15-TONE SCALE SYSTEM (1991)
As everybody knows, alternative communication channels opened up in the 1960s, and one consequence of this was that about 27 years ago an informal Xenharmonic Network of People came into being and it is still going strong--why, just this afternoon my phone rang, and it was long-distance from Florida, clear across the country. So I got to hear David Hill's newest computer music experiment with just intonation septimal chords using the ratio 48:49.
Even during the last few weeks: concerts here and a Microfest Even in New York City are providing the Network with many new members. Everything from quartertones to exotic oriental or Third World scales and the latest things out of electronic laboratories and the computer people getting into the act with MIDI (there is a new group here in San Diego for that and it is growing fast) and all kinds of new computer tables and ways of modifying commercial instruments to permit new scales on them.
Also I spent the last few weeks with a frequency-counter, a hacksaw, an electronic calculator to re-work some computer-generated frequency-tables, a vise on the garage workbench, an assortment of galvanized conduit pipe and old heavy-walled water-pipes, and came through with a 3 & 1/3-octave 15-tone tubulong set. (The term tubulongs is from Erv Wilson of Los Angeles, who got me started making instruments in new scales and re-fretting guitars to non-twelve, some years ago.)
Why 15 tones per octave? Some time back I had refretted guitars to a number of scales--most of them in the scales suitable for harmony as well as melody, such as 19, 22, and 31; but also whatever else seemed worth experimenting with, and having had a chance to borrow for a short time the very rare book by Augusto Novaro of Mexico, published in 1951 and almost never seen, Sistema Natural de la Musica, saw his reference to 15-tone guitars and their use in conjunction with orthodox 12-tone guitars to get many of the intervals of 60-tone.
So one fine Smoggy Day in Glendale CA I went down the street to a sleazy crummy Thrift Shop and got a guitar for a mere song, and detwelvulated it and soon it was a Fifteen. A couple of years later a young fellow tried it at an impromptu meeting of ours, and played mean ol' Blues on it as though he had it all his life! Currently it hangs on the wall some 2.5 meters to the right of this typewriter. Novaro in his book had devised a 15-tone keyboard and 15-tone notation, but that was way back in the 30s and 40s, and few people ever knew about it, so we don't have to go into that here.
Let's "face the music" right here! 15-tone equal temperament is not as important as just intonation or meantone or the 17, 19, 22, 24 and 31-tone equal temperaments or certain unequal temperaments that deserve to be composed in and made available on instruments or computers. Nor, in having 15-tone available on and just building another instrument for it and compiling labels for it, would I be insulting the memory of the late Harry Partch, nor would I be injuring the successes of Just Intonation or the recent progress a number of people, myself included, have been attaining with 19, 22, and 31 notes per octave. It is no longer a question of making agonizing decisions or giving up one tuning for the sake of having another! Rather, it is a matter of having many tunings available, for the sake of variety and CONTRAST.
It is time to get out of the 12-tone-equal rut and EXPLORE anything and everything so that composers do not have to repeat what their predecessors have ALREADY SAID. Variety is the spice of life.
Those who mainly want to make old music sound smoother will object that the fifth and the fourth in the 15-tone system are 18 cents, or 2/11 of an ordinary semitone, out of tune, and the major third is 1/7 of a semitone, too sharp, exactly like the regular 12-tone-equal-tempered major third. I could counter that the minor third is very good indeed and the 7th and 11th harmonics are very well represented in 15-tone, but that just isn't the point. We have no intention of trying to play Schubert's Serenade or Home Sweet Home or Beethoven's Fur Elise on any 15-tone instrument. No, the point is having something for use now and then to contrast with 12 or 17 or 19 or 22 or whatever.
Other facts are more relevant: 15 = 5 x 3 and 15 = 3 x 5. There is a 5-tone-equal scale and other scales very close to 5-equal found all around the globe. Africa, parts of Asia, South Sea Islands, elsewhere...people just naturally stumble on it. And of course there are unequally-spaced five-tone scales, such as the black keys on our conventional 12-toe keyboards, and many Scottish and Irish melodies and those found in China and other places.
However, 12--the basis of much ordinary music--is NOT divisible by 5. So we in the conventional Western-European-derived musical world, have been starved for 5. Now a 5-tone-equal scale doesn't have too much in the way of harmonic and melodic resources so how about a multiple of 5? Ten has been tried to a very limited extent. Gary Morrison some years ago built a 10-tone flute and a 10-tone guitar and some other things. 10-tone is said to have been tried during the French Revolution when everything was going decimal. I made a 10-tone set of metal bars; it turns out that the MOOD of 10 differs from that of 5 more than the mood of 15 does, so I planned on making some 15-tone affairs and trying it on synthesizers some time ago, and now this tube-set gives 15 a fair shake.
