is

assumed

that

with ports

as

wide

as

the/

holes in the standard

violin,

this

is

a

negli-

gible

effect.

Loss

within the wood.

In

the

simplified

circuit of

Fig.

2,

a

transient in HG would suffer

loss

from resis-

tance

Ri

unlesswall motion were

blocked

during

meas-

urement.

Calculation

suggests

theeffect to be

appreci-

ablebut

possibly

not

large.

However,

it

seems desirable

to excludefrom the

definition

of this

decrementeffects

of important

circuit

elements

such

as

Rb,

which

are

shown

explicitly.

One

would include

effects

of

modes,

if

any,

that

are

not

directly

excited

by

the

bridge.

Discussion. The

losses

contributing

most

to the

decre-

ment

of the

air

circuit

as

thus defined

seem,

therefore,

to be wall-surface

loss and radiation.

For

a

given

fre-

quency

a

change

in

volume

affects these

components

oppositely,

one

varying inversely

and

the

other

directly.

Account

also

must

be

takenof the

fact

that

B

may

be

a

function

of volume. A

question

.often

raised

concerns

the

best

height

of

the

ribs,

dimensions of

plates being

determined

by

other

considerations.

In

Fig.

3 are

plotted

computed

values of these components and

their

sum.

Account

was

taken of

the

fact,that

S

includes

the

area

of the ribs. Resonance frequency (wavelength) is held

constant

by

changing

width of

/holes

or

by

use

of addi-

tional

ports.

The

used is

0.04,

the

value

for wood

floors

on

solid

foundation,

1411

architecturally

a

small

value.

For assumed

values of parameters, the two

compo-

nents

are

equal

for

arib

height

of5

cm.

Their

sumhas

a

minimum

between3

and 4 cm.

This

may

be

compared

with the rib

height

used

by

Stradivarius,

3.0

cm.

It is

true that theminimum is nota

sharp

one,

and that

its

calculated

value

will shift somewhat with better data.

Nevertheless,

the

agreementseems

significant, as does

the

consistency

with Saunders' data.

His median

value

of

0.115

contains

a

significant

amount

resulting from

wall

motion.

The value shown

by Fig.

3

is 0.105. It

would,

of

course,

be

a

mistake

to

lose

sight

of the con-

siderable

spread

from instrument to instrument

—

from

0.09 to0.14

—

and the

fact

thatthe

computation

depends

on

choice

of

particular

values

of

a_»

and

/.

Other

air

modes. Because

air

resonance is

important

in the

lower

register,

it

is

sometimes

supposed

that the

many

natural modes

of

the

cavity

must

play

an

impor-

tant part in the

upper ranges.

It is

argued

that

the

volume

is

large

enough

to support

dozens

of modes

within

the

range,

and

that these

must be

helpful.

The

experimental

evidence, however,

is that

they

are of

little

or no

value. Saunders

10

reported

that "there

ap-

peared

to

be

upper

resonances

near

1300,

2600,

and

3660"

in

a

certain

violin,

but his

general

conclusion

was

that the

output

from the

/

holes is

unimportant

except

near

the

lowest

resonance.

To

be effective

a

natural

mode

has

to

satisfy

two re-

quirements:

it

must

be

energetically

excited

by

the

walls,

and it

must

be

"impedance-matched"

to the

/

holes.

The

lowest mode

satisfies

both

by

design.

It is

excited

because

the

wall

motion

provides

thenet

changes

in

volume

7,816

required

to induce

"zeroorder"

pressure

changes.

Secondly, its

very

existence

depends

upon

there

being

an

air

flow

through

the

/

holes,

that

is,

upon

radiation.

By

contrastconsider the

other

modes

:

their

geometric

structures,

except

by

accident,

are un-

related

to

those

of the

wood,

and there

is

no

obvious

basis for

expecting

power

transfer

to the air

within.

Moreover,

such

excitation

as

may

fortuitously

occur

will not

necessarily

cause

the

breathing

through

the

/

holes

neededfor

radiation

;

theholes

are

apt

to be too

small

or

too

large

or

in

the

wrong place.

V. COMBINATION OF AIR

AND

BODY MODES

Air and main

body

resonances are

not

isolated

means,

but

in

good

instruments are matched

for

best

total

effect

to

insure

a

strong

lower

register.

In

studying

cir-

cuit

behavior,

they

need to be considered

together.

The

problem,

which is

complicated,

will

here

be limited to

simple

conditions.

To this

end,

consider thecircuit

of

Fig.

2

in

which

one

resonant

body

mode is assumed

to

predominate,

its

series

circuit

being

in

series

with

the shunt

resonant

cir-

cuit

representing

the air

circuit,

and

its

impedancebeing

sufficiently great to control

wall

velocity.

17

Here the

acoustical circuit HG has been transformed

into

its

mechanical

equivalent

in terms of linear

velocity

at

C,

thetop of the

bridge. Assuming

the

configurationof the

body

mode to be

independent

of frequency,

radiation

resistance of the

plates

(without

contribution

from the

/

holes)

is

proportional

to

frequency

squared.

'0'

O 2 4 6

8 10

12

14

cm

HEIGHT OF RIBS

Fig.

3.

Two

main

components

of

air

decrement.

»

H.

Backhaus,

Z.

Physik

62,

143

(1918);

72,

218

(1931).

17

A

more

refined

calculationwould

forego

the

last

assumption.

The

impedance

measurements that

Eggers*

made

on

a

cello

are

of interest

in

this

connection.

*„=

0.027&W

Vf~

0.027Sa

w

\/V.

(2b)

1-0.2-

;

cr

0.1

-

\

|

xs°

-~

O

-

£>-<

—

8/17/2019 2001 N.3 VOL.4 CASJ


18

CASJ

Vol.

A,

No.

3 (Series II),

May

2001

Schelleng

-

The Violin as a Circuit

1/5

-j

oj

a.

v

U

1

1.5

2

3

FREQUENCY

ELATIVE

Fig.

. 4.

Relativesound

pressure,

air

resonance,

and

one

body

resonance. I n

the

violin

other

peaks

occur at

the

right.

Following

the method of

Appendix

I,

relative

performance

is calculated

for

the following

typical

condition :

Air

resonance

atrelative

frequency

Q»tr(mean

of

Saunders'

values)

Body

resonanceat

relative frequency

Qbody

(Saunders'

mean)

1.0

«12.

The

dotted

curve of

Fig.

4

depicts

radiated

response

without

air

resonance,

a

condition that

might

be

real-

ized

by

usingvery

large

volume

or

by

closing

the/

holes

;

the

violin now

has the

advantage

of

enclosure,

but

not

of

air

resonance. If resonance is

now

permitted

and

ad-

justed

to

an

interval of

a

fifth (frequency ratio

of

3/2)

belowbody

resonance,

the light

solid

line

gives

the im-

provement in

decibels.

Finally,

the

combination

is

shown

by adding

the

two,

giving

the

heavy

solid line.

The air

curve

has

several

features

to notice.

Most

prominent,

of

course,

is

the

resonance

peak.

At lower

frequencies

the air

advantage

falls

off

until,

atrelative

frequency

0.7,

half

an

octave,

it becomes

zero.

Within

practical

bounds,

a

differenceof

Q(ot

8)

would

notaffect

this

conclusion,

though

it could

change response

radi-

cally

within

10%

of resonance.

In

violas

air

resonance

is

not

infrequently placed

eleven

semitones

(frequency

ratio 15/8)

above

the lowest

fundamental,

which

con-

sequently

suffers

an

"air-resonance

disadvantage"

of

8

dB,

though

the second and third

harmonics can be

in

a

very

strong

position.

The

curve

is

somewhattoo

opto-

mistic

at its

high-frequency

end

because

of

oversimpli-

fication in

circuit

representation.

It seems safe to

say,

however,

that there

is some

gain

over an

entire

octave

and 9 dB

ormore

over

half

an

octave.

The

curve for

body

resonance

alone,

instead

of fall-

ing

to

very

low

values

at

high frequencies,

approaches

a

horizontal

asymptote, a

point

of considerable

signi-

ficance.

This

behavior,

whichholds

for all modes

above

resonance

and which

has its

counterpart

in direct-

radiation

loudspeakers,

is the

result

of

two

opposing

tendencies.The conformation of amode

and, therefore,

its

equivalent

mass are taken tobe

independent

of

fre-

quency

;

hence,

the

velocities

set

upby

a

given applied

force

vary inversely

with

frequency.

But the sound

pres-

sure

radiated

by

a

given

velocity

is

directly

proportional

to frequencyand thus annuls the effectof

the

decline

of

velocity.

Thewayin

which

thevarious

modes

will

com-

bine

depends

upon

the

phase

relations

of their

simple

sources;

it is

plausible

to

suppose,

however,

that the

lower

modes

thus

provide

a

more or

less

leveltable

land

on

which the

higher

ones

erect their

peaks,

and that

this

is

an

important

contributor

to violin tone.

Another

result

of

Appendix

I is

an

expression

for the

ratio

of

sound

pressures

produced

at

body

and

air

resonances

:

pMv/pair^h/fcnQb/Qa).

(3)

This

agrees reasonably

well with ratios

found from

single-frequency

curves

by

Saunders

(see

reference 11,

p.

173).

How

important

are

the

(?'s?

In

Fig.

4

the

effect

of

an

increase in either

Q

beyond

usual values

produces

an

elevation

of level within

a

very

narrow

band at

reso-

nance,

an effectas apt to be

harmful

tonally

as

helpful.

Thereseems little to seek

in

a

Q

higher

than that

which

gives

a3-dB

bandwidth

of

one tone

—

a

QofB

or9

—

and

there

may

be

something

to

avoid in bandwidths

that

can be straddled

by adjacent

semitones.

The

impor-

tanceof

resonances,

in

other

words,

is

to

provide

broad

foothills

rather than

sharp

peaks.

What is the best

volume

to be used?

It

is

significant

thatin

approximate Eqs.

(1), (2), and (3) of

Appendix

I,

volume

does

notappear

as

an

explicit

term affecting

radiation. It is

true

that

resonant

impedance

of

the

shunt

circuit increases asvolume

decreases,

suggesting

an

advantage

because more

power

can be abstracted

from the constant

velocity

source. But this is

opposed

by

reduction of radiation

decrement

and, therefore,

of

radiation efficiency,

leaving

a

change

of

only

second-

order

importance.

There is

another

consideration,

however.

In

good

in-

struments

the

"piston

area"A

(see

Sec. Ill) is made

as

large

as

possible,

so

large

in fact that the

impedance

offered

to the

motion

of thetop

plate

by

airresonance is

by

no means

negligible.

The

sign

of its

reactance com-

ponent

at

a

frequency somewhat

below

resonance

is

positive,

so as to

tend

to cancel

the

negative

reactance

of the

body.

If thevolume

is

now

made

too

small,

this

cancellation

can

be

complete,

so that the

impedance

into

which the

string

works is

a

relatively

low resistance

capable

of interferingwith the

normal

operation

of the

bow. Somethingof this

sort

seems

to

be

the

reason

for

the

airtone

"wolfnotes."

18

11

The

behavior

andelimination ofairtone wolfnotes

have been

studied

by

F. A. Saunders (private

communication). Impedance

measurements

byEggers,*

Fig.

18,

areof interestin this

connection.

1.5

=

14.5.

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3

(Series

II),

May

2001 1

Schelleng

-

The Violin

as a Cir

Fig.

5. Elementsof

wolfnote

circuit.

VI. THE WOLFNOTE

The most troublesome

wolfnote,

however

—

a

cyclic

stuttering response

to

the

bow on

the

heavier

strings,

particularly

in cellos

—

can occur whenthe

fundamental

is

within

a

half-tone or

less

of

the

main

resonance;

it

may

occur in

otherwise

fine instruments.

Its

behavior

immediately

suggests

beating

and

coupled

circuits. The

best

explanation

has

beenone

published

by

C.V.

Raman

45

years

ago.

Having

much

in common with his

theory,

the present

one,

which is stated in the

language

of

circuits,

differs

in

one

important

respect.

Through

most

of

the frequency

range

the

impedance

presented by

the

bridge

is

high compared

with the

characteristic

impedance

of the

strings,

perhaps

ten

times or much more.

Trouble

may

ensue

at

resonance

when

this

ratio is

well below

ten,

and

the

Q

is in the

range

found

by

Saunders.

In

this

study

it is the

impedance

presented

to thebow

that

is the

most

informative.

Calculations

must

take

account of the

distributed nature

of the

mass

and

com-

pliance*

of the

string,

hence

requiring

standard methods

of

computation

for

transmission

lines,

as

indicated in

Fig.

5 and

Appendix

11. Resistance in

the

string

itself

is

neglected.

19

For

generality,

.equations

are

written in

terms

of

dimensionlessratios:

impedance

relative

to

X,

the

Q

of the

bridge

circuit,

ft and

ft,,

and the fractional

part of the

string length

between

bow and

bridge.

Since

wolfnote is not sensitive

to

the

latter,

two

parameters

Q

and

K/'SiMb)*

remain

as

thefundamental

data

pre-

scribing

circuit

behavior when

impedance

seen

by

the

bow

is considered

as

a

function

of frequency.

In the

normal

situation,

the

string

presents

to

the

bow

an

unambiguous

impedance

;

it

is thatof

a

simple

series

tuned circuit

having positive

resistance

low

enough

to

be

matched

by

the

negative

of the

bow-string

contact,

and

reactance

that

passes through

zero

at

thefrequency

of operation

as

shown

for

the

fundamental

by

the

broken

line

in

Fig.

6(b).

Though

still

not

a

simple problem,

in

view

of the

complicated

impedance

pattern

inwhich the

various

components

must

seek

a

compromise

frequency,

the situation

contains no

obviously

tempting

invitation

to misbehavior.

By

contrast,

consider the

impedance

pattern at the main resonance as shown

in

Fig.

6,

in

which

for

a

given

string length

(e.g.,

1.028) there

is

not one

but

three

frequencies

at

which reactance

is

zero. Steady

oscillations

can

conceivably

occur at

any

»

H.

Backhaus,

Z.

Physik

18,

98

(1937).

of

these

frequencies.

20

If

the

negative

resistance is

in-

sufficient

to

cope

with the

high

resistance at the

point

of

tuning,

it

may,

nevertheless,

be

adequate

at

the

two

outside

points.

That

is to

say,

if bow

pressure

is in-

sufficient

for the

normal

vibration,

itstill

may

be

enough

for

the outside

pair

because of

their

lower

resistance.

Let

these frequencies

be

(jy+A/2)

and

(ft'

-A/2).

If

amplitudes

are

equal,

total

string

velocity

will be

pro-

portional

to

the

familiar

expression

for

a beat.

Speaking in

terms

of

"instantaneous"

frequency instead of

Fourier

compo-

nents,

this is

a

wave of

average

frequency

ft'

pulsating

at frequency

A.

Frequency

is

always

ft',

but there is

a

phase

reversal in

passing through

zero

amplitude.

Raman

9

criticized G.

W. White's

suggestion

21

that it

is

a

beating

process

on

the

ground

that

one of

the fre-

quenciesmust

be

that

of afree oscillation

thatwill

soon

decay.

I

believe

the conclusion incorrect that there is

no

beating.

The

two

oscillations

suggested

here

are

equally

forced.

These two

oscillations

(referred

to as

the"fundamen-

|l

J

1

iS

20-

A

<

J \

(a)

fc

10

y

V

£

OX )

i

c

.92 .96

10

Ijo4

IjoB

1.12

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FREQUENCY

A

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L r

oj

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or

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Fig.

6.

Impedance

seen

by

bow

(Z\+Zi

of

Fig. 5); (a)

and

(b)

fora

bad

in

(c),

1,2,

and

3 show

consecutively

im-

proved

conditions.

"Even

though

the

negative sign

of

reactance

slope

raises

a

question

of

stability,

with

the

highly

nonlinear

behavior

of the

bow-string

contact,

the

stabilizing

effect ofharmonicson

a

string

free

of

phase

distortion

wi ll i n

borderline cases

probably permit

oscillations

in

spite

of

the

slope.

«

G.

W.

White,

Proc.

Cambridge

Phil. Soc.

18,

85-88

(1915).

bow

.bridge

i. i.

|-Z,I

M

m

body

(inqer^

T

»j

2**

(sm>Vq

?

■

*_

Hi

,

£

1

J

cos2tt

(ft'+

A/2)

+

cos2jt

(ft'

-

A/2)

-2cos2irft'coS7rA/,

(4)

1

X*

0.0122

2

„

=

12.5 X

«

"

3

=

12.5

X

=0.0074

8/17/2019 2001 N.3 VOL.4 CASJ


20

CASJ

Vol.

A,

No.

3

(Series ),

May

2001

Schelleng

-

The Violin

as a Circuit

tal

pair )

are not the

only

sinusoidal

components

that

move

through

the whole

beat

cycle

substantially

un-

changed.

The

same is true

of

the even

harmonics

of

ft.

Raman

showed

that the

octave

becomes

prominent

at

thebeat

minimum.

Curiously

enough,

this

prominence

is

notbecause the

even

terms have

grown,

butbecause

the

odd

terms

have

subsided

;

the sawtooth

at

its maximum

amplitude

contains

even terms ofaboutthesame

ampli-

tude

and

phase

asat theminimum. This is

brought

out

clearly

and

simply by

a

graphical

separation

ofodd

and

even

terms

in

the waveshown

in

Fig.

7(a).

22

Themaxi-

mum

displacement

of the

even

components shown in

Fig.

7(b)

is abouthalf thatin

Fig.

7(a), and

the

slopes

of the

long

sections are the

same,

matching

the

same

bow

velocity.

Addition

of

Figs.

7(b)and 7(c)

shows

how the

intermediate

discontinuities have been

cancelled

by

the

odd

terms

of

Fig.

7(c).

Removal of

the odds

will,

there-

fore,

bring

the "octave"back.

An

important

differencebetween

a

linear and

a

non-

linear

generatorneeds

mention.

In

the

former it

is

pos-

sible

for

oscillation to

occur at

one

of the

fundamental

pair

alone.

The

principle

of

superposition gives

them

complete

independence.

But with

bowing,

therecurrence

rate

depends by

virtue

of

the

necessary

harmonics on

the

string length

and the

string's simplephase

character-

istic. Neither

of the

pair

can

exist

without the

other

because its frequency

is so differentfrom

a

recurrence

rate

possible

on

the

string.

On the other

hand,

by

co-

operation they

can

produce

an

instantaneous

frequency

acceptable

to the

string,

equal

to

half

the

trigger

rate

of

Fig.

7(b).

Like Siamese

twins,

they

can

exist

as

a

pair,

but nototherwise.

If

this

theory

is

correct,

it shouldbe

possible

from ex-

perimental

evidence

to

show

that

an

epoch

of

maxima

has

undergone

a

phase

shiftof

t

relative

to

the

preceding

one. This

can,

in

fact,

be seen

in

Raman's

oscillograms

(Plate

I

of

reference

3),

which

show simultaneous

mo-

tion

of

bridge

and

string,

that of the

string

being

sug-

gested

in

Fig.

8.

At

the

epoch

where

the

amplitude

of the

bridge

motion is

growing

most

rapidly,

the

string,

as

Raman

indicates,

has

a clean sawtooth

displacement.

At

this

moment

bridge

amplitude

is

matched

to

bow

velocity

and

pressure.

The

amplitude

of

bridge

motion

continues

its

growth

for

a

time,

but the

sawtooth

shows

signs

of

deterioration

in the form of new

discontinuities

midway

between those of the series

just

considered.

Fio. 7.

Separation

of

evenandodd

terms

of

ideal-

ized

string

displacement.

H

Odd

components

of

J (pl)- [J (pt}-f{pt+ir)y2]

even

components

-

tf(pt)

+/(#+*)

j/2.

0101010101010 1010

amplitude

t

maximum t

rnoximum

growth

rote

decoy

rate

Fig.

8. String displacement

through

one

wolfnotebeat.

This

new

series

is

destined

to

be

the

sole series

of

dis-

continuities

during

the next

period

of

bridge-motion

growth.

To

see this in the

original

oscillograms

requires

close

examination,

preferably

with

a

magnifying

glass,

23

but it is

readily

followed in

Fig.

8. If

we

place

a zero

adjacent

to each

clearcut

discontinuity

at the

left

and

a

1

midway

to the

next

later

discontinuity,

and

con-

tinue

this alternate

naming through

the

octave

period

to the

nextclearcut

stage, we

find

that the

discontinui-

ties

of thelatter

are named

1,

not

0.All

threetransitions

shown in the

original give

the same result.

This indi-

cates

a

phase

shift

of

180°

in instantaneous frequency

in

passing

through

the

minimum,

and

this,

of

course,

is

what

a

beat

requires.

The bad situation

shown

in

Figs.

6(a)

and (b) is

greatly improved

in

Fig.

6(c)

byreducing

Q

from 25

to

12.5.

Though

the

S

shape

remains,

the

reactance

curve

is

nearly

flat in

the

region

of

interest,

thefundamental

pair

closer

together,

and their

resistances

just slightly

less

than

at

midband.

It is doubtful

that

a

wolf could

occur.

Curve (3)

shows the

further

advantage

of

re-

ducing

characteristic

impedance

of the

string

through

reduction of

weight.

The

side

frequencies

have

now

dis-

appeared.

That

light strings'

help

is,

of

course,

well

known.

The

rate

at

which

beating

occurs is consistentwith

the

difference

in frequency

within the fundamental

pair.

Applying

Fig. 6(c)

to

the

cello,

the

indicated

rates

for

conditions (1) and (2)

are,

respectively,

16

and

8

per

sec.

The

delays

of

bridge

maximum

with

respect

to

string

maximum

are

calculated as

0.36

and

0.17

of a

beat

cycle

for the

same

respective

conditions,

agreeing

with

Raman's

8

0.25,

which

would have been

found here

had

Q

been

taken

at

the

more

typical

value

of

17.5.

Finally

it should be

re-emphasized

that

conditions at

harmonic

frequencies

may

have some

connection with

wolfnote,

and

that

(1)

the

distance of the

strings

from

the

nodal

line about

which the

bridge

swings

and (2)

the

angle

of

bow

motion

certainly

do

have an

effect.

One

experimental

condition

was

to

bow

the cello

C

string

(the

lowest)

underneath

rather than over the

strings,

with hand

held

as

high

as

possible

without

the

bow

touching

the

wood.

On this

most "wolfish" of

strings,

the

wolftone,

as

expected,

disappeared.

Wolf

one

criterion.

It

is

desirable

to show

graphically

the relations

prevailing

under

different conditions of

susceptibility

to

wolftone.

To this end

Fig.

9

provides

dimensionless coordinates

onwhich

can

be

exhibited

es-

sential

parameters

applying

to all

instruments

of the

violin

family,

viz.,

K/'SbM

b

)*

and

logarithmic

decre-

M

The

reproductions

in

a communication

to Nature

are

notclear

enough.

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

A,

No.

3 (Series ll)

;

May

2001

2

Schelleng

-

The Violin

as a Cir

10

Q

■

its

patternof wood resonances with

respect to those

of

string

and

air.

If

he is

designing

an

instrument

to

occupy

a

new

frequency

range,

all

of

these

resonances are

changed

with

respect to

those

of instruments

that

have

become

conventional

to him.

If

hewishes

to

change

size

without

changing

frequency

range,

either to

accom-

modate

smaller

hands

or

to

allow

larger

ones

to

work

to

better

advantage,

an

understanding

of the

principles

governing

modified

dimensional

scaling

will

be

helpful.

Complete scaling

is

theoretically

no

problem;

all

that

is needed is

thoroughgoingchange

of all dimensions in

proportion

to

change

in air

wavelength,

and

use

of iden-

tical

materials.

(Actually

the difficulties of

even one-to-

one

scaling—

that

is,

copying—are

considerable,

partly

because

of

unavailability

of identical

materials;

this

ever-present

problem

is notconsidered

here.) In

general,

complete

scaling

is not

practicable

because of the im-

possible

demands

that it

places

on

strength

or size

of

the

player,

or

for other

reasons.

Failure

to understand

scaling

leads

to

errors in

construction

;

for

example,

in

making

a

viola

24

luthiers have

sometimes chosen

a

plate

thickness

in

proportion

to

that of a

violin; however,

this is

too

much.

10*

,

6,0

Fto.

9.

Wolfnotecriterion.

ment. The

heavy

line shows

the

locus of conditions for

which

the

midpoint

of the

5

curve in

Fig.

6

is

horizontal,

i.c:,

on

the

verge

of

having

three

intersections;

it is the

boundary

between

safe

and

questionable

conditions.

On thebasis of

data

previously

cited for

one

cello and

Saunders'

median

8, points

are

plotted for

the three

strings

that

are

used

to

produce

the

frequencyof main

resonance.

For

the

cello

D

string,

the

point

falls

close

to

the safe

area as

one expects

from

experience.

For the

heavier G

string,

the

point

is definitely

away

from

the

"safe"

region,

also in

agreement

with

experience

;

being

much used in this

position,

this

string

causes the cellist

the

most

annoyance.

In

going

to

the

C

string,

one

would

expect and

one

finds

that it

may

be

very

difficult in-

deed.

Fortunately

this

note

is

played

on

this

string

rel-

atively

infrequently.

The

point representing

a violin

indicates

relative freedom from wolftone.

Before

undertaking

to

scale,

it is

necessary

to

decide

on

basic

aims

and

the

compromises

one

is

willing

to

accept. Discussion

here

will be

limited

to conventional

instruments

;

for concreteness

we

shall

rather

arbitrarily

regard

the violin

as

the

most suitable

starting point,

and askwhat this leads

one

to

expect

about the viola

and

cello

and

their

strings.

There

are

three

basic ratios

to

consider:

Eliminating

the

wolftone.

The

instrumentalist is

rarely

interested

in

an

explanation.

What

he

wants is to

have

the

curse

removed.

The

idea

occurred

to

the

author

and

to

others'

to insert a narrow-band

suppressing

circuit

in series

with

the

bridge

motion.

This is

most conven-

iently

done

by

attaching

to

one of the

strings

between

bridge

and

tailpiece

a

mass

of a few

grams

chosen

to

tune

the

string

end

to

thewolfnote. On

the

cello

tuning

can

bedone

by

ear

by

tapping

the load with the

eraser

of

a

pencil

used endwise.

Without

tuning

there

is

no

guide

to

adjustment.

A second

precaution,

not

always

necessary

butto be

recommended,

is use of

a

suitably

lossy

or

nonringing

substance such as the rubber

of

a

large

pencil

eraser. Calculation indicates

a

desirable

Q

to

be

10

or

less,

soas to

give

a

wider

band

than the

main

resonance.

The

less

obstinate

thewolf, the

farther

the

load

may

be

placed

from

the

bridge.

Hutchins finds

molding clay

very

convenient,

since

it has desirable

loss

and

its mass is

easy

to

adjust.

Avoidanceofwolftone

by

means external to the

body

may give

more

freedom

to themaker

in other

respects,

such as

ability

to

use

wood

of

high c/p

(see

Sec. VIII).

(1)

The lowest

frequencyof

the newinstrument is

to

equal

that

of the

violin

divided

by

c.

