1.
GUITARS and LUTES
MUSIC 318 MINICOURSE ON PLUCKED STRING INSTRUMENTS
Physics of Musical Instruments Chap 9
Science of Sound Chap. 10
“Guitar as a reflex enclosure,” G. Caldersmith,
JASA 63, 1566 (1978).
Computational Mechanics of the Classical
Guitar, R. Bader (Springer, 2005)

2.
LUTE-TYPE INSTRUMENTS HAVE A LONG HISTORY.
VARIOUS TYPES OF NECKED CHORDOPHONES WERE IN USE IN ANCIENT EGYPTIAN, HITTITE,
GREEK, ROMAN, TURKISH, CHINESE, AND OTHER CULTURES. IN THE 9TH CENTURY, MOORS
BROUGHT THE OUD (UD) TO SPAIN.
IN THE 15TH CENTURY THE VIHUELA BECAME POPULAR IN SPAIN AND PORTUGAL. ABOUT
THE SAME TIME GUITARS WITH FOUR DOUBLE STRINGS BECAME POPULAR. ITALY BECAME
THE CENTER OF THE GUITAR WORLD.
THE EARLIEST KNOWN SIX-STRING GUITAR WAS BUILT IN 1779 BY GAETANO VINACCIA IN
ITALY. STRADIVARIUS IS KNOWN TO HAVE BUILT SEVERAL GUITARS. COMPOSERS WHO
PLAYED THE GUITAR INCLUDE ROSSINI, VERDI, VON WEBER, AND SCHUBERT. FERNANDO
SOR WAS THE FIRST OF A LONG LINE OF SPANISH VIRTUOSOS AND COMPOSERS FOR THE
GUITAR.
THE SPANISH LUTHIER ANTONIO DE TORRES JURADO (1817-1892) CONTRIBUTED MUCH TO
THE DEVELOPMENT OF THE MODERN CLASSICAL GUITAR WHEN HE ENLARGED THE BODY
AND INTRODUCED A FAN-SHAPTED PATTERN OF BRACES TO THE TOP PLATE. FRANCISCO
TARREGA (1852-1909), PERHAPS THE GREATEST OF THE 19TH CENTURY PLAYERS,
INTRODUCED THE APOYANDO STROKE AND EXTENDED THE EXPRESSIVE CAPABILITIES OF
THE GUITAR.

3.
THE GUITAR

4.
TYPES OF ACOUSTIC GUITARS
CLASSICAL NYLON
FLAMENCO STRINGS
FLAT TOP
ARCH TOP
STEEL STRINGS

5.
CLASSICAL GUITAR FOLK GUITAR
(STEEL STRINGS)
PATTERNS OF GUITAR STRUTTING

6.
THE GUITAR AS A SYSTEM OF COUPLED
OSCILLATORS

7.
STRING PLUCKED
AT ITS MIDPOINT

8.
STRING
PLUCKED 1/5
OF ITS
LENGTH
FROM THE
BRIDGE

9.
ESTIMATING
FORCES ON
THE BRIDGE

10.
FREQUENCY RESPONSE OF A GUITAR
SOUND SPECTRUM FOR A SINUSOIDAL FORCE APPLIED PERPENDICULAR TO THE BRIDGE.
NOTE STRONG PEAKS AROUND 100 AND 200 Hz, SEVERAL PEAKS AROUND 400-700 Hz, AND
A COLLECTION OF PEAKS IN THE REGION OF 1500 TO 2500 Hz.
PEAK LEVELS OF THE RESONANCE NEAR 400 Hz CORRELATES ESPECIALLY WELL WITH THE
QUALITY RATING OF THE GUITAR BY LISTENERS (Meyer, 1983).

