Dept. for Speech, Music and Hearing

Quarterly Progress andStatus Report

Eigenmodes and tone qualityof the double bass

Askenfelt, A.

journal: STL-QPSRvolume: 23number: 4year: 1982pages: 149-174

http://www.speech.kth.se/qpsr

I N P U T ADMITTANCE AND EIGENMODES

Frorn studies of the input admittance of violills (Alonso Moral &

Jansson 1982a), it is clear that essential information on the proper-

t i e s of the viol in can be extracted from the input admittance curve.

The ce l lo has been investigated successfully with the same method by

Lundberg (1982). The data on the ce l lo included i n t h i s paper a re from

h i s study, which has not been published in English previously. To the

author's knowledge input admittance neasurernents of the double bass have

not been published earlier.

Eiyenmodes

The vibration pmperties of a string instrument can be described by

its eigenmdes. In a recent work the eigenmodes of the violin have been

mapped by means of a novel interferometry technique (Alonso Moral &

Jansson 1982a). It was found that the violin exhibits different kinds

of eigenmodes, Fig. 1. In the low frequency region below 800 Hz, the

viol in vibrates as i f it were made of a homogenous material. These

eigenmodes are labelled body modes, abbreviated C (Corpus). In the

lowest body mode ( C l ) the violin vibrates as the fundamental mode of a

f ree bar. The next higher node ( N ) derives from the neck together with

the fingerboard. These two eigenmodes are one-dimensional and do not

radiate sound. The next higher body modes C2, C3 and C4 are two-dimen-

sional. The C3 and C4 mode can radiate sound. Above (300 H z the eigen-

modes of the viol in a re limited t o e i ther the top or the back plate

(plate modes). In addition t o these recently explored modes there is

the well-known cavity resonance, labelled as the Helmholtz a i r resonance

(AO) . A t t h i s resonance the top and back plates nove i n opposite phase

and alternatingly enlarges and shrinks the enclosed a i r volume in the

instrument. The Helmholtz resonance often fa l l s close to *-he neck re-

nance and an interaction between -these modes can thus take place. Anot-

her prominent eigenrnode is the f i r s t top plate resonance (TI), which

shows a complicated vibration pattern, the major vibratiolls beeing

located a t the bass bar side of the top plate. The eigenmodes of the

violin, with the exception of C2, have been verified t o exis t a lso in

the cello (~undberg 1982).

Measurement of input admittance

The ~aechanical admittance a t a certain point on a vibrating object

i s defined as the r a t i o between vibration velocity and force a t tha t

point. In the present measurements the admittance was measured a t tlie

same point on the instrument as the driving force was applied, hence the

tenn input admittance.

The driving unit consisted of an externally mounted coil, together

with a small, very strong, magnet (weight 2 g) mounted on the bridge of

the instrument with a piece of wax, Fig 2. The c o i l was fed from a

constant current source which gave an almost constant driving force

(+/- 0.5 dB) througklout the frequency rarige used (40 - 3000 HZ). The

vibrations of the instrument were measured with a light accelerometer

(B&K 4374, weight 0.65 g) attached to the magnet. This combined driving

and measuring system, developed by Jansson, possesses almost ideal

properties for admittance measurements of string instruments, featuring

low weight and no disturbing internal resonances or losses. me drawback

however is the massloading due t o the magnet and accelerometer which

l i m i t s the possibilities to study the properties of light objects, such

as the viol in bridge, cf. Fig. 2.

The velocity was obtained by integrating the acceleration signal in

a passive network. A s the driving force was kept constant the admittance

was d i rec t ly proportional t o the velocity measured. A chdrt of the

admittance versus frequency could thus be plotted d i rec t ly on a X-Y

recorder as the frequency of the driving signal was swept through the

frequency range. The input admittance curves of the basses presented in

this stu<ly were recorded with the driving a t the low E-string side of

the bridge in parallel with the top plate as illustrated in Fig. 2. This

was found to be the rnost efficient driving point for cellos arid basses.

As some bodymodes were weakly excited by this arrangement, complementary

measureinent3 were undertaken on the body with the driving perpendicular

t o the top plate.

Curing the measurements the instrments were suspended in rubber

bands or resting on the r ibs on foam rubber supports. The eigenmoiles

were regarded as pract ical ly undisturbed when the il~strurnerlt was

hanging. It was found that the frequencies and levels of the eigenmodes were essentially uninfluenced by restiny the instrument on the ribs. me

strings were damped during the masuremnts.