That

is,

air

wavelength

is

multiplied

by

that factor. For the viola

c=l.s,

for cello 3.0.

(2)

The

instrument

being

thought

of

as

lying

on

its

back,

its

shape

as seen

from

above,

is similar to that of

the

violin,

and all horizontal

dimensions

are

multiplied

by

a.

Fora

16$

-in. viola a-

1.17,

for

a

typical

cello 2.1.

(3)

The

pattern of

body

resonances

is to

remain

the

same

logarithmically,

and

wavelength

of themain reso-

nance

is to be

multiplied

by

tj.

Usual

practice

places

-n

at 1.33 for the viola and 2.66

for

the cello.

Thesefactors are

defined

so

astobegreaterthan

unity

in

going

to viola

orcello. Plate

shapes

not

being

strictly

the

same,

a

involves a small

compromise.

In

a

completely

scaled

instrument,

the air

resonance

takes care of itself.

Incompleteness

will be

evident

in

width and

thickness

of

ribs and width

of/

holes. It

seems

desirable to

scale

length

of

/holes.

Ribs

can

be scaled

according

to

principles

of

air resonance (Sec.

IV).

A

reservation

with

respect

to thearch

needs

mention.

The

rigidity

of

a

plate depends

on

(1)

its stiffness in

flexure

and

(2)

its two-dimensional

curvature.

With a

flat

plateonly

thefirst

enters.

(The

effect

onresonances

IL

DIMENSIONAL

SCALING

The

process

of

tuning

a

violin includes

more

than

adjusting

string

tension;

the

luthier

must

first

tune

**

I

amindebted

to

C. M. Hutchins for

informationon

this

and

other

matters.

25 20 17.5 15 12.5

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3

(Series II),

May

2001

Schelleng

-

The Violin as a Circuit

is somewhat

analogous

to

that in a

piano

string

where

two forms of

stiffness,

tension, and

rigidity

occur.)

While our

analysis

in

strictness, therefore,

applies

only

to

a

flat

violin

(thickness

graded,

however),

it

is be-

lieved to

give

numbers

of significance

even

considering

the arch."

For

a

flat

plate of

arbitrary

shape

and

graded

thick-

ness,

thebasicrelation isthatthefrequencyof

a

flexural

mode

is

directly

proportional

to

the

scale

of thickness

and

inversely

to the

square

of

a

horizontal

dimension.

We

assume

that themain effect of the

ribs,

aside

from

providing

enclosure and

coupling

between

plates,

is

that

of

mass

loading

atthe

edges,

which

are

by

no

means

immobile.

7

1

The

idea

that,

in

scaling,

total mass of ribs

should

remain

proportional

tomass

of

plates

is

suggested

by

the

fact

that in the cello

they

are

proportionately

thinner

than in the

violin,

their

height being propor-

tionately

greater.*

4

Thickness.

Subscripts

1

and

2

refer

respectively

to

the

model

and

the

"new"

instrument.

H

is

thickness

at

some reference

point.

We now have

/i-MTi/P

and

■/«-**«/*_*,

(5)

I

being

length,

and

since

/i//s= =Hio^H^

Stiffness.

Consider

design

in

two steps

—

first

to

an

intermediate instrument

completely

scaled

by

factor

a-

ancj

indicated

by

primed

symbols.

A

general

relation

for stiffness S

of

dimensionally

similar

shapes

is

Altering

intermediate

to

new*

change

of

thickness affects

stiffness in

proportion

to

the

cube,

or

and from

(6) and

(7),

the ratio of stiffness

entering

into

corresponding

resonances.

Mass.

Corresponding

masses

are

proportional

to

total mass of the

plate

:

The

tendency

for deformations

to

be*

predominatelyinexten-

sional

(potential

energy

purely flexural)

is discussed

in

Rayleigh's

Theory

of

Article 235 b.The factthatthearchdoeshavean

effect

in acoustical

behaviorhas

recently

suggested

that

similarity

of behavior shouldresult

if in

scaling

wemaintain thesame

ratio

between

flexural

and

extehsional

potential

energies.

An

elementary

analysis

indicates

that

this

is obtained

simply

by scaling

alti-

tudeofarchaccording

to

aYi*

thesame

factorused

in

Eg. (6)

in

scaling

thickness;

that

is,

by

holding

constant the

ratio,

arch/

thickness,

rather than

the more

naturally

used

ratio,

arch/

horizontaldimension.

Since arch is a means

of

adjusting

promi-

nence

of high

frequencies

with

respect

to

lows,

and since low-

voiced instrumentsdonot

necessarily

requirethe same

balance as

high-voiced,exact scaling of

the

arch

may

notbe

the

best.

Body impedance.

CMf«)VCSitfi)*-»

4

M

(ID

Ultimate

strength.

Ratio

of

ultimate

strength

of

forms

completely

scaled is

and

if

as in

the

flexural

strength

of

isotropic

materials,

This is

the

same as

for

body

impedance,

Eg.

(11).

Strings.

General

opinion,

borne out

by

the

need

of

old

instruments

for stronger bass

bars,

is that

string

tension T with afactor of safety

is

set

with

relation

to

ultimate

strength

of the body.*

4

Therefore,

from

Eg.

(14)

It

follows from

Mersenne's law

for

strings

that

M*/mi*<tVM

(16)

From

(16)

and (15)

ratio of

characteristic

impedance

is

K ^K o*

(17)

"Wolf

ratio."

Finally

taking

ratio

of

Eqs.

(17)

and

(11), we have

iKt/iSiMtVytKi/iSiMi)*]**

e/<r,

(18)

expressing

the

relative

impedancepositions

in

Fig.

8.

In

order to check

these

relations

experimentally,

in-

struments

compared

must

embody

the

uniformities

of

construction

assumed.

In

individual

instruments

this

is difficult assurance to

gain.

However,

certain

general

relations

may

be

tested.

Thus,

Eg.

(6)

indicates

why

in violas

and

cellos

thickness

is less than for

complete

scaling

since

i}><r.

Again according

to

Eg.

(15),

one

ex-

pects

cello-string

tension

to

be 2.7

times

as great as

in

the violin (<r=2.l,

*j=2.7);

for

two sets of

strings

com-

pared,

the

ratio was 2.4.

Equation

(18)

is

particularly

interesting

since

it

ex-

plains

why

wolftone

trouble increases in

going

from

violin to viola to

cello;

the

reason

is

simply

that

the

sizesof the instruments have not

been

increased in

pro-

portional

to

theair

wavelength,

andmaximum safe

ten-

sion has

been

insisted

upon

in the

strings.

Thechronic

susceptibility of

the

cello to

this

trouble

is

the

price

paid

for the

convenience

of a small

instrument,

small com-

pared

with

one

completely

scaled.

Since with

scaling

A is

proportional

to o-

4

,

and

/at

body

resonance

to

1/ij,

radiation

resistance that

de-

pends

on

_4*/

is

proportional

to

o*/if.

This is identical

with the

expression

that

Eg.

(11)

gives

for

body

im-

pedance.

It

follows

that

a

body-resonance

radiation

dec-

rement,

which

is

theratio of

these

quantities,

is

invari-

ant.

If

it

is

truethat

body

losses

dependprimarily

on the

wood,

we

may

conclude

thattotal decrement is

also

in-

H

i

/H

I

=o*/v

.

(6)

_?75i-r.

(7)

Vs'=

(ff

_/#)'= (Ht/cHtf; (8)

Si/Si-o*/*,

(9)

Mt/Mi**

o*.ff*/ii=a*/n.

(10)

r'/FW ,

(12)

F

2

/F'=

'Hi /H y o*/? , (13)

Yt/Yi****/?.

(14)

iyri-«*M (15)

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3

(Series

II),

May

2001

2

Schelleng

-

The Violin

as a

Cir

variant in the

scaling

process,

since

Rohloff finds

the

decrement

of wood to be

independent

of

frequency.

26

Within these

limits,

this

justifies the

name

"wolfratio

used

with

Eg.

(18). In absence

of

scaling,

we

require

measurementof

both decrement

and K /{S M)*

for

the

application

of

Fig.

9 to individual

instruments.

Vm.

ON

THE

REQUIREMENTS

OF WOOD

Violin

makers have

always

attached

great

importance

to

the selection

of

wood,

not

only

as to

species

but also

the

characteristics

of the

particular piece

to be used.

Acousticians have measured elastic

properties,

density,

and

damping

coefficients,

and the

more

scientifically

minded

makers

are

trying

to

take

advantage

of

such

procedures.

It is

important

to

relate

thesemeasurements

to

the luthier's

problem

in

as

simple

a manner

as

possible.

An

important question

is: When

are

two

pieces

of

wood

acoustically equivalent?

Should

one

try

to

match

both

the

elasticmodulus and

the density?

Along

and

across

the

grain

elastic

properties

are

dif-

ferent

velocities

of

compressional

waves

appearing

to

be in

the

orderof three or

four

toone. We

assume a

fixed

ratio

and

consider

theelastic behaviordetermined

by

a

single

modulus

E,

density,

and

scale

of

thickness.

As

in

the

previous

section,

flat

plates

of

graded

thickness

are

assumed.

Flexural

similarity

and

c/p. Having

given

a

reference

plate

(subscript

zero),

letitbe

required

to

duplicate

its

acoustical behavior

in

a

plate

of

different

material

(sub-

script

1).

Consider

any

point

and

a

line

through

it in

the

plane

of

the

plate,

the line

being

part

of

the

linear

wavefront

of

a

flexural

wave. Such

a wave

is

character-

ized

by

a

torque

per

unit

length

lying along

the

front

and

trayeling along

with it. This

torque

is

directly

re-

lated

to

the

potential

energy

of

the

medium,

which

is

momentarily

located

in

the

stiffness

at the

point

under

consideration.

Thekinetic

energy

is

similarly

associated

with

the

transverse

velocity

of the

mass

per

unit area

(rotational

energy being

negligible

in the

thin

plates

of

the

violin).

Flexural

behavior

is

similar

in the

two

plates

when

their stiffnesses per

unit

length

and

densities

per

unit

area are

equal.

Stiffness

per

unit

length

is

propor-

tional

toE

and

to

thecube of thickness (asin the

analo-

gous static

problem

of thebeam).

Hence,

EoHf E tHt.

(19)

Equal

densities

per

unit area

require

thatH

(i

p

(i

=Hip

h

or

Hi/Ha—

po/pu

(20)

This

means that even

if

we

are notable to

duplicate

c

and

p

separately,

reactive behavior

remains the same

if

»

E.

Rohloff,

Ann. Physik,

No.

5, 38,

177-198

(1940).

Fig.

10.

c/p

vs

Q

for various

species

of wood

(based

on

Barducci and

Pasqualini).

their

ratio remains

invariant.

However,

ratio of thick-

ness must

change

as

required

by

Eg.

(20).

c/p

and circuit parameters. The

ways

in

which

c,

p,

and

c/p

enter

into circuit

relations

may

now

be

indi-

cated. Consider

a

violin

plate

of

standard

shape

(width

vs length) and

assume

it

distorted in the

pattern of a

tap-tone

vibration.

A

stiffness

and

a

mass

will

be

in-

volved whose

changes

with

certain variables

are

in-

dicated

by

the

following

proportions:

Stiffness

S

«

EH3 *

Mass

M

a

pHP

Tap-tone

frequency

/&«

(S /M xcHl- *

Thickness H

(l/c)/^

(22)

Impedance

(SM)**

(Ep)KH**

(p/c)f

b

H*

(23)

Mass

M«(p/

)ftf

(24)

Since

f

b

and /

are

determined

by

considerations

un-

related

to

the

wood,

plate

impedance

mass and stiff-

ness

depend

on

the wood

only through

theparameter

c/p,

thickness on

c.

Comparison

of

species.

Barducci and

Pasqualini

27

measuredc and

p

for

85

species

ofwood.

In

Fig.

10 their

data

have been

adapted

to

display

the violin-wood

parameter

c/p

as

a

function of

its

Q.

Most

of

their

species

are

plotted,

but

to

avoid

confusion

only

those

represented by

four or more

specimens

and indicated

by

black

circles

are

numbered. (Numbers

give

theorder

in

their

table.)

A

fact

immediately

evident is

thatPicea

excelsa

(the

spruce

which

in

Europe

has

traditionally

been

used in

topplates)

is

high,

whereas

Acer

pUUanoides

(the

maple

used in backs) is

low.

The

former

has few

neighbors

to

be candidates for

substitution,

the latter several.

For

reasons to

be

mentioned,

horizontal

separation

of

points

is

difficult

to

interpret.

Comments

largely

drawn from

Howard's

Timbers

of

the

World (MacMillan and

"I. Barducci and

G.

Pasqualini,

Nuovo cimento

5,

416-446

(1948).

With (£/p)*=c,

itfollows that

Cl/pi=Co/pO.

(21)

Stiffness

S *

(p/c)f

bH*.

(25)

8/17/2019 2001 N.3 VOL.4 CASJ


24

CASJ

Vol.

A,

No. 3

(Series

II),

May

2001

Schelleng

-

The Violin as a

Circuit

Company

Ltd.,

London,

1951)

are

listed

below forsome

neighbors

of

Picea

excelsa.

#58

Populus

alba

Close,

hard,

tough

texture.

Sounds

promising.

#60

Populus nigra

Same characteristics as

#

58.

#59

Populus

canadensis

#51 Pinus

cembra

Knots

prevalent,

otherwise

promising.

#81

Thuja

plicala

A cedar.

Perhaps good,

ex-

cept

for

splits

and shakes.

#82

Tilia

europaea

A linden. Sounds

good.

Thecraftsman

may

rule some

of these

out

for

nonacous-

tical reasons.

Relation

of

top and back. Measurements

by

Meinel

(Fig. 16 of

reference 7

;

also

reference

8) show thatat

main

resonance

(and

presumably

generally) the back

contributes

materially

to

the equivalent

simple source

of the

violin.

Though

the

top

is

themore

important

as

radiator,

theback

can

by

nomeans be

neglected

as

a

contributor;

and the

proper

matching

ofone to the

other

seems essential

to

insure

a

strong,

simple

source

over

the frequency

range.

The

conjecture,

therefore,

appears

justified

that the

relation

of

impedances

of

the

plates

[Eg.

(23)3

needs

to

be

maintained

bykeeping

thevalues

of

c/p

in the same

approximate

ratio of

2

to

1,

which

practical experience

has led

to,

andwhich

Fig.

11 shows

for

Picea

excelas and Acer

platanoides.

Othervalues

of

c/p.

28

On

the

assumption

of some

such

balance between

top

and

back,

what is

to

be

expected

when,

instead of

using

the customary spruce,

the

c/p

of the

top

of anew

violin

is

made lower,

as

it

sometimes

is,

by using

woods lower

in

Fig.

10?

Equation

(23)

in-

dicates that

its

body

impedance

will be

increased.

The

oscillating

force that

a

string

is

able

to deliver

to the

bridge

for

a

given amplitude

of

string

motion

is

pro-

portional

to

tension.Hencewith

unchanged

strings

the

velocity

produced

in the

radiating

surfaces

and

hence

the

sound

pressure

will be

correspondingly

lower.

The

extent to

which

this

disadvantage

can

be

overcome de-

pends

on the

willingness

of the

performer

to

use

heavier

strings

and

the

ability

of the

structure

to

withstand the

greater

load. These

considerations make it

obvious

why

maple

would be

a

very

bad

choice for

the

top

plate.

The

2-to-l

impedance

increase

that

was

mentioned

in the

previous

paragraph

wouldcause

a

6-dB loss

unless

pos-

sibly

cancelled

by doubling

string

tension,

and it

is

not

obvious

whatmaterial

having

a

still

lower

c/p

would

be

suitable

for

the

back. The

weight

of the box would be

almost

doubled.

Oppositely,

higher

ratios make more

power

available

and

deservecareful trial.

However,

the

problem

is

not

simple.

The

same

lowering

of

impedance

which

adds to

"

Gleb

Znatie-Sila

(February 1961). According

to

a

summaryby

G.

Pasqualini,

the

importance

of

c/p

was

emphasized

by

Mr.

Anfiloff.

acoustical

output

increases

vulnerability

to

wolfnote.

Though probably

acceptable

in

a

violin,

this

might

be

serious

in

a

cello unless

a wolf

eliminator

is

used.

Strength

of

wood is

anotherconsideration. When

string

tension

is

proportioned

to

strength

of

structure,

it

ap-

pears

that

a

different

wood

parameter,

4>/{cp),

measures

relatively

the upper

limit of

sound pressure

produced.

Here

<>

is

the

strength

function

of thewood (e.g., bend-

ing,

shear,

tension

across

grain,

etc.),

in

which

thestruc-

ture is most vulnerable

as

used in the

violin.

Damping requirements

of

wood.

In

measurements

of

elastic characteristics

of

wood,

the

usual

emphasis

on

properties

along

the

grain

has

led

to

a

preponderance

of

values

quoted

27

between

60 and

130,

whereas the

Qof

the

principal body

resonance of the assembled instru-

ment" ranges from

10to

20. It

has,

of

course,

been ap-

preciated

that

cross-grain

Q's

are

the

lower

by

a

factor

near

4 and must

certainly depress

the resultant. The

difficulties

of the

problem

have

precluded

an

estimate

of

what

resultant

Q

one

should

expect

from

a

plate.

There

is one

qualitative

consideration worth mention-

ing;

namely,

the

relative

narrowness of

the instrument

and

its

vibrational patterns in

comparison

with

length,

and

the

resulting

tendency

to

emphasize

the

effect

of

cross-grain

constants,

both

as

regards

to

potential

en-

ergy

ofvibration and energy

loss.

Consider

a

flat,

rectangular

plate

of wood

"sup-

ported"

(hinged)

along

its

edges

and

vibrating

in

its

lowest flexural mode.

sb

We

may suppose

that if ratio

of

length

a

to width

b

equals

thatof

length

to average

width of the

body

of the

violin,

the

energy

relations

will be somewhat

comparable.

At the

centerof

the

plate,

the

principle

curvatures

lie

parallel

a nd

perpendicular

to

the

grain,

and,

if we

ignore

Poisson's

ratio,

the

potential

energy

of

deformation

120

per

unit

area

is

W

cc

EH

3

(r

a

~

2

-{-

r

b

~2

)

for

an

isotropic

material,

r

being

radius of curvature.

For

wood (anisotropic), with

c— (£/p)*

and,

for

a

given

s,

fa a

1

,

and

rjoc

J

5

,

Here the first

term

corresponds

to

the

long

dimension

a,

thesecond

to

theshort

oneb.

It is

immediately

evident

that

although

c

b

in

wood

is

much

smaller than c

ai

the

inverse fourth

power

of

width

can be

a

powerful

in-

fluence in

emphasizing

cross-grain

energy

if width

is,

in

effect,

much

smaller

than

length.

Similarly,

it

follows

that

rate

of

energy

loss

at

the

center

is

dW/dt

oc

st&p'cS ar Q +cfb- tQr

1

). (27)

The

cross-grain

term is

now

further

emphasized

rel-

ative

to the

other

by

the inverse of

its smaller

Q.

We

should,

therefore,

expect

the

Q

of

a

violin (corrected for

radiation resistance) to lie nearer to that indicated

by

cross-grain

wood

samples

than

to that

obtained

with

samples

cut

along

the

grain

;

that

is,

nearer

to

some

com-

promise

value

between

30

for

the

spruce

plate

and 20

for

the

maple,

than to

a

compromise

between

125 and

80.

W

a

3?H*p(e

a

*o-

4

+eh*lr

4

). (26)

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

A,

No. 3 (Series

II),

May

2001

2

Schelleng

-

The Violin

as a Ci

The

effectof the

arch

may

be to

lower

the

Q

still

further.

It

may

be,

therefore, that

simple

wood

loss

and

radia-

tion

are

enough

to account for the low

Q's

of

violins.

The

very

fact

that

these instruments

are

built-up

struc-

tures

may

accentuate

unfavorable

strains

not as ye t

sufficiently

studied,

perhaps

such

as shear

along

the

grain.Other

mechanisms

for

increasing

losses,

of

course,

deserve

consideration,

such as

pre-stressing

of bassbar

and

top-plate,

as

proposed

by

Rohloff.

28

ACKNOWLEDGMENTS

It is a

pleasure

to

expressmy

indebtedness to Pro-

fessor

F.

A.

Saunders for

the

benefit of his

long

and

fruitful

experience

in

this

field,

and

to Mrs.

Carleen

M.

Hutchins

for

her

insight

into the

problems

of

scien-

tific

violin

making.

APPENDIX I

Refer

to

Fig.

2,

right half, beginning

at

C

where force

F is

applied

by string.

Subject

to

approximation

that

impedance

of air

circuit is

negligible

compared

with

reactanceof

body,

Current-producing

radiation

is

(«

x

-w

a

) (external

sur-

faces

and/

holes)

and

equals

(u%+u

4

). Its

radiation

re-

sistance

is

thatofa

simple

source

:

where

/S=po_4

s

/4tc.

Since

impedance

of S

a

=-iS

a

/a),

R*=S*Qa/(>>a

t

and

impedance

of

Af.=t-So

0)/a.

a

it

follows

This

is a

function

of V

only

insofar as

Q

a

depends

on

it

implicitly

(see

Fig.

3)

or

above

approximation

unacceptable.

With

/holes

closed,

power

radiated

is

(1)X

(2).

With/

holes

open, power

radiated

is (1)X

(2)X

(3).

Except

near

resonance,

relative variation

of

radiated

power

with frequency

is

[1-

(«

6

/

w

m[l-

(«

a

/«)

J

]-

s

. (A

4)

By

use of

Eqs.

(l)-(3),

the

ratio

of

sound

pressures

produced

atthe

two resonances assumes

a

simple

form

:

P h/P Wf.y'iQt/Qa).

(A5)

APPENDIX

H

Refer

to

Fig.

5

and take

22=

{SM^Q,

vu

b

=

{S /M )\

2

b

=Z

b

/(SM)*=l/Q+i(Q-

I/O).

The

line

over

other

impedances

indicates

similar

nor-

malizing

to

(SM)K

With

this

nomenclature,

calculations

were

made

as

follows

:

Erratum : The

Violin

as a

Circuit

U.

Acouat.

Soc Am. 35.

326-338

(1963)]

J ohn

C.

Schelleng

301 Bendermere

Asbury

Park,

New

J ersey

AT

several

points

in

thepaper,use

was

madeof

measurements

made

by

F. A. Saunders

on

logarithmic

decrementsof

violins

I

have discovered

that,

whereas his

results

are

in

terms of the.

Naperian

base,

I

erroneously interpreted

them

as

to

the

base

10.

This does

not affect

the

theoretical

developmentsof

the

paper,

but

it does

affect

some numerical

comparisons

covering power

losses,

as

follows

:

can no

longer

besaid that

the

calculationfor

air

decrement

agrees

with

his

measurementunless we

use a

con-

siderably

lower

absorption

coefficient than

0.04,

the value

for

wood

floor

on solid

foundation

borrowed

from

architectural

acoustics.

A

lower

value,

however,

is

credible.

The

radiation

effi-

ciency

at

the

principal

body

resonance should

be

28%

or

more,

rather than

12% or

more. In

Fig.

9,

theSaunders

comparison

data

should be

moved

to

the

left

by

a factor of

2.3.

This

means that

curves such

as those

in

Fig.

6will

in

typical

casesbemoreS-shaped

than

those

in

Fig.

9.

On

page

337

under

"Damping Requirements

of

Wood,"

the

range

of

Q's

for

the

assembled

instrument

should

be 20

to

50

instead

of

10

to

20.

Reprintedfrom

The

J ournal

of the

Acoustical Societyof

America,

Vol.

35,

No.

3,

326-338,

March

1963

Copyright

1983

by

theAcoustical Society

ofAmerica

Printed

in

U.S.A

\ui\***F*/{s

i

Moli/Qf+

(«/«i-«t/«)D).

(Al)

R r=ktf,

(A2)

that

«i-«*IVM

2

-[iA2.*+

(«/«■)»]/

[l/&M-(«/«

a

-<V«)

2

].

(A3)

ai-4irli/l

bt

and

at=Airh/lbt

.

\+i{2

b

/R)

tana.Q

22/R=Z2

/K =-icota&.

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3

(Series

II),

May

2001

ON P O L A R I T Y OF

R E S O N A N C E

by

J ohn

C.

Schelleng

(as

published

in

CAS

Newsletter

#10, November

1968)

fiddle

acoustics,

the

conspicuous-

ness

of

vibrational

modes

at

their

fre-

of resonance

has tended to

what

takes

place

away

from the

of

response.

There are

two

cases

especial interest,

1)

response

between

and

2)

response

below

them.

—

Between Peaks

years

ago

Hermann Backhaus

attention to

the

peculiar

nature

of

low

in

the

spectrum

of

some good

near

the

"open

E (660 eps)

in

spite

of

lack

of

support

from

the sound

produced

does

not

toward

a

sharp

zero

but holds to a

value

because,

he

said,

the

instru-

acts

like

a "Nullstrahler". The

has

been

confirmed

by

later

but no

theoretical

explanation

to

have been

offered.

In

making

the

comparison

to

a

Backhaus

was

thinking

the zero-ordervibration

ofa

sphere

in

all radii

pulsate

in

phase

and all

of

thesurface

conspire

without

cancellation to

produce

the vol-

e

change

necessary

for

a

powerful

source. He found that in two

good

violins

onea

Stradivarius,

"at

83 eps

almost

the

whole

body

swung

in

phase .

[1]

None of thewriters on

subject

seem to have tried to recon-

the

idea

of

a

Nullstrahler

with

the

picture,

which

obviously

must

be

to

explain

whatever does

take

It

has

no

resonance

and

obviously

not

one ofa setof

orthogonal

resonant

[2]

We

may

think

ofthe

manifold

wood

as so

many series

resonant

circuits

in

parallel,

all

responsive

to

the

same

force

exerted

on

the

bridge

by

the

strings.

Each

mode

will

be

characterized

by

a

change

in

displaced

volume

propor-

tional

to its

shift

in

bridge

position,

i.e.,

each has

a

component

that is a

simple

source.

Not

only

will

the

proportionali-

ty

constants

differ

in

magnitude

for

dif-

ferent

modes,

but

they

will

also

differ

in

sense;

a

priori

at least the

sign

is as

apt

to be

negative

as

positive.

For eachmode

the

radiating

surface is

divided

by

nodal

lines

into

two sets

of

fields,

the

two

being

in

opposite phase

insofar

as

they

contribute

to

the

totality

of

volume

change.

There

is

no reason to

suppose

thatwhen

the

top

of the

bridge

moves

to the

right

the

volume

will

always

in-

crease,

though

that

is

what

happens

at

the

principal

resonance.

[3]

We

shall

refer to

the latter

as a

mode

of

positive

polarity.

Obviously

what

takes

place

at

frequencies

between

adjacent

peaks

that

have the same

polarity

will

differ

from

behavior

when

they

have the

opposite.

For the

sake of

concreteness,

a

cal-

culation

has been

made

for

a

situation

that is

intended

to

resemble

the

open-E

region

of

a

violin.

The

numerical

assumptions

may

notbe

accurately rep-

resentative: our

real

interest

at

this

point

is

in

illustrating

a

principle.

