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GUITARS and LUTES

GUITARS and LUTES. MUSIC 318 MINICOURSE ON PLUCKED STRING INSTRUMENTS. Phys ics 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

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GUITARS and LUTES

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  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 9THCENTURY, 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 FLAT TOP ARCH TOP STEEL STRINGS CLASSICAL NYLON FLAMENCO STRINGS

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

  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 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: 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

  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. GUITAR BY GRAHAM CALDERSMITH SMALLMAN GUITAR

  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. Ha(w) [dB (uncalib.)] Hv(w) [dB (m/s2/N)] D VIBRATIONAL BEHAVIOR ACCELERANCE OF PORTUGESE GUITAR 275 Hz 360 Hz 635 Hz

  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

  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 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)

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