Fig. 2. View of the driving unit (magnet + coil) and vibration sensor (accelerometer) used in input admittance measurements of the violin ( le f t ) and double bass (right). The mssloading of the bridge due t o the magnet and accelerometer is about 30% of the weight of the bridge for the violin and 3% for the bass.

Interpretation of input admittance curves

Apeak in the input admittance curve at a certain frequency haplies

a high vibration velocity and hence also a high vibration amplitude.

Thus, the input admittance curve illustrates how easily the instrument

vibrates at different frequencies. An eigenmode of the instrument is

manifested in the input admittance curve by a peak. It is possible to

identify such a peak as a specific eigenmode of the instrument by

comparisons with interferometry measurements.

The sound radiatian from the instrument may be estimated from the

input admittance curve. However, the radiation efficiency of the

different eigenn~odes is not equal. A correction must be added to the

levels of the peaks in the input admittance curve in order to give the

radiated sound fro111 the instrument. The effect of this correction for

the violin is mainly to raise the radiation at the Helmholtz resonance

and to lower the radiatian at high frequencies (Jansson 1982).

Comparison of in~ut admittance violin - cello

In a study of the violin by input admittance measuremerits (Alonso

Moral & Jansson 1982a) it was found that instruments of high tone

quality were characterized by input admittance curves with tall, equally

hish resonance peaks in the lower frequency range, followed by a steep

slope from 1.4 kHz to 3 kHz. These characteristics of a high quality

violin can easily be observed in Fig. 3 (top), which shows the input

admittance of a violin made by Andreas Guarneri. The prominent peaks

have ken identified by means of real time interferometry as the first

top plate resonance (Tl) and corpus three (C3) and four (C4). It was

concluded that the steep slope derives from the principal bridge

resonance.

The input admittance curve for the Guameri-violin can be cornpared

with the input admittance of a high quality cello (Lundberg 1982), Fig.

3 (middle). Also for the cello the input admittance curve exhibits

prominent peaks in the lower frequency region followed by marked rise in

the curve, in this case starting at 1 kHz. But in contrast to the

2 STL-QPSR 4 / 1 98 2

violin, T1, C3 and C4 are clustered close together in the cello and

constitute the second prominent peak. The lowest prominent peak is the

Helmholtz a i r resonance which is more pronounced as compared to the

violin. The higher prominent peaks mnsist of one or two plate modes.

From the comparison between the violin and cello it may be

hypothesized (Lundberg 1982), that the input admittance curve of a high

quality cello and violin respectively should show the same principal

characteristics, w i t h high, distinct peaks in the lower frequency ratlge,

a l i t t l e separated in frequency. These similarities i n the responses of

the two instruments are lmwever achieved in somewhat different ways. In

the violin each prominent peak consists of one single resonance. In the

cello some prominent peaks are assen~bled of several resonances. Yhese

differences between the input admittance curves of the violin and cello

indicate that the cello cannot simply be considered as an enlarged

violin.

comparison of input admittance ce l lo - double bass

If the input admittance curve of a double bass of high quality,

Fig. 3 (bottom) i s compared with the input admittance curve of the

cello discussed earlier (middle), striking similarities can be observed.

'=he f i rs t top plate resonance (Tl) in the bass forms a prominent peak a t

approximately 100 Hz together with two other resonances, probably C3 and

C4. Thereafter follows a range between 150 - 400 Hz with higher plate

males. In this frequency range the input admittance curve of this bass

sllows almost equally high and equally spaced resonances. Finally, above

400 Hz, the influence from the bridge resonances can be seen as two wide

humps i n the m e . The similarities w i t h the input admittance curve of

the cello make it reasonable to conclude that the double bass is more

closely related to the cello than to the violin. A plausible explanation

for this would be characteristic constructional details shared by the

cello and bass, e.g. the high ribs.

Comparison of input admittance amongdouble basses -- -

Input admittance curves of four basses of conventional design but

of varying quality are corxpared i n Fig. 4. The instruments are ordered

INPUT ADMITTANCE LEVEL (10 ~ B / D I V )

INPUT ADMITTANCE LEVEL (10 d ~ l f l l v )

INPUT ADMITTANCE LEVEL (10 dB/D IV )

INPUT ADMITTANCE LEVEL (10 dB/DIV)

according to price with the rnost expensive instrument a t the bottom. The

prices vary between approximately $ G O O - $20,000. Input adr~littance

curves of the newly designed basses of the New viol in Octet ( ~ u t c h i n s

13G7) are shown se,mrately i n Ficj. 5.