[4]

The

assumptions

are:

1)

Tone

of

the

lower

resonance

is B (494

eps);

2) tone

of

upper

resonance is F# (740

eps);

3)

the

Q's

of

both are

40.

It

will

also

be

assumed

that

both

modes

produce

the

same sound

pressure

at

resonance. We

need

to

know how

the

volume

velocity

that

produces

radiation

changes

in

response

to

force

on

the

bridge

and

shall

refer to

volume

velocity

divided

by

force

as

transfer

admittance.

The

equivalent

circuit is shown in

Figure

1.

The

method of

calculation consists

in

finding

the

transfer

admittance

for

each

mode

separately

(in-phase

compo-

nent

+

j

90° component)

over

the fre-

quency range

in

the

standard

manner

and

combining

for the two

modes

in

two

ways

—

addition and

subtraction.

If

the

two

modes

are

of the same

polarity

(bridge

moving

to

right

increases both

volumes or

decreases

both)

the

separate

transfer admittances are added

alge-

braically

to

give

the

resultant.

If

one has

positive

and

the

other

negative

polarity

(one increases

in volume

and the other

decreases)

the

transfer admittances

are

subtracted.

[5]

In

Figure

2 relative sound

pressures

are

plotted

for

the

components

in

phase

with

force

on

the

bridge

(curves

labelled

C)

and those at

90°

(labelled

S),

for

both

resonances.

Polarities

are at first

assumed the same.

[6]

When

the modes

are

ofthe

same

polarity,

resultant sound

pressure

is

obtained

by algebraic

addi-

tion

as

in

curve

SI

+

S2.

Of

particular

interest

is

what

happens

near

"relative

frequency"

1.3,

where CI and

C

2

re

both

negligiblysmall.

Here

the

sum

SI

+

S2

passes

through

zero andwe shall find

a

deep

"sound hole" in the

response

of

the

instrument.

Contrasted

with this

unfavorable

situation

is theresultant

when

polarities

differ: at the

same

frequency,

response

SI

-

S2 is

by

no means

negligible.

With

our

numbers

amplitude

is

0.125

as

com-

pared

with

1

.0 at

resonance.

While

thus

1

8

db

down

from its value atthe narrow

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No. 3 (Series

II),

May

2001

2

Schelleng

-

On

Polarity

of Resona

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

A,

No.

3

(Series II),

May

2001

Schelleng

-

On

Polarity

of

Resonance

of

resonance

(which may

be too

to

be

of

much

use) it is

large

to be

significant.

In fairness it

be

compared,

notwith

the

peak,

withsome

kind of

average

over

that

of

the

spectrum.

Note

that

it

is

27

above the

sound

hole in SI

+

S2.

way

of

representing

this

type

of

is

shown

in

Figure

3

which

the absolute value of the total

pressure

in

the

same coordinates

in

Figure

2,

and shows the difference

result

as

it would

appear

on the

usual

curve.

Behavior

illustrated

is

not

to

be

con-

with

that

of

the

admittance of

the

itself,

which

will

always

have

an

between

peaks.

The

zero

admittance will

in

general

occur

at a

frequency

from

that

of

transfer

A

method

canbe devisedfor direct-

identifying

the

polarities

of

the

vari-

resonances. In

principle

it would

the

phase

at

a

point

a

wave-

or

two

from the

instrument

with

phase

proper

to the time

delay

at

point,

using

the

principal

resonance

standard.

Analogous

phenomena

can also be

with

free

plates

with radiation

We

are

then

dealing,

not

with

sense

of

a

volume

change

but

with

sense

of radiation.

Since

shapes

of

patterns

are

involved,

behav-

will be

more

complicated

than

with

assembled

instrument.

In

conclusion,

theresultant

between

of

opposite

polarity

is

always

than between similar

peaks

of

polarity, regardless

of

frequency

or

relative

strength

of

peak.

separation

is

not

small

(e.g.,

when

is

twenty

times the

bandwidth

ex-

in

cents)

deep

sound

holes

can

between

peaks

ofsimilar

polarity,

not between

peaks

of

opposite

po-

A more

thorough study

of the

should

bemade.

II

—

Below

the

Wood Peaks:

Air

Resonance

The

same

question

of

polarity

should

be

asked

in

considering

the air

resonance,

the

lowest

in

frequency

of

all,

if it

is

excited

by

more

than

one

body

mode.

The

way

in

which it is

excited has not

been

studied in detail and

will

not

be

attempted

here

sincean

exacting

experi-

mental

study

of

particular

instruments

would be needed. Since its

frequency

is

remote

from the

wood resonances

as

measured

inbandwidths ofthe latter itis

their

reactive

parameters

rather

than

their decrements of

Q's

that are

of

sig-

nificance.

Thus

it is conceivable

that

a

mode

higher

in decrementbut

lower

in

frequency

than the

principal

resonance

might

contribute

as

much

or moreto the

air

resonance,

either

positively

or

nega-

tively.

We

shall

limit

present

considera-

tion

to

simple

cases.

Consider

first

an air resonance

excited

by

a

single

mode in the

wood,

onewhose

resonance lies a

musical

fifth

higher

in the scale.

There will now

be

two

components

of

simple-source

radia-

tion: volume

velocity

caused

by

expan-

sion

and contraction oftheexternal

vol-

ume

of

wood,

and

volume

velocity

breathed

in and

out

through

the

f

holes.

Between

the

two resonances do

these

two

components

addor subtract?

First,

ask

a

simpler question:

what do

they

do

at

very

low

frequencies? Obviously

an

increase in

body

volumewill

require

air

in

equal

amount to be drawn inward

through

the

f

holes;

that

is,

the

effects

cancel

each

other.

Therefore,

as

rising

frequency passes through

and

beyond

the

frequency

of

air

resonance,

the

180°

shift

in

phase

will

cause the effects

to

cooperate.

In

this

range

as a

result

no

deep

sound

holewill

usually

be

found.

It

is in the

nature

of

air

resonance

above

its

resonance

frequency

not to

oppose

the

volume

velocity

set

up by

the

outer

wood surfaces.

With

respect

to the

wood

resonance

that

supports it,

the

air resonance

thus

acts

somewhat like a

resonance

of

oppo-

site

polarity,

and

itis

its

strengthening

of

thesound

between

peaks,

as

much

as at

them,

that

measures

its acousticaluseful-

ness.

If

it

tended

toward

cancellation

air

resonance

might

not

be

used. The

impli-

cation

therefore is

that both above

and

below

principal

resonance

this

wise old

instrument

has

mechanisms

for

avoiding

cancellation between

peaks.

The

numerics of the

problem

are

approximated

as

follows:

In "TheViolin

as a

Circuit

[7]

Equation

(3)

relates the

sound

pressure

at air resonance

to

the

pressure

at

a

body

resonance

assumed

to

support

it.

Qualitatively

at

least

it

will

be

true

thatwhen

more

than one

body

res-

onance

affect

air

resonance,

the

compo-

nents

atairresonance

will

be

algebraical-

ly

additive

with little

interaction.

Thus

the

sound

pressure

produced

by

some

standard

amplitude

of

force

on

the

bridge

is:

Pair

=

f

a

2

Q

a

2

Pb

/(f

b

2

Q

b

)

Here

p

b

is the sound

pressure

at a

given body

resonance

taking

due

ac-

count

of

its

polarity:

it

may

be

positive

or

negative.

A

numerical

example

may

be

sug-

gestive.

Consider the two

body

reso-

nances

assumed

in

I

above,

separated

in

frequency

by

a

musical

fifth,

the lower

one

being a

fifth

above

the

airresonance.

The

calculation

is

as

follows:

Wood

resonance

p

b

f

b

/f

a

Q Q,,

p

a

Lower

1.0

1.5

1.2

0.370

(1)

Upper

1.0 2.25 1.2

+0.164

(2)

Upper

-1.0

2.25 1.2

-0.164 (3)

If

both

resonances

are

of

the same

polarity,

thecombined sound

pressure

at

air

resonance is (1)

+

(2)

=

0.534,

that

is,

5.5 db below

sound

pressure

at

either

wood

resonance.

If

they

are

of opposite

polarity,

the combined

sound

pressure

at air resonance is

(1)

-

(2)

=

0.206,

or

13.7db down.

This decreasewill

be

exaggerated

if

the two wood

peaks

lie

close

to

each

other.

It is

commonly

felt

that in the

best

fiddles

the

principal

resonance is

a

clus-

ter.

Such

a

cluster

has not

beenexamined

from the

present

viewpoint,

but

what if

it

should

include a

peak

of

negative

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No. 3 (Series II),

May

2001

Schelleng

-

On

Polarity

of

Reson

polarity?

Imagine

an

extreme case:

let

REFERENCES

there

be two

components

of

opposite

L

ForscbungenundFortschntte,

14,

No.

4.

Discussion

is

limited

to

sim

polarity equal

in

sound

pressure p

and

?o n

-j

l7

r\

rt

inio

Wing

Q-s

in

inverse

ratio to the

square

2

.

m

'

uthier

_

f

taptQnes

-urce

radiation

At

high freq

_.1

... £

___

I_ .

1 -r

n_«

firm

rh_=>

Hnnh

of their

frequencies.

For

example,

let

them

be

separated

by

a whole

tone,

and

let

Q's

be

50

and 40

respectively

for

lower and

upper

one.

The

equation

above

says

that

the two

components

of

sound

pressure

at

air resonance

will be

equal

and

opposite,

and that

therefore

therewill

be no

response

whatever

at

air

resonance.

Although

these

examples

intention-

ally

exploit

our

ignorance

of the basic

cies

radiation of the

doublet

he

refers

to

the

relaxation

frequen-

...

.

r

.

r 1

rill

1 1

11

■

n

will be

or

cies

or

the

fiddle

body,

usually

mtlu-

enced

somewhat

by

the tension

of

5>

frequencies

have

been

normaliz

the

strings

but

not

by

their

reso-

that

of

the lowerresonance

freq

nances,

whichhe

avoids.

With

string

cy

taken

as

unity.

The

sound

material of

sufficient

strength,

such sure

at

any

desired

frequency

f

as "Rocket

Wire",

he

could use

tive to

that

atthe lower resonan

strings

so

light

that

they

would tune

w

ju

equa

i sounc

j

pre

ssure

at

well above

the

highest

taptone

of

res

onance

multiplied

by

Af/

usual interest

with

tension

at

normal

,

A

.

r

,

.

_

,

where

A

is transfer

admittance

facts,

themoral

nevertheless

seems

clear:

values.

Ihe

only advantage

however

.

„

r

'

.

,

.

,

■1^

1

-i

11

6.

F or

eitherresonance

a

plot

oftra

We

ought

to knowwhat

these

facts

are.

might

be to

avoid

quibbles.

r

Perhaps

some

member

of

this ancient

3. This is

a

deduction

from measure-

admittances

on

xy

coordinates

ments

by

Hermann

Meinel,

Elect.

the

familiar

circle

diagram.

nd

honorable

society

will

undertake to

clarify

the

matter

by

studyingpolarity

experimentally.

■

CASJ

Nachrichten-Technik,

14,

No.

4,

pp.

7.

J .C.

Schelleng,

J our.

Acoust.

Soc.

1

19-134,

Fig.

16a

and

b,

April,

1937.

35,

No.

3,

pp.

326-338,

March,

CASJ

35,

No.

3,

pp.

326-338,

March,

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3

(Series

II),

May

2001

ON

H I G H E R

AIR

MODES

IN

THE

V I O L I N *

by

Erik

J ansson

(as

published

in

CAS

Newsletter#19,

May 1973)

resonant box of the violin consists

a

top

plate

and

a

back

plate

glued

to

ribs,

thus

enclosing

an

air

volume.

In

top

plate

two sound holes are

cut,

the

F-holes. The total area

of

the

sound

holes

taken

together

is

about

cm

2

and

that

of the total

area

of

the

walls

about

1200

cm

2

Thus

the

between

the

two

areas

is

about

This small ratio

implies

that

only

small

portion

of the stored

energy

of

waves set

up

into the

air

vol-

e is

likely

to

radiate

through

the

F-

and that

several

higher

air-modes

ay

be

expected

in

the enclosed

air

cav-

of

the violin.

However,

it is

usually

that

the

shape

and

the

position

the F-holes

are

such

that

higher

air-

cannot

effectively

influence

the

producing

mechanism

ofa

violin,

for

example

a

theoretical

study

of

violin

by Schelleng

[I].

In

earlier

by

Saunders

traces

were found

higher

air-modes,

but

these

modes

to

give

little influence

on

the

behavior of theviolin

[2].

Prelimi-

experiments

with a

rectangular

box

that

the

energy leakage through

the

does

not

remove

higher

air-

in general.

This

means

that

the

inimpedance

seen

from

the

maybe

important

although

the

radiation

through

the

sound

holes

negligible.

Therefore

the present

study

was

to

remove the

ambiguity

of the

summarized results and

to

give

an

understanding

of

the

higher

air-modes.

In

this

paper

we

shall

limit

the discussion

to

the

frequency

range

below

2

kHz.

Experiments

with

violin-shaped

cavities

The

first

main

question

to

answer

is:

Does

it or does it notexist several

high-

er

air-modes

in a

violin-shaped

cavity

with "F-holes"?

To

find

the

answer

to

this

question

we

measured

the

acoustical

input impedance

of the air

volume

of

a

violin

encased in

plaster

thus

blocking

the

motion of

thewalls

and

allowing

the

examination of the

air

cavity

in isola-

tion. The

impedance

was measured

by

means

of

a

specially designed

measure-

ment

probe

containing

an

STL-iono-

phone

and

a

B&K

4133

microphone

with a

short

and

thin

sond

(length

about

2

cm and

effective

diameterabout

0.025

cm). The

impedance

was measuredboth

with

closed

and

with

open

F-holes.

When the

F-holes

were

open,

the

areaof

top

plate

between

the c-bouts (at the

waist)

and

around the F-holes was

free

from

plaster,

so

thatthe

radiation

at

the

F-holes

should be

the

same as

in

playing.

The result

is

exemplified by

two meas-

ured

impedance

curves,

the

upper

one

with

closed and

the

lower

one

with

open

F-holes

(Fig.

111-C-1).

The

upper

and

the lower

diagrams

show

grossly

the

same number

of

peaks

but

the lower

impedance

curves

have

slightly

less

marked

peaks.

The

peak

frequencies

and the

-3

dB

bandwidths were

accurately

measured

Figure

111-C-1

■Acoustical

inimpedance

measured

close

to the

end

button

ofa

violin encased

in

plaster.

Top

curve

—

closed

F-holes

Lower

curve

—

open

F-holes

by

means

ofa

frequency

counter for

all

resonances. From

these

measurements

the

Q-factors

were

calculated.

The

Q-

factors

obtained

in this

way

are

plotted

as a

function of

peak

frequencies

in

Fig.

111-C-2.

For

simplicity

the

modes

are

numbered

starting

from

zero for

the

Helmholtzmode.

From

the

diagram

we

find that

the

peak

frequencies

are

only

slightly

changed by

the

F-holes.

The

on

apaper

given

at

the

84th

meeting

of

the

Acoustical Societyof

America,

Miami

Beach, Florida,

Nov.28/

Dec.

1,

1972.

study

was

performed

in

cooperation

with the

Instituteof

Optical

Research,

KTH,

Stockholm.

Issued as

a

STL-QPSR

Report.

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No. 3 (Series II),

May

2001

3

Jansson

-

On

Higher

Air

Modes

in the

V

150

.30.

so

A*.

SOUNDPI.E

0

MIN.

SOUNOPRE

PHASE 0

Figure

111-C-2■

Q-factors

and

frequencies

of the first sevenair

modes

of

a

violin

encased in

plaster.

PHASE

IX

Figure

111-C-3

■

Standing wave

patterns

of theseven

lowest

modes

of

a

violin-shaped

flat

cavity.

Q-factors

are

moderately

lowered

by

plate.

The

resonance

frequencies

of this

ume,

at

some

other

ones

weak

and

the

F-holes in all modes

but

two,

name-

cavity

approximate

within

a

few

percent

energy

is

solely

stored in

either

o

ly

the third

and the

sixth mode.

In the those of the violin

encased

in

plaster.

upper

or

lower

cavity.

third

mode the

Q-factor

is

considerably

This

indicates

thatthe

arching

of

the

top

The

F-holes

are

grossly

situ

lowered

and

in

the

sixth

mode

no

traces

and

back

plates

is

not

very

important

to

between the

c-bouts.

This is at

abou

of

a

peak

show

up.

These

results

support

the

seven

lowest

modes.

The

different

border

area

between the

upper

the

hypothesis

previously

introduced;

standing

waves were

excited

and the

lower

cavity

estimated from

Fig.

11

-there

are

several

resonances

and

these

sound

pressures

at

different

positions

3,

i.e.

an

area

of

low

sound

pressure

resonances arein

generalonly

moderate-

were

measured

through

small holes the

second,

the

fourth,

and

the sev

ly

affected

by

theF-holes. drilled in

thewalls.

The

different

stand- modes.

These

modes

will

therefore

The next

question

we

asked

was:

ing

wave

patterns

estimated are

present-

little

affected

by

the

sound

holes. F

Why

are

just

the

third and

the

sixth

ed in

Fig.

111-C-3. The

first,

the

third,

thermore,

the first and fifth modes

modes

so

affected

by

the

F-holes?

The

and

the

fifth

modes

correspond

to the sound

pressure

minimum between

th

oscillation

modes of

a

cavity

can be

first

three

modes

of

a

pipe

closed

in

both

bouts and are thus

little

affected.

O

greatly

affected

by

holes

in the

cavity

ends

althoughmoderately

perturbed

by

the

third and

the sixth modes

h

walls.

Not

only

the

size

but also

the the

swelling

and

shrinking

of the

cross- sound

pressure

maximum in the

vici

place

of the

hole

are

important,

as

point-

sectional area.The second

and the

sev-

of

the

F-holes,

which

explains

why

t

ed

out

by Schelleng

[I].

A hole

drilled

at enth

modes

are resonances

of

the

cavity

Q-factors

drop

considerably

when

a

sound

pressure

maximum can affect the

below

the

narrowing

section

between

the F -holes

are

opened.

The

rule

regard

standing

wave

considerably

while

a

hole c-bouts.

The

fourth

mode

is

the

mirror

theposition

of

holes

in

relation

to

so

at

a

sound

pressure

minimum will

have

image

of the

second

mode in

the

cavity

pressure

maximum has

thus

proved

little

effect on

the

standing

wave.

Thus

part

above

the

c-bouts. The

sixth

mode

is

give

results

in

agreement

with

the

ex

we shouldfirst

record

the

standing

wave made

up

by

a

combination

of

vertical

iments.

patterns.

Therefore

we

can see

if

these

and

horizontal

standing

waves. The

To

summarize,

we

may

say

that

patterns

explain

what

happens

when

the

results allow

the

volume

of

a

violin

tobe

garding

the

resonances

ofa

cavity

sha

F-holes

are

opened.

To

simplify

our

regarded

as

consisting

of two

coupled

like

a

violin

and

with

F-holes,

higher

measurements

we

made these

experi-

cavities.

At

some

resonances

the

cou- modes exist

andmost

of

them

are

m

ments with

a

cavity

shaped

like

the

inside

pling

between

these cavities is

strong

and

erately

affected

by

the

F-holes.

of

a

violin

but

with flat

top

and back the

energy

is stored in

the

whole

air

vol-

properties

of

the air

modes

obey

at

l

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No.

3

(Series

II),

May

2001

Jansson

-

On

Higher

Air

Modes

in

the

Violin

the

simple

rules

regarding

in

cavities with

standing

waves.

with

violins

far

we have

studied

the

modes

of

a

with

rigid

and

heavy

walls.

In

a

violin

this is

not

a

good

approxima-

From

earlier

studies

by

J ansson,

and

Sundin

[3],

we

know

that

are

vibrating

with little

motion

at

ribs at least

for

higher frequencies.

air-modes

of theviolin

shaped

cavi-

have

sound

pressure

maximum

gen-

at the

"ribs,"

i.e.

at the

places

the

plate

motion

is

small. The fact

the

places

ofmaximum

sound

pres-

and

maximum

plate

motion

are

dif-

indicates

that the

coupling

plate

motion

and

air-modes

is

and

that

the

higher

air-modes

are

present

in

theviolin.

In

our

experiments,

not

yet

finished,

have

begun

with

a

detailed

study

of

e

air-mode

1,

which

is

at

about

500 Hz

thus

close

to

a

major

resonance

peak

violins

—

the so-called

main

wood

We

built

a

new

measuring

probe

of

an

STL-ionophone

and

a

2

1/4

inch

microphone

with

a sond.

we

mounted

on and into an

"end

of

plexiglass.

By

means

of

this

"end

button

we were

able

to

the

air vibrations

with

a

well

acoustical

input

on

violins,

even

and tuned

instruments.

With this device

the

acoustical

input

at

the

end button

of

six

vio-

was

measured

in the

frequency

range

air-mode 1. A

clear

peak

showed

up

in

instruments.

Tests

with

a

sond

micro-

in

different

positions

inside the

verified that

this

was

the

air

The

frequencies

and

Q-factors

of

peaks

are

displayed

in

Fig.

111-C-4.

frequencies

are

lowered

compared

thoseofthe violin

shaped

cavity

with

and

fall

close

in

frequency

to

A

i.e.

just

in the

region

of the main

peak

generally

found

in

good

vio-

The

Q

-factor

averaged

for

six

vio-

is

only

slightly

lower

than

the

Q-fac-

for the

violin

shaped

cavity,

i.e.

the

through

the

walls

are moderate.

Fig.

111-C-4■

Q-factors

and

frequencies

of

thefirst air-mode

in

six

complete

violins.

Thus

we have

proved

that

air-mode 1

is

set

up

in

complete

violins.

Our next

question

is:

Can

this

air-

mode be

excited

by

the

plate

vibrations?

We

excited

the

bridge electromagnetical-

ly

and

measured

the

frequencyresponse

by

the

microphone

in

the end

button

in

the

frequency

range

of

air-mode

1.

Probe measurements

proved

that

theair

was

oscillating

in air-mode 1.

The

pres-

sure minimum of

the

air-mode

was

found

to

be

roughly

in

the

place

of

the

bridge.

A

peak

wasstill

generally

found

(5 out

of

6)

corresponding

to

the

air-

mode.

Furthermore

the

inside

of

the

lower

part

ofthe

top

plate

was

found to

be

coupled

in

phase

with

the

sound

pres-

sureoftheair-mode.

Conclusion

In

a

previous

study

of

our test

instru-

ment

HS

71,

it

was

found that

the

wall

vibrations

are

mainly

in

the first

top

plate

mode

in the

region

of the main

wood

peak

[4].

In

the

present

study

we

have found that the first

air-mode

above

the Helmholtz mode falls in

the

same

region.

The

experiments

have

proved

that

the

two

modes

are

coupled.

Stand-

ing

wave

patterns

of

the two

nodes

are

drawn for

comparison

in

Fig.

111-C-5.

The entire

top

plate

moves

in

phase,

whereas the

sound

pressure

in the

upper

Fig.

111-C-5

■a. Thefirst air-mode (470

Hz,

Q

=

65),

and b. thefirst

top

plate

mode

ofviolin

HS

71

(480

Hz).

(Fig. 111-

C-5b

is

from

J ansson-Molin-Sundin,

PhysicaScripta,

Vol.

2,

pp.

243-256,

1970.)

and

the

lower

parts

are

180°

out of

phase.

Thus

a

simple

and

direct

coupling

between the

sound

pressure

of

the air-

mode

and the vibrations

of

top

plate

is

not

possible.

However,

an

estimate

of

the volume

displacement

by

the

top

plate

above and below

the

bridge,

i.e.

the

pressure

minimum,

gives

a

difference

of

about

10%,

the

lower

part

giving

the

greater

displacement.

The

phase

rela-

tions

of

such

a

coupling

agree

with

the

experimentally

determined

phase

rela-

tions,

the sound

pressure

of

the

air-

mode

1

being directly

coupled

to

the

lower

part

ofthe

top

plate

vibrations.

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No. 3 (Series II),

May

2001

Jansson

-

On

Higher

Air

Modes

in the V

Thus

we

have

proved

that at

least

Especially

as

themode

falls

in

a

frequen-

influences

the

main

wood

peak

one air

mode

above

the

Helmholtz

cyrange

of

interest,

the

range

where

vio-

wolfnote,

and

thus

the

quality

o

mode is

present

in

violins,

that this

lins

have

a

peak

in their

acoustical out-

instruments

■

mode

is

coupled

to

wall

vibrations.

We

put

and

where the so-called

wolfnote is

have

also

given

an

explanation

of

the

to

be

found.

coupling

mechanism.

Although

the air- Our

investigations

are

continuing

ACKNOWLEDGMENTS

mode

does

not

radiate

through

the

F-

to

study

the

importance of

the

higher

This

work

was

supported

by

the Swedish

holes,

the acoustical load on

the

top

air-modes

and

how

the

relation

between

Humanistic

ResearchCouncil and

the Swedi

plate

vibrations

may

be

important.

the

top plate

mode

and

the

air-mode

Natural

Science

Research

Council.

REFERENCES

1.

Schelleng,

J .C.:

"The

Violin

as a

Cir-

cuit, /,

of

the

Acoust.

Soc.

Am.

35

(1963).

pp. 326-338

and

1291.

2.

Saunders. R: Recent Work

on

Vio-

lins,"

/.

of

the

Acoust.

Soc.

Am.

25

(1953).

pp.

491-498.

3.

J ansson,

E.,

Molin,

N-E.,

and

Sundin,

H.: "Resonances of a Violin

Body

Studied

by Hologram

Interferome-

try and

Acoustical

Methods,"

Physics

Scripta

2

(1970).

pp.

243-

-256.

4.

J ansson,

E.:

An

Investigation

of a

Violin

by

Laser

Speckle

Interferom-

etry

andAcoustical

Measurements,"

Acustica

(in

the

press).

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No.

3

(Series II),

May

2001

THE

C AVI TY

(AIR) MODES

OF

THE

V I O L I N

by

Carleen

M.

Hutchins

(as

published

in

CAS

J ournal

Vol. 1, No.

5,

May

1990)

or

a

long

time it

was

thought

that

with two

openings,

one

circular with

one

f-hole,

with both

open.

It

often

there is

only

one so-called air

sharp

edges

and one

with

a

tube-like

helps

to

identify

the

pitch

by

closing

the

in the

violin

and

that was

labeled

protrusion

that

could

be

fitted

into

a

other f-hole

and

listening

as

the

pitch

Helmholtzmode.

Research

of the

piece

of waxinserted in the

ear,

see

Fig- goes

down

with

the

smaller

opening,

20

years

has shown

that

there

are

a

ure

2. These

resonators were tuned to An

important

AO-B0

interaction is

of

higher cavity

modes

above

certain

frequencies

so

that

by

listening

described

in

this

issue

as

well as

in

"Helmholtz." These

higher

modes

through

them

in

sequence,

the observer Hutchins (1985) and

Spear

(1987).

first

described

by

Erik

J ansson could

hear

clearly

any

partial

that

might

The

frequency

of

the

Al

mode

sson,

1973),see

Figure

1.

coincide

with

the

frequency

of

a

given

depends

primarily

on

the

length

of the

The

term

"cavity"

is now

preferred

resonator. inside of

the violin box

as

well

as

the

describing

these

modes instead

of

The

frequency

of

the

Helmholtz

flexibility

of

the

walls,

particularly

in

the

or

"Helmholtz,"

since

they

are

not

or

A

0ode in

a

violin

is based

on

the

upper

and lower

plate

areas.

