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From: mclaren

Subject: Combining different tunings and "transferring" between different tunings

Thierry Rochebois asked whether anyone had thought of combining different tunings--for example, 12/oct and 19/oct equal temperament. As it happens, the idea of combining different tunings has a long history. Unless memory betrays me, Archytas described (with contempt!) a Greek composer who built a rotating table on which were mounted kitharas in all of the three Greek genera. The composer apparently kicked the table to rotate the required kithara into his grasp. If true, this would be the first known example of movement between different tunings in the course of a musical performance. In France, the keyboardist Jean Titelouze built a 19-tone equal-tempered harpsichord in the 17th century: his work is mentioned by Mersenne. Titelouze advocated performing 19- tone equal tempered harpsichords with ordinary stringed instruments. Since violins, violas, celli, etc., tend toward Pythagorean intonation and since their fifths are tuned just (701.955 cent fifths versus the 694.73684 cent fifths of 19-tone equal temperament or 1/3 comma meantone, whichever description you prefer) this was tantamount to suggesting that different tunings be combined. Titelouze' s ideas were thought radical at the time: and he himself thought of 19 as a sort of expanded 1/3-comma meantone. He reportedly used his 19-tone harpsichord to perform in a wider variety of tunings than would otherwise be the case on a 12-note 1/3-comma meantone harpsichord.

Costeley's chromatic chanson, composed circa 1560, clearly used 19-tone equal temperament but it is less clear whether the vocal parts were accompanied and if so, with 12-tone equal tempered instruments. Were this the case, Costeley's chanson would be the 1^ere known example of combining 12-tone and 19-tone equal temperament.

In the modern era the Mexican microtonalist appears to be the first to suggest combining 12 and 15 tone equal temperament. In his 1951 magnum opus Sistema Natural, Novaro points out that 15/oct and 12/oct share 3 notes: the familiar augmented chord, C, E, G#. (Because every 4th note of 12/oct is also every 5th note of 15/oct.) So Novaro suggested moving from 12/oct to 15/oct by using the C-E-G# chord as a "pivot point," or by using any of the three pitches as a means of departing from 12 for 15, or vice versa.

Novaro published "Sistema Natural" in 1951 and does not appear to have received much recognition. Ivor Darreg, in his 1975 Xenharmonic Bulletin Number 5, proposed that all equal temperaments exhibit a distinctly audible "sound" or "mood." Ivor further proposed that composers add to the range of melodic and harmonic possibility by moving from one equal tempered scale to another during the course of a composition, either by building different instruments (metallophones, for example) and moving from one pitch on one instrument to an equivalent pitch on another instrument, or by using tape overdubs.

In 1975, in his "Xenharmonic Bulletin Number Five," Ivor proposed the term "transfer" for moving between different equal temperament--the term "modulation" doesn't apply, obviously, since we're no longer moving between different *keys* but different *tunings.* When I used to visit him, Ivor would often pick up his mallets and sound a set of notes on one of his 17- or 19- or 14-tone metallophones, then strike the equivalent pitch on his 10-tone or 24-tone or 22-tone metallophone and continue playing the same melody but in a different tuning. Ivor also combined just intonation with various equal temperaments on his many hundreds of reels of recordings.

One of Ivor's favorite methods of combining and moving between different tunings employed the two stacked Farfisa electric organ keyboards sent him by Buzz Kimball. Ivor had both keyboards set up in his living room so that the tuning slugs at the backs of the Farfisa combo organs were exposed: Ivor would spend an hour or two with an oscilloscope, a StroboConn tuner, and a screwdriver to get one tuning set up on one Farfisa, then another tuning on another Farfisa. Finally he would sit down and play extremely exotic yet perfectly consonant chords by alternately fingering one key on one keyboard and another on the other keyboard. Both keyboards sat literally on top of one another, with keys so close that it was simple to reach up with the thumb or the index finger and get a C in one meantone or just intonation tuning, and an Ab and an Eb in another meantone or just intonation tuning. On many occasions Ivor would greet visitors who argued that the "wolf" tone was impossible to avoid in meantone, or that it was impossible to modulate through different keys in a just tuning--Ivor would merely smile and sit down and adroitly finger exactly the intervals that the visitor had just claimed were impossible. Of course, the reason these intervals "seemed" impossible is that everyone assumes only one keyboard tuned to only one tuning at a time--with two or more keyboards, or with tape overdubbing, the sky's the limit.

To my knowledge, the other people who have combined different tuning systems are:

Julian Carillo (various divisions of the whole-tone combined; "Preludio a Cristobal Colon," for instance, uses a vocal part in 24/oct with a harp part in 72/oct and string parts in 36/oct)
Rick Sanford (12-tone and 19-tone equal temperament, 19-tone equal temperament and 7-limit just)
Warren Burt (almost every equal temperament combined at one time or another with almost every other equal temperament; many different species of just intonation combined with many different other kinds ofjust intonation. Warren is likely the king of combined simultaneous tunings. One of his pieces pits a melody in 19/oct against every other tuning from 5 through 19 tones per octave; *another* of Warren's compositions runs through every single mode of all three Greek genera in turn.)
Jonathan Glasier (pelog and slendro, just intonation with 19 tone equal temperament, 31-tone equal temperament with 43-note 11-limit Partch JI)
Myself (John Chalmers has mentioned some of the tunings I've combined: also 15-tone and 17-tone at once, every 2nd prime harmonic and every 3rd prime harmonic at once, &c.)
William Schottstaedt (11-tone, 13-tone and 36-tone equal temperament at once in "Water Music I," Pythagorean just intonation with 13-tone equal temperament in "Water Music IV," many other combinations in other computer music compositions)
Bill Wesley (Pythagorean just intonation with the Lydian mode of the Greek Enharmonic; 12-tone equal temperament combined with 15-tone equal temperament)
John McBryde (Various divisions of the golden section, 1.6180339, e, pi and Feigenbaum's constant 4.6692106, at once)
Wendy Carlos (Her composition "Beauty In the Beast" transfers between two different non-octave scales, while her piece "just imaginings" moves between 12 different transposed just intonation arrays over the course of the piece.)

Warren Burt and William Schottstaedt appear to have produced the most memorable music combining different tuning systems.

These two composers could almost be called pan-intonationalists, since they move with complete fluency between a vast variety of different tunings and seem almost always to use more than one different tuning at the same time.

The idea of combining or moving between different tunings has been little discussed in the music theory literature, but it is clearly a compositional technique of great potential promise.

In particular, Warren Burt and William Schottstaedt would do us a considerable service by describing some of their compositional methods in moving between & combining different tunings.

--mclaren