The secolld bass fron che top i n Fig. 4 (ELI) I.lay serve as a

representative of a mediurn quali ty bass. 'i'he character of the input

acinittance curve of this bass differs from the character of hie curve of

the I l i y l ~ quali ty bass (SI)) , a t the bottoln of the figure. In the input

admittance curve for the taediun quali ty bass several small peaks

interfere with the high peaks. A general tendency towards rnore ileveloL@

and d i s t inc t peaks i n the input adlnittance curves of experlsive

instruments i s discernable as tnoving downwards i n the figure. I t is

especially irlteresting t o notice that only the high quali ty bass

( b t t o ~ n ) shows a regular structure with equally spaced peaks between 150

- 400 HZ.

The resonance frequencies of C1, N, A0 and T1 for the six basses in

Fig. 4 and 5 are compared in Fig. 6. Typical frequencies of the

EIelnholtz resonance (AO) and the f i r s t top plate resonance ( T l ) for

basses of normal s i z e a r e 65 Hz and 110 tIz r e spec t ive ly . The

corresponding frequencies for the high quality bass (SD) are a l i t t l e

lower than could be expected according t o the moderate s ize of t h i s

instrument. The Large Bass of The New Violin Octet (CEIII LE), which has

extraordinary dimensions (length 214 cn) , has very low resonance

frequencies, k0=42 Hz and T1+1 Eiz.

I t can be noted tha t the neck resonance (N) and the Helmholtz

resonance (AO) f a l i close together for three of the basses in Fig. 6.

'=he exceptions are a bass of poor quali ty i n which the N-resonance i s

considerably lower than the AO-resonance, and the basses of the New

Violin Octet which both have a rather high C?-resonance, indicating a

s t i f f neck. The frequencies of the C 1 and PT-resonance of the huge Large

Bass are strikingly high with respect t o the body length, but the

relat ively short neck of t h i s bass may be responsable for th is . Tile

implications for the sound and playing properties of the instrw~ent of

the frequetlcy r e l ~ t i o n s betwen A0 and tJ are not yet understood. R

coup1 iiig betwerl these resonances i s possible i f tlle resonarlce

frequencies are sufficiently close. I t xilay be hypthesized that a neck

resonance we1 1 separated f ror~ the HeL nhol t z resotmlce would benef i~ tile

playing properties of the instrument, i f this decreases the vibrations

of the neck, i.e. the s t r ing su,2port. The bow-string interac tiorl would

then be less disturbed.

STL-QPSR 4/1982

The lowest body nodes, C 1 and N, were recorded wit11 the driving

attached to the end of thr? fingerboard. The rnotion of the fingerboard

is larger at the N-resonace than a t the Cl-resondnce. Tnus, these rcales

can easily be identified by attaching a weight t o tile end of the

fingerboard. %is massloading w i l l have a considerable hlfluence a1 the

N-resonance, leaving the C1-resonance essentially undisturbed, cf Fig.

7.

The eiyen~nodes of a s t r ing instrument are not independent. For

example, a 'bass with a low AO-resonance w i l l automatically have a low

Tl-resonance. I n order to obtain the low AO-resonance the bass :nust have

a large body and also preferably thin top and back plates. This design

of the instrument with a large and thin top plate w i l l inevitably give a

low T'l-resonance, although the maker can ad just this frequency within a

ratlye of approximately 10 % by sk i l fu l adjustments of the top plate.

The strong dependence between the A0 and T1-resonance is illustrated in

Fiy. 8. Apart from one clear exception, which probably is due t o at1

uilusual design of the top plate of t h i s bass, it seems possible t o

predict both the resonance frequency and level of the f i r s t top plate

resonance for a bass i f the corresponding data on the Ilelmholtz

resonance are known. The sarne strong connection between the A0 and

Tl-resonance has also been found in the viol in (Jansson, personal

camuriication) . m i c a 1 values of the resonance frequencies of the C1, N, AO and T1

resonance for the violin, ce l lo and double bass are plotted in Fig. 9.