The

air

is

air or Helmholtz modes because

volume

of the

box,

the

area

of the

f-

alternately expanding

and

contracting

at

contain

contributions

from

both

holes,

the

thickness

of

the

f-hole

edges

the twoends so there is a

pressure

max-

airandthewood

of

the

violin

as

well

(which

Sacconi

indicated that

Stradivari

imum

first at

one

end and then

at

the

interactions

with the outside

air

always

kept

at 3mm

all around

in his

other

with

a node

in

the

middle.

This

is

the

f-holes.

violins

regardless

of

top

plate

thickness)

similar

to the air

vibration

in

a

closed

True

Helmholtz

resonators

have (Sacconi,

1961)

and

the

compliance

tube,

see

Figure

3.

walled cavities

which,

in

the

form

(flexibility)

of

the

walls

—

particularly

In

a violin

the

pitch

of

the Al mode

by

H.F.

Helmholtz,

were a

of

the

top

and

back.

The

pitch

of

the

A

c an

be

identified

approximately

by

of

different

size

glass

spheres

each

mode

can

be

heard

by blowing

across

humming

(near

A

440

Hz)

into

an

f-hole

Figure

1

Figure 2 ■Helmholtz

resonators

HIGHER

AIR MODES

IH THE

VIOLIN

vJ )

y

j

in

sogatMissuat

_

XII SCUPiDKi-S-H

I I M - S I

D

9979*92

PNMi Tl

e.V.J AIiSSOH

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No.

3

(Series II),

May

2001

Hutchins

-

The

Cavity

(Air) Modes of the V

Figure 3

A IR

COLUMN

CLOSED A T

BOTH

2L

F

=

Frequency

L

=

Length

=

Velocity

sound

while

feeling

the vibrations

in

top

and

REFERENCES

back

at

both ends with thumb and fin-

Hutchins,

CM.

(1962),

"The

Physics

of

Hutchins,

C.

M. (1990),

Work

gers.

There

is

considerable

interaction of

violins,"

Sci.

Am.

78-92,

Nov.

progress.

the

Al mode

with

the

nearby

large

Bl

Hutchins,

C. M.

(1967),

"Founding

a

J ansson,

E.V.

(1973), On

highe

body

mode.

However,

this

interaction

family

of

fiddles,"

Phy. Today

20,

modes in the

violin,"

Catgut

Ac

depends

on

a

variety

of factors such

as

2

3-27. Soc. NL

19,

13-16,

May.

the

frequency

spacing

between Al and

Hutchins,

CM.

(1985), "Effects

of

an

Sacconi,

S.A. (1961), Personal

comm

Bl

modes (Hutchins,

1989,

1990) and

air-body coupling

on

the

tone

and

cation.

the

tuning

of

the

free

top

andback

plates

playing

qualities

of

violins,"

/.

Spear,

D.2.

(1987),

"Achieving

an

(Hutchins,

1990).

Catgut

Acoust. Soc.

44,

12-15.

body

coupling

in

violins,

violas

The

frequency placement

in

relation

Hutchins,

C.

M.

(1988),

"The

acoustics

cellos:

A

practical

guide

for

the

to

string

tuning

of the Al mode has been

0

f

t

he viola,"/.

Amer.

Viola

Soc,

lin

maker,"/.

CatgutAcoust.

Soc

found to

be

very

important

to overall

Vol.

4,

No.

2 (summer).

4-7,

May.

instrument tone

and

playing

qualities,

Hutchins,

CM. (1989), A

measurable

especially

for the

viola

(Hutchins,

1988)

controlling

factor

in

the

tone

and

and for the

development

of the instru-

playing

qualities

of

violins,"

/.

ments

of

the

violin

octet

(Hutchins,

Catgut Acoust. Soc.

Vol.

1,

No.

4,

1962,

1967).

(Series II),

10-15,

Nov.

Further work is

being

done to

Hutchins,

C M.

(1990),

A

study

ofthe

understand

more

about these relation-

cavity

resonances

of

a

violin

and

ships

and

other

important

interactions

their

effects on

its tone

and

playing

between the

cavity

and

body

modes of

qualities,"

/.

Acoust.

Soc.

Am.

87,

the

violin.

■

CASJ

392-397.

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3

(Series II),

May

2001

PRO JECT

T I N Y

—

AN

OVERVIEW

by

Mary

Lee

Esty

and

Carleen

M. Hutchins

(as

published

in

CAS

Newsletter#31,

May

1979)

the article

entitled

"Project

Tiny"

(CAS

Newsletter,

#

30,

November

some

methods

for

improving

the

of small violins were

presented.

was

placed

on

raising

the

air

resonance

(AR)

frequen-

to

provide

second

harmonic

rein-

of

the

lower

G

string

range

as

powerful

method of

improving

the

of tone on

some

small violins.

are,

however,

several

factors to

be

in

deciding

exactly

what

steps

beused to

improve

the

tone

of

any

small violin. Size is the most

variable

to

be

taken

into

for

manipulation

of

the

AR

fre-

is

not

needed

in

all

small violins.

article outlines

factors to

be

consid-

when

attempting

to

improve

the

ofa small

violin.

Figure

#

1

includes

a

sound level

chart

[1]

and

frequency

resonance

[2]

of

a

good

3/4violin. This vio-

has had theback and

top

plates

grad-

to

exhibit

good

Chladni

patterns.

sound level

meter (SLM)

results

that

the wood resonance (WR)

at B

l

on

the A

string

and the

air

(AR)

near

the

open

D

string.

is the

arrangement

of

resonances

found

on

good

full-sized

violins.

relatively

small difference

in

size

a

3/4 and4/4

violin

is not

alone

to

be

detrimental to

good

cal characteristics

in a 3/4

violin.

effects of

regraduation

of the

plates

this 3/4 violin canbe

seen

by

compar-

of the

frequency

response

curves

in

#1. These

curves,

made

before

after

plate

regraduation,

show

an

amplitude

of

response

in

this

lower

range

and

a

decrease in the

high

frequency range.

This

violin

has

been

played

by

several

teachers and is

judged

to have

an

excellent

tone

quality.

If

it is

necessary

to

try

to

improve

the

toneof

a

Figure

1■

3/4

size

violin

100

sir.c

wave

input

open

strings

C 9

A

S

95

db

90

bowed

string input

(after

plate

tuning)

v

(

196 Us 293 440 639

3/4

violin,

work should be

limited

to

regraduation

of the

plates.

No

manipu-

lation ofthe

AR

is

needed.

Figure

#2

upper

line shows

portions

of five

frequency

response

curves

of a

1/4 size

violin which

has

four

holes

drilled

in

the

ribs

in

order

to

raise

the

AR

3

.

The

lower

two

charts (SLM)

made

with

bowed

string

input

show first that

the

frequency

of the

AR

of

this violin

with all

four

holes

closed

(duplicating

the

untreated

violin

body)

occurs

mid-

way

between the

open

D

andA

strings.

The second

chart,

made

when

all four

holes

are

open

shows the

AR

moved

up

enough

in

frequency

to

provide

second

harmonic

reinforcement of the

lower

G

string range

an

octave

below.

Moving

the

AR

on

this

violin

improved

the

sound

of

the

lower

strings

dramatically.

The

1/8

violin

also

lends

itself

to

improvement

by

raising

the

AR fre-

quency. Figure

#3 includes two SLM

charts,

the

first made after

the

plates

were

regraduated

but

with

normal rib

height

of

22.5

mm.

Reducing

the

rib

height

to

20.0

mm(lowerchart) moved

the

AR

up

in

frequency

so

that

it

pro-

vides second

harmonic

reinforcement

of

the low

G

string.

The

AR

frequency of

the

1/4

and

1/8sizes

can

be

changed

very easily,

but

the movementofthe AR

alone

will not

magically

transform

a

weak violin into

an excellent one. The

negative

effect of

plates

that

are

too

thick

cannotbe over-

come

by merely

raising

the AR

into

a

position

to

provide

second

harmonic

reinforcement.

Raising

the

AR of

a

small

violin without

also

graduating

the

plates

is

virtually

wasted

effort

as

20000

. Altar

plata

tuntna

«

I.J

Wood ft

\\i\i

■—

*—

-~<-W.i4.L

I

l___l

I_| ._j,

J j J ,

■ loo

°

i o

«»„„.,

2001

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3

(Series II),

Moy

2001

37

Esty

and

Hutchins

-

Project

Tiny—

An

Overvie

Figure

2 ■

1/4

size

violin

Figure 4 ■ 1/2

size violin

no

holes

in

ribs

A

Holp-s

I rt

Ribs

„

,_„,„.

...

ever,

leave

the

plate

thicknesses

figure

3

■

1/8size

violin

i_i

i i r

roughly the

same

as those

or

much

larger

violins.

The

end

,

a u

|

result

is

a wood

thickness that

95^

y,.

o<»

\JY~7^

plates

tuned

makes the

plates

much

too stiff

db

901A-J.-V

j

*

\jl

\i

V

rib

height

in

Proportion

to

the

instru-

\

/

i

V

22.5

mo

ment's size

to

vibrate

well, in-

85

j

Sc_J

j

hibiting

an

already

small

tone.

1

Several

very

small

"Project

Tiny"

violins

have

had

the

1

w

,

plates

regraduated

and we re

95

A'

v

i

A WOO4I

greatly

improved.

The

AR

of

\/

iW'

\

fflv\ \

B^ning

ate

1/10 and

1/16

size

violins

falls

db 90.--V-—

|-V

IWAJ -&-

\

—

A-t-

naturally

where

it

contributes

open strings

Bowed

string input

Figure

5

1/16

size

violin

196 Hz 293

440 659

No

rib

height

P lates tuned

change

(

-2.8

gr)

be

taken

not to

move

theAR too

high.

jofV-,

-V-i-lW4*

U-Ar

naturally

where

it

contributes

be tak

f

n

not to

move

theAX to

°

hl

§

h

I

V

b

0

h

"

Bht

to

overall

tone

production,

so

complicating

factor arises from

pla

65

-«

,

L«

that

any

a

ttQ

aker

sub

_

regraduating

which

reduces the AR fre

-0

i

i

1

stantially

the

normal

AR

of

U Q n c

l

f

iakl

"S

the

walls

ofthe

bo

open strings

these

sizes is

unnecessary.

,

more

flexible

All of

these

factors

mu

_

.

be

considered

when

deciding

exact

owed

string

input

The

1/2size

yiolin

;

s a

spe

_

what

J /2

size

cial

case which

must

be han-

To

summarize

for

those

who

ma

died

carefully.

The

frequency

want to work

with

small

violins

wit

1 1

,

.t

.

,

.

...

of the AR of 1/2

sizes

falls

poor

tone,

it is

always

necessary t

work

we

haye

done

with

1/10

and

1/16

around

E

320

Hz

on

the D

string,

well

reg

raduate

the

plates

unless

they

a

violins

vividly

demonstrates

below

the 392Hz needed

for

the AR to

al

read

y

too

thin,

in which

case

nothin

The 1/10

and

1/16

violins

are

so

produce

second

harmonic reinforce-

c an be

done

for the instrument.

Th

small

that

the

AR

frequency

is

high

ment.

Figure

#5)

It

is

necessary

to

do a

1/16, 1/10,

and

3/4

violins

need

onl

enough

to

produce

second

harmonic

considerable

reduction

ofrib

height

on

pl

a

te

regraduation.

The

AR

frequenc

reinforcement.

(Figure

#4) Present

man-

these

instruments

to

introduce

second

needs to

be

raised in

only

the

1/2 1/

ufacturing

methods

of

these

sizes,

how-

harmonic

reinforcement,

and

care must

and 1/8

sizes.

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No.

3

(Series II),

May

20018

Esty

and

Hutchins

-

ProjectTiny

—

An

Overview

It

is

possible

to

improve

the

playing

qualities

of

small

violins

greatly

by

regraduating

plates

and

by raising

the

AR

incertain

cases,

however,

raising

the

AR

frequency

is

not

auniversal

solution

to

all

small

instruments'

tone

problems.

Manipulation

of

the

AR

must

be

applied

selectively

andbe combined

with effec-

tive

plate

graduations

to

produce

better

sounding

small

violins.

FOOTNOTES

1. A

sound level meter

chart

is

a

loud-

ness curvemade

by bowing

thevio-

lin

normally,

but

without

vibrato,

at

1/2

steps

for

one

octave

plus

one-

half

step

on each

string.

Each

note

is

played

as

loudly

as

possible

andthe

resulting

decibel level

is

read

on a

sound

level

meter.

2.

For

explanation

see

Esty

and

Hutchins,

"Project

Tiny,"

CAS

Newsletter

November

1978.

3.

The

location of rib

holes,

used for

experimental

purposes

only,

must

be

chosen

with

care

in

order

to

avoid

complicating

effects that

would

arise

if

inner air

modes

were

disturbed.

See

J ansson

On

Higher

Air Modes in the

Violin,"

CAS

Newsletter

#19,

May

1973.

L

-

R:

Maureen

J ohnson

J ohn

Selway

Anne

Kornblut

Karen

Terio

1/4.

These

four children are

students

ofMrs. Ronda Cole

of

Arlington,

Virginia,

shown

just

before

performing

at

the annual

Christmas

Recital,

December

1978.

Photograph

Credit:

Maurice

J ohnson,

Chevy

Chase,

Md.

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No.

3

(Series

II),

May

2001

39

EVIDENCE

FOR

THE

C O U P L I N G

BETWEEN

PLATE

AND

ENCLOSED

AIR

VIBRATIONS

IN

VIOLINS

by

G.

Bissinger

and

C.

M. Hutchins

(as

published

in

CAS

Newsletter

#39,

May

1983)

A

transducer

on the

bridge

of

violin SUS #180was used

to

initiate instrument vibrations. The

output

of

a

small

acoustic

driver

placed

in

the

lower

bout was

used

to initiate internal

air

oscillations.

An

accelerometer

placed

at

various

positions

on the

top

plate

and

a

small

pickup

microphone

insertedinsidethe

instrumentwere

used to measure

top

plate

and

enclosed

air

vibrations,

respectively.

By tracking

thevari-

ousresonances

using

a

combination

of

thesetestmethodswhile

alternating

between air

and C0

2

inside the

violin,

we

are

able

to

show

that

some

of

the

resonances

heretofore

labeled

"air,"

"wood"

and

"top

plate

are

caused

by

complex

couplings

between

the wood

of

the

body

and

its inside

air

modes.

The

significance

of

possible

"impure"

character

for

an

important

resonance

is

discussed.

Introduction

preted

as the "wood

prime,"

the

"main evidence for

significant

enclosed ai

Moral and

J ansson

[1]

have

recently

aif

/'

an

d

the

"main

wood"

resonance

oscillation

when

there is

also

significa

made

a

significant

contribution

to

our

[2,4].

(The

"wood

prime"

peak

is

strong

plate

oscillation

[6].

What kind

of

ev

understanding

ofthevarious

vibrational

mthe

bowed-string

tone

becauseofsec-

dence is

there

for

enclosedair oscilla

modes of a

violin

with the aid of such

on

d

harmonic

reinforcement

by

the tions

"forcing" significant

plate

oscilla

modern

experimental techniques

as

TV

main

wood

resonance an

octave

higher).

tions?

An

attempt

to

answer

th

speckle

interferometry.

They

have

at-

The main

air

resonance,

also

called

question

led

us

to

the

experimen

tempted

to

deduce

the

character of

the

the

Helmholtz

resonance,

AO,

or the

described

herein,

resonance

peaks

in

input

inadmittance

"breathing"

mode,

has

generally

been

curves and

also

to deduce

the

impor-

considered the

only

air

resonance

that

Apparatus

andMeasurements

tance of these

resonances

to the acoustic

contributes

significantly

to

the acoustic

The

"guinea"

SUS

(violin

SUS

#180)

fo

output

ofthe

violin. For

theoretical

pur-

output

of

the

violin,

because it

commu-

the

experiment

was

suspended

horizon

poses

the exact

character

of these reso-

nicates

to

the outside

world

through

the

tally

with

thin

rubber

bands

from

ama

nances

is of the utmost

importance,

f-holes

of

the

instrument.

Higher

air

si

ve

fixture

(designed

for use

previous

since

"scaling"

of violins

[2]

must

be

modes

typically

have nodes

around

the

f

or

optical

sensing

experiments

on

strin

done

according

to the

character

of the f-hole

region

[5]

and

so

are

not

consid-

instruments

[7]). The

microphonepick

resonance.

A

mislabeled

resonance

be-

ered to

contribute

directly

to

the

output Up

for

internal

air

oscillations

was

comes

a

serious

matter

in

this

context,

of

the

instrument.

The

question

that

small

Knowles

microphone

slipped

i

e.g.

the

mislabeling

of

the

Helmholtz

must

be

answered for

these

higher

through

an

f-hole and

suspended

off

main

air

resonance of

the cello

led

to

modes

is

basically

the

question

of how

center in

the

lower

bout

region

so

that

propagated

errors in

the

scaling

of

effectively

c an "enclosed

air

oscilla-

did not

lie

on

any

of

the nodal

position

dimensions

for

the

baritone

member of

tions,

coupled

to

the

plates, produce

top

for

the

enclosed

air

resonances.

Th

theviolin

octet

[3].

(and

back)

plate

vibrations and how

accelerometerwas

placed

eithercentere

For some

time

now,

the

three

major

effectively

do

they

radiate?

When

the

directly

in

front of

the

bridge

or

off

resonance structures

observed

for an

top

plate

is

forced to

move

due to trans-

center

in

the

middle

of the

upper

o

assembled

well-tuned

violin in

the

pitch

mitted

bridge

vibrations

it is

clear that lower

bouts.

The

transducer to mechan

range

of

196-660

Hz,

labeled via

the

air

enclosed in

the "container" must

ically

drive the

bridge

was

a

cylindrica

Saunders

loudness

test,

have

been inter-

move

also.

There

is

direct

experimental

coil

placed

between the

G and

D

strings

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3

(Series

II),

May

2001

Bissinger

and

Hutchins

-

Evidence

for

the Coupling

Between

Plate

and

Enclosed AirVibrations in Violins

connected

to the

output

of

a

swept-fre-

quency

sine

wave

generator,

andwith

a

cylindrical

magnetic

structure

slipped

inside thecoil

(basically

the voice

coil

-

magnetic

structureofa

loudspeaker)

[B].

The

acoustic

driver for the enclosed

air

was an

earphone

transducer

system

cou-

pled

to

theenclosed

air

through

a

length

of

tubing

inserted

through

the other

f-

hole

[3].

The

aperture

ofthe

tubing

was

suspended

off-center in the

part

of the

lower bout

opposite

the

pickup

micro-

phone.

Additionally,

in

place

of the

transducer

positioned

on

the

bridge,

an

accelerometer unit with

a

small rare-

earth

magnet

attached,

could

be used

to

mechanically

drive

the

bridge

and simul-

taneously

pick

up

bridge

motion. This

technique,

due

to

J ansson

[I],

measures

the

input

inadmittance,

which

is

the

driving

point

velocity

for

a

driving

force

of constant

amplitude.

These

measure-

ments wereall conducted in addition to

the usual measurements

on

instrument

acoustic

output acquired

by placing

a

calibrated

microphone

one

plate-length

away

from the instrument

while

it

was

mechanically

excited

via

a

transducer

on

the

bridge.

With this

collection

of

apparatus

connected

to

the

violin,

and

swept

sine

wave

driving signals

fed

to

the

transduc-

ers,

it was

possible

to

initiate

bridge

oscillations

and

pick

up

plate

motions

with

the accelerometer

or

interior

air

oscillations

with

the

microphone.

Alter-

nately,

it was

possible

to initiate

en-

closed

air

oscillations with

the

acoustic

driver and

pick

up

plate

motions with

theaccelerometer

or

enclosed

air

oscilla-

tions

with the

microphone.

All of

these

measurements weremade

with

all of the

apparatus

connected

and

in

place;

the

effect

of

the

apparatus

on

the

resonance

properties

of

the

system

was

thenshared

for

all

measurements. Wewere

primarily

interested here

in the

changes

in

system

resonance

behavior

that

occur

when the

air

inside

the violin is

replaced

with

C 0

2

,

since

changing

the

internal

gas

from

air

to C 0

2

(same

temperature

and

pressure)

does

not

change

the

compli-

ance of the

gas

in

the

internal

cavity,

nor

does

it affect

plate

resonance behavior

(although

it

will

change

the

internal

humidity

which,

over

the

duration

of

the

scan,

should

not

significantly

affect

the

plate

response).

The

technique

employed

to

replace

the air

with

C 0

2

was

very

simple.

Using

"dry

ice"

from a local

dealer,

a

rubber

stopper

with

one hole and

a

long

plastic

tube,

a

glass

jar

and

a

warm

water

"bath,"

the

dry

ice

was

placed

in

the

glass

jar,

which

was

then

stoppered,

placed

inthe bath and the tubeextended

to blow the

escaping gas

into the hori-

zontally-suspended

violin.

Since the

C 0

2

vapor

is heavier

than

air,

it

will dis-

place

the

air

from

the violin.

Care must

be taken

that

the

gas

does

notcome out

too

rapidly

(increase

tubing

inside

diam-

eter), and thatit is

at

room

temperature

(a

long

piece

of

tubing

with

a

coil

run-

ning through

room

temperature

water

should suffice).

Finally,

to

help

understandhow the

enclosed

air-plate

coupling might

affect

the sound

of

the

instrument,

we

employed

a

Bruel and

Kjaer

Real Time

Fourier

analyzer

to

analyze

theacoustic

output

of

the instrument. To

eliminate

the harmonic

structure

associated

with

sustained

tones,

we

played

"slide

tones"

on

the

G

string

—

covering

the

frequen-

cy

range

(fundamental)

off=l96-~550

Hz and

back in

1-2

seconds,

all

the time

"weaving"

the instrument

around. The

pickup

microphone

(a

companion

B &

X

microphone)

was

placed

in

the

corner

of

the

Hutchins

living

room

(which

those

of

you

who

have visited know

to

have

many

non-parallel,

unusually

shaped

objects

to reduce

standing

wave

effects).

To

help

eliminate

thevagaries

of

bow

velocity, pressure,

position,

etc. on

the

results,

we took

advantage

of

the

accumulating (averaging)

capabilities

of

this

instrument

and

collected

128

sepa-

rate

frequency-analyzed

spectra.

In this

way

we

could examine

differences

in the

resonance structure of the actual

acoustic

output

ofthe

played

instrument

for air-

versus

C 0

2

-

filled.

Results

and

Discussion

For

the reader

to

observe the effect th

the

substitution

of

C 0

2

for air

(N

2

an

0

2

) had

on

the resonance

structure

the

enclosed

air

oscillations

the result

are

probably

best

presented

graphicall

In

Figure

1

(a)

we

show

the

enclosed

a

resonance

curve

obtained

by

the

intern

microphone

when the enclosed

air

wa

internally

excited

by

the

acoustic

drive

in

Figure

1

(b)

C 0

2

has

replaced

the

a

all otherconditions

are

exactly

the

sam

There

is

a

noticeable

downward shift

some

peak positions

with

the introduc

tion of C 0

2

. This

shift

is

due

to

th

change

in

the

velocity

of sound

wit

mass ofthemolecule (oratom)

compri

ing

the

gas

(or

gas

mixture). Here th

average

mass

of

an

air

molecule"

is

2

while

that

of

the

C 0

2

molecule

is

4

The

velocity

ratio is

just

inversely

pro

portional

to the

square

root

of the

ma

ratio

(temperature and

pressure

the

sam

for

both

gases),

i.e.,

Equation

1

Also in

Figure

1

(a)

and (b)

are

th

accelerometer

readings,

superimpose

on the same

frequency

scale

for air an

C 0

2

gases,

for the

bridge

and

upper

an

lowerbouts combined.

Significant

plat

motion,

as

indicated

by

the substanti

accelerometer

reading,

was observed

the same

frequency

(-255 Hz) as th

lowest

frequency

air

resonance,

th

Helmholtz resonance

or

AO

mode,

an

was also

observed

atthesame

frequenc

(-463

Hz)

as

that

for

the

Al

air reso

nance

mode

[s].

This

indicates that th

air

oscillations

are

coupled

to

the

plate

forcing

the

plate

to

move also.

This

made

even

clearer

in

Figure

1

(b),

wher

we see

that

the

frequency

of the

plat

oscillation

maximum

"tracks" th

downward

frequency

shifts of the

AO

andAl

modes. This shift in

plate

"reso

nance"

frequency

is due

to

"enclose

air-plate"

coupling,

notto the air

res

VCO_

I

[mair]

U2

v

air

~

[m

C0

2

]J

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No. 3

(Series

II),

May

2001

41

Bissinger

and

Hutchins

-

Evidence for

the

Coupling Between Plate and Enclosed AirVibrations in

Violin

Figure

1

■

(a)

Internal

microphone

output

(solid

line) andaccelerometer

output

(dashed

band

gives

range of

accelerometer

readings

—

dotted

line

gives

bridge

accelerometer

reading)

obtained

with

internal acoustic

driver

excitation

of SUS #180

overfrequency rangeof-130

-

1950Hz.

Internal gas

is air.

All

outputs

are

in

db.

(b)

Same

as

in (a)

except

internal

gas

is

C 0

2

.

Note

in

particular the downwardshift

of the

two

lowest

peaks

in

the

internal

microphone

output.

These

are

theAO and

Al internal

airnodes.

(HZ)

onance

shifting

downward to

coincide

difference can

be understood from the

with

another

plate

resonance.

(At

the

character of

air motion associated

with

endofthe

run,

when

the

C 0

2

was run-

these

two

oscillatory

modes.

The

A

ning

out

and

there

was an

air-C0

2

mix-

mode,

descriptively

called

the

"breath-

ture,

the

air resonance

peaks

all

shifted

ing"

mode,

is

characterized

by

the in-

up

slightly

in

frequency

and

so

did

the and-out

sloshing

motion

of

the

gas

accelerometer

peak

position). From the

through

the f-holes. This will mix

the

curves

in

Figure

1

(a)

and

(b) it

might

be internal andexternal

gases

in

the

f-hole

noted

that the

frequency

reduction

for

region,

reducing

the "mass

plug"

of

the

theA0ode is

not

quite

as

high

as that

A0ode.

Also

when

the internal

gas

is

for theAl

mode,

being

about

.86for

the

different

than

air,

this

sloshing

will

tend

A

0ode and

.81

for the

Al mode.

This

to

produce

a

gas

mixture

and

change

the

should

be

compared

to

the

value

of

average

mass

of

the

molecules in

the

(29/44)

=

.81

from

Equation

(1).

This

mixture.

For the caseof C 0

2

the

change

is toward

a

lighter

mixture and th

toward

a smaller

velocity

change

fro

that of

air. Whereas for

the

Al

mod

there

is a

node

at

the

f-holes,

very

litt

airmotion

in this

region,

and

very

litt

mixing.

