BETWEEN U S: A HyperHistory of American Microtonalists

A tremendous amount of work remains to be done in the realm of determining the tunings of non-Western musics. This is my academically acceptable way of professing ignorance. I have made some attempts on my own to match tunings of various non-European musics on my synthesizer, and to analyze pitch structures in terms of tuning. Not only is this sometimes difficult (especially when the music is fast or more than one pitch is sounded at a time), but the appropriate methodology varies from culture to culture. Many non-Western musics do not hold sustained pitches in place the way European music does, but slide and glissando and even yelp from one word to the next. An entire generation of musicologists could devote themselves to this problem without exhausting it. However – I’ll tell you what I know, and what I’ve found.

At Bard College we have a gamelan. Its official slendro scale is as follows:

Ab 16/15 = 112 cents
G 1/1 = 0 cents
Eb 8/5 = 814 cents
D 3/2 = 702 cents
C# 11/8 = 551 cents

These cent measurements arrived with the gamelan – the ratios I supplied myself. The gamelan instruments are in pairs, tuned about 30 cents apart to create the characteristic shimmering of gamelan music, but this tuning applies separately to each half of the pairs. I once wrote about gamelan music in terms of ratio tunings, and received an irate letter from some gamelan maven who informed me that gamelan musicians don’t tune in terms of ratios, and that I was imposing a foreign notion. And yet I’ve heard Lou Harrison talk about gamelans in terms of ratio tuning, and the cent-sequence 551, 702, 814, 0, 112 can only be interpreted as intending the ratios above. Not my field, but this particular bit of evidence leaves little room for interpretation.

Among Americans, Lou Harrison, Barbara Benary, Evan Ziporyn, and Jarad Powell, and many others, have written music for gamelan, and inspired by gamelan. With more than 200 Indonesian gamelans operating in the U.S., gamelan must really be considered a major current in American music.

Arabic music is well known for its use of 11-based intervals which sound, to our ears, like fairly exact quarter-tones. Treatises on Arabic music make reference within a scale on, say, G, to pitches halfway between Bb and B (11/9, or 347 cents) and halfway between F and F# (11/6, or 1049 cents). Modern transcriptions of Arabic songs and violin music sometimes use fairly standard quarter-tone notation for these pitches of the scale, and the quarter-tones are easily audible and very distinct on recordings.

That Indian ragas use a scale of 22 pitches is well known, but the exact tuning seems to be in doubt. The Hindu specialist Alain Danielou lists a tuning for the 22 pitches with some authority, but a student of mine (Jane Gilvin) researched Danielou and couldn’t locate any such tunings in the Sanskrit treatises he supposedly derived them from. Danielou, in his Music and the Power of Sound, interprets the Indian scale as pairs of notes, some five limit and others drawn from a cycle of 53 perfect fifths, and thus within three-limit tuning:

1/1 = 0 cents
256/243 = 90

16/15 = 112
10/9 = 182

9/8 = 204
32/27 = 294

6/5 = 316
5/4 = 386

81/64 = 408
4/3 = 498

27/20 = 520
45/32 = 590

64/45 = 610
3/2= 702
128/81 = 792

8/5 = 814
5/3 = 884

27/16 = 906
16/9 = 996

9/5 = 1018
15/8 = 1088

243/128 = 1110

Several of the paired notes are separated by the syntonic comma of 21.5 cents, or 81/80. It is unclear what authority Danielou asserts for these ratios, but he is a fascinating figure nonetheless.

Finally, many musicians believe that the “blue” notes that jazz singers and sax players play – bending the third, sixth, and seventh steps of the minor scale downward a touch – is a return to a seven-limit scale inherited from Africa. I have analyzed a few recordings by Billie Holiday with inconclusive results. There are certainly points at which she distinctly sings about a third of a half-step flat on those scale steps, with reference to the piano – and other places at which she sings in tune with the piano. My impression, drawn from the most modest evidence, is that sometimes she bends the third, sixth, and seventh scale steps downward for expressive purposes, and that she may find there “notches” representing the ratios 7/6 (267 cents), 14/9 (765 cents), and 7/4 (969 cents). Ben Johnston has written some jazz arrangements couched in such specific “mis-tunings.”

Through the spread of pop music, the Euramerican 12-pitch equal-tempered scale is in danger of wiping out indigenous tunings in much of the world, especially India and Southeast Asia, even in Arabic countries. At the same time, however, more and more American musicians are studying Eastern cultures, becoming experts in Indian or Indonesian performance, and absorbing new tunings. It is clear that if we want American music to join the rest of the world rather than squashing it, we need to get out of our 12-pitch equal-tempered RUT.

With that depressing thought you can go to the just intonation page, the historical European temperaments page, the equal temperaments page, or back to the tuning page.

From BETWEEN U S: A HyperHistory of American Microtonalists
by Kyle Gann
© 2001 NewMusicBox

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