The relations between the eigerunde frequencies are seen t o be si:nilar

for the three r~ernbers of the s t r ing ensemble and also matched rather

closely to their tonal range. This is indicated 11y the filled s P h l s

above the frequency scale which give the frequencies of the open

strings of the instruments. I n a l l three instrments the C1-resonance

fal ls close to the lowest open string and the N and AO-resonances close

t o the second lowest string. The Tl-resonance shows the largest

variation, ranging fror:l the highest open s t r ing in the bass t o the

second highest open string i n the violin.

Tie eigenrnodes of the bass are influenced by the ?layer. Ttlis i s

I illustrated i n Fig. 10 which sllows a cori lpr i~r l of ule iinput ahitkance I

curves of a clouble ixss when the instrument is suspended i l l rubber bmds I

(top) and held by the player i n nori~al playing position (bottom). %e

influence by the player on the input admittance is stro~ly around GO I Iz 2

STL-QPSR 4/1982 161.

30 40 50 60 70 FREQUENCY (Hz)

2 ' . 7. Input admittance of a double bass with the driving attached to the end of the finger- board. The tm lowest body mdes, Corpus 1 (C1) and Neck (N) , are excited. The broken curve shows the influenceof a l i g h t weight fastened to the end of the finger- board, see text.

Fig. 8. Caparison of input admittance levels and resonance frequencies of the Helmholtz a i r mde (AO) and the f i r s t top plate mode (TI ) for the six basses in Figs. 4 and 5. Data points for the individual instruments are connected with straight lines. The data points represent the AO-resonance ( l e f t ) and TI-resonance (right) . The abbreviations t o the right of the sym- bols refer t o the names of the makersinFigs.4and5.

STL-QPSR 4/1982

d W

24 -J

W u - 5 2 + 0 E 2 0 a e - I- 3 n z

50 100 200 500 1000 2000 FREQUENCY (Hz 1

-I W

2 -J

W U - 2

25! t g IT 0 0 a Z I- =, n z

50 100 200 500 1000 2000 FREQUENCY (Hz

Fig. 10. Comparison of the input admittance of a double bass when the insfxurent is suspended in rubber bands (top) and held i n normal playing position (bottom). The horizontal lines correspondtothe same admittance level. The driving point is marked w i t h a triangle.

!

STL-QPSR 4 / 1 982

( N and AO), which rnay be clue t o a disturbance of the neck resonance by

the player's supporting arm. A c lear difference between the curves is

a lso seen above 200 HZ, probably ref lect ing the influence of the

player's supporting knee on the plate modes.

Eigenmodes of t h e br idge

The properties of the bass bridye i tself have been studied with the

bridge clamped to a rigid support. By driving a t appropriate positions

three eigenmocles of the bass bridge were found, Fig. 11 a) . A s the bass

and cello bridge are of very similar design it i s reasonable to conclude

that these eigemndes are the same as those of the cello bridge reported

by Xeinecke (1973), Fig. 11 b). The lower resonance frequencies of the

bass bridge due to larger dimensions reflect a necessary matching of the

bridge t o the lower resonance frequencies of the bass body. This is

illustrated in Fig. 1 2 which shows the frequencies of the three hridye

resonances together with the f i r s t top plate resonance (T1) for two

basses and two cellos. Corresponding typical values for the violin are

also included in the figure. The influence of the bridge resonances on

the input admittance curve can be seen as wide humps around the rneasured

resonance frequencies of the bridge, cf Fig. 4.

Desirable c h a r a c t e r i s t i c s of t h e i n ~ u t admittance curve f o r basses

Some desirable characteristics of the input admittance curve of a

double bass can be summarized from Fig. 4, 5 and 6. The inpt admittance

curve should show high, d i s t inc t peaks in the low frequency region, a

l i t t l e separated in frequency. The rnab resonances in this range are tile

FIelmholtz a i r resonance (AO) and the f i r s t top plate resonance (Tl), the

l a t t e r probably i n combination with body resonances C3 and C4. More

specifically it is desirable that the resonance frequency of A0 is not

higher than GO H z and the T1-C3-C4 group not higher than 100 Hz.