The

time

interval

between

t

swept

sine

wave

generator

passin

through

the

AO mode

and the

Al

mod

was

sufficient toreduce

the

aircontam

nation

almost

completely.

How

strongly

are these

variou

enclosed

air resonances

excited

b

bridge-transmitted

vibrations such

arise

from

string

vibrations or

the

bridg

transducer? To

answer

this

question

w

ran

a

separate

series

ofruns (on

anoth

day

—

the

slightly

different

temper

tures

and,

possibly,

local

humiditie

could

easily

give

the

few

Hz

variation

in resonance

positions)

to

investigate

th

strong

enclosed

air

oscillations

set

u

when

the

violin

bridge

was

transduce

driven

and

to

investigate

the

strong

plat

vibrations set

up

when

the

enclosed

a

was

driven

by

the

acoustic driver.

I

Table

I,

we

list

the

resonances

observe

in

these

two measurements.

From

Table

I it is clear

thatthere

a

only

two

resonances

below

1200 H

that

coincide

in

frequency;

these ar

justthe

same

two

resonances

that

sho

such

strong

frequency

shifts

in

Figure

Furthermore,

the accelerometer

reading

at the

bridge

for

the

same interna

microphone

output

were within

0.5 d

of

each

other for

both

transducer-on

bridge

and

internal

acoustic

driver

exc

tation of these two

resonances.

Th

accelerometer

readings

obtained

at

an

other

resonance in

Table

I,

for

the

sam

internal

microphone

reading,

were

n

closer than 3.5

dB.

This

implies

tha

essentially

all

of

the

plate

motion

at

fre

quencies

coinciding

with

the

A

0nd

A

internal

air

modes

is

due

to the

enclose

air

driving

the

top

plate.

Further

information on

the

reso

nance

behavior

of

the violin SUS

#18

was

gotten

from

the

inadmittance

meas

urements

with

the

accelerometer

placed

on

the

bridge

(outside

theG

string).

The

information from

these inadmittance

curves on

the

interchange

of

the

air and

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3

(Series

II),

May

2001

Bissinger

and

Hutchins

-

Evidence

for

the

Coupling

Between Plate

and Enclosed

AirVibrations in Violins

TABLE

I

■

Strong

Air

Oscillations

(Transducer

onBridge)

compared

to

Strong

Plate Oscillations

(Acoustic Driver

inside

LowerBout).

C 0

2

is not the same

as

that obtained

from

the direct

measurement

ofinternal

air

oscillations or

plate

motions.

First,

many

of the

peaks

in

the inadmittance

curvesdo

not

fall atthesame

frequencies

as

those for the

enclosed

air

or

plate

motions,

although

there is

a

structural

similarity

in some instances. For exam-

ple,

there is

no

peak

at463 Hz.

The

clos-

est

peaks

are

at

422

and

532

Hz.

There

is

a

peak

atabout -242

Hz

which is all

by

itself and

almost

certainly

corresponds

to theA0ode. When C 0

2

is flowed

into

the

violin this

peak

appears

to

split,

with

one

component

dropping

down

to

209

Hz

andthe

other

staying

at

246

Hz;

both

peaks

are

considerably

smaller

than

the

single

original

peak

(peak heights

about

5-7

dB

less).

The inadmittance

curves

are

essentially

copies

of one

another

up

to

-720

Hz,

with this

one

exception,

and then

over

the

range

730-

-2000

Hz

they

are

quite

different,

finally

becoming

quite

similar

again

above

this

frequency.

Itis clear in

the

case

oftheA

0

mode

that

the inadmittance

curve

shape

and

strength

are

strongly

affected

by

the

change

of

gas

inside;

the

situation

for

the other

structures

is

as

ye t

not

clear.

What

is

clear

is that these curves offer

different

information about

the

reso-

nancebehaviorof the

violin and for

that

reason alone

are

quite

interesting

and

important.

Finally,

we

present

the

results

of

the

real

time

analysis

ofthe acoustic

output

of

the

violin SUS

#180,

played

with air

or

C 0

2

as the internal

gas.

In

Figure

2

are

the

averaged

slide-tone

spectra

for

these

two

cases.The

C 0

2

curve

shows

a

30Hz

shift

downward

in the lowest

res-

onance,

almost

certainly

theA0

ode,

which

lay

atf

=

260

Hz on

the

air

curve

(as read off the

screen

of the

analyzer

right

on

top

ofanoth

resonance

at

-380

Hz

This slide-tone

te

agrees

quite

well

wi

the

results of the

i

admittance

test

me

tioned

earlier.

It

h

been shown

by

Beld

[9]

that

the

inadm

tance

curve is

relate

with

the

aid of

a

cursor).

Prominent

tance

curve

is

relat

peaks

in

the

air

frequency

spectrum

to

the radiated

power

of

the

violin

below

1kHz

lay

at

-380

Hz,

460

Hz,

low

frequencies

(note

that one

of t

610

Hz,

765

Hz,

and

965

Hz.

A

glance

at

instruments he tested was SUS

#180).

Table I shows that

many

of

these

same

an

eigenmode

can be driven

effective

resonances

show

up

also in

plate

vibra-

from the

bridge,

the inadmittance cur

tions

induced

by

enclosed

air oscilla-

will show a

peak

at

that

eigenmode

fr

tions. However it

should

also be noted

quency.

The

absence of such a

peak

that

while

there are

changes

in the rela-

the inadmittance

curve

at463 Hz is

co

tive

amplitudes

of

these

same

resonance

sistent

with

the

results

of

the

frequen

peaks

associated

with the

interchange

of

analysis

of

slide-tones,

and also

wi

gases,

some

of

the

quite

large

peaks

do

holographic

measurements

of

SUS

#1

not

show

as

large

or, indeed,

any

netfre-

which show an

eigenmode

with

nod

quency

shift.

Unfortunately,

when

anair

around the

bridge

(Moral and

J anss

resonance

shifts

its

position

downwards,

also

see

somewhat

similar results

in

the

it is

possible

for

it

to then

fall

"under"

a

holographic

measurements

onothervi

plate

(or

other) resonance.

For

example

lins).

the

Al

mode

frequency

forair

inside the

Ideally,

of

course,

measuremen

instrument is -463

Hz;

for

C 0

2

the Al

that

involve

shifting

air

resonance

fr

mode

slips

down to .81

x

46-

=

375

Hz,

quencies

while

not

affecting

plate

res

Figure

2 ■

Fourier

analyzed

slide-tone

spectra

for

violin

SUS

#180

(see

text)

over

the

frequency range 0-2000 Hz.The vertical

scale

is

linear.

The

curves

shown

are

for

air

(solid line)

and

C 0

2

(dotted line)

as the

internal

gas.

(Hz)

AIR

OSCILLATIONS

(Hz) 258

343

370 409

463 655 743

1032 1220

PLATE

OSCILLATIONS

(Hz)

256 463

-612 -761

963

-1100

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No. 3 (Series II),

May

2001

43

Bissinger

and Hutchins

-

Evidence

for

the

Coupling

Between

Plate and

Enclosed

Air

Vibrations inViolins

nance

frequencies

should be a tremen- is

quite

possible

in

our

case

since there

affects

the

acoustic

output

of

the instru

dous

aid

in

accurately

labeling

the

char-

already

was

a

strong

peak

at -380

Hz

ment

only

in

the

case of

the

AO

mod

acter of

the

observed

instrument

reso- and the

CO2

interchange

would

drop

a

However

the

accelerometer

readings

fo

nances.

It

would

appear

from

ourresults

peak

at463

Hz down to

-370

Hz.

plate

motions whose

frequencies

"trac

that

the

useof

more

than

one

gas

would

changes

in

air mode

frequencies, give

clear

indication

that

some

of

the

reso

e

a

further

improvement

since it

would

Summary

considerably

reduce

the

probability

that

The

information

gathered

here,

in

a

vari-

nances heretofore

labeled

"air,"

"plate

the

enclosed

air

resonance would

always

ety

of

ways,

indicates

thatthere

is

signif-

or

wood

vibrations

by

variou

be shifted

just

the

amount

needed

to

icant

"enclosed air

-

plate"

coupling

in

researchers

are

caused

by

complex

cou

accidentally

coincide with

some

other

violins at

least

for

some

of

the

lowest

air

plings

between

the wood

and

th

type

resonance.

This

"shadowing

effect"

modes.

Our

results

show

how

this

enclosed

air.

B C A S

REFERENCES

1.

J .

A. Moral and E.V.

J ansson,

CAS

NL

34,

29

(1980)

(also

submitted

to

Acustica).

6.

CM .

Hutchins

—

numerous

unpub-

lished

tests on all

types

of

string

instruments.

9.

LP.

Beldie,

CAS

NL

22,

13 (1974).

2. C M.

Hutchins,

Set. Amer.

207,

78

(1962).

3.

CM .

Hutchins,

CAS

NL

26,

5

(1976).

4. F.A. Saunders,/.

Acoust.

Soc.Amer.

9,

81 (1937).

5. E.V.

J ansson,

Acustica

37,

21

1

(1977).

7.

R.E

Menzel

and

CM.

Hutchins,

CAS

NL

13,

30

(1970).

8.

CM . Hutchins

and EL.

Fielding.

Phys.

Today

21,

34

(1968).

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3

(Series II),

May

2001

FURTHER

EVIDENCE

FOR

C O U P L I N G

BETWEEN PLATE

AND

ENCLOSED

AIR

VIBRATIONS

IN

STRING INSTRUMENTS

by G.

Bissinger

and C M. Hutchins

(as

published

in

CAS

Newsletter#40, November

1983)

The

interior

airin

four

different

string

instruments

(standard

violin,

long-pattern

Stradivarius

model

violin,

mezzo-violin

and

16

viola)

was

interchanged

with

C0

2

andCC l

2

F

2

to

examine

the

coupling

of

plate

vibrations to interior gas oscillations

by

shifting

the

frequency

of

these oscillations.

The lowest

fre-

quency

air

modes,

AO,

Al

and

A

2, could

be

identified

reliably by

correlating the

results

for

all

interior

gases.

These

gas

oscillations also showed

significant

plate

coupling

as

evidenced

by

accelerometermeasurements

at three

points

on the

top

plate.

Introduction

duced

a

broader

cross section of

string

period

ofthe waveand so the oscillati

In a recent work

we

reported

on an

instruments

toexamine

the

generality

of

frequency

drops.

If

the

interior

gas

osc

experiment

to determine the

significance

this

coupling

for

other

string

instru-

lations

couple

strongly

to

the

instrume

of

"enclosed

air-plate"

coupling by

ments.

We

felt

that

a

quick

look

at

these

plates,

then the

frequencies

of the

pla

interchanging

the

air inside

a

violin

with

new

results

would

be useful

for

those

vibrations

will

drop

also.

While th

C 0

2

gas

[I].

The fundamental idea of

with an interest in this

subject,

even

seems

straightforward,

there are

serio

this work

was

to

show whether

or

not

though

many

of the details

will

have

to

difficulties

in

determining

the

exact

cha

the interior

gas

oscillations

could

force

be

filled

in

later.

acter

ofthe resonance

peaks

in

the

prob

significant

plate

vibrations.

Using

an

microphone

or accelerometer

outpu

acoustic driver

slipped

thru

an

f-hole

Results

and

Discussion

that arise

from the lar

§

c

numbers

into the lower bout

off-center,

a

probe

c

. .

„

j«.

l

peaks

in the

spectra.

, ,

.

l

Since the

apparatus

and

techniques

were

t .a.

■

i i

v

t

m

microphone slipped through

the other

-i v

j jj j

In the

on

g

inal

work h

Y

J ansson

[2

r

i

i-

.

i

-ii-11

so

similar to

those

used,

and

discussed,

-t

.i

+'

w^ .

f-hole

into

the

opposite

side of

the lower

. .

, ,

'

,'

identifying

the

interior

air

modes,

t

bout and an

accelerometer

positioned

P '

6

IJ8 l

J

1]

'

*

c reader should

consult

stHng

instmment

was

encased

in

plast

at

three

points

on the instrument's

top

at

WOrk

f ^

«P«imental

details

tQ

eliminate the influence of

pkte

vibr

plate,

we were

able

to monitor

interior

Here we

wIU dl

f

uss

onl^

the

matters

,

of

tions on

the

interior

air

oscillations.

He

air

oscillations

and

plate

vibrations.

Our

interest newto thls

experiment.

Since

the

we have

nQ

such

simplification

and w

results

clearly

showed that

the

lowest

velocit

y

of

sound

in

a

gas

varies inverse-

observe

that

the

probe microphone

giv

frequency

air

modes

[2],

AO

and

Al,

did

as

the

sc

l

uare

root

of the molecular

significant

outputswhen

the

plate

osc

indeed

produce

strong

plate

vibrations

weight

for that

gas,

for C 0

2

the

velocity

lations

are

strong.

We

havealso

observ

that

tracked

the

downwardshift

in reso-

°*

sound is

only

0.812

that

for

air

that,

in

general,

when

there

is

strong

co

nant

frequency

associated

with

the sub-

(same

temperature

and

pressure)

and

for

pH

ng

between

air

and

plate

vibrations

t

stitution

of

C 0

2

for

air.

We have now

CC1

2

F

2

theratio is

0.492.

When the

air

in

accelerometer

output

and

probe

micr

extended

thesemeasurements to

include

an

instrument

is

replaced

with a

heavier

phone

output

are

large.

When the co

gas interchange

with

a

much

heavier

gas,

gas,

the "transit" time for

the

waveto

go

pling

is

very

weak

the

outputs

are

cha

CC1

2

F

2

,

which

will

drop

the

air reso-

from

boundary

to

boundary

inside the acterized

by large

dissimilarities

nant

frequencies

even

further,

and

intro-

instrument

is

increased.

This extends

the

magnitudes,

with the

ratio

depending

o

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No. 3 (Series

II),

May

2001

45

Bissinger

and

Hutchins

-

Further Evidence

for

Coupling

Between Plate

and Enclosed

AirVibrations

in String Instruments

the

character

of

the

resonance,

i.e.

plate

regions.

For

the

A

2

ode clear correla- C 0

2

are

referred

to our

previous

wor

resonances

producing very

low

micro- tions

were noted

only

when

the

A

2

for the standard

violin,

SUS #180

[I],

o

phone

outputs

and

air

resonances

pro-

mode

dropped

to

frequencies

below

600

the

more

recent results

obtained

wit

ducing

weak

plate

vibrations. In some

Hz,

i.e.,

only

for

the

CC1

2

F

2

spectra.

It CC1

2

F

2

for

this

same

instrument

[3].

cases

we

have

had

difficulty

in

identifica-

was then

a

straightforward

task

to work

Referring

to Table

1

below we

se

tion

of

resonance

peaks

due

to

the

large

from

the

CC1

2

F

2

spectra

back

to

the air

that

the

frequencies

for

the

AO ,

Al,

an

number

of

peaks

occurring

in certain fre-

and C 0

2

spectra.

During

this

identifica-

A2

odes

for

the

various instrument

quency

regions,

in

particular

above

tion

procedure

it

was

noted that

general- usually

fall

close to the

frequencies

ca

about

700 Hz.

This

made

identification

ly

the

peak

in

the

probe

microphone

out- culated

from

Ref.

2,

which were

for

of theA2

ode difficult for the air and

put

associated

with the A2mode

"standard"

violin

encased in

plaster;

th

C 0

2

spectra,

but

for the CC1

2

F

2

spectra

appeared,

relatively

speaking,

to

grow

exception

was

the mezzo-violin.

W

theA

2

eak

was below

the

"clutter" weaker

as

the

resonance

frequency

have

normalized

the

frequencies

of

J ans

(probably

due to various

plate,

rib

and

increased

(the

mezzo-violin,

SUS

#159

sonto

theA

0

nd

Al

mode

frequencies

"body"

resonances) and

was

easily

iden-

was

the

only exception).

for all

instruments

except

the

mezzo

tified.

An additional

aid

in the

identifica- Inthis

work

we

are

going

to

restrict

violin,

SUS

#159,

where

only

the

middle

tion

of

the

type

mode

in the

spectra

was

ourselves

to

"air-plate"

coupling

for

just

mode

Al

was

used

for

normalization

the

relative

accelerometer

readings

at the

AO ,

Al

and

A

2

odes,

which

are

pri-

These

normalized

frequencies

were

then

peaks

in

the

plate

response

curves that

marily

a

volume

mode,

a

length

mode

multiplied

by

0.812

for

C 0

2

and

0.49

appeared

to

be associated with

interior

and

a

width

mode

(lower bout

only),

for

CC1

2

F

2

for

comparison

with these

gas

oscillations.

Using

the

nodal-antin-

respectively [2].

In

the

interest

of

brevi-

gas-interchanged

cases.

Again

it

should

odal

patterns

for the interior

gas

oscilla-

ty

we will

present

our

results

in

the

be

noted

that the

A0

ode

always

la

tions from

Ref.

2,

we observed that

the

Table

below for

these

air modes in all

above

the

predicted

values

for the

C 0

accelerometer

readings

for

theA0

nd

Al the instruments.

Those

interested in

a

and

CC1

2

F

2

cases.

This effect

probabl

modes

always

showed

strong

plate

graphical

presentation

of the air and

was

dueto

the

intermixing

of

the

airand

motion

in the antinodal

region

and

rela-

plate

mode

frequency

and

response

vari-

interior

gas

at

the

f-holes

in this

so

tively

weaker

response

in

the

nodal

ations

under

the

interchange

of

air

and

called

"breathing

mode."

The

results ofthis

work

show

clearly

that for

frequencies

below 600

Hz,

strong

Table 1

■

Enclosed

air-plate

coupling

frequencies

(AO,

Al

andA2odes only)

—

All

frequencies

shown are

plate

motions

are

as

for air

modes;

plate

vibrations

generally

fell within a

few

Hz

ofthese

frequencies.

sociated

with interior

*

-

From

the

workof

Jansson

[2]

with

encased

violin,

normalized

to

A0 andAl

modes,

a

-

evidence forthree

peaks

at

262/276/290

Hz.

-

evidence

for

three

peaks

at

276/285/303 Hz.

+

-

predictions

based on

Al mode

only

gas

oscillations,

and

will

track

decreases

in interior

gas

oscilla

tion

frequencies,

i.e.

the

plate

acts

very

much

as a

loudspeak

er

does.

What

is no

clear

at

present

is how

much

of a

contribu-

tion this

coupling

makes

to

the

overall

acoustic

output

ofthe

instrument.

Our

ear-

lier

work

indicated

significant

downward

shifts,

for

C 0

2

vs.

air,

in

the

AO-associated

peak

frequency

ofthe

Fourier-

analyzed

acoustic

output

of

standard

violins;

we

INSTRUMENT

(SUS#)

MODE

AIR

This Work

Pred.*

co

2

CC1

2

F

2

This Work Pred.*

his Work

Pred.*

#180 AO

258 264

224 214

150 130

(standard

Al 465 455 383 369

229 224

violin)

A

1047

992

804 803

490 480

#250 A

276

a

277

236

225

154

136

(long

pattern

Strad)

Al

478

477 383

388 230 235

A 2

1070 1040 780 845

484

511

#159

AO

285

b

251+

236 204

158/166

123

(mezzo-

Al

433 433 352

352

222 213

violin)

A

2

753

944

718/740

767

418/429

464

#212

AO

234 237 201

192

138

117

(16" Al

413 408 335

331 201 201

viola) A

2

849

890

663

723 413

438

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No. 3 (Series II),

May

2001

Bissinger

and

Hutchins

-

Further Evidence for Coupling

Between

Plate and

Enclosed

Air

Vibrations

in

String Instruments

have seen

this

sameshiftformezzo-vio-

relative

to

AO ,

thanthe

violins

or

violas.

air

and

"plate"

modes

is

still

not

a settl

lins and

violas

also.

Unfortunately

we

If

higher

airmodes are

an

audible

con-

question

in

terms

ofthe

acoustic

outp

do

not

have

any

such measurements

for tributor

to

the acoustic

output

of the

f

, ,

.

,

.

.

t.

i

wr

i i

1

i i-i-i i

oi

the

instrument,

what is settled is t

CC1

2

F

2

interchange.

We also see that

the

violin,

then,

on

this basis

alone,

the

mezzo-violin has

considerably

different mezzo-violin

will

sound

different than

a

matter of

coupling

between

interior

a

frequencies

for

the

Al

and

A2

modes,

standard violin.

The

interplay

between oscillations and

plate

motion.

■

CA

REFERENCES

G4S

NX

39,

7

(1983).

2.

E.V.

J ansson,

CAS

NL

19,

13 (1973);

Acust. 37,211(1977).

Proc.

Stockholm Mus.

Ac.

Conf,

J uly,

1983

(to

be

published).

1.

G.

Bissinger

and

C.M.

Hutchins,

3.

G.

Bissinger

and C.M.

Hutchins,

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No. 3 (Series

II),

May

2001

47

EFFECTS

OF

AN

AIR-BODY

C O U P L I N G ON

THE

TONE

AND

P L A Y I N G

QUALITIES

OF

VIOLINS

by

Carleen

M.

Hutchins

(as

published

in

CAS

Newsletter

#44,

November

1985)

The

response

curves

of

many

violins

and

violas show

evidence in

some

instruments

of close

coupling

between

the

so-called "Helmholtz"

mode

(here

designated

as

AO

mode)

and

a

body

mode (here

designated

as

BO

mode).

This

coupling

c an be observed

as a

distinct

dip

in the

response

curve

of

the lowest

strong fundamental

air

resonance,

the

AO

mode,

making

a

double

peak

of

this

resonance which in

violins

occurs

around

270-280Hz.

Such

condition is

indicative

of

goodcoupling

betweenthe

A

0

mode

and the

B0

node. In

some

instruments

there

is

evidence

of the

B0

mode

being

somewhat

lower in

frequen-

cy

thantheA0

ode,

while

in

others

the

B0

mode

is

higher.

Figure

1

shows the

response

curves of

three Stradivarius vio-

lins

tested

by

Frederick

A. Saunders in

the

Harvard Laboratories when

he

was

working

with

J ascha

Heifetz

in the

1930s

[I].

The

upper

and

lower of

these

show

thedouble

peak

in

the

lowest

strong

res-

onance,

the

AO,

while

the center one

shows

the B0 to

be

lower in

frequency

than

theA0ode.

Saunders often

spoke

of

this double

peak

of the

A

0

ode in

such tests

and wondered

atits

cause

and

possible

significance.

The same

double

peak

is

found

in

many

of

the

several

hundred

response

curves

of

violins

and violas of

varying

musical

qualities

belonging

to both

pro-

fessional and

amateur

players.

These

tests

were

made in

my

laboratory

over

the

last

15

years.

The

interesting

feature,

however,

is

that

the

violins

and

violas

selected

and

playedby

many

profession-

als

as well

as

some fine amateurs

very

often

show evidence of

this

close cou-

pling

in their

response

curves.

These

response

curves are made

by

suspending

the violin

vertically

on

rub-

ber

bands

at

the four

corners

and at the

neck,

with

a

light-weight

transducer

coil

clipped

to the

bridge

between the

C

and

D

strings

of the violin

with an

electro-

magnet

inserted into

the

coil,

but not

touching.

The

violin

is

activated

by

a

sine

wave

sweeping

from 20Hz

to20kHz

fed

through

thecoil

with

the

response

of

the

instrument

picked

up by

a

microphone

placed

14

inches

off

the

back.

The testis

made in

a

constant

position

in

a

heavily

curtained

room,

which tests

show to

have

little

if

any

reverberation

in

the

fre-

quency

range

below

600

Hz.

We now

know,

thanks to

the tech-

niques

of

modal

and

finite element

analy-

sis which

have

been

applied

to the

violin

by

Marshall

[2],

Roberts

[3]

and

others,

that

the

B0 mode is

a

bending

of

the

whole

violin,

particularly

the

neck,

oc-

curring

around

260-300

Hz. This

mode

shows

a

nodal line

just

below

where

the

neck

joins

the

body

and

another across

the

widest

part

of

the lower

bout,

as

well

as

bendingof

the

neck,

scroll

and finger-

boardwith

another

nodal

line

just

below

thenut

(Figure 2).

The

B0

mode

is in

effect

a beam

node

of

thewhole

instrument

with

the

addition

of

vigorous

bending

of

neck

and

fingerboard. By holding

the

violin

in

thumb

and

forefinger

upside

down at

the

nodal

line across

the lower

part

of

the

body

and

tapping

on

the

end

of

the

scroll,

the

pitch

of the

B0

mode

can he

heard

fairly

clearly.

Then

if

one

blow

into one

f-hole,

the

pitch

of

theBO mod

and that

of

the AO node

can

be com

pared.

When

the

pitch

of

these tw

modes

can

be

heard

to

coincide,

there

a

clear

ringing

sound

which affects

th

whole

instrument.

Further

studies

to document th

effect

more

precisely

have

been

made

Since the

B0

node

imparts

a

strong

rock

ing

and

bending

notion

to the neck an

fingerboard,

there

is

considerabl

motion

at

both

the scroll

and

the

bridge

endofthe

fingerboard.

With violin#29

suspended

vertically

on

rubber

band

an

accelerometer

(0.68

gr)

was

fastene

on

the

bridge-end

ofthe

fingerboard

an

a

tiny

recoma

magnet

waxed

to

the

en

of

the

scroll

in

such

a

way

that

a

co

could

be

placed

over

it

without

touch

ing.

With

a

sine

wave

sweeping

from

20Hz

to

20kHz

fed

through

the

coil,

th

accelerometer

showed

the

motion

ofth

end

of

the

fingerboard

as

recorded

in

Figure

3.

With

the

violin

in

the sam

position,

a

test

was

made

immediately

using

a

tiny

loudspeaker

(Knowles

#CI

-1955)

suspended

through

one

f-hole

inside

the

lower

end,

and

a

tiny

micro

phone

(Knowles

#

XL

9073)

suspende

through

the

other

f-hole

also

in the

lower end of the

violin.

Figure

4

shows

the

cavity

resonances

of

this

instrumen

tested inthis manner

which

are

a

combi-

nation

of the

air

inside

the

box and

the

vibrations

of

the

wooden

walls,

bu

since

the test is

from

air

to

air,

the

vibra-

tions

of the inner

air

predominate.

In

violin

#297,

the

A0

ode

at 271

and

286

Hz

and

the B0

node

at

278 Hz

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No. 3

(Series II),

May

2001

Hutchins

-

Effects

of

an

Air-Body

Coupling

on

the

Tone

and

Playing

Qualities

of

Violins

Figure

1■

Response

curves

by

new

method

of

three

Strads,

and

three

new

violins which led

inthe

Heifetz

test.

FREQUENCY

are

very

close

in

frequency.

The

response

curve of this

same

violin

made under sim-

ilar conditions of

tempera-

ture

and

relative

humidity

shows the double

peak

in the

A

0

ode

of

Figure

5

(similar

to

the

response

curves of

Saunders) indicating

close

coupling

of the

BO

and

A

0

modes.

Violin

#299 was test-

ed

by

the same three

meth-

ods.

