GUITARS and LUTES

MUSIC 318 MINICOURSE ON PLUCKED STRING INSTRUMENTS

Physics of Musical Instruments Chap 9Science 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)

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.

THE GUITAR

TYPES OF ACOUSTIC GUITARS

CLASSICAL NYLONFLAMENCO STRINGS

FLAT TOPARCH TOPSTEEL STRINGS

CLASSICAL GUITAR FOLK GUITAR(STEEL STRINGS)

PATTERNS OF GUITAR STRUTTING

THE GUITAR AS A SYSTEM OF COUPLED OSCILLATORS

STRING PLUCKED AT ITS MIDPOINT

STRING PLUCKED 1/5 OF ITS LENGTH FROM THE BRIDGE

ESTIMATING FORCES ON THE BRIDGE

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).

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.

VIBRATION MODES OF COMPONENT PARTS

VIBRATION MODES OF A GUITAR PLATE BLANK (WITHOUT BRACES) WITH A FREE EDGE

VIBRATION MODES OF COMPONENT PARTS

CLASSICAL GUITAR TOP PLATE WITH FAN BRACING

HOLOGRAPHICINTERFEROMETRY

MODAL TESTING WITHINPULSEEXCITATION

VIBRATION MODES OF COMPONENT PARTS

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

MODES OF TOP PLATE, BACK PLATE AND AIR CAVITY

VIBRATIONAL MODES OF A CLASSICAL GUITAR

CLASSICAL GUITARS WITH RADIAL BRACING

Torres Hauser Eban

MODES OF A GUITAR WITHRADIAL BRACING

ANATOMY OF A STEEL STRING ACOUSTIC GUITAR

COUPLING IN A MARTIN D28 FOLK GUITAR

THREE LOWEST MODES OF A MARTIN D28 FOLK GUITAR

(BASED ON (0,0) MOTION OF TOP AND BACK)

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

MODES OF A STEEL STRING GUITAR

(0,0) MODE AT 97 Hz

(0,0) MODE AT 205 Hz

(1,0) MODE OF A STEEL STRING GUITAR

DREADNOUGHT GUITAR AT 390 Hz

(1,1) MODE IN STEEL STRING FOLK GUITAR

DREADNOUGHT BODY 450 Hz

RESONANCES OF CLASSICAL AND FOLK GUITARS

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.

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 HOLEV IS AIR CAVITY VOLUME

3 RESONANCES WITH 2 ANTI-RESONANCES BETWEEN THEM

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

APOYANDO AND TIRANDO STROKES

IN THE APOYANDO STROKE, THE FINGER COMES TO REST ON AN ADJACENT STRINGIN THE TIRANDO STROKE, IT RISES ENOUGH TO CLEAR IT

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

SOUND RADIATION

SOUND RADIATION PATTERNS AT THREE RESONANCES IN A MARTIN D28 GUITAR

SOUND RADIATION AND SOUND DECAY

COMPARISON OF THE SOUND LEVEL OF THE FUNDAMENTALS OF PLAYED NOTES (BARS) TO THE FREQUENCY RESPONSE FUNCTION (SOLID CURVE)

QUALITY

1. PEAK LEVEL OF THE THIRD RESONANCE (AROUND 400 Hz)2. AMOUNT BY WHICH THIS RESONANCE STANDS ABOVE THE RESONANCE CURVE3. THE SHARNESS (Q-VALUE) OF THIS RESONANCE4. THE AVERAGE LEVEL OF 1/3-OCTAVE BANDS IN THE RANGE 80-125 Hz5. THE AVERAGE LEVEL OF 1/3-OCTAVE BANDS IN THE RANGE 250-400 Hz6. 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:

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

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.

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

VIBRATIONAL BEHAVIOR

DHv(w) [dB (m/s2/N)]

Ha(w) [dB (uncalib.)]

275 Hz 360 Hz 635 Hz

ACCELERANCE OF PORTUGESE GUITAR

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.

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

ELECTRIC GUITARS

EARLY ELECTRIC GUITARS

FenderStratocaster ~1952 Stevie Ray Vaughan

“Lenny”

GibsonLes Paul ~1957

Eric Clapton

Rickenbacker model 325 ~1958

John Lennon

FenderStratocaster ~1952 Stevie Ray Vaughan

“Lenny”

GibsonLes Paul ~1957

Eric Clapton

Rickenbacker model 325 ~1958

John Lennon

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.

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

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.

LOVER’S HUMBUCKING PATENT

(ISSUED 1959)

HUMBUCKING PICKUPS

S N N S

N

S

NS

S N N S

N

S S N

s

N

single coilsingle pole

two magnets

two coilstwo poles

three magnets

(a) (b)

S N N S

N

S

NS

S N N S

N

S

NS

S N N S

N

S S N

s

N

single coilsingle pole

two magnets

two coilstwo poles

three magnets

(a) (b)

HUMBUCKING PICKUP

TOP VIEW

BOTTOM VIEW

MAGNETIC FIELD ABOVE A MAGNET

FUNCTION OF VERTICAL DISPLACEMENT FUNCTION OF HORIZONTAL DISPLACEMENT

SPECTRUM INDUCED IN PICKUP BY VIBRATING WIRE

SINGLE COIL PICKUPPICKUP WITH MULTIPLE COILS

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.

SIGNAL PROCESSING AND SPECIAL EFFECTSNEARLY 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.

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.

ELECTRIC GUITARS: Body vibrations

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.

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).

LUTES

FREQUENCY RESPONSE OF A LUTE

MOBILITY (INPUT ADMITTANCE) AT THE TREBLE END OF THE BRIDGE SOUND PRESSURE LEVEL 1 m FROM TOP

PLATE (BELLY)

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)

TURKISH TANBUR (LONG LUTE)

IMPULSE RESPONSE OF TANBUR

VERTICAL IMPULSE RESPONSE SPECTRUM

HORIZONTAL IMPULSE RESPONSE SPECTRUM

LONGITUDINAL IMPULSE RESPONSE SPECTRUM

FOURIER TRANSFORM OF VERTICAL IMPULSE SPECTRUM