11.
VIBRATIONS OF THE GUITAR BODY
THE COMPLEX VIBRATIONS OF THE GUITAR BODY CAN BE DESCRIBED IN TERMS OF
NORMAL MODES OF VIBRATION. NORMAL MODES ARE INDEPENDENT WAYS IN
WHICH A STRUCTURE VIBRATES. THEY ARE CHARACTERIZED BY NODAL LINES AND
ANTI-NODES, AS WELL AS BY MODAL FREQUENCY AND DAMPING.
MODE SHAPES ARE UNIQUE FOR A STRUCTURE, WHEREAS THE DEFLECTION OF A
STRUCTURE AT A PARTICULAR FREQUENCY, CALLED AN OPERATING DEFLECTION
SHAPE, MAY RESULT FROM THE EXCITATION OF MORE THAN ONE NORMAL MODE.
MODAL TESTING IS A SYSTEMATIC METHOD FOR IDENTIFICATION OF THE MODAL
PARAMETERS. IN GUITAR TESTING, THE EXCITATION IS USUALLY A SINUSOIDAL
FORCE OR AN IMPULSE. DETECTION METHODS INCLUDE:
MEASURING ACCELERATION WITH AN ACCELEROMETER;
MEASURING SURFACE VELOCITY WITH A VIBROMETER;
DETERMINING DEFLECTION BY MEANS OF HOLOGRAPHIC INTERFEROMETRY;
DETERMINING MODE SHAPES WITH CHLADNI PATTERNS.

12.
VIBRATION MODES OF COMPONENT PARTS
VIBRATION MODES OF A GUITAR PLATE BLANK (WITHOUT BRACES) WITH A FREE EDGE

13.
VIBRATION MODES OF COMPONENT PARTS
CLASSICAL GUITAR TOP PLATE WITH FAN BRACING

14.
HOLOGRAPHIC
INTERFEROMETRY
MODAL
TESTING WITH
INPULSE
EXCITATION

15.
VIBRATION MODES OF COMPONENT PARTS
VIBRATION MODES OF A CLASSICAL GUITAR GOP PLATE GLUED TO FIXED RIBS BUT
WITHOUT A BACK.

16.
MODES OF TOP PLATE, BACK PLATE AND AIR CAVITY

17.
VIBRATIONAL MODES OF A CLASSICAL GUITAR

18.
CLASSICAL GUITARS WITH RADIAL BRACING
Torres Hauser Eban

19.
MODES OF A
GUITAR WITH
RADIAL BRACING

20.
ANATOMY OF A STEEL STRING ACOUSTIC GUITAR

21.
COUPLING IN A MARTIN D28 FOLK GUITAR

22.
THREE LOWEST MODES OF A MARTIN D28 FOLK GUITAR
(BASED ON (0,0) MOTION OF TOP AND BACK)

23.
TWO MODES BASED ON (1,0) MOTION OF PLATES

24.
MODES OF A STEEL STRING
GUITAR
(0,0) MODE AT 97 Hz
(0,0) MODE AT 205 Hz

25.
(1,0) MODE OF A STEEL STRING GUITAR
DREADNOUGHT GUITAR AT 390 Hz

26.
(1,1) MODE IN STEEL STRING FOLK GUITAR
DREADNOUGHT BODY 450 Hz

27.
RESONANCES OF CLASSICAL AND FOLK GUITARS

28.
COUPLING OF TOP PLATE TO THE AIR CAVITY:
THE TWO-OSCILLATOR MODEL
Kp and mp ARE STIFFNESS AND
MASS OF TOP PLATE.
mh IS MASS OF AIR IN SOUND
HOLE.
V IS VOLUME OF AIR CAVITY.