Figure

6A

shows that

the BO mode

of this violin

at

308

Hz is

higher

in

frequen-

cy

than its A0ode at 276

Hz.

To

lower the

frequency

of

#299'sB0

mode,

an

appro-

priate sized

lump

of

oil

clay

was

fastened

under

the end

of

the

fingerboard thereby

adding

mass

to

a

vibrating

part

and

reducing

the

B0

mode

frequency

to

287

Hz

as

in

Figure

68.

A

comparison

ofthe

response

curves (radia-

tion)

of

violin

#299 are

shown:

Figure

7A without

clay;

Figure

3 with

clay

on

Fingerboard

to

lower the

B0

mode

frequency.

Notice

the

increase

of

amplitude

up

to

7

kHz

and

decrease

above

10

kHz

when

A0

nd

B0

modes

couple

as in

Figure

78.

Further

tests to docu-

ment this mode

coupling

were

done on

violin

#299

with the collaboration

of

George

Bissinger using

the

interior

gas exchange

tech-

nique

as

described in refer-

ence

[4].

With the driverand

microphone

inside the

lower

end,

the violin

was

suspend-

ed

horizontally

on

rubber

bands.

Using

a

sine

swept

input

to

the

driver and

recording

the accelerometer

output

vs.

frequency

for

two

interior

gases:

(air,

molecular

weight

29

and

Freon

22

molecular

86.5)

produced

the

Figure

2 ■

Violin

#295. First

bending

o

neck,

rigid body

pitching

of

corpus and

bending

of

body

(K.D. Marshall

with

permission).

Violin # 295

n

P itch Ax

(node)

charts shown

in

Figures

8

A

and

Notice

that

theA

0

ode

dropped

infr

quency

from 282

Hz

withair

to

197

H

with the

Freon

22;

while

the

B0

mode

306 Hz went

only

to

304

Hz.

(Data

n

shown,

see

reference

[4]). These fr

quency changes

clearly

indicate

that

t

A0

ode

is

primarily

a

mode

of

the in

rior

air

and

the

B0 mode

that

of

t

wooden

instrument

body.

Displacing

the

interior

air

w

Freon 22

should

drop

the

velocity

sound

by

a

factor

of 0.58 and hence t

A0ode should

drop

from

about 2

Hz to about

160

Hz. To check the actu

frequency

displacement,

the

tiny

lou

speaker

and

microphone

described

abo

were

suspended

through

thef-holes in

the lower

end

of

the

body

cavity.

Itw

observed

that theA0mode

was

abo

23%

high

due

primarily

to

gas

inte

change

through

the

open

f-holes

[4].

As

mentioned

earlier,

the music

effects of

this AO-B0

mode

couplin

have

interesting

implications.

Six

Hutchins violins

were

made

on

the

sam

Stradivarius

pattern,

of

the

same

lot

50

year

old

spruce

and

maple,

with

t

free

plates

tuned

to

havemode

#2 in

to

and back around 180

to

185

Hz

a

8/17/2019 2001 N.3 VOL.4 CASJ


8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3

(Series

II),

May

2001

Hutchins

-

Effects of an

Air-Body

Coupling

on

the

Tone and

Playing

Qualities

of

Violins

Figure

6A

■

Violin

#299

showing

motion

of

end

of

fingerboard

without

clayweight.

Figure

7

A

■

Response

curve

of violin

#299

without

clay

on

fingerboard.

Notice increase

of

amplitude

up to 7

kHz

and decrease

above

10

kHz whenAO

and

BO modes

couple

as

inFig. 7

Figure

6B

■Violin

#299

showing

motion

ofendof

fingerboardwith

clayweight.

Figure

7B

■

Response

curve

of

violin

#299

with

clay

weight

on

end of fingerboard.

words,

it

is

practically

impossible

to

pre-

the end

of the

fingerboard.

To

lower the have

already

preferred

it

in

this

cond

diet

during

construction

what

the rela-

B0

mode

in

frequency,

mass can be tion

evenover#297.

tion

of

these

two modes

will

be

in

the added

to

the

scroll orto

the undersideof

It

should

be

emphasized

that a

fin

finished

instrument. Once

the

instru-

the

fingerboard

end

or

the

neck

thinned. instrument need not

necessarily

ha

ment is

finished,

then

some

adjustments

In the

experiment

referred to above

an

this condition of

mode

matching,

f

c an be

made such

as

changing

from

appropriate

massofoil

clay

was

fastened

there

are

many

fine

violins and viola

ebony pegs

andchinrest

to

lighter

rose-

to

the

underside

of

the

fingerboard

end

being

played

today

which do

not

have

wood ones to raise

the

BO

mode fre-

ofviolin

#299

so as to

match the

AO

and

The

concept

is

offered

here as

an

ext

quency,

or

removing

woodfrom under

B0 mode

frequencies.

Several

players

dimension

in

the

response

and

FEEL

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No. 3

[Series

II),

May

2001

51

Hutchins

-

Effects

of

an

Air-Body

Coupling on the Tone and

Playing

Qualities

ofViolins

Figure

8A ■

Cavity

resonances of

violin

#299with

AIR.

(Molecular

weight

29)

Courtesy

G.

Bissinger.

violin

|

299

8B■

Cavity

resonances

of violin#299with

(Molecular

weight

86.5)

Courtesy

G.Bissinger.

an instrument

which

seems

to be

impo

tant to certain

players.

Further

docu

mentation

is

a

challenge

to

the

psychoa

cousticians,

for

it

is a

measurab

parameter

that

may

be

of

importance

the

great

instruments.

Also,

it

is

hope

that both

makers

and

players

wi

explore

the

frequency matching

of th

AO

modeand the

BO

mode

bybecomin

expert

at the

tapping

and

listening

te

described

above

and

let us

have

som

feedback

ontheir

findings.

■

CAS

REFERENCES

1.

Saunders,

F.A.,

"Mechanical

Actio

of

Instruments

of

the

Violin Fam

ly,"

/.

Acoust.

Soc. Amer.

Vol.

1

No.

3, 169-186,

J anuary

1946.

2.

Marshall,

K.D.,

"Modal

Analysis

of

Violin,"/.

Acoust. Soc. Amer.

77(2

695-709,

February

1985.

3.

Roberts, Gareth,

Personal

Commu

nication.

4.

Bissinger,

G. and

C.M.

Hutchins

"Air-Plate-Neck

Fingerboard

Cou

pling

and the 'Feel

of a Good

Vio

lin,'"/.

Catgut

Acoust.

Soc. No.

44

November,

1985.

5.

Hutchins,

C.M.,

"The

Acoustics

o

Violin

Plates,"

Scientific

American

October,

1981.

Hutchins,

C.M.

"Plate

Tuning

for

th

Violin

Maker,"

Catgut

Acoust. Soc

NL

#39, 25-32,

May,

1983.

■

CAS

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3

(Series

II),

May

2001

AIR-PLATE

-»

N E C K

FI N GE RB OARD C O U P L I N G

AND

THE

"FEEL"

OF

A GOOD

V I O L I N

by

G.

Bissinger

and

C.M. Hutchins

(as

published

in

CAS

Newsletter #44, November

1985)

One

aspect

of

the elusive "feel" of a

fine violin thatseems to

be

impor-

tant

to

many

players

is the

feeling

of

vibration transmitted

to the hand of

the

instrumentalist

through

the

neck finger-

board.

The

possibility

that

air-body/

plate

coupling might

contribute

signifi-

cantly

to

the "feel"

of

a

good

violin has

been the

object

of

investigation by

one

ofus

(CMH)

for

over

15

years

[I],

As

an

offshoot

of

our

previous

investigations

into

the

coupling

between

enclosed

air

oscillations

and

plate

vibrations

[2],

we

have

applied

the same

techniques

to

scrutinize

neck

fingerboard

motion

instigated

by

internal

gas

oscillations.

For identification

of

the neck

finger-

board

modes,

we have used the

modal

results

presented

in

a

recent

article

by

Ken

Marshall,

who

described

the dual

FFT-derived

modes of

vibration for the

violin

SUS #295

[3].

In

these

measure-

ments,

a

neck

fingerboardbending

mode

vas

observed

near

300

Hz,

which is not

far

from

the

typical

Helmholtz airmode

(A0)

frequency

of

270-280 Hz.

If

the

body/plate

oscillations

set

up by

the

internal

gas

oscillations

are

effective

in

driving

neck

fingerboard

motion,

it

could

be of

significance

to

the instru-

ment

maker.

Since

theA

0ndAl modes

are

already

known to drive

plate

motion

quite

strongly [2],

it would

be interest-

ing

to know

whether these internal air

oscillations

are

also

capable

of

indirectly

inducing

significant

neck

fingerboard

vibrations.

Utilizing

the

very

same

technique

of

interior

gas exchange

described in

Ref.

[2]

to

drop

the

interior

gas

mode

frequencies,

and

placing

an

accelerome-

ter

in

the

center

of

the

bridge

end

of

the

fingerboard,

we

have

monitored

neck

fingerboard

vibrations

in

violin

SUS

#299

induced

by

gas

oscillations

set

up

by

an

acoustic

driver

placed

off

center

in

the

lower

bout.

Using

a

swept

sine wave

input

to

the

acoustic

driver and

record-

ing

the accelerometer

output

vs.

fre-

quency

for

the interior

gases

of

air

(molecular weight

-

29) and

Freon-22

(MW

-

86.5)

produced

the

response

charts

shown in

Figure

1

.

Displacing

the

interior

air

with

Freon-22

should

drop

the

velocity

ofsound

by

afactor of0.58

andhence the

A0

ode

will

drop

down

from

280 Hz

or

so to

-160

Hz,

whereas

the Al

mode

frequency

should

drop

from -480

Hz

to -280 Hz. To

check the

frequency

displacement

of

the

interior

gas

modes,

a

small

microphone

was

sus-

pended

in

the

opposite

side

ofthe lower

bout from the

driver,

and

it

was

observed

that

the

displacement

for

both

the

A

0

nd

Al

modes

was

not

as

great

as

predicted

due

primarily

to

gas

inter-

change through

the

open

f-holes

[2].

This

effect is

particularly

noticeable for

theA0ode

where

the

Freon-22

result

was

about 23%

high,

whereas the Al

mode

frequency

was about 12%

high.

(These

results indicate

that

the

Freon-22

flow

rate

might

not

have been

high

enough.)

Comparing

the

resonance

plots

air and

Freon-22 in

Figure

1,

we obse

peaks

in

the neck

fingerboard

respon

at

frequencies

corresponding

to

the

and

Al

modes (the

arrows

in

the

figu

point

to

themeasured

AO

and

Al

mo

frequencies).

The

peak

at

-175

Hz

in

neck

fingerboard response

for bo

gases

is almost

certainly

the

"rig

body"pitching

mode

[3].

For the

Freo

-22

plot,

the

peak

at

-200

Hz

is

a

stro

neck

fingerboard response

activated

the AO mode internal

oscillations;

t

peek

at

-300 Hz

is

the

Ist

neck

fing

board

bending

mode

which

happens

coincide

with

theAl mode

frequency.

heightened response

at

-300

Hz

observed in

this

case,

indicating

an A

contribution

to

the

amplitude

of t

mode.

It is

also

interesting

to

note th

the

interior

gas

resonance

plot

w

Freon-22

(not

shown) also shows

ad

tional

structure

in the

region

of the

A

peak,

indicating

possible

neck

finge

board-air

mode

coupling

(via

bod

plate

motion).

The

results

obtained

in

this

expe

ment

present

strong

evidence

enclosed

air

-

neck

fingerboardcoupli

for

both

gases.

The

fact

that the

A

mode lies

quite

close in

frequency

to t

Ist neck

fingerboard bending

mode

air

suggests

that

significant

changes

thefeel

of

aninstrument

can

be achiev

by adjusting

the

frequencies

of

the

ne

fingerboard

vibrational

modes.

Since t

feel

and sound

of

aninstrument

are

n

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No. 3 (Series

II),

May

2001

53

Bissinger

and Hutchins

-

Air-Plate

->

Neck

Fingerboard

Coupling and the Feel of

a

Good Violin

FIGURE 1 ■

Output

of

accelerometer

(mounted

at

center

of

bridge

end

of

fingerboard) versus

frequency

of acoustic driver (placed

off-center

inside

lower

bout)

for airandFreon-22

internal

gas

in

violin SUS #299.

The

AO and

Al air

mode

frequencies

shown for

each

internal

gas

come

from

microphone

measurements of

thegas

oscillations

inside.

50

100 200

500 1000

FREQUENCY

(Hz)

necessarily

correlated,

an

interestin

extensionofthis

experiment

would

be

t

choose

good-feeling,

poor-sounding

an

good-sounding,

poor-feeling

violins an

subject

them to

the same

sort

of

meas

urements

to

determine

the

relative

place

mentof

these

resonances. ■CAS

REFERENCES

1.

C M.

Hutchins,

this issue

J ourna

Catgut

Acoustical

Society,

CASNL

40,

12

(1985).

2. G.

Bissinger

and

C.M.

Hutchins

C A S N L

39,

7

(1983);

ibid.,

40,

1

(1983); Proc.

Stockholm Mus. Ac

Conf.

(1983), Vol.

11,

(editors

A

Askenfelt,

S.

Felicetti,

E.

J ansson

and

J .

Sundberg),

p.

145.

3.

K.D.

Marshall,/

Acoust.

Soc.

Am.

77

695 (1985).

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No.

3

(Series II),

May

200

4

A l

C AVI TY- M OD E - E N H AN C E D FUNDAMENTAL

IN

BOWED

V I O L I N

AN D

V I O L A

SO UND

by

G.

Bissinger

and

C.M.

Hutchins

(as

published

in

CAS

J ournal

Vol. 1,

No.

2, November

1988)

Fourier

analyses

were

performed

of

bowed

instrument

sounds

produced

by

two

violins,

a mezzo-

violin

and a

viola both when

the

internal

cavity

was

filled

with

air

andwith CC l

2

F

2

which reduces the

cavity

mode

frequencies.

The

results

generally

demonstrated

significant

strengthening

of

the

fundamental

of

a

bowed

note,

when it

coincided

with

the

pertinent

Al

cavity

mode

frequency

for

both

gases,

irrespec-

tive

of

the

presence

or

absence

of

strong

corpus

resonances.

Introduction

tively

obscured

any

possible

Al

contri- This

recording

setup,

in a

room

w

Recently,

we

reported

on

a

series

of

bution

M-

man

y irregular

pieces

of furniture

experiments

involving

gas

exchange

in

To

clarify

whatcontribution the

A

1

numerous

objects

hung

on

the

wa

the

cavity

of

the

corpus

of violins

cavity

mode

makes

to

the

overall

was

intended to

integrate

the

acou

mezzo

violins

and

violas.

A

significant

acoustic

output

ofthe

violin,

we

present

outputof

the instrument overall dir

aspect

ofthese

experiments

involved

the

theresults of

a

Fourier

analysis

of fixed

tions

and

simultaneously

reduce

measurements of

plate

vibrations

in-

tones

of

two bowed

violins,

a

mezzo

vio-

destructive

interference effects assoc

duced

in assembled instruments

by

an

n anc

l

a v

i°l

a

>

w

ith thefundamentalfre-

ed

with

standing

waves

[A.

Benade,

p

acoustic

driver

placed

inside the

instru-

quency

fj

ofthebowed

tone

coinciding/

sonal

communication].

The

violin,

tu

ment

cavity

in the

lower

bout

region

of

above/below

the

frequency of

the

Al

to

A

=

440

Hz,

was

played

strongly

the

violin

or

viola

[1,2,3].

The

plate

mode

f(Al),

while

interchanging

airand

manner

similar

to

that

used in

a

Sa

vibrations were

monitored

as the

driver

CC1

2

F

2

in

the

instrument

cavity

to

move

ders loudness curve

measurement,

v

was

excited

by

a

swept

sine

wave

signal,

the

resonant

frequency by

a

factor

of

at

or

near its maximum

sound

inten

with an accelerometermounted on

the

approximatelytwo,

i.e.,

an

octave.

Fouri-

levels,

in order

to minimize

any

par

upper

bout,

bridge

or

lower bout

er

analysis

of

these

sounds

was

then

used

strength

variations

due

just

to

change

regions

of

the

top

plate.

Strong

plate

to estimate the

quantitative

change

in

dynamic

level.

motions were observed to

track the

strength

of

the

fundamental

as the

The

recorded

sound

of

the

fo

internal

cavity

AO and Al

oscillations

as

bowed-tone

fundamental

frequency

was

instruments

(SUS#

violins

#269, #2

the

internal

air

was

displaced

with heav-

shifted

to

either

side

of

f(Al). This

analy-

mezzo-violin

-

#107;

viola

-

#231) w

ier-than-air

gases

which

lowered the

res-

sis

also

§

ives

a measure of the

impor-

t

h

en

Fourier-analyzed

with

a

Rapid

S

onance

frequencies

of

these

modes.

By

tanceof the

A

1

cavity

mode

to the

over-

terns-Apple

11-based

FFT

syst

using

"slide tones"

(extended

portamen-

all

acoustic

output

of

the

instruments.

Analysis employed

512

lines

(1

to)

to cover

a

continuous band

of

fre-

points),

Hanning-weighting

with

a

quencies

in

conjunction

with air or

C 0

2

Experimental

Measurements

kHz

sampling

rate

over

a

0-5

kHz f

inside

the

cavity,

the

effects

of

theA

0 The

violin

sound was

measured

with

a

quency range.

Samples

of

these

plots

cavity

mode

shifts

were

easily

seen

in

the

pressure

zone

microphone

(Radio

shown

in

Figure

1(a)for

air and

Fig

Fourier-

analyzed

spectra.

Unfortunate- Shack)

placed

about

8'

away, midway

up

1(b)

for

CC1

2

F

2

exchange

in the

cavity

ly,

those

cavity

mode

shifts

for

the

Al

against

the

wall

in the corner

of the

SUS

#269. This

Figure

clearly

shows

mode

coincided

with

another

corpus

Hutchins

living

room,

and

recorded

on

(quite

audible)

effects of the

gas

int

resonance

peak

already

present

in

the

MA

(metal)

tape

with

an

Aiwa

3500

cas-

change

onthe

spectrum

of

partials

—

acoustic

output.

This coincidence

effec-

sette

tape

recorder

for

later

analysis.

most

significant changes

under

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No. 3 (Series II),

May

2001 55

Bissinger

and Hutchins

-

Al

Cavity-Mode-Enhanced Fundamental

in

Bowed

Violin

and Viola

Sound

Figure

1

■

Fourier

analysis

of thebowedopen

G

for

violin

#269with: (a) air

inside,

and (b)

CCl

2

F

2

inside.The numbers over

the

peaks

denotethe

partial.

Note

that thefundamental

(fl

=

196

Hz)

is

much

stronger

for

CC1

2

F

2

inside

because f(Al) has

dropped

to

-230

Hz.

The

arrows

in

(a)

and

(b)

denote the

expected

frequencies

of theAO

and

Al

cavity-mode

resonances

(however(b) suffers from

some

air

mixing

whichwill

raise

these

calculated

frequencies).

FREQUENCY

(kHZ)

exchange

are

the

17dB

strengthening

of

were

bowed

for -20 seconds.

Recorded

the

fundamental in

the

CC1

2

F

2

spectrum

passages

were

later

extended

to two

as

well

as a

substantial

reduction

(10-23

semi-tones

above

and

below the

note

dB)

in

partial

strength

in

the

region

2.5 1

whose fundamental

frequency

f

x

most

The

fundamental is

augmented closely

coincided with

the

cavity

mode

more

strongly

than

any

other

partial

in resonance

frequency

because

of the

gas

igure

1

(b);

in

fact

only

two

other

par-

interchange

problem

(particularly

severe

(5, 12)

are

stronger

in the

CCl

2

F

2

for the

A0

mode). Sixty-four

of

these

than the air

spectrum.

recorded

notes

were

chosen

for

analysis,

The

CC1

2

F

2

should

drop

all the

although

a

considerably larger

selection

y

mode

frequencies

by

a

factor

of

0.492,

was

recorded.

cavity

mode

frequencies

are

of wall

compliance)

hence

Results

he

A0ode

that

normally

occurs

at The

partial

strengths

for

each of the

Hz

should

drop

to -140

Hz

and

recorded notes

can beextracted

from

the

he

Al mode should be

dropped

from

Fourier

analysis

plots

such

as

shown in

Hz to -230 Hz. This of

course

Figure

1,

although

here we

have chosen

no

air-gas exchange through

the toconcentrate

our

attention on

the

fun-

f-holes,

in

agreement

with

what

we

observed

(factor

of

0.51)

for

the

Al

cavity

mode

which

has

a

nodal

region

around the

f-holes,

but

defi-

nitely

not

the

case

for

the

AO

cavity

mode

which

has

antinodal

regions

at

the f-

holes.

To have

the funda-

mental

overlap

these

low-

ered

cavity

resonance

frequencies,

the

violin

and

viola

strings

were all

tuned

down

a

fifth for

the CC1

2

F

2

measurements.

This

tuning

allowed

us tocover

frequen-

cies

ranging

from

130

Hz on

up

for

the

violins

and

from

87 Hz

on

up

for

the viola.

This

was sufficient

to

cover

the

CC l

2

F

2

-lowered

AO cav-

ity

mode

frequency

for all

the

instruments.

Due to

the

significant

gas

interchange

through

the

f-holes

during

actual

playing

it

was

necessary

to

bow

the

instrument

at the

playing

level

for

a few seconds

prior

to

recording

to allow

the

average

gas

level

to

stabilize.

Notes

at, immediately

above

and

immediately

below the

expected

cavity

mode fre-

quencies,

f(A0)

and

f(Al),

damental

only.

In

Figure

2(a,b,c)

w

show

the

plots

of

Fourier-analyzed

spectra

of

SUS

#298

for

air,

and

in

Figure

2

(d,e,f)

for

CC1

2

F

2

,

when

the bowe

tone fundamental coincides/lies

above

falls

below f(Al).

Figure

2

clearly

show

that the

strength

of the fundamenta

peaks

when

its

frequency

coincides

with

the

Al

cavity

resonance

frequency

fo

both air

and CCI2F2.

Moreover the

strength

of

the

fl

component

on

this

semi

log

plot

is

clearly

a

major

contribu-

tor

to the

overall

strength

ofthese

notes

particularly

when

fl

coincides

with

f(Al).

Analyzing

equivalent

plots

from

the

other

instruments and

presenting

the

rel-

ative

intensity

changes

of

the

fundamen-

tal

in

Figure

3(a)

for

air

and

3(b)

for

CCI2F2,

we see

that the

results

of

ou

analysis

of the

partial

structure

of

the

two

violins,

mezzo-violin

and

viola for

the

Al

mode

are

quite

similar

-

where the

fundamental

of the bowed instrumen

coincides

with the

frequency

of the

Al

cavity

mode

it

is

enhanced

in

strength

[s].

It

is

noteworthy

that there

are no

other

strong

contributors to

the

acoustic

output

of

the

violin

in

the

Al

frequency

region

around 230

Hz

for

CCI2F2

exchange, i.e.,

no

plate

or

corpus

reso-

nances

with

strong

associated acoustic

output

[4],

and that the

fundamental ofa

G

(196

Hz)

or

A (220

Hz)

on

the

violin

G

string

is

relatively

weak

in

violins

as a

class

when

air is inside the

cavity.

Behavior similar to

that

notedabove

was

also

observed

for the AO

cavity

mode in the

case

of the

air-filled

instru-

ment.

However,

the

measured

funda-

mental

intensity

of the instrument

for

the

CCI2F2

interchange

wasreduced

by

-20

dB or

more

for all

the instruments

relative

to

that

for

air

and

some

hum

background

intruded. This

effect was

probably

due

in

part

at least to the low-

ered

tension in the

strings

which

then

coupled

less

effectively

to

the instru-

ment at

these

very

low

frequencies.

Summary

By

moving

the

Al

cavity

mode reso-

nance

frequency

with

gas

interchange

it

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No. 3 (Series

II),

May

2001

Bissinger

and Hutchins-

Al

Cavity-Mode-Enhanced Fundamental in Bowed

Violin

and Viola

Sound

Figure

2 ■Fourier

analysis

of notes

played

onviolin

#298

with thefundamental

lying

in

the

region

of the

Al cavity

mode

with

a ir o r

CCl

2

F

2

inside:

FREQUENCY

(kHZ)

Figure

3 ■

Variations

in

strength

offundamental for

bowednot

played

with

fj

ranging

from

below to

above

f(Al):

(a)

with air

inside,

(b)

with CC1

2

F

2

inside

[#269(»),

#298(A),

#107(H),#231(T)].

The

line

joining

the

points

is

meant to

guide

eye

only.

Note thatall

frequencies

have

been normalized to the

frequency

of

maximum

response

which

coincides closely

with

f(

for violins

#107

(mezzo)

and viola

#231.

The

mezzo

violin

points

havebeen

omitted for

the

air

case

because there

wa

no obvious maximumat

the

expected

f(Al)

-430

Hz.

f/f(A1)

was

possible

to observe enhancementof

nearby corpus

contributions.

Moreover,

3.

Bissinger,

G. and

Hutchins,

C M

the

fundamental in

the bowed

tone

the

entirety

of

ourwork

on

gas

exchange

whenever

a

note

was

played

that

satisfied

on

string

instruments

strongly

suggests

f

=

f(Al).

In

the

case

of

airand

CC l

2

F

2

,

that

the

heretofore labeled "main

wood"

the

typical

enhancement of the

funda-

resonance

[6] largely

depends

on oscilla-

mental

compared

to

notes

just

below

the

tions

ofthe Al

cavity

mode for

its

over-

just

above

f(Al)

was

roughly

10 dB for

all

strength.

■CASJ

air and 20 dB

for CC1

2

F

2

.

This

magni-

"Tracking

'enclosed

air-plate'

co

pling

with interior

gas

exchang

Stockholm

Music

Acoustics

Co

ference

(SMAC

'83),

Royal

Swed

Academy

of

Music

No.

46:2, 1

(1985).

4.

Marshall,K.D.,

"Modal

analysis

o

.

-ill

n_B___

,

_Bn_B___..__Mß__>

oijiciii,

___✓

ciiicti

y

aia

tudeor

change

was

perceptibleto

the

ear

REFERENCES

.

„

T

.

b

.

r r

,

.

violin,

/.

Acoust.

Soc.

Am.,

77

and

in

some

instances

meant

that the

l.

Bissinger,

G.

and

Hutchins,

C M . ,

695

—

£

1985)

enhanced fundamental

was

the

major

"Evidence

for the

coupling

between

c

„,

'

...

contributor

to

the overall sound

intensi-

plate

and enclosed

air

vibrations in

5

*

The

u

me2ZO

vlohn

dlffe^

d t

ty

level.

Our conclusion then is

that

the

violins,"

CatgutAcoust.

Soc.

#39,

7,

°

ther

instruments

in

that

«

dld

n

Al

cavity

mode,

whether

aided

by,

or

(1983).

show

anobvious

peak

in

fundame

aiding,

the

plate/corpus

acoustic

output

2.

Bissinger,

G. and

Hutchins, C M . ,

tal

strength

at

the

expected

430

H

is

capable

of

producing

a

very

signifi-

"Further

evidence

for

coupling

be-

frequency

for the

Al

cavity

mode

cant,

even

dominant,

contributionto the tween

plate

and

enclosed

air

vibra-

6.