Expressed i n bass making terms this rneans a large instrument with thin

top and back plates. In tile r.lic1-frequmicy range between 150 - 400 Hz it 1 is advantageous i f the input admittance curve exhibits a p t t e r n with

I I equally spaced peaks. The properties of trlis frequency range is set by I

higher plate modes. Finally, above 400 Hz it is desirable with a strong

t

STL-QPSR 4/1982 1'66.

influence from the lowest bridge resonance, giving a pronounced rise in

the curve.

The term desirable has been used above only with the price of tile

instrument as a guide. No formal tes t has been undertaken as regards the

correlation between the ck~aracteristics of the input admittance curve,

stated as desirable above, and the tone qual i ty of the instrument.

However, it can be assumed tha t the price of the instrument is a

reasonable re l iab le indicatior of the tone quali ty of the instrument

with few exceptions. Inforr:~al playing t e s t s by a professional bass

player a lso support the rank ordering according t o prices. The

connection between the characteristics of the input admittance curve and

the tone quali ty of the instrument w i l l be discussed i n the next

section.

Tone a u a l i t v versus i n ~ u t admittance

The measurement of the input admittance is a re l iab le and

straightforward way of recording a "fingerprint" of tile eigenmodes of

an instrument. Ilowever, knowledge of the connections between tlle tone

quali ty of an instrument and the characteristics of the mrrespnding

input admittance curve is however yet rudimentary. One question i s

whether the tone quali ty of an instrument car1 be predicted by

considering only a few parameters of the input admittance curve.

In a recent work on the tone quality of tlle violin incorporating a

large number of instrurnents (Alonso Moral & Jansson 1982b), it was

found that a weighted sum of four parameters extract& from the input

admittance curve cmrrelated well with the tone quality of the instrument

as rated by experienced violin players. Tall, equally high peaks in the

low frequency range followed by a steep r i s e a t higher frequencies of

the input admittance curve was found to correspond t o high rates of tone

quality, cf Fig. 3 (top).

Only preliminary suggestions have bee11 made as t o why these

characteristics favors the tone quality of the violin. 'The high ,peaks a t

low frequencies nay give a strong response in the low regis ter of the

I instrument. Equally high peaks nay give an even response between !

adjacent notes. A steep r i s e i n the input admittance curve towards

higher frequencies rnay be rlecessary t o compensate for a decreasing

radiation efficiency ( Alonso T,loral & Jarissorl, personal corfi~,~unicatiorl).

The input admittance curves of the violin, ce l lo and bass i n Fig.

3, which are a l l of high quali ty, show a s imilar pattern. Prominent

peaks i n the lower frequency region, a l i t t l e separated in frequency are

followed by a marked r i s e in the curve a t higher frequencies. The

criteria of the input admittance curve which were f o u l favorable to

the tone quality of the violin can thus be assumed apgly also t o the

ce l lo and bass. Support for these assumptions can be found in Fig. 4,

where input admittance curves of basses with prices ranging from low

(top) t o very high (bottom) were compared. A n ap2lication of the

characteristics given above w i l l give esser~tially the same rank order as

the prices.

TONE OUALITY

One desirable character is t ic of a double bass i s a " fu l l bass

sound" i n the low register. This section is focussed on this aspect of

the tone quality. The term "full" here is used t o describe a deep bass

sound, whose character resembles a low organ flue pipe.

Radiated swectra

All members of the bowed string family are small as compared to the

wavelenyth of the low spectral components of the lowest riotes of the

instrument. This leads t o a weakly radiated fundamental in the lowest

register. A s an example it can be mentioned that the violin radiates a

fundarnerltal i n the lowest register which is a u t 25 dB weaker than the

strongest partial (Meyer 1972). This fact is especially embarrassing

as regards the bass, as there is rlo instrument in the string ensemble to

substitute partials in the low-frequency region.

The most efficient way t o produce and radiate a strong fundamental

i s t o make a large instrument. However, i f a rnusician is t o be able t o

play the i~lstrurnerlt a limit for the s ize of the bass is set . The Large ' Bass of the New Violin Octet (CMH LB) with an overall length of 214 cm I touches tllis l i r n i t of "playability". On the otl~er l w d this bass offers

l

a fully developed ful l bass tone quality i n the low register, as judged

by professional bass players. The fundame~ltal radiated from this bass on

the lowest note is however not especially prominent as cumpard to the

higher partials. This is illustrated in Fig. 13 which shows a comparison

of spectra of isolated tones from some of the basses in ~ i g . 4 and 5,

recorded in an anechoic chamber. On the lowest note E l (upper half of

the figure) the Large Bass (CMH LB) radiates a fundamental which is

almost 20 d B weaker than the second par t ia l . Siinilar proportions

between the fundamental and the higher harmonics a re seen in the

spectras of the valuable bass (SD) discussed earlier and the bass (BL).