29.
COUPLING TO THE BACK PLATE:
THE THREE-OSCILLATOR MODEL
mp and Kp ARE MASS AND STIFFNESS
OF TOP PLATE;
mb and Kb ARE MASS AND STIFFNESS
OF BACK PLATE;
Mh IS MASS OF AIR IN SOUND HOLE
V IS AIR CAVITY VOLUME
3 RESONANCES WITH 2 ANTI-RESONANCES
BETWEEN THEM

30.
STRING FORCES
FORCES PERPENDICULAR
AND PARALLEL TO THE
BRIDGE EXCITE
DIFFERENT RESONANCES
AND RESULT IN TONES
THAT HAVE DIFFERENT
DECAY RATES.
PLUCKING PARALLEL TO
THE BRIDGE PRODUCES
A WEAK BUT LONG-
LASTING TONE.
PLUCKING AT AN ANGLE
GIVES A COMPOUND
DECAY RATE

31.
APOYANDO AND TIRANDO STROKES
IN THE APOYANDO STROKE, THE FINGER COMES TO REST ON AN ADJACENT STRING
IN THE TIRANDO STROKE, IT RISES ENOUGH TO CLEAR IT

32.
SOUND RADIATION
MARTIN D28 FOLK GUITAR DRIVEN BY A SINUSOIDAL FORCE OF 0.15 N APPLIED TO THE
TREBLE SIDE OF THE BRIDGE. SOLID CURVE IS SOUND SPECTRUM; DASHED CURVE IS
ACCELERATION AT THE DRVING POINT

33.
SOUND RADIATION
SOUND RADIATION PATTERNS AT THREE
RESONANCES IN A MARTIN D28 GUITAR

34.
SOUND RADIATION AND SOUND DECAY
COMPARISON OF THE SOUND LEVEL OF THE FUNDAMENTALS OF PLAYED NOTES (BARS)
TO THE FREQUENCY RESPONSE FUNCTION (SOLID CURVE)

35.
QUALITY
1. PEAK LEVEL OF THE THIRD RESONANCE (AROUND 400 Hz)
2. AMOUNT BY WHICH THIS RESONANCE STANDS ABOVE THE RESONANCE CURVE
3. THE SHARNESS (Q-VALUE) OF THIS RESONANCE
4. THE AVERAGE LEVEL OF 1/3-OCTAVE BANDS IN THE RANGE 80-125 Hz
5. THE AVERAGE LEVEL OF 1/3-OCTAVE BANDS IN THE RANGE 250-400 Hz
6. THE AVERAGE LEVEL OF 1/3-OCTAVE BANDS IN THE RANGE 315-5005 Hz
ACCORDING TO JANSSON (2002), “TONAL STRENGTH” OR CARRYING POWER IS THE
MOST IMPORTANT QUALITY CRITERION WITH TONE LENGTH AND TIMBRE ALSO BEING
IMPORTANT.
Meyer (1983) FOUND THE FOLLOWING OBJECTIVE CRITERIA TO BEST CORRELATE WITH
QUALITY:

36.
TOP PLATE THICKNESS
RICHARDSON (1998) FOUND THAT REDUCING “EFFECTIVE MASS” HAS A GREAT EFFECT
ON RADIATION OF HIGH-FREQUENCY SOUND.
AUSTRALIAN LUTHIER GREG SMALLMAN, WHO BUILDS GUITARS FOR JOHN WILLIAMS,
USES LIGHTWEIGHT TOP PLATES SUPPORTED BY A LATTICE OF BRACES WHOSE
THICKNESSES ARE TAPERED AWAY FROM THE BRIDGE. SMALLMAN GENERALLY USES
CARBON-FIBER-EPOXY STRUTS IN ORDER TO ACHIEVE HIGH STIFFNESS-TO-MASS RATIO.
SMALLMAN GUITAR GUITAR BY GRAHAM CALDERSMITH

37.
FAMILY OF SCALED GUITARS
GRAHAM CALDERSMITH (AUSTRALIA) HAS CREATED A FAMILY OF GUITARS ESPECIALLY
DESIGNED FOR ENSEMBLE PERFORMANCE. HIS CLASSICAL GUITAR FMILY, INCLUDING A
TREBLE GUITAR, A BARITONE GUITAR, AND A BASS GUITAR IN ADDITION TO THE
CONVENTIONAL GUITAR, HAS BEEN RECORDED EXTENSIVELY BY THE AUSTRALIAN
GUITAR QUARTET.
HE HAS ALSO CREATED A FAMILY OF SCALED FOLK GUITARS.

