MANDOLINS

MUSIC 318 MINICOURSE ON PLUCKED STRING INSTRUMENTS

“The Acoustics of Mandolins” (D. Cohen, T. Rossing, Acoustical Science and Technology 24, 1 (2003).The Classical Mandolin, Sparks (1995)

MANDOLIN FAMILY

THE MANDOLIN FAMILY INCLUDES FOUR INSTRUMENTS, EACH HAVING EIGHT STRINGS IN FOUR DOUBLE COURSES. THE COURSES ARE TUNED IN INTERVALS OF FIFTHS, AS ARE VIOLINS.The mandolin is tuned G3, D4, A4, E5THE MANDOLA IS TUNED C3,G3,D4,A4THE OCTAVE MANDOLIN IS TUNED C2,G2,D3,A3THE MANDOCELLO IS TUNED

A VARIANT OF THE MANDOCELLO IS THE FIVE-COURSE LIUTO TUNED C2,G2,D3,A3,G2A MANDOBASS WAS ALSO MADE DURING THE EARLY 20TH CENTURY

MANDOLIN FAMILY

MANDOLIN FAMILY BY DAVID COHEN: F MANDOLIN, A MANDOLA, C# OCTAVE MANDOLIN, A MANDOCELLO

HISTORY

THE MANDOLIN APPEARS TO HAVE DESCENDED FROM THE GITTERN IN ITALY, WHERE IT TOOK TWO FORMS. ONE WAS THE MILANESE MANDOLIN WITH SIX DOUBLE COURSES OF STRINGS TUNED IN 3RDS AND 4THS. THE OTHER WAS THE NEAPOLITAN MANDOLIN WITH FOUR DOUBLE COURSES TUNED IN 5THS (LIKE THE MODERN MANDOLIN). THE NEAPOLITAN MANDOLIN ULTIMATELY PREVAILED.

THE MANDOLIN BECAME A CONCERT INSTRUMENT IN 19TH CENTURY EUROPE. VIVALDI, MOZART, BEETHOVEN, MASAGNI, LEONCAVALLO, PUCCINI, AND OTHER COMPOSERS WROTE MUSIC SPECIFICALLY FOR THE MANDOLIN. THE MANDOLIN WAS BROUGHT TO AMERICA DURING THE 19TH CENTURY BY ITALIAN IMMIGRANTS. C.F.MARTIN, LYON & HEALY, AND OTHERS MANUFACTURED MANDOLINS.

IN 1895 ORVILLE GIBSON APPLIED FOR A PATENT FOR A NEW TYPE OF MANDOLIN. HE DISPENSED WITH THE BOWL BACK AND CARVED AN ARCHED TOP AND BACK FROM SINGLE OR BOOK MATCHED PIECES OF WOOD, AS IN THE VIOLIN. GIBSON MANDOLINS BECAME THE DOMINANT TYPE OF MANDOLIN IN AMERICA. LLOYD LEAR DESIGNED THE STYPE 5 FAMILY OF INSTRUMENTS (INCLUDING THE F5 WHICH HAD f-HOLES LIKE A VIOLIN.

BRACING PATTERNS USED ON TOP PLATES

TYPES OF MANDOLINS

NEAPOLITAN MANDOLIN—ALSO KNOWN AS “BOWLBACK” MANDOLINS, THESE INSTRUMENTS HAVE DEEP BOWL-SHAPED BODY MADE FROM STRIPS OF HARDWOOD ASSEMBLED OVER A MOLD. THE BOWL IS USUALLY NOT BRACED BUT MAY BE LINED WITH PAPER. THE TOP IS USUALLY LADDER BRACED, AND THESE MANDOLINS HAVE A SINGLE OVAL OR ROUND SOUND HOLE.

FLATBACK MANDOLIN---ALSO KNOWN AS “PANCAKE” MANDOLINS, THE TOPS AND BACKS MAY BE TRULY FLAT OR WITH A SLIGHT ARCH . TOP AND BACK ARE USUALLY LADDER BRACED, ALTHOUGH THE TOP PLATE MAY HAVE A SINGLE TRANSVERSE BRACE BETWEEN THE BRIDGE AND A SINGLE OVAL OR ROUND SOUND HOLE.

