Monday, December 15, 2008

Vibrating strings

Throughout history, billions of strings have been plucked, bowed or hammered on citarras, pandouras, violins, pipas, biwas, đàn tỳ bàs, barbats, qins, giterns, citerns, sarods, rawabs, rebabs, rebeks, rubabs, basses, bajos, banjos, washtubs, lutes, ouds, koras, harps, lyres, saungs, tamburas, tamburs, tamburitzas, banduras, dombras, dobros, clavichords, harpsichords, monochords, autoharps, zithers, tars, ektars, dutars, sitars, setars, santoors, doshpulurs, mandolins, mandolas, mandocellos, ukuleles, vihuelas, kotos, zhengs, khims, qanuns, yangqins, cimbaloms, zhus, cellos, erhus, zhonghus, dahus, jinghus, dulcimers, bazuqis, kayagums, psalteries, hurdy-gurdies, crwths, kamanches, ghijeks, masenqos, morin khuurs, gojes, balalaikas, ses, sazes, changs, çengs, charangos, đàn bầus, ruanxians, yueqins, sanxians, shamisens, berimbaus, sarangis, veenas, cuatros, inangas, qumuz, qobuz, tiples, valihas—I could go on—not to mention chicken-cookers, rubberbands strung over shoeboxes, and of course the guitar.
Whether by plucking, hitting, scraping, being blown on or stimulated electronically, these strings have moved in patterns determined by their physics. The finger, pick, bow or hammer imparts energy to a string, dislocating it slightly from its straight resting position. After the impact, the tiny bend in the string propogates along its length, hits the nut or bridge, flips and bounces back again, continuing back and forth in this fashion until its energy is expended. When thus set in motion, any specific point along the string simply oscillates back and forth in a direction perpendicular to the line of the string itself. But when viewed a whole, the twangling string moves in waves, producing a fundamental frequency and a series of integral multiples of it known as overtones. The frequency and its harmonic overtones can be defined as a function of the length of the string, its tension and its mass; a longer, fatter or looser string gives a deeper note, shorter, thinner or tighter stings vibrate faster. These frequencies are joined by other, unrelated frequencies from the scraping of the pick or bow on the string—interesting noise, to a stringed instrument player. These "noises" too are waveforms.
All these waves are conveyed through the bridge into some kind of box or drum, where they are amplified in an enclosed space between hard walls and picked up in turn by whatever more flexible membrane the instrument employs: a softwood soundboard, a stretched skin or mylar head, or a vibrating plate. The visible motion of the string has now been turned into pulses of air, radiating outward from the instrument in invisible pressure waves. The original set of overtones has been further shaped by the materials in the string, bridge, box and resonating membrane, which have a character all their own, amplifying some frequencies and repressing others, resulting in a unique sound. Few stringed instruments sound exactly alike.
Most of these billions of vibrations over thousands of years have been heard by somebody; many of them have, moreover, been listened to. If heard, that means that the pressure waves from the instrument's sounding membrane made their way to a person's eardrum, which conveys the frequencies of moving air molecules into the inner ear. There, hair cells keyed to the specific frequencies fired, converting the wave's kinetic energy into electrical signals (the same thing accomplished by an electric guitar pick-up). The cells sent these electrical signals into the auditory cortex, where a set of neurons likewise designated to particular frequencies registered their highness or lowness—their pitch. But that was just the beginning. Many different parts of the brain then started processing the sound, sorting out the different overtones, determining one fundamental tone from the mass of harmonic multiples, estimating how far away the sound was and what direction it was coming from, determining whether or not it constituted something dangerous, recalling that the man had heard that sound before and what it was called, or if he hadn't happened to have heard a crwth or a qobuz, noting that fact while suggesting things that sound similar. The sound and its recognition triggered a series of additional memories and images in our hearer (heavenly hosts, seancing shamans, or screeching animals, for example.)
If the string is vibrated again, in a pattern with rhythm and a sequence of different pitches—that is, if it was used to make music and the man was listening—the brain would have fired millions more neurons, involving brain stem, cerebellum, amygdala, nucleus accumbens, frontal cortex and other areas associated with movement, language, pleasure and reward. The listener may have recognized the tune or its style and been able to predict where it was going based on rhythmic and melodic patterns; he may have felt happiness or dread; he might have been moved to dance, sing, love, or fight by the sounds themselves and the webs of associations they evoked. He might have felt the urge to drop whatever he was doing and pick up an instrument to play along.
Hominids have always heard sound. We don't know when humans first listened to strings, or struck objects, or columns of air in flutes or other things intentionally vibrated to make music, but it is likely to have been a long time ago. On the wall of a cave painted 12,000-15,000 years ago is this drawing of a ox-headed biped (presumed to be a man in a mask and called the petit sorcier). He seems to be playing a bow (the bow-and-arrow kind) pressed to his nose or mouth, using his own skull as the resonator.

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