38.
PORTUGESE GUITARS
PEAR-SHAPED PORTUGESE GUITARS ARE ESPECIALLY USED TO ACCOMPANY FADO
MUSIC. THEY HAVE 6 COURSES OF DOUBLE STRINGS AND HAVE BEEN USED IN
PORTUGAL SINCE THE 13TH CENTURY. THE TOP PLATE MAY BE SLIGHTLY CURVED,
WHILE THE BACK PLATE IS USUALLY FLAT.
PORTUGESES GUITARS (left to right): LISBON, COIMBRA, AND PORTO MODELS

39.
VIBRATIONAL BEHAVIOR
D
Hv(w)
[dB
(m/s2/
N)]
H
[d
(u
b
275 Hz 360 Hz 635 Hz
ACCELERANCE OF PORTUGESE GUITAR

40.
GYPSY GUITAR
THE GYPSY GUITAR, KNOWN IN FRANCE AS THE
MANOUCHE GUITAR, GAINED POPULARITY IN
THE LATE 1920s. PLAYED BY DJANGO
REINHARDT THROUGHOUT HIS CAREER, THE
INSTRUMENT HAS SEEN A REVIVAL IN
INTEREST.
A GYPSY GUITAR MEASURED BY LEE, et al
(2007) SHOWED RESONANCES AROUND 120 Hz,
230 Hz, AND 420 Hz.

41.
SYNTHETIC MATERIALS
TRADITIONALLY GUITARS HAVE TOP PLATES OF SPRUCE OR REDWOOD WITH BACKS
AND RIBS OF ROSEWOOD OR COMPARABLE HARDWOOD.
OVATION GUITARS (BY KAMAN) HAVE BOWLS OF FIBERGLASS .
CHARLES BESNAINOU AND HIS COLLEAGUES IN FRANCE HAVE CONSTRUCTED GUITARS
USING COMPOSITE MATERIALS

42.
ELECTRIC GUITARS

43.
EARLY ELECTRIC GUITARS
Fender
Stratocaster ~1952
Stevie Ray Vaughan
“Lenny”
Gibson
Les Paul ~1957
Eric Clapton
Rickenbacker
model 325 ~1958
John Lennon
Fender
Stratocaster ~1952
Stevie Ray Vaughan
“Lenny”
Gibson
Les Paul ~1957
Eric Clapton
Rickenbacker
model 325 ~1958
John Lennon

44.
MAGNETIC PICKUPS
THE INDUCED VOLTAGE WILL BE ROUGHLY PROPORTIONAL TO THE VERTICAL
VELOCITY OF THE STRING. TRANSVERSE MOTION WILL INDUCE A SMALLER SIGNAL
AT TWICE THE FREQUENCY OF THE STRING VIBRATION SINCE THE FLUX CHANGE
WILL BE THE SAME WHICHEVER DIRECTION THE STRING MOVES.

45.
MAGNETIC PICKUPS
 = 1/20
 = 1/10
 = 1/7
 = 1/5
 = 1/2
string partial n
DEPENDENCE OF THE SENSITIVITY OF
THE nth PARTIAL OF A PLUCKED
NOTE FOR A MAGNETIC PICKUP
LOCATED AT A FRACTIONAL LENGTH
ß OF THE VIBRATING STRING FROM
THE BRIDGE

46.
HUMBUCKING COILS
THE “HUMBUCKING” PICKUP WAS PATENTED IN 1955 BY SETH LOVER FOR GIBSON.
TWO CLOSELY-SPACED PICKUPS ARE PLACED ALONG THE STRING WITH THEIR
OUTPUTS ADDED, BUT WITH THEIR SENSING COILS WOUND IN OPPOSITE DIRECTIONS
SO THAT PICKUP FROM EXTERNAL MAGNETIC FIELDS (“HUM”) IS CANCELLED.
HUMBUCKING COILS HAVE A LARGER INDUCTANCE THAN SINGLE-COIL PICKUPS AND
THUS HAVE A LOWER RESONANCE FREQUENCY, RESULTING IN A “MELLOWER”
SOUND.