CYLINDERBACK MANDOLINS---THE EARLY 20TH CENTURY SAW A NUMBEER OF UNIQUE DESIGNS INTENDED TO IMPROVE VOLUME AND/OR TONE QUALITY. ONE SUCH DESIGN WAS THE VEGA “CYLINDERBACK” MANDOLIN WITH A FLAT TOP PLATE EXCEPT FOR A PLIAGE AT THE BRIDGE LOCATION AND A MODIFIED LADDER BRACING.

NEAPOLITAN MANDOLIN WASHBURN FLATBACK MANDOLIN

VEGA CYLINDERBACK MANDOLIN GIBSON F4 ARCHTOP MANDOLIN

TYPES OF MANDOLINS

ARCHTOP MANDOLINS WITH OVAL SOUND HOLE---TOP AND BACK PLATES ARE CARVED INTO AN ARCH AS ARE VIOLIN PLATES. TOP PLATES MAY HAVE A SINGLE TRANSVERSE BRANCE, THOUGH SOME LUTHIERS USE X-BRACING. BACK PLATES ARE NOT BRACED.

ARCHTOP MANDOLINS WITH f-HOLES---TOP AND BACK PLATES ARE CARVED INTO AN ARCH. TOP PLATES ARE COMMONLY BRACED EITHER WITH PARALLEL LONGITUDINAL TONE BARS OR WITH X-BRACING. BACK PLATES ARE NOT BRACED. BOTH OVAL-HOLE AND f-HOLE ARCHTOPS HAVE BEEN MADE IN THE A-BODY (TEARDROP) STYLE AND THE F-BODY (TEARDROP WITH UPPER BOUT IONIC SCROLL) STYLE.

MANDOLAS, OCTAVE MANDOLINS, AND MANDOCELLOS---THE LARGER MANDOLIN FAMILY INSTRUMENTS ARE FOUND IN ALL OF THE ABOVE VARIETIES. MANDOLA SCALE LENGTHS VARY FROM THE ORIGINAL GIBSON SCALE LENGTH OF 400 mm TO 432 mm AND EVEN LONGER. OCTAVE MANDOLINS VARY FROM 480 mm TO 620 mm. THE MOST COMMON SCALE LENGTH FOR MANDOCELLOS IS THE ORGINAL GIBSON LENGTH 630 mm.

MANDOLIN FAMILY

MANDOLIN FAMILY BY DAVID COHEN: F MANDOLIN, A MANDOLA, C# OCTAVE MANDOLIN, A MANDOCELLO

MODES OF VIBRATION

THE COMPLEX VIBRATION OF A SYSTEM CAN BE CONVENIENTLY DESCRIBED IN TERMS OF NORMAL MODES OF VIBRATION. A NORMAL MODE IS CHARACTERISTIC OF THE VIBRATING OBJECT ITSELF AND IS NOT DEPENDENT ON HOW THE OBJECT IS EXCITED OR OBSERVED. FOR A MANDOLIN, A NORMAL MODE IS DETERMINED BY THE COUPLED MOTION OF ITS STRINGS, BRIDGE, TOP AND BACK PLATES, SIDES, ENCLOSED AIR CAVITY, AND THE NECK/HEADSTOCK/FINGERBOARD ASSEMBLY.

THE DEFLECTION OF AN OBJECT AT A PARTICULAR FREQUENCY IS CALLED AN OPERATING DEFLECTION SHAPE (ODS). AN ODS MAY RESULT FROM THE EXCITATION OF MORE THAN ONE NORMAL MODE. A CURVE FITTING PROGRAM MAY BE USED TO DETERMINE THE INDIVIDUAL NORMAL MODES FROM THE ODS.