The tone q u a l i t y of these two basses were never the less a l s o

characterized as full.

The inexpensive i n s t m a l t (GK) produces a very weak fundamental on

the lowest note, and the second hannonic is also weak as compared with

the other basses. Three semitones higher, Fig. 13 (lower ha l f ) , the

fundamental has gained considerably in a l l basses. still the inexpensive

instrument (GR) radiates a relatively weak fundamental.

The tone characteristics of the three basses with a pronounced ful l

tone quali ty (CMH LB, BL, S D ) seem t o be related t o the low resonance

frequencies oE the Helmholtz resonance and the f i r s t top plate resonance

in these instruments, cf Fig. 4 and 5. These resorlances w i l l enhance

the fundamental and second partial respectively in the lowest register.

However, the promotion of the furrdamental by the Helmholtz resonance is

not sufficient to make the radiated fundamental as strong as the other

pa r t i a l s on the lowest notes. The d i f f i cu l t i e s associated with the

radiation of a low fundamental i s always considerable, as can be

inferred fran the following.

The wavelength of the Eundamerltal of the lowest mte on the bass

is 8 m. This should be compared with the dimensions of the body of the

instru~nent, roughly 1 x 1 m. The source is undoubtedly small as

cor~~pared t o the wavelength a t t h i s low frequency , which l i m i t s the

possibilities of radiating sound. For the second partial tJle dimensions

of the source are almost a quarter of a wavelength which gives a much

more efficierit radiation.

The spectrum analysis yields as a resul t tha t the fundamental

i tself contributes to a f u l l tone quality. However, it is not necessary

tha t the fundamental is stronger than the other pa r t i a l s in order t o

i ensure a ful l bass tone sound. I t is sufficient that the fundanlentdl is 1

I present i n tlie radiated sound w i t h reasonable strength and tilat the 1

instrument radiates a strony second arld possibly also a strong third I

harmonic.

STL-QPSR 4/1982

0 500 IWO FREUUtNCY I H z I

0 500 FREOUENY I H z I

:41Hz]

FREWENCY l H z l FREWENCY 111~1

;: 2 3 0

8 s t - 2 m $; a o z 0

n u a z 5 E

-- -. . . .

0 so0 1000 0 500 loo0 FREOUENCY IHZ I FRLOUENCY I Hz)

s 2 3 0 g 2 5 ; C -_ a o

? m n u

5 E 5 E

SO0 l M 0 0 MO WO FREOUENLY 111z 1 FRCOUENCI (Hz1

Fig. 13. Radiated spectra of four double basses showing the note El =41 Hz (upper half of the figure) and GI =49 Hz ( lowr half) played mezzoforte. The recording was made approxi- mately 1 m in front of the instnrment in an anechoic chamber. The abbreviations refer t o the names of the makers in Figs. 4 and 5.

I

STL-QPSR 4/1982

Long T i m e Average S p e c t r a (LTAS)

The radia ted sound was a l s o inves t iga ted using an a l t e r n a t i v e

method. Chromatic two octave scales from seven basses were recorded with

four i,licrophones i n a l a rge , very reverberant room. l'he s c a l e s w e r e

analyzed by means of LTAS, which gave an es t ima t ion of t h e rad ia ted

sound p w e r i n 1/3-octave bands. In tihis way differerlces i n the radiated

sound among t h e instruments could be observed a s a funct ion of

frequency. I t was hypothesized t h a t the varying tone q u a l i t y of t h e

instruments tested should be reflected i n the LfFM. More specifically,

t h e acoust ic c h a r a c t e r i s t i c s of t h e f u l l tone q u a l i t y of some of t h e

instmnent was expected t o show up clearly i n these measurements.

The r e s u l t i s shown i n Fig. 14 i n which LTAS of t h r e e basses a r e

cornpard. Each LTAS is an average over several recordings and over the

four recorded channels. A s expected t h e rnethod d i sp lays t h e in£ luerice

frorn t h e unusually low resonance frequencies of A0 and T1 i n t h e

radia ted sound f o r t h e two basses (CMH LB) and (BL), c f Fig. 4 and 5.