Hutchins, C M . ,

The

Physics

overallsound of the

instrument

for

cer- tions in

string

instruments,"

Catgut

Violins,"

Scientific

Amer.

207, 7

tain

fingered notes,

independent

ofa ny Acoust. Soc.

#40, 18,

(1983). (1962).

Air

-

(a)

fj

=

f(Al), (b)

f, <

f(Al),

(c)

f, >

f(Al);

CC1

2

F

2

-

(d)

f

a

=

f(Al), (c)

f,

<

f(Al), (f)

f,

>

f(Al),

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3

(Series

II),

May

2001

57

SOME

OF

THE

EFFECTS OF

ADJ USTING

THE

AO

AND

THE

BO

MODES OF

A

V I O L I N

TO

THE

SAME

FREQUENCY

by

Carleen

M.

Hutchins

(as

published

in

CAS

J ournal

Vol. 1,No.

5,

May

1990)

number of

violin

makers

have

reported

that

they

are

getting

results

from

matching

the

AO

d

BO resonance

mode

frequencies

in

violas

and

cellos.

Comments

are

when

the

modes are

matched,

the

is

more

"friendly,"

easier to

rings

all

over,

and has increased

of

tone

throughout

its

range.

A

for

matching

mode

frequencies

reported

in CAS

J ournal

#47

(Spear,

Some

researchers

are

particularly

that

matching

the

frequencies

two

of

the

lowest

modes

in

an

instru-

c an

have

such overall effects. Al-

there

is

as

yet

no

exact

documen-

of the

mechanisms

causing

such

there

are

good

indications

that

two

strong

resonances areclose

in

there

is increased mass

load-

g

as well as increased

damping

of

the

Such

effects

could

very

well

to

the

changes

described.

Methods

three

charts

—

A,

B,C

—

in

Figure

1

the

changes

caused in the reso-

spectrum

from

100

Hz

to

10

kHz

three

different

tests.

(Dotted

lines

tuning;

solid lines after).

Chart

A

(wood-wood)

shows the

of

the

free

end of

the

finger-

vertical

to the

top

of the instru-

It is

made

by waxing

an ac-

unit

to

the

top

of

fingerboard

end. A

small

coil

activat-

ed

by

a

sine wave

from

an

audiogenera-

tor,

sweeping

from

100

Hz to 10

kHz,

is

positioned

over,

but

not

touching

the

magnet,

which

is

waxed

to

the

top

ofthe

accelerometer.

The

resulting

I N P U T

ADMITTANCE

test

is

recorded on

a

strip

chart.

Chart B shows anair-air

test

made

witha

tiny

magnet

and

tiny

microphone

inserted

through

the

f-holes and sus-

pended

inside

the lower

end

of

the

violin

cavity,

but

not

touching

the wood or

each other. The

speaker

and

microphone

are

activated as

above.

Chart

C

is

an

I N P U T

ADMIT-

TANCE testmade

in

the

same

way

as

in

Chart

A,

but with the

accelerometer-

magnet

unitwaxed to

the

top

of

the

vio-

lin over

the

bassbar 5 mm tailwards

of

the G-foot

of

the

bridge.

The

tests in

Chart

A,

made

with

the

drive unit

on

the

end

of

the

fingerboard,

show the

B0

mode

loweredin

frequency

from 292

Hz to

275

Hz to

nearly

match

theA0odeat

272

Hz. This

change

was

accomplished

by chiseling

1.7

grams

of

woodfrom

under

the

fingerboard

where

it

joins

the

neck.This

removal

of

wood

reduced

the stiffness of

the

fingerboard

between

the

free

end and the neck

joint,

thereby

reducing

the

frequency.

A

simi-

lar

reduction in

frequency

could

be

achieved

by

thinning

the

fingerboard

and/or

theneckwhere

they

are

bending

between the nut

and

the

upper

edge

of

the

violin,

Figure

2.

The

amplitude

decrease in

the

B0

peak

is due

mainly

to

the

interaction of the

two resonance

modes,

AO and 80. Note

especially

in

Figure

1,

ChartA,

with

thedrive

unit

on

the

end of the

fingerboard

that above 6

kHz

the free

end of

the

fingerboard

is

acting

like

a

clamped-free

beam.

Thus

all

these

higher

resonance

frequencies

moved down

a

fair amount.

In Chart

B,

with

the

air-air

test

inside the

violin

cavity,

notice that

very

few

of

the

resonance

peaks

changed

fre-

quency,

although

someof the

details

of

the

curve

did

change.

In

Chart

C,

the

I N P U T

ADMIT-

T A N C E

test,

with the

drive

unit

over

the bassbar

near

the

G-foot of the

bridge,

there

are

some

changes

in

fre-

quencies.

But

mainly

the

changes

are in

increased

amplitudes,

particularly

for

the

peaks

in

the 700-1100 Hz

range,

and

decreased

amplitudes

in

the 3

kHz to 6

kHz

range.

Conclusion

It is

becoming

clear

that there are

extremely

important

relationships

be-

tween

thebody

resonances and

the

cavi-

ty

resonances

affecting

tone

and

playing

qualities

in theviolin. A recent

report

of

a

long-term

study

based

on

the

so-called

"Swiss

cheese

violin,

Le Gruyere

(Hutchins,

1990)

gives

some

interesting

details

oftheeffectsof

various

changes

in

these

relationships.

Seealso the

following

references:

(Bissinger

et.

al.,

1983),

(Hutchins,

1985,

1989), (J ansson,

1973),

(Shaw,

1

990),

(Spear,

1987).

■

CASJ

CASJ

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No. 3 (Series II),

May

2001

Hutchins

-

Some

of

the

Effects

of

Adjusting

the

AO

and

the

BO

modes of

a

Violin to the

Same

Frequenecy

FREQUENCY

REFERENCES

Bissinger,

G.

and

Hutchins,

CM.,

Paying qualities."/.

Acoust. S

(1983), Evidence

for the

cou-

Am.

87,

No.

1,

392-397.

igure

2 ■

First

Bending

ofNeck

and

Body.

pling

between

plate

and

enclosed

J ansson,

E.V.

(1973), On

higher

air

vibrations

in

violins,"

Catgut

modes

in the violin. Cat

Acoust. Soc. NL

#39,

7-11.

Acmst

Soc NL

#1%

13

.

15

Hutchins,

CM. (1985), "Effects of

shaw>

£AQ

(1990)>

«

c

re

an

air-body coupling

onthe tone

,

.

,

T

i

,

.

.

°

.

„ nances in

the

violin:

Netw

and

playing

qualities

of

violins,

/.

CatgutAcoust. Soc.

#44,

12-15.

representation

and

the effect

Hutchins,

CM .

(1989),

A

measura-

damped

and

undamped

ble

controlling

factor in the

tone

holes,"

/.

Acoust. Soc. Am.

and

playing

qualities

of

violins,"

No.

1,

398-410.

BO MODE

/.

CatgutAcoust.

Soc. Vol.

1,

No.

Spear,

D.2.

(1987),

"Achieving

4 (Series

II),

10-15,

Nov.

air/body

coupling

in

violins,

v

Hutchins,

CM.

(1990),

A

study

of

las and

cellos.

A

practical

gu

the

cavity

resonances of a

violin

f

or t

he

violin

mak

er

,"

J .

Cat

and

their effects on its tone and

Acomt

Soc

#47j

4

_

7j

May

Courtesy

of

Kenneth

Marshall

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No. 3 (Series

II),

May

2001

59

A C O USTI C A L

EFFECTS

OF

"DRESSING

DOWN

A

F I NGE RB O A RD

AND/OR

THINNING

THE

V I O L I N N E C K

by

Carleen

M.

Hutchins

(as

published

in

CAS

J ournal

Vol.

1,

No.

5,

May 1990)

e

to demands for

greater

facility

ning

will

reduce

the

BO

mode

frequency

than thatoftheAO tostart

with:

namely,

in

performance,

many

players

are

and

spoil

the

desirable

effects

of

the

that

the

neck-fingerboard

thinning

will

for

thinnernecks,

particularly

on

mode

matching

(Spear,

1987).

bring

the

tWQ

modes

to^

r^

thereby

Also,

the traditional

"dressing

T]

"

reduction

in

frequency

can

he

enhand

tQne

y

A§

w{±

a

fWprhnsrrl wl_pn tlnp

sm'nac

offset either

by

removing

some

wood

„

.

,

own

ofa

fingerboard

when

the

strings

>

6

all

adjU

stments

m

violins,

what

one

worn

ridges

from

long-term play-

3

unuer me

rree

ena or tne

nnger

,

f-

,

r l /

board

or

by

cutting

a thin

slice

off the

does

depends

on

what

one has

to start

results

in thinningthe fingerboard. ,

..

,

i

T

,

m i

1

, , ,

free

end,

thereby

raising

the

BO

mode

with.

BCASJ

It

should

be realized

that

this

thin-

r

~

.

,

.

. .

,

. .

,

frequency. Changing

to

lighter

fittings

lowers

the stiffness ofthe neck

and i

v

i

v i

i en

.

&

.

and

chm

rest

can

also

help

raise

the

BO

REFERENCES

with the

result that

the

mode f

somewhat,

(for exam-

c

7

,

1Q

_

frequency

of the

BO mode

(see

ples

by replacing ebony

pegs?

tailpiece

Spear,

D.Z.

(1987),

Achieving

an

2in

previous

note) is

reduced

and

chin rest

with

lighter

rosewood

or

air/bodycoupling

in

violins,

violas

Thus if

the

BO mode

fre-

boxwood

ones).

and

cellos.

A

practical

guide

for

the

violinmaker,"/.

Catgut

Acoust.

Soc.

#47, 4-7,

May.

has

been

"tuned"

to

that

of

the

Another

possibility

exists

if

the

BO

mode,

this

neck-finger-board

thin- mode

frequency

is

somewhat

higher

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No. 3 (Series

ll],

May

200

T UNI NG

THE

BO

MODE

IN

F O U R

NEW

V I O L I N S

by Carolyn

Wilson Field

(as

published

in

CAS

J ournal

Vol.

2, No. 7,

May 1995)

In

November

1993,

there

appeared

in

the CAS

J ournal

a

most

remarkable

article

by

Carleen

Hutchins

[1]

in

which

she

recalls results of her work with

Frederick

Saunders

40

years

ago,

inte-

grates

these with results of her

own

work

over

many

succeeding

years,

and

produces

a

rational

and

practical

guide

to

the

origin

and

identification of

sever-

al

modes

of

vibration in the

finishedvio-

lin

and

to

the

possibilities

of

matching

one mode to another.

At

the

time I

read the

Hutchins'

arti-

cle,

I

happened

to

have in

my

shop

a

group

of

four

essentially

identical

new

violins allmade

by

me,

No.

15

from

1992

and

Nos.

21,

22 and

23

from 1993.

Using

them

to

experiment

on,

I

deter-mined

to

match

body

and

air

modes

as

well

as

pos-

sible and

to test

the

assumption

that

quality

is

improved

by

thesematches.

I

hadknown since the

appearance

of Bob and Deena

Spear's

research

[2]

about

the

desirability

of

matching

the

neck-fingerboard

vibration

(BO

mode)

to

what

they

and

I

suppose

most other

builders

thought

was

the

first mode

of

vibration

of the

inner

air,

the AO

or

Helmholtz mode.

However,

far

from

the

equipment

in

Carleen's

laboratory,

I

had

great

difficulty finding

thesereso-

nances.

Pitches

produced

by

tapping,

blowing

and

humming

were

remarkably

hard to

pin

down. The first

help

came

from Ake

Ekwall

[3]

who offers

a reli-

able

technique

for

identifying

the

BO

mode

using

an

audio

oscillator

which I

and

many

other

makers

keep

in our

shops

for

tuning

plates.

Although

Ekwall also

suggests

a

way

in

which

the

AO mode

c an

be

identified,

this

proce-

dure

does not

work

for

me.

Thus,

I

could

only guess

at

the

frequency

of

AO

until the

appearance

ofCarleen's

article

above

in which

she

explains

that

there

are

not

one

but

two

modes

in the "main

air

region.

One is the AO mode which

can

beactivated

by blowing

across

an

F-

hole

as

across

a

flute or

bottle.

The other

is

the "wood

prime"

(W) mode. It is

a

subharmonic

of

the

Saunders

"main

wood"

mode,

a

combination

of

air

and

wood

resonances.

The

pitch

of

this

W

mode can

be

fairly easily

identified

by

humming

into an

F-hole,

thus

activating

both the air

and

the wood

At

the

right

pitch,

the

instrument will

buzz under

the earand vibrate in thefingers.

When I

knew

what

to

look

for,

I

was

able to

identify

both

W

andAOwithin

a

few

hertz. Not

surprisingly,

all

four

vio-

lins

werethe same

with

AO at

about275

and

W' at

about 260

Hz.

The

challenge

was

to

match the BO

modes

to

one

ofthe

above.

In

these

instruments,

which were

all

complete

including

varnish

when I

began

the

experiment,

the

BO modes var-

ied

between

240

and 283

Hz. I had

made

some

attempts

at

fingerboard

tuning

before

completion

but had notfollowed

through.

Therefore,

only

one

violin,

No.

23,

was

well

matched

from

the

begin-

ning,

both

modes W'

and

BO

lying

at

about 257

Hz.

This

violin,

which

by

the

tuning

and

activity

of

its

plates

had not

been

predicted

to

be

the

best

of the

group,

was

noticeably

freer, smoother,

and

more

eventhan its brothers.

No.

21

started

with

a

low

BO

fre-

quency,

about

240 Hz.

The

neck and

scroll had

been carved

from

a

piece

of

European

woodwhich

was

not

quitebig

enough

to

accommodate

a

full stand

neck

thickness

and the

fingerboard

i

was

also

flexible,

though

of nor

dimensions.

I

replaced

the

fingerbo

with

a

thickerone

and,

after

having

i

and on

three

times,

succeeded in

plac

BO

at

261

Hz

where

it

coupled with

The

violin came alive

and

took

its

p

dicted

place

attheheadofthe

group

No.

22

had

been

equipped

wit

scroll

and

neckofhard

American

ma

Its

original

BO

mode

was

quite

hig

283

Hz.

Being

a

little tired

of

fing

boards at the

time,

I

merely

reac

under

with

a

gouge

and

chipped

the

low

back to the heel

of

the

neck,

p

ducing

a

BO

of

275 Hz

which matc

the

AO

mode.

I

hadbeen

toldbefore

operation

that this violin did

not

"rin

No

one

would

say

that

now.

No.

15

was

the

mostdifficult

to

with.

It

had beenaround

for over

a

y

not

played

much,

very

pretty,

and

ev

but not

exactly

assertive.

Its

BO m

fell

at

250 Hz.

I

removed the

fing

board

and first tried the

one

left

o

from

No.

21.

That

being

no

bette

picked

out

a

new

high-frequency

bl

and started

over. This

fingerbo

turned

out

to

be

too

stiff and

the

quency

of

B0 much

too

high.

The

gerboard

had

to

be

thinned

more

tha

usually

do

and

the hollow

extended

the heel of

the

neck

and

widened

deepened

several

times

before

the

mode could

be

brought

down to

Hz.

At

this

point,

I set

up

theviolin

tried

it,

finding

the bass

and

trebl

good

bit

improved.

Later when

the f

gerboard was

trimmed,

smoothed

beveled on the

edges

and the neck

n

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No. 3 (Series II),

May

2001

61

Field

-

Tuning

theBO

Mode

in

Four New

Violins

slightly

and

well

sanded,

the

BO

mode

was

found to

beabout

262

Hz

and

theviolin sounded

even

better.

It is

my

conclusion that

theeffort

to

tune a

fingerboard

to the AO or to

the

W'

mode is wellworthwhile.The differ-

ence

in

these

violins

tuned

anduntuned

very

noticeable

even,

or

especially,

untutored ears. The tuned

finger-

makes the instrument

instantly

open,

friendly,

and

popular.

I

agree

with Carleen's

suggestion

that

the

fingerboard

(BO) to

W'

works

ter than

to AO.

Only

oneviolin in

group

is

tuned

BO to

AO ,

but

I have

with

several other

instru-

including

a

couple

of

cellos.

I can't documentthe

experience

now,

I

have

the

impression

that

I

never

happy

with

my

fingerboard

efforts

until

I

was

able to

identify

e

two

separate

peaks

and

try

to

match

,

the

"hum

tone."

Let me now

make

some

points

may

help

othermakers

avoid

my

problems

with

new instruments.

or

adjustment

of

old

instruments,

see

Spear's

excellent

article

[2].

1)Do all

your

work

before

varnish-

2)

Consider

the

wood

of

your

scroll

d

neck.

If

you

can

remember

to

weigh

before

gluing

it

in,

you may

beahead.

also

that

each

fingerboard

has

its own

personality.

The

fre-

of the

bar mode

of

a

blank

can

be

determined

by

tapping

or

by

on

your

speaker.

The

ones

I

varied

between

460 and 535

Hz.

8) Thin the

fingerboard moderately

do

not extend

the

hollow

or bevel

he

bridge

end.

Put

a

narrow

groove

its centerand

glue

it on

tight

over

l its

surface,

using

very

light

glue.

If

it

not

been

on

long,

it

will

not

be

hard

remove.

4)

Set

up

the

instrument

completely,

a

firmly

fitted

soundpost,

semi-

pegs,

and

final

tailpiece

and

chin-

At

this

stage,

to

avoid wear

on

the

fittings,

I would mount old

strings

an

inexpensivebridge.

5) With

the

instrument

set

up,

damp

strings

(not

against

the

fingerboard)

and

hunt for

the

resonances.

Tap

or

vibrate

for

80.

Hum

into anF-hole for

W'

andblow

across for AO. Do

this

sev-

eral times

over

a

day

or more.

Compare

with

a

similar

instrument.

Incidentally,

although

the

Spears

report

that these

resonances can

be

determined

without

strings

and

tailpiece,

oneof

my

violins

would

not vibrate

easily

at BO

until

it

was

under

tension.

6)

If

BO

is lower

than

W,

remove

the

fingerboard

and start over

with

a

stiffer

blank.

It is

possible

to

raise

BO

by

trimming

the

free end of the

fingerboard

but on these

violins

I could not

bring

myself

to cut off

enough

to

make

any

difference in

frequency.

With a

viola or

cello where

dimensions are not

so

rigid,

I

might

do

it.

7)

If

BO

is

higher

than

W',

remove

the

fingerboard

and extend its

hollow

toward

the

neck.

Making

the neck end

of

the hollow

wider and

deeper

will also

drop

frequency.

Thin the whole

finger-

board if

necessary;

from

top

or

bottom,

leaving

the

bridge

end

thick.

Every

now

and

then,

glue

the

fingerboard

back

on,

let

it

dry

an hour

or

so,

and retest

it

without

strings

but not

forgetting

end

button,

pegs

andchinrest.

When

you

get

close,

put

the

strings

on

and

play

a

little.

If

the

low

string

rattles

your

teeth and

the

high

one

hurts

your

ears,

you

have

made it.

8)

If

you

can't reach the

frequency

of

W',

stop

atAO

which

is

usuallyhigh-

er.

Or

stop

in

between.

There

is still

moreto

this than

we

know.

Postscript

My

scientific

husband

surmises that W'

works better

for

matching

because

it,

like

80,

is (oris descended

from)

what

is

largely

a

body

resonance.

I

myself

have

a

suspicion

that

all this mode

tuning

has

an

effect

onaninstrument

which is

relat-

ed

to

that

of

years

of

playing.

Is it

possi-

ble that all these

old and new

European

fiddles,

so

dearly

loved

by

their

owners,

have

matching

AO and W' modes? I

intend

to

find

out

as I meet

them,

and

would

appreciate

information

from

readers.

References

1.

Hutchins,

C M.

and

Voskuil,

D.

(1993) "Mode

tuning

for

the violin

maker,"

/.

Catgut Acoust.

Soc.

Vol.

2,

No. 4

(Series 2),

pp.

5-9.

2.

Spear,

D.Z. (1987)

"Achieving

anair-

body

coupling

in

violins,

violas

and

cellos:

a

practical

guide

for the

violin

maker."

Catgut Acoust.

Soc.

J .

#47,

pp. 4-7.

3.

Ekwall,

A. (1990)

"Tuning

air-body

resonances

for the

violin

maker,"

CatgutAcoust. Soc.

J .

Vol.

1,

No.

6

(Series

2)p. 37.

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3

(Series

II),

May

2001

V I O L I N

V A R N I S H

EDITED

BY

J OSEPH

AND

R E I N E R

HAMMERL

George

Stoppani

Anyone

who

triesto

varnish

a

musical

gloss

lacquer

is desired we fill the

wood

the

materials

suggested.

Our

nexttas

instrument soon

discovers that

there

pores

with

fine

mineral

powder

in a

var-

to

choose

a

priming

coat

thatwill

p

are

aninfinite

variety

of

approaches.

This

nish

medium. When

partially

dry,

this is

vent later

colored

coats

from

sinking

book

only

partially

satisfies

the

hunger

rubbed off

leaving

the filler

lodged

in

the Various mixtures

of

shellac,

resi

among

beginners

for

practical

instruc-

pores

and surface

irregularities

(Note

propolis,

and

other

compounds

are

s

tions

and

the

need among

professionals

that

this

is

a

procedure

used

in

polishing

gested.

Instructions

are

rather

confus

for reliable information

on

materials.

furniture and

is

not

to

beconfused with

although

it c an

be

deduced that

Mainly,

it offers a window

into modern

the much thicker

particle

layers

found

should

pick

harder resins

for

prim

German

practice

mainly

inherited

from

on

samples

from

old

instruments). Next coats.

Priming

coats

are

rubbed do

the

1

9th

century.

Many

resins,

dyes,

we

impregnate

the wood

(although

it is

with

pumice

or rottenstone

and

wa

volatile

oils,

balsams and othermaterials

unclear whether we

should

use a

pore-

We now

apply

the

spirit

coloring

v

are

described

with

information

on coun-

filling

procedure

beforehand). The

book nish.

Options

here

are

again

rather

op

tries

of

origin,

different

qualities

and

suggests

a weak

potassium

silicatesolu- ended. An

assortment

of

resins,balsa

usage.

There

are

sections on

wood

prepa-

tion

or

solutions of

resins such

as san-

colored

resins,

aniline

dyes

and

extra

ration

and

varnishing

procedures

includ-

darac, mastic,

or

propolis

(dissolved in

of

natural

dyes

are

employed.

We

sho

ingbleaching, removing

iron,

glue

andoil

alcohol or

potash

solution).

A

further

apply

a

large

number of

thin

coats

ru

stains,

filling pores, impregnation

of the

possibility

that

highlights

annual

rings

is

bing

down

in

between.

Finally

we

ap

surface,

highlighting

annual

rings,

stain-

linseed oil

or

linseed oil varnish

applied

a

clear

"spirit

finishing

varnish."

Int

ing,polishing,

and

varnishing

with

both

in

thin coats

and

rubbed

in

gently

with

a

mediate

rubbing

is

recommended

plu

spirit

andoil varnishes.

However,

readers

cloth.

A

variety

of

staining

methods

are final

rub down

with oil

insteadof

wa

hoping

for an

overall,

step-by-step

described that should

have

been done

Possible drawbacks to thebook

methodwill have

to

extract

this

for

them-

before

or

instead

of

surface

impregna-

the lack of historical

perspective

a

selves from various

strategies

presented

tion.

First we

lightly

seal the wood

with

information

on

Cremonese

or

Ital

for

each

stage

of

the

process

and

there

a weak

gelatin

or

gum

tragacanth

solu-

varnish,

what

distinguishes

one

st

may

not be

enough

information

for a

tion.

The

possibilities

for

stain are

water

from

another,

and information

beginner

to

successfully

implement

them or

spirit

soluble aniline

dyes

and

a

range

acoustical effects

of

varnishes.

We

or to

understand theusageof

materials. of

natural

dye

materials

such

as turmer-

told

that:

A

reading

of

the

varn

The

varnish

process,

according

to

ie

or

orlean.

They

also have a

category

of

recipes

from

the old

Italian

masters

w

this

book,

might

go

as

follows:

We start

"primer

stains"

such as

gamboge

or

show

that

in

addition

to

spirit,

they

a

by making

the

instrument

from

dry,

sea-

aloes

and

this

seems to

mean

stains that

used volatile

oils."

Presumably they

soned

wood. Wood

stains

are

bleached

have

some

body

and

seal

the

surface

a

referring

to

numerous

old

manuscri

with a

mixture

of

hydrogen

peroxide

little as

opposed

to

stains

that

justpro-

that

contain

recipes

forvarnishes

inten

and

ammonia

applied

with

a

wooden vide color. There

is

also

"double

stain-

ed for miscellaneous

purposes,

beca

stick.

Other

stains,

such

as

rust,

are

c ut

ing"

an

example

of

which

is a5%

tannin

recipes

for

violin

varnish

are sca

out

and the

cavity

filled with

plastic

solution

which

is

allowed

to

dry

fol- before the 18th

Century.

In anoth

wood

or lycopodium

powder

mixed

lowed

by

a

5%

potassium

dichromate

place:

"Gum

benzoin

can

also

be

used

with

glue

or

varnish. Glue stains are

solution. There

is

no

information

about

a

polishing

agent.

It is dissolved in al

removed with

a

soft

soap

solution or the

compatibility

of the

processes given.

hoi

and

applied

very

lightly

as a

poli

Oxalic

acid;

oil

stains with a

paste

of For

example:

what

might

happen

if

we As can be

seen fromold

treatises on

magnesium

oxide

and

gasoline.

If a

high

applied

potassium

silicate

oversome

of

subject,

gum

benzoin was

alreadybe

8/17/2019 2001 N.3 VOL.4 CASJ


8/17/2019 2001 N.3 VOL.4 CASJ

http://slidepdf.com/reader/full/2001-n3-vol4-casj 67/76Vol.

4,

No.

3

(Series

II),

May

2001

65

Book

Review

THE

ART

OF

V I O L I N

MAKING

CHRIS

J OHNSON

AND

ROY COURTNALL

J eff

Loen

beautiful

book

is

concerned

with

Partthree

describes

violin

construe-

instructions

on

installing pegs,

nut,

and

how

to "finesse"

a violin

using

a

tion,

start-to-finish.

The rib

assembly

is

saddle,

carving

a

bridge,

and

setting

a

level

of

craftsmanship,

understand-

constructed on

al2 mm thick

mold.

soundpost.

The

chapter

on sound

and

sensitivity.

It

goes

far

beyond

Operations

such

as

rib

bending

and

adjustment,

by

Gerald

Botteley,

gives

engineering

approach

of

most

how-

block

fitting

are

described in

detail,

i

nstruct

ions

for

fine-tuning

stringlength

violin-making

books,

into the realm

including

many

tips

to achieve well-fit-

i

in i

fiii

i

ii-i-

-i

cii«

i

i

based on

the

effects

tightening

and loos-

scholarship

and

a real

kinship

with

ting

parts,

subtleties

regarding arching,

.

,

.

,

°

makers

of

past

ages.