HOLOGRAPHIC INTERFEROMETRY

EXPERIMENTAL MODAL ANALYSIS MY BE ACCOMPLISHED USING ANY TRANSDUCER CAPABLE OF DETECTING MOTION, BUT HOLOGRAPHIC INTERFEROMETRY OFFERS THE BEST SPATIAL RESOLUTION. ELECTRONIC TV HOLOGRAPHY IS A FAST AND CONVENIENT WAY TO RECORD ODSs FROM WHICH NORMAL MODES CAN BE DETERMINED.

SYSTEM USED FOR TV HOLOGRAPHY

NORMAL MODES OF VIBRATION

(1,0) MODE IN TOP (left) AND BACK PLATE (right) AT 474 Hz

(2,0) MODE AT 796 Hz (left) AND (3,0) MODE AT 929 Hz IN MANDOLA TOP PLATE

MODE SHAPES IN A 1924 GIBSON F5 MANDOLIN

TOP PLATE

472 Hz

868 Hz

1118 Hz

BACK PLATE

278 Hz

778 Hz

1118 Hz

MOTION OF AIR IN A MANDOLIN

AIR MOVES IN AND OUT OF SOUND HOLE(s)

AIR MOVES FROM UPPER TO LOWER BOUT WITH A NODE AT THE CENTER (DASHED LINE)

AIR MOVES FROM ONE SIDE OF CAVITY TO THE OTHER

PLATE/AIR PHASE RELATIONSHIPS IN AN OVAL HOLE MANDOLIN

HOLOGRAPHIC INTERFEROGRAMS SHOWING VIBRATIONAL MODES OF A MANDOLINTOP (left) BACK (right)

ONLY FOR THE LOWEST TWO MODES ARE THE PATTERNS SIMILAR IN TOP AND BACK

FREQUENCY RESPONSE

ACCELERANCE OF MANDOLIN (upper) AND MANDOLA (lower)

RANGES OF MODAL FREQUENCIES IN MANDOLINS AND MANDOLAS

Instruments Neapolitanmandolins1,2

Vega 205 cylinderbackmandolin3

Archtop4-8 Archtop9-11 archtop mandola12 archtop mandola13

soundhole round or oval oval oval f-holes or c-holes oval c-holes

bracing ladder modified ladder single soundhole tone bars or asymmetric radial

single soundhole(has Virzi)

asymmetric radial

mode

(0,0) (a) (b) ©

496-549529-618

202403439

200-210358-441465-491

237-318345-452

173346

234368

(1,0) (a) (b)

792-1012 876 446-603 472-482605

439540

402

(0,1) (a) (b)

658-769 599 717-819902

620-774767-824

485568

558666

(1,1) (a) (b)

13571471

730 746-876873-1033

821-896933-953

771 728

(2,0) 1092-1380 not observed 1005-1089 837-1118 not observed 796

f0 183-200 209 205-211 283-301 185 218

f1 815 795 725-875 747-913 629 556

f2 not observed 1050 978-10601280-1300(with Virzi)

1050-1082 1157 792

SUSTAIN

THE VIBRATIONAL ENERGY STORED IN THE STRING IS TRANSFERRED THROUGH THE BRIDGE TO THE PLATES (AND THE ENCLOSED AIR) WHICH RADIATE THE SOUND. SOME OF THE ENERGY IS LOST AT EACH STEP. THE RADIATED SOUND DECREASES EXPONENTIALLY WITH A CHARACTERISTIC TIME OR DECAY TIME WHICH IS THE TIME FOR THE AMPLITUDE TO DECREASE TO 1/e (37%) OF ITS INITIAL VALUE.

Frequency, Hz

100 200 300 400 500 600 700 800 900

Cha

ract

eris

tic

tim

e, s

0.0

0.1

0.2

0.3

0.4

0.5

1920 Calace (Neapolitan) mandolin

CHARACTERISTIC (DECAY) TIMES vs FREQUENCY FOR TWO MANDOLINS

MEET DAVID COHEN IN HIS MANDOLIN SHOP