47.
LOVER’S
HUMBUCKING
PATENT
(ISSUED 1959)

48.
HUMBUCKING PICKUPS
S N N S
N
S
N
S
S N N S
N
S S N
s
N
single coil
single pole
two magnets
two coils
two poles
three magnets
(a) (b)
S N N S
N
S
N
S
S N N S
N
S
N
S
S N N S
N
S S N
s
N
single coil
single pole
two magnets
two coils
two poles
three magnets
(a) (b)

49.
HUMBUCKING
PICKUP
TOP VIEW
BOTTOM VIEW

50.
MAGNETIC FIELD ABOVE A MAGNET
FUNCTION OF VERTICAL DISPLACEMENT FUNCTION OF HORIZONTAL DISPLACEMENT

51.
SPECTRUM INDUCED IN PICKUP BY VIBRATING WIRE
SINGLE COIL PICKUP
PICKUP WITH MULTIPLE COILS

52.
PIEZOELECTRIC PICKUPS
A PIEZOELECTRIC CRYSTAL HAS AN ASYMMETRIC MOLECTURE STRUCTURE SUCH THAT
A COMPRESSIVE OR BENDING STRAIN CAN INDUCE A VOLTAGE ACROSS THE CRYSTAL.
PIEZOELECTRIC PICKUPS MAY BE MOUNTED ON THE BRIDGE OR ON THE BODY OF THE
GUITAR NEAR THE BRIDGE. THE OVATION ACOUSTO-ELECTRIC GUITAR IS OFTEN GIVEN
CREDIT FOR POPULARIZING PIEZOELECTRIC PICKUPS.
PIEZOELECTRIC PICKUPS HAVE A VERY HIGH OUTPUT IMPEDANCE, AND THUS REQUIRE
PREAMPLIFIERS WITH A HIGH IMPEDANCE INPUT. THEY ARE RELATIVELY FREE OF HUM
DUE TO PICKUP OF STRAY MAGNETIC FIELDS. THEY ARE SUSCEPTIBLE TO IMPULSIVE
FORCE APPLIED TO THE GUITAR BODY.

53.
SIGNAL PROCESSING AND SPECIAL EFFECTS
NEARLY ALL ELECTRIC GUITARS HAVE VOLUME AND TONE CONTROLS MOUNTED ON THE
INSTRUMENT ITSELF.
A FUZZBOX IS A SPECIAL EFFECTS PEDAL THAT COMBINES AN AMPLIFIER AND A CLIPPING
CIRCUIT, WHICH PROVIDES DISTORTION (TURNS A SINE WAVE INTO A SQUARE WAVE) TO
CREATE THE CLASSIC “FUZZ” TONE. SINCE CLIPPING IS A NON-LINEAR PROCESS,
INTERMODULATION WILL ALSO OCCUR, LEADING TO SUMS AND DIFFERENCES OF THE
FREQUENCY COMPONENTS IN THE INPUT SIGNAL. THESE WILL NOT, IN GENERAL, BE
HARMONICALLY RELATED TO THE INPUT SIGNAL, LEADING TO DISSONANCE. TO
MINIMIZE DISSONANCE, SIMPLE CHORDS ARE PREFERRED TO FOUR-NOTE CHORDS WHEN
USING A FUZZBOX.
A PHASER DIVIDES THE OUTPUT SIGNAL INTO TWO PATHS AND CHANGES THE PHASE IN
ONE PATH SO THAT “NOTCHES” OCCUR IN THE SPECTRUM OF THE RE-COMBINED SOUND.
A FLANGER IS A PHASER WITH A GRADUALLY CHANGING DELAY IN ONE CHANNEL THAT
PRODUCES A SWEPT “COMB FILTER” EFFECT. THE NAME COMES FROM THE ORIGINAL
METHOD OF CREATION. A SIGNAL WOULD BE RECORDED ON TWO TAPE MACHINES
SIMULTANEOUSLY; THE OUTPUTS FROM THESE TWO RECORDERS WERE COMBINED AND
RECORDED ON A THIRD RECORDER. PLACING A FINGER ON THE FLANGE OF ONE OF THE
TAPE REELS PROVIDED A VARIABLE DELAY.