These resonances can thus be assuned t o give i rnpr tant co~ltributions t o

the f u l l bass sound of these instruments a s discussed earl ier .

Tie curve f o r t h e bass ( E F J ) is t y p i c a l f o r t h e o the r f i v e basses

analyzed. The d i f fe rences i n LTAS among these o the r basses w e r e not

significant, although the instruments represented a wide range of tone

quality. In a s i r ~ i l a r experiment with the viol in ( W r i e l s s o ~ l & Jarlsson

1979) it was found t h a t c e r t a i n c h a r a c t e r i s t i c d i f fe rences i n LTAS

between high a113 low q u a l i t y r a t ed instruments could be observed. The

nunber of instruments in t h a t inves t iga t ion was however considerably

larger tlml in t h i s study.

Further, it is known t h a t t h e usefulness of t h e LTAS a n a l y s i s f o r

t h e purpose of es t imat ing tone q u a l i t y is l a r g e l y dependent on t h e

maruler of playing the instruments (Jarlsson, personal comtnunication) . The

variations between players and between d i f ferent recordings of the same

player can ue considerable a s shown i n Fig. 15. This f igure sllows a

cornpar ison between a professional and a non-profess iona l bass player.

1 The professional player is seen to produce a stronger fundarnerltal in t;t~e 1 low r e g i s t e r (40 - 00 Hz) than t h e non-professional player . The I

di f fe rence between the two recordings of t h e profess ional player is ,

r a t h e r l a rye i n t h e low freyilerlcy range. This is probably due t o

STGQPSR 4/1982 171.

LEVEL

10dB

FREQUENCY ( Hz I

LEVEL

10 d?

PROFESSIONAL REC 1 - - - PROFESSIONAL REC 2

50 100 200 500 1000 2000

FREQUENCY (Hz

Fig. 14. Ung T i m Average s .ctra (LTAS) of c h r m t i c scales of three double basses ! played in a very reverberant I

room. Each LTAS is an aver- I

age over four microphones and several recordings. The ab- 1 breviations to the right of the symbols refer to the nams i I of the rrakers in Figs. 4 and 5.

F . 15. Conparison of LTAS of different record- ings of the same instru- mt.

BRIDGE Fiq. 16. Conparison of the magnitude of the vibrations a t the driving point (top) and end pin (bottom). 'Ikbe driving point is m k e d with a triangle. The accelero- mte r measured the vertical conpnent of the end pin vibrations.

FREQUENCY ( Hz 1

be obtained from the end pin vibrations depends on the properties of the

suppr t ing floor. A s tlle vibration amplitude is s r n a l l a large area rnust

be s e t i n v i b r a t i o n i f any s i g n i f i c a n t con t r ibu t ion to the r a d i a t e d

sound i s t o b e o b t a i n e d . The p r a c t i c a l e x p e r i e n c e i s t ha t t h e

reinforcement of the the low frequerlcy reg is te r may be substant ial under

s u i t a b l e cmnditions.

Summarv o f t o n e a u a l i t v

The a n a l y s i s of t h e tone q u a l i t y h a s focussed on t h e a spec t of a

f u l l bass tone. It was found t h a t an instrument which was characterized

by a f u l l bass tone q u a l i t y i n the low r e g i s t e r , r ad ia t ed a s t ronger

fundamental than o t h e r basses. Ilowever, even t h e basses possessing a

f u l l tone qual i ty radiated a fundamental considerably weaker than the

second and t h i r d p a r t i a l s . Low values of t h e Helmholtz and f i r s t t o p

p l a t e resonance were found t o favor t h e fundamental and t h e lower

par t ia l s .

An analysis using LI'AS gave an estimation of the spectral content

of t h e r ad ia t ed sound. A boos t a t l o w frequencies due to t h e in f luence

of low A0 and T1-resonances could be observed i.11 the LTAS of two basses

with pronounced f u l l tone quality. N o other connections between a tone

qual i ty and radiated sound could -be observed i11 this analysis.

Acknowledgements

Tne author thanks Erik Jansson, Jesus Alonso Moral, Garan Lmdberg

and Alf ~e te r se 'n for generous cooperation.

- I 1 STL-QPSR 4/1982

174.

References

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