The

handsome

channeling,

andf-hole

flutings

are

effec-

° ° °

"

re

'

of

this

hardback

volume

tively

illustrated

using carefully

shaded

and

useful

is given

for

a coffee

table

book,

but it is

photographs.

The authors

recommend

adjusting

soundpost

position,

length,

an

outstanding

shop

manual

using

wood

purfling

rather

than

fiber,

and

wood

density

to

modify

particular

on

the

approach

taught

at

Eng-

and describe

how

to

make

your

own sound

qualities.

However,

no

discussion

Newark

School

of

Violin

Making. purfling.

The sections on

plate

gradua-

is offered

regarding improving

tone

by

is

filled with

hundreds

of

fine

photo-

tion

and

tuning

offers

so

much

informa-

acoustical

mode

matching,

or

artificial

and

drawings

that

clarify

impor-

tion

(someof it

contradictory)

thatsome

playing-in using

electronic

equipment.

points,

and

the

textis

peppered

with

readers

may

be

paralyzedby

indecision.

Appendices

include

a

list

of

suppli-

to

pertinent

literature

Both

traditional and

electronic

plate

ers

of

toolss

plans>

and

joumaJ s

in

±c

Part

one

clearly

and

logically

de-

tuning

methods are

discussed,

with

sev-

tt iz j

ttc

jt

i

,

/

.

,

&

.

J

.

, , ,

„

,

'

.

.

,

United

Kingdom,

U.S.,

and

Europe,

and

what a

violin

is,

how

it

works,

eral

pages devotedto

Carleen

Hutchins

r

7,

r

. ..

jji

i

rii

i

a .

j

i

j i

a

l is t o f

collections

of musical

mstru-

d the

historyof

development

by

mas-

methods,

plus

an

excerpt

from

J oseph

makers.

A

chapter

on

classic

makers

Curtin's talk

"The

Trouble

with

Plate

ments

B^

mcludm

§

no

full

s ize

P

lans

>

lavishly

illustrated

with

full-page Tuning."

Carving

a

neck and scroll is

the authors seem to be

gentlyprodding

photographs

of

violins

by

Nicolo

explained

using

dozens

of

excellent

pho-

l

-

c r ea

der to

personally

research the

Stradivari,

Andrea

Guarneri,

and

tographs

and

drawings.

In

the section

topic

and

to

investigate

instruments in

ob

Stainer.

Biographical

sketches

of

on

varnish,

the

authors

suggest

using

literature and

collections,

rather

than

contemporary

violin

makers

con-

ready-made

varnish,

although

they

simply tracing

an

arbitrary

plan

in

a

useful

information on

their

working

include

interesting recipes

for

oil

and

how-to book.

This

refreshing scholarly

and individual

approaches

spirit

varnish.

Severalmethods

of stain-

approach

to

violin

making

is

what

models,

wood

selection,

plate

tuning, ing

wood,

preparing grounds,

and

makes

this

book

indispensable

to

begin-

varnishing.

adding

color

are

explained

in

adequate

ni and intermediateviolin

makers

.

Part

two

covers

workshop,

tools detail

for

the reader to

produce

results,

materials.

These

authors

arededicat-

although

the authors

generally

stop

...

to

the

use

of

sharp

edge

hand

tools,

short

of

recommending

particular

meth-

P ublication

Intormation

rarely

do

they

mention

the

use of

ods.

Nomention is

made

ofthe

popular

Published

by

Robert

Hale,

London,

tools,

jigs,

and other modern

"Rubio

ground"

recipe.

The

chapter

on

setup

and

adjustment

gives

detailed

1999,

253

p.

Available from

the

Strad

Library.

Price

$130.

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

A,

No.

3 (Series

II),

May

20

6

The New Violin

Family

Association,

Inc

112

Essex

Avenue,

Montclair,

NJ

07042

©9~

Phone:

(973)

744-4029

Fax:

(973)

744-9197

Best

wishes to all for the

new millenium

from The New

Violin

Family

Association,

Inc

Requests

for

information

about

the New Violin

Family

instruments

keep

us

very

busy.

We

are

excited

about

many

new

opportunities

that

are

developing. Anyone

interested

in

keeping

in touch

with

the

NVFA

and the

progress

o

the instruments can receive

a

copy

of our

semi-annual

newsletter

by sending

us a contribution

of

$25.00

There is lots

happening

For further

information,

contact

the office

at

the

address above on

a

Thursday,

o

you

can

explore

ourwebsite at

www.newviolinfamilv.org.

THE

HUTCHINS

CONSORTresident

The

Hutchins

Consort

will tour

the US Midwest

in

April

2002.

The

centerpiece

will

be

a

concert at

one

o

the

top

five

concert

halls

in the

nation,

theLied Center

in

Lawrence,

KS .

The commitment

includes

a

3

to

5

day residency

to

conduct

workshops

and

master

classes

at the

University

ofKansas.

Discussions

are

underway

with the

Washington

Center

in

Sioux

Falls, S.D.,

and

the Shrine

to

Music Museum

in

Vermillion

S.D.,

to

present

a similar

program.

Venues

in

Colorado, Missouri,

lowa,

and additional

cities in Kansas

are

also

under

negotiation.

AllenAlexander

Ist

st

Vice

President

Robert

J .

Miller

2

nd

VicePresident

J oseph

F.

II

Artistic Director J oe

McNalley

has

met

with

personnel

from the

instrument

department

of

the

Metropolitan

Museum of

Art

in

New

York

City

with

the

hopes

and

expectations

of

presenting

a

three-day

series

o

concerts

and

educational

programs

at the

museum

in

May,

2002. Also

under consideration are a

tour t

Australia,

a 90

th

birthday

celebration concert

honoring

Dr.

Hutchins,

a concert

featuring internationally

renowned oboistAllan

Vogel

as

guest

soloist,

and

a

possible

collaboration of

Consort musicians

with the

Cerritos

Performing

Arts

Center

to

develop

an

educational

outreach

program.

Secretary

Margaret

H. Sachter

Treasurer

Charles

J .

Rooney,

J r.

Members

of

the Consort are

developing

outstanding

educational

programs,

which can be

adapted

to

various

age

levels.

The

strong

pedagogical

backgrounds

of the musicians and

the

application

of

acoustica

science

in

the

design

of

the

instruments

easily

enable the

musicians

to

present interdisciplinary

programs

that

foster

understanding,

interestand

appreciation

of

science,

history

and

music.

Executive

Director

Carleen

M. Hutchins

Executive

Assistant

Deborah

C.

Anderson

Pleasecheckthe

website,

www.hutchinsconsort.org.

for

updates

on

future

activities.

Trustees

CONSTANCE

COOPER

Dennis

Flanagan

Frances

J .

Furlong

Paul

R.

Laird

Constance

Cooper,

an

American

microtonal

composer

of

opera,

orchestral

pieces,

and chamber

musi

for

voice

and

instruments,

had

the

premiere

of

her

composition

collectively

entitled

Coming

From Us

at

New

York City's Church

of

the

Holy

Apostles

on

February

10,

2001.

Of

the

thirty

pieces

for various

chambe

ensembles,

ten

were

designed

specifically for

instruments

of the Violin

Octet

and featured

the

new

pizzicato-bow

designed

by

Ms.

Cooper.

In a

concert format

pioneered

by

First

Avenue,

improvised

commentaries

alternate

with

composed

works

both

in

reaction

to and

as extensions

of

the

compositions

This concert

was

made

possible

by

The New York State Council

on

the

Arts,

the

Mary Flagler

Car

Charitable

Trust,

The Aaron

Copland

Fund,

and

the

American

Composers

Forum.

For

more

information

on

First

Avenue,

please

visit theirwebsite

at

www.firstavenue.org.

Andre

P.

Larsen

Donald J oseph

McNalley

Edith

Munro

J oseph

Peknik,

111

Pamela

Proscia

D.

Quincy

Whitney

DOMINICDUVAL

Dominic

Duval,

a

virtuoso

improviser

and

one of

the

finest and

most

prolific

bassists

on

the

contemporary

scene,

had

the

first

public

performance

of

his

new

Pyramid

String

Quartet

at

the

Knitting

Factory

in

New

York

City

on

December

21,

2000.

On his international

tours,

his instrument

of choice

is the small

bass

o

the New Violin

Family.

More

information can be

found on his website at www.saxofonismusic.com

ROBERT

MILLER

Bob Miller

is

developing

a

catalog

of

music

composed

and

arranged

for

the

Violin Octet

instruments

compositions

thatare also

playable

on

traditional

string

instruments.

Be

sure to

check

our website

to

se

what

is available.

Deborah

Anderson,

Executive

Assistant

Carleen

Hutchins,

Executive

Director

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

A,

No.

3 (Series

II),

May

2001 67

ISM

A

2001

symposium

entitled

"Musical

Sounds

from

Past

Millennia"

will

be

held

September

10-13,

2001

in

Perugia,

Italy.

Approximately

150

participants

are

expected

for

this

retrospective

overview

of

acoustical

characteristics

of

musical sounds

(i.e.

sounds that

man

s

carefully

selected

in

the

course

of

history

for

creating

music). Attentionwill be focused

mainly

on

issues

regarding

the

need

keeping

this

cultural and

scientific

heritage

alive and

available

to later

generations.

For

more

information,

see

the

web

page:

kshops (Preliminary

Schedule)

Violin

Makers and

Simplified

Wind

Instruments:

series

of

workshops

on

specific

musi-

Violin

Acoustics

for

Luthiery

building,

playing

and

combining

acoustics

subjects

will beheld

during

Lecturer: PioMontanari

musical acoustics with

performance

he

last

three

days

of

the conference.

Duration: 9

hours

Lecturer:

Leonardo

Fuks

are

intendedfor

instrument mak-

Groups

o

participants

will

analyze

and

Duration:

4

hours

researchers and

students

interested

I°T,

AA

V

USm§

tl

hands

°

n W

°

rksh

°

P

alWs

'

Chladm

method.

In

addition,

modal

j

ont[

kn_l__

y^ KC A

applied

aspects

ofmusical

instrument

anal

is

wi

„

be

demonstrated o

n

a

com

.

tZZIT^

f

7

r

j

_

« .

,

}

,

,

instruments

(oboe,

clarinet, rlute,

cor-

and

construction

or

computer

pleted

violin

(a

trebleviolin of

the

Italian

j-j

m

u-

t

j

■

-i

y

v

netto,

didgendoo, etc.),

measure

their

used in musical

acoustics.

Octet). .

,

,

.

,

.

length

of

the

workshops

will

vary

2to

20

hours

depending

on

the

Virtual

Acoustics

and

Virtual

Musical

Instruments

Lecturer:

Lamberto

Tronchin,

Course onArchitectural

Andreas

Langhoff

physical

and

physiological

variables in a

laboratory,

present

ashort

lecture,

com-

pose

music,

and

finally perform

a

piece

written for it or thewhole ensemblefor

the

ISMA

2001 audience.

"Blending

Sound

Sources,

Duration: 3

hours

Fields

and

Listeners"

f

methodology

of virtual

acoustics

Gestural

Interfaces

and

Con

rol

of

YiochiAndo

and virtUal musical instruments

will

be

Expressiveness

in

Microtonahty

ec urers. ioc

in o

illustrated

for

violin

and

wind

instru-

Lecturers: Leonello

Tarahella,

Sakai,

Shm-ichi

Sato

m^

sound

bg

compared

Diego

Gonza

lez

17hours

with

original

sounds

made

in an

ane

_

Duration: 3 hours

on a book

by

1

rot.

Ando,

this

choic

chamber

by

violinist

M.

Fornacia-

New

gestural

interfaces for

musical

covers

theoretical

background

oi

r

[

t In

addition,

the

virtual

sound

of

applications

are

presented

with an

he

field of

architectural

acoustics,

Baroque

trumpet

will be

compared

with

emphasis

on

performance

of

microtonal

application

of

theories to

the

actual

sounds

in the

anechoicchamber.

music. LeonelloTarabellawill

introduce

of concert

halls and theaters.

wireless interfaces for

real-time

control

of

electro-acoustical

music,

which

allow

rass Instrument

Optimisation

Instrument

Analysis

System

and

BoreReconstruction

System

iomi instrument

analysis system

««.

—

--

—

-7—

the

performer

to

«

touch

thesound

.»The

GregorWidholm

Lecturer:

Gregor

Widholm

.^

subject

of

this

workshop

is

a

meas- a

ion.

ours

system

for violin makers and

Diego

Gon2ale2

and

a

comparison

of

based on

admittance

at

the

khm

for

optimizi

intona

.

the role

playedby

musical

proportions

by

a

laser

system.

The

system

ome

q{

instruments

among

different art

branches.

Finally,

it

possible

to

compare

different

Additional

discussions wiH focus onthe

-

Leonello

Tarabellawill

explore

the

con-

to differentiate between

oretical

foundations of

BIAS,

bore

trol of

expressiveness

in

microtonal

and

non-radiating

modes,

to

reconstruction,

and various

problems.

music,

and

workshop

participants

will

for

wolf

tones,

and

other

acousti-

Finally,

participants

will be

invited to

be

invited

to

experiment

with

gestural

applications.

use the

system.

interfaces.

8/17/2019 2001 N.3 VOL.4 CASJ


CASJ

Vol.

4,

No.

3

(Series

II),

May

200

MeetingAnnouncement

-

ISAM 2001

Selected

Preliminary

Abstracts

Reverberating Strings:

Echoes

of

Apollo

LindaArdito

Bows and timbre

—

myth

or

reality?

Anders

Askenfelt

and

Knut

Guettler

The sound

qualities

of

string

instruments: a new

approach

bybody

non-linearities

Charles

Besnainou

Vibrational

dynamics

of

the

resonance

of

the

guitar:

modal

analysis

andfinite

elementmethod

Thickness

graduation

systems

of

violin

family

instruments:

Preliminary

Statistics

and

M.J.

Elejabarrieta,

A.

Ezcurra,

and

C.

Santamarfa

Conclusions

J effrey

S. Loen

The

Australian

Didgeridoo

Directional timbre

spaces

ofviolin soundseville

Fletcher,

Lloyd

Hollenberg,

J oe

Wolfe,

and

J ohn

Smith

Zdenek Otcenasek

and

J an

Stepane

Measuring

mechanicalnon-linearities

Reviving

the

Baroque

baryton

—

n

stringed

instruments The

instrument,

playing

techniqu

he

instrument,

playing

technique

Vincent

Gibiat,

J oel

Frelat,

and

unique

sound

quality

and

Charles Besnainou

TerenceM.

Pamplin

ow to achieve sound

quality

and

Charles Besnainou

TerenceM.

Pamplin

by

non-linearity

feeds

by

active

control on musical instruments

Microtonality, non-linearity

Violin

quality

assessment

Charles

Besnainou

an

d

golden

scales

with an

objective

criterion

using

D.

Gonzalez,

D. BonsiandD.

Stanzial the

constant-Q

transform

Admittance

measurements

Rafael

Sando,

in

the fretbar

of

a classical

guitar

Physical

aspects

of

perception

j

ose

R

0

y

erto

deFranca

Arruda

Ricardo R. Boullosa

ofviolin

quality

Colin

Gough

Sound

source

perception

Anacoustical

study

on double

bass

and

physicalmodeling

bridge

height

adjusters

Measurements

of acoustical

Gary

p

Scavone,

Stephen

Lakatos,

Andrew

W. Brown

parameters for

theclassical

guitar

an

j

Perry

R Coo

£

Toby

Hill,

Bernard

Richardson,

Relationship

between the

inorganic

and

Stephen

Richardson Sound

directivity

spectral

components

of

cellular

wall

and the

spaces

ofviolins

acoustic

properties

of

wood

forviolins

Prediction of

violin

radiation

j

an

Stepanek

and

Zdenek

Otcenasek

Voichita

Bucur

properties

in

the

200-700

Hz

range

Erik V.

J ansson,

Lars Henrik

Morset,

The

relationship

between

sound

andKnut

Guettler

post

adjustment

and

resonator

non-linearity

in the

violin

J oseph

Curtin,

Vincent

Gibiat,

and

Charles

Besnainou

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No. 3 (Series II),

May

2001

69

Acoustics

Australia

V

01.28

N0.3

Dec

2000

contains:

N.

Fletcher,

A

History

of

Musical

Acoustics

Research

in

Australia,"

97-102

N.

Fletcher,

"Other Branches

of

A

Tubis,

C.L.

Talmadge,

C.

Hong,

Effects

of

Basilar Membrane

Non-

KTH

Royal

Institute

of

Technology,

linearity

and

Roughness

on

Stimu

Deph

of

Speech,

Music

and

Hearin

lus

Frequency Otoacoustic Emis-

sionFine

Structure,"

Vol.

108

No.

6

contains:

Dec

2000,

2911-2932

A.

Askenfelt

"1999 in

Summary," Ann

al

Report

1999,

1-2

Acoustics,"

113-114

I-

Dhar,

On

the

Relationship

Be-

J .

Sundberg,

"Music

Acoustics,"

Annu

tween the

Fixed-fl,

Fixed-f2,

and

Report

1999,

13-20

American Lutherie

Fixed-ratio

Phase

Derivatives

of

the

a.

Friberg,

J .

Sundberg,

L.

Fryde

No. 60Winter

1999

contains:

2fl

f2

Distortion

Product

Otoa-

Motion

in Music: Sound

Lev

„

„, ,

.

,

„

.

,

._

T

. . coustic

Emission,"

Vol.

108

No.

4

-c

i

r

T

r

tv

G.

Caldersmith,

Arching

and

Voicing

n

Envelopes

ol

Tones

Expressing

H

Violin

Plates

16-18

„w,

.

'

TT

.

..

,

ma n

Locomotion,"

TMH-QPS

T

,-,

.

K r

,

.

r

. ,

Mft

G.

Wemreich,

C.

Holmes,

M.

Mellody,

J .Curtm,

Project

Evia,

30-35

«

A

ir-Wood

Coupling

and

the

J an

2000,

73-82

Swiss-Cheese

Violin,"

Vol.

108

M.

Thalen,

J .

Sundberg,

A

Method

f

J ournal

Ot

the

No

6pt

1

Noy

20Q^

2

389-2402

Describing

Different

Styles

Acoustical

Society

of

America

E

G Win

iamSj

B .H.

Houston,

P.C.

Singing,"

TMH-QPSR

J an

200

contains:

Herdic,

S.T.

Raveendra,

B. Gard- 45-54

M.R.

J ones,

Book

Review,

The

Psychol-

ner,"lnterior

Near-field

Acoustical

P.

White,

J .

Sundberg, "Spectrum

Effec

ogy

of

Music,

Vol.

108

No.

3

Sept Holography

in

Flight,"

Vol.

108

0f

Subglottal

Pressure Variation

x a

-°

0

'

87

T

9

;

T

BB

l

„

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No.

4

Oct

2000,

1451-1463

Professional

Baritone

Singers

J .

A. Mann

111,

Book

Review,

Fanner

TMH-QPSR

April

2000,

29-32

Acoustics: Sound Radiation

and

J ournal

of

TheViolin

Society

Nearfield

Acoustical

Holography,

#

A

mA

>n

Vol. 108

No. 4

Oct.

2000,

1373-1374

America

Michigan

Violinmakers

Association

C.A.

Shera,

C.L.

Talmadge,

A.

Tubis,

VoL

XVII

Na

1

contains:

contains:

"Interrelations

Among

Distortion-

T.

Croen,

Audio

Calipers:

Interpreting

._.

.

„

,

_,

_

,

t W7

i r

t

i

\r

j

i«i

»

D. Brownell, Inlet

Scroll Chee

Product

Phase-Gradient

Delays:

the

Work ol Isaak

Vigdorchik,

t-,,

.

r,

■

ore

c

i Repair, No. 42 an

2001,

6

Iheir Connection

to

Scaling Sym-

>-_£/

r

metry

and

its

Breaking,"

Vol.loB

J .

Curtin,

"Innovation

in Violin Mak-

L-

Tews,

A

Tuscon

Experience,"

No.

4

No. 6Dec

2000,

2933-2948

ing,"

75-83

Oct

2000,

1

0-1

1

C.L.

Talmadge,

A.

Tubis,

G.R.

Long,

C.

N.

Pickering,

AHolistic View

ofViolin

C.

Traeger,

"Varnish

Touchup,"

No.

4

Long,

"Modeling

the

Combined

Acoustics,"

29-53

J an

2001,

7-8

Thomas

D.

Rossing

was

the

recipient

ofthe

2000RobertA. MillikanMedal. This

medal

is awarded

annually

for

notable

an

creative

contributions

to

the

teaching

of

Physics.

TheAmerican

Auditory

Society

presented

Daniel

Ling

with its

Life

Achievement

Award

at its Annual

Meeting

at

Scottsdal

Arizona

onMarch

16,

2001.

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No. 3 (Series

0

May

2001

(Note:

Please

contact

the

editor

with

information about additional courses not

listed)

THE

C H I M NE YS WORKSHOP

F OR

V I O L I N MAKERS

Sponsoredby

theViolinMakers Association

ofArizona, International

This

is a

workshop

for

makers

with

at

least

minimal

experience,

held in

Tucson,

Arizona

each

Spring.

The

workshop

is

taught

by

Edward

C. Campbell

of

the

Chimneys

Violin

Shop.

Four one-week

workshops

are

presented

on

a

variety

of

topics. Workshops

include

lectures

and

demonstrations

of

varnishing,

bow

making,

plate

bending,

etc.

For information

contact

Ed

Campbell,

The

Chimneys

Violin

Shop,

614

Lerew

Road,

Boiling Springs,

Pa.

17007-9500,

(717)

258-3203,

[email protected].

Please

note

that the

workshop

is

followed each

October

by

the annual convention

and

contest

of

the

Violin

Makers Association

of

Arizona

International.

For

additional

information

on eitherthe

workshop

or

the

competition,

see the

web

page:

www.vmaai.com

V I O L I N

B U I L D I N G

WORKSHOP

at theViolin

Craftsmanship

Institute

CAS

TrusteeA.

Thomas

King

will be

assisting

Master

Craftsman

Karl

Roy

in

the Violin

Building

Workshop,

held

J une

11-J uly

27

in

Durham,

New

Hampshire.

Tom

King

began

studying

violin

building

with

Karl

Roy

in

1983and

has

operated

his

own

shop

in

Maryland

for

a

number

of

years,

specializing

in

the

construction

of

violins

and

violas.

The

course is

designed

for

beginning,

intermediate,

andadvanced

students.

Students

work

on

two instruments

simultaneously,

oneunder the

guidance

of the

instructor,

and the second

intheir free

time. At

the end

ofthe first

year

thestudent

has

completed

two

rib

assemblies

and

two

roughly

arched

sets of

plates.

During

the

second

year

two

violinbodies

are

completed

"in

the

white,"

and

in

the third

year

two violins are

completed

and varnished. Please

see the

web

page

for more

details

and

registration

information:

www.learn.unh.edu/violin.

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No. 3 (Series II),

May

2001

71

0

:

The

new CAS

J ournal

Editor,

Dr.

J eff

Loen,

began

his

professional life

as

anearth scientist

forthe

U.S.

Geological

Survey,

conducting

field

studies

throughout

the

Rocky

Mountains.

The

USGS

had

high

standards

for

technical

writing,

drafting,

and

editing,

and

Loen

worked

at

those

skills,

eventually

publishing

more

than 25

scientific

reports

and articles. He earned

a

Ph.D.

in Earth Resources

from

Colorado

State

University

in

1990.

Subsequently,

while

living

in

Butte,

Montana,

Loen

gravitated

toward

his love

of

music.

He

learned

that

Butte

hada

good

supply

of

old

violins,

left from

the

days

when

the

city

was

a

wealthymining

town.

Loen

eventually

opened

his

own

shop

to

repair

instruments

and

bows.

He also

began

to

make

instruments,

studying

withmakers invarious

parts

of

the

United

States.

When Loen

joined

CAS in

1997,

he

felt,

as

a

scientist,

a

kinship

with

researchers ofmusical

acoustics.

Loen now

lives in

Seattle,

where

he

operates

his own

shop.

He

has

begun

a

significant

research

project

that

involves

compiling

thickness

data

of

old

masterinstruments.

He is confi-

dent

that

a

scientific

approach

can reveal much about the

workings

of

fine

instruments,

andhe

looks

forward

to

sharing

the

results

of

his

research with

other

violin

enthusiasts.

As

Editor,

Loen

hopes

to

fill

the

J ournal

with

practical,

easily

comprehensible articles

that

coverthebroad

range

of

material of

interest

to

CAS

members.

A.

Thomas

King

8/17/2019 2001 N.3 VOL.4 CASJ


Vol.

4,

No.

3

(Series II),

May

2001

2

ITEMS

AVAILABLE

FROM

THE

CAS OFFICE

(see

CAS

Website

www.marymt.edu/~cas

for

the latestupdate)

Past Issues

of

the CAS Newsletters

/

J ournal

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Set

of

Newsletters

and

J ournals

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Specific

issues:

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issue)

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Selected

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dealing

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practical application

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Volume I:

1964

-

1978

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/

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60

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Volume

II: 1979

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1986

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/

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"Acoustics for theViolinmaker":

8/17/2019 2001 N.3 VOL.4 CASJ


Editorial Procedures

for

Publications

The

CAS

J ournal

is

a

peer-reviewed

publication.

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means

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the

Editor

will

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topic

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paper

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744-0375,

email

[email protected].

The

J ournal

Editor

ca

be

contacted at

CASJ [email protected].

OFFICERS

TRUSTEES

ADVISORY

CO U NCI L

President

Gregg

T.Alf

Dennis

Flanagan

J ulius

VandeKopple

Pamela

J .

Anderson

FrankLewin

ExecutiveVice

President DavidL. Chrapkiewicz Gabrielweinreich

Paul

Ostergaard

Christopher

Chafe

Treasurer

Sam

R. Compton,

J r.

COMMITTEES

J .

Maurits

Hudig

J oseph

Conrad

Research

Secretary J osephCurtin

°

liver

E

Rodgers

Elizabeth

McGilvray

Uwe Hansen

J ournal

Permanent

Advisor

A.

Thomas

King

GreggT.

Alf,

Associate

Editor

CarleenM.

Hutchins

Daniel

Ling

Virgink

Benade

'

Associate

Editor

,

„

.

EvanB.

Davis,

Associate

Editor

General

Manager J osephRegh

_,

.

„„

'

,

.

r

,.

t\

ti

/~>

■

_

Robert

T. AssociateEditor

DeanaR.

Campion

OliverE. Rodgers

_

_ _

. .

A

Catgut

Musical

Acoustics

Gary

Scavone

l

t

-l

Research

Library

Robert

T.

Schumacher

J oan

E

MiUer

INTERNATIONAL

VICE PRESIDENTS

Canada:

Warren

Reid

France:VoichitaBucur

Germany:Volkmar

Tetzner

HongKong:

Anton

Sic

Italy:

Domenico

Stanzial

J apan:

Isao

Nakamura

Netherlands:

Adrian

M. Houtsm

Scandinavia:

AndersAskenfelt

U.K.:

J im

Woodhouse

8/17/2019 2001 N.3 VOL.4 CASJ


2001 N.3 VOL.4 CASJ

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