54.
SPECIAL EFFECTS
IN 1945 LEO FENDER INTRODUCED WAH-WAH BY MEANS OF A FILTER WITH A
FORMANT STRUCTURE SIMILAR TO THAT OF THE HUMAN VOICE. BY MODIFYING THE
STRENGTHS AND POSITONS OF SUCH FORMANTS WITH A FOOT PEDAL, THE GUITAR
CAN BE MADE TO SOUND LIKE THE HUMAN VOICE.
A VIBRATO ARM (SOMETIMES CALLED A “WHAMMY ARM”) IS A LEVER THAT MAKES
SMALL CHANGES IN STRING TENSION TO PRODUCE A VIBRATO EFFECT.

55.
ELECTRIC GUITARS:
Body vibrations

56.
PEDAL STEEL GUITAR
A PEDAL STEEL GUITAR USES A METAL
SLIDE (THE “STEEL”) TO STOP OR
SHORTEN A STRING RATHER THAN A
FINGER ON THE STRING. IT USES FOOT
PEDALS AND KNEE LEVERS TO AFFECT
THE PITCH, HENCE ITS NAME.
THE MOST POPULAR CONFIGURATION IS
ONE OF TWO NECKS HAVING 10 STRINGS
EACH, BUT 8-STRING AND 12-STRING
NECKS ARE ALSO COMMON.
A PERFORMER USUALLY SITS ON A STOOL OR SEAT. THE RIGHT FOOT IS USED MAINLY TO
OPERATE A VOLUME PEDAL, WHILE THE LEFT FOOT IS PRIMARILY USED TO PRESS ONE OR
MORE OF THE FOOT PEDALS. THE STEEL IS SLID UP AND DOWN THE NECK WHILE TOUCHING
THE STRINGS, LEADING TO A CHARACTERISTIC SLIDING PITCH SOUND.

57.
LAP STEEL GUITAR
LAP STEEL GUITARS MAY BE
EITHER ELECTRIC OR RESONATOR
TYPE. THE STRINGS ARE RAISED
AT BOTH THE NUT AND BRIDGE
ENDS OF THE FINGERBOARD.
THE PLAYER HOLDS A METAL
STEEL SLIDE (OR TONE BAR) TO
CHANGE THE PITCH WHILE THE
RIGHT HAND STRUMS THE
STRING.
BLUES AND ROCK PLAYERS USUALLY TUNE THEIR STRINGS TO D-G-D-G-B-D OR TO E-A-
E-A-C#-E. BLUEGRASS AND COUNTRY PLAYERS MORE OFTEN TUNE TO G-B-D-G-B-D.
(CONVENTIONAL GUITARS ARE TUNE E-A-D-G-B-E).

58.
LUTES

59.
FREQUENCY RESPONSE OF A LUTE
MOBILITY (INPUT ADMITTANCE) AT THE
TREBLE END OF THE BRIDGE
SOUND PRESSURE LEVEL 1 m FROM TOP
PLATE (BELLY)

60.
VIBRATIONAL MODES OF A LUTE
BARRING PATTERN AND NODAL PATTERNS
AT FIVE RESONANCES LOCATIONS OF NODES COMPARED TO THE
BRIDGE AND THE BARS (Firth, 1977)

61.
TURKISH TANBUR (LONG LUTE)

62.
IMPULSE RESPONSE OF TANBUR
VERTICAL IMPULSE
RESPONSE SPECTRUM
HORIZONTAL IMPULSE
RESPONSE SPECTRUM
LONGITUDINAL IMPULSE
RESPONSE SPECTRUM

63.
FOURIER TRANSFORM OF VERTICAL IMPULSE SPECTRUM