A Aaar - Carlos Sampaio Microtonal & Unknown Sounds

Alternative Composer,Csounder, Sitar Player. Instrumental and sometimes microtonal musician. Updated to Unknown Genre in December 14th 2004.
If you know his true genre, please, let him know.
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There is nothing that musicians take more for granted than the fact that there are twelve pitches to an octave, and that these pitches divide the octave into twelve equal steps. Apparently few musicians question this arrangement, and only a tiny minority can explain whence it arose, why, and from what principles its authority derives. This 12-pitch assumption, however, is far from innocent. Twelve-tone equal temperament, as this common tuning is called, is a 20th-century phenomenon, a blandly homogenous tuning increasingly imposed on all the world's musics in the name of scientific progress. In short, twelve-tone equal temperament is to tuning what the McDonald's hamburger is to food.

How can this be so? What is so unnatural about twelve-tone equal temperament?

The basis of any natural system of tuning is that two pitches sound consonant (that is to say, sweet, or intelligible to the ear) when their sound waves vibrate at ratios of relatively small whole numbers. In an octave, for example, two pitches vibrate at a ratio of 2 to 1, one pitch vibrating twice as fast as the other. In a perfect fifth, such as C up to G, the ratio is 3 to 2. In a major third C to E, the ratio is 5 to 4.

The great problem that nature bequeaths to us in the mathematics of tuning - not an obstacle, but a wonderful challenge when viewed the right way - is that these simple intervals aren't divisible by each other. To illustrate, we need a perceptual measure of interval size. The one invented by the great acoustician Alexander Ellis in the late 19th century is called a cent, and is equal, by definition to one 1200th of an octave, or 1/100th of a half-step.

An octave: (ratio 2:1) = 1200 cents
A perfect fifth: (ratio 3:2) = 701.955 cents
A major third: (ratio 5:4) = 386.3 cents

In the equal temperament we're used to, three major thirds - C to E, E to G#, G# to C - equal one octave. But as you can see, three pure major thirds of 386.3 cents do not equal one octave, because 3 x 386.3 does not equal 1200. So equal temperament, our McDonald's hamburger tuning, stretches every major third out to an arbitrarily out-of-tune 400 cents, somewhat the way McDonalds standardizes every patty to a flat quarter-pound of dubious relation to beef. These means that every major third on the piano is out of tune by 13.7 cents, creating busy little beat patterns between the overtones of every major third we hear. Unless you've had some exposure to Indian or Indonesian or some other non-Western musical tradition (or authentic barbershop quartet music, the last pure-tuned tradition in America), it's quite likely that you've never heard a true major third in your life, nor a true major or minor triad.

Music schools teach that this Big Mac tuning has been around for centuries and represents an immutable endpoint of progress. It's a lie. History, even in Europe, has provided many alternatives, Arabic and Asian cultures have provided rich tuning resources unknown to us, and many recent American composers have explored alternative tuning possibilities.

There are many reasons to write in other tunings, seemingly as many as there are composers who do it. La Monte Young seeks absolute purity of pitch so he can explore complex combinations of distant overtones never heard before. Harry Partch wanted to imitate in melody the subtle contours of the human voice, without compromise. Lou Harrison wants to recapture the sensuous presence that true intervals had before the 20th century. Ben Johnston wants his music perfectly in tune so it will have a healthful psychological effect on the listener. Myself, I enjoy the expanded composing resources of 30 or so pitches to the octave, and the option of creating amazing chromatic effects through minimal voice-leading. Some composers are seeking a magical harmonic alchemy written about in ancient treatises. Others just enjoy exotic out-of-tuneness. One of the exciting things about the microtonal field is that, despite its grounding in natural laws of acoustics, its diverse practitioners hardly agree on anything.
by Kyle Gann
©2000 NewMusicBox
(Visit Kyle Gann at http://www.kylegann.com)
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