The MOOD of 5-equal differs from that of 5-out-of-12, which latter is the familiar pentatonic scale in use by most musicians around here. The moods of 5, 10, 15 or anything else could not be predicted by theory, by silent ink on paper, by extrapolating from known or familiar musical practice nor by attempting to construct new rules of harmony. They had to be discovered by building and playing instruments!
Now: one property of 15 should be obvious from the above..if 12 = 4 x 3, 15 = 5 x 3, which means that 12 and 15 share in the 1/3-of-an-octave interval. This further means that if you have 12- and 15-tone instruments at hand, or you can have your synthesizer or computer go from one to the other, you have three points at which you can enter or leave either system to go into the other. In order to use the standard A=440 Hz pitch and its octaves, I have chosen the 12-tone pitches F, A & C# to be the 3 points-in-common.
This does not commit either you or me to calling the 15-tone pitches any name familiar or strange. You can number them 0 through 14 if you want. Or you can avoid naming them entirely. As for me, I will evade the issue by improvising and recording what I improvise and copying the tapes and sending them out. Why write it down at all? Any notation I might use would only confuse and mislead and maybe discourage you or the bellow behind the lamp-post. At age 71 I just don't have the time to write new music out when I can play it on real instruments with real sounds and copy the recordings. Nor do I have time to learn or read or use or practice notation for 15 or the obvious way to use 15 and 12 together, 60-tone.
Many of you who have access to computers could use various published information to make your computer sound the 15-tone scale or 14 or 19 or 41 or 53 for that matter, so I don't have to run on for many pages to give that information here.
15 is one of the systems which we surely do not want to call "microtonal"! Indeed, this size of unit-interval, 80 cents or 4/5 of a standard semitone, is not too small to be taken intentionally by a violinist as a leading-tone half-step. It is a possible first stopping-place for someone trying out the first steps beyond the half-step. Xenharmonic enough to be different from 12, but not as strange as its neighbors 14 and 15. The major and minor thirds and therefore the sixths, the fourth and fifth are still recognizably there. Something does happen to the major second, and then there is a new little animal that appears even in simple 5: the subminor third.
We can conceive of 15-tone as a pattern of the equal 5-tone scale on three levels, or the ordinary Augmented triad with thirds-of-an-octave on 5 levels. Or take your familiar concept of 12-tone as 3 x 4 and ask yourself: "What would happen if the 4 in 3-times-4 was replaced by a 5?" The 4-tone scales is not usually thought of as a scale, although it could be; it is ordinarily thought of as a chord and called the Diminished Seventh Chord and its pile-of-minor-thirds structure is usually given a back seat. In 12-tone, of course, quarters of an octave. The pile of minor thirds in 15 does not come out even at the octave any more than minor thirds in 19-tone do. This becomes interesting when used as a melody. It exceeds the octave. In the 16-tone scale, the 12-tone pattern of equal quarters recurs of course. The 6-tone or whole-tone scale made by taking every other note of 12, is not usually thought of as a chord, but surely Debussy used it as a chord as much as he used it as a scale. Take then this idea of the whole-tone six-tone scale as a chord and backtrack to the five-tone scale and call THAT a CHORD and see what happens when you compose in 15 or just improvise, trying it in open spacings. Then alter this 5-note chord by raising or lowering one of its notes, since you now have 3 sets of 5 to work with!
Its sounds as a chord will be difference enough from familiar twelve to get your imagination in gear.
15-tone frequency tables and 15-tone fretting tables are available from me. Indeed, I have condensed tables for every system, 13 through 24, and more for many other tuning systems including of course just intonation. But just as I saw over and over with respect to the more resourceful systems such as 17, 19, 22, 31 and the rest, don't expect me to aid and abet anybody who wants to use only 12 out of 15! That cripples it and makes it dreadfully lopsided and does not do a thing for musical progress. It is absolutely inexcusable in these days of available guitars and synthesizers and computers and means of automatically tuning anything you want or need. I wouldn't recommend tuning 15 by ear. Why give yourself all that trouble now that we have electronic tuning-devices in wide variety?
I wouldn't bother giving 15 this much space if having it meant you had to invest lots of money on something dedicated to 15. But we now have freedom of Choice hitherto out of the question for me or you. I've been waiting over 50 years for such freedom and now that I can have it, everybody else can too. Don't ask me "What is your FAVORITE system? or even worse, "What is the BEST tuning system?" Discover your favorites by HEARING them. There isn't any BEST, but each piece of music may have a tuning that will bring out some aspect you will like. Never mind whether anybody else agrees. I don't have to give up the exciting possibilities I have discovered composing in just, or 31, or 19 or 22 if I play a little 15. It's not a case of either/or. Explore!