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From: mclaren

Subject: Intonational heresy

In Tuning Digest 685 Brain Belet (oops, typo--but appropriate in this case) asked whether JI, Golden Mean and equal temperament tunings could co-exist together.

Warren Burt and Your Humble E-Mail Correspondent appear to be the xenharmonists currently combining the largest possible number of different tunings in a single composition.

My upcoming concert series includes several pieces which employ non-just non-equal-tempered, microtonal equal tempered, and JI tunings simultaneously (in one case, one performer in each tuning; in another case, Sound Globs algorithmically generates a backing track with simultanous different melodic lines in each tuning). However, Warren Burt is the acknowledged master of this art. To my knowledge no one has combined more different kinds of tunings simultaneously than Warren-- certainly not with better musical results. (Although Bill Schottstaedt has come close to combining that many different tunings simultaneously and seriatium in certain of his computer compositions, notably "Water Music.")

Several comments:

[1] James Tenney has astutely pointed out in META + HODOS that combining different tempo-streams and different polyphonic melodic lines often produces a "resultant" as entirely different from the components as is a vector resultant's direction from those of its component vectors. My experience in combining different tunings simultaneously appears to indicate that exactly the same is true with intonations. That is: take 5-TET and play it simultaneously with 7-TET and the audible result is RADICALLY different from either 5-TET or 7-TET. Ditto different classes of tuning: viz., Tibetan tunings overlaid with slendro & pelog, the Wilson 2,4 [17,19,23,29] hexany overlaid with 35-TET, etc. For audible examples, see my latest two cassette compilations, "Toward Unknown Regions," Vols. 1 & 2. Warren Burt's cassettes are riddled with this kind of intonational miscegenation--his compositions "Journeys through the jungle of intonational injustice," "Justice, equality and beatings," and "Microtonal computer research music" are all notable examples of combining many different tunings (if memory serves--hope the titles are correct, Warren).

In fact, Warren recently sent a letter in which he exulted at the possible heretical number of different combinations.

The diagram looked something like this:

ET partials                     ET tunings
JI partials                      JI tunings
N-J N-E-T partials      N-J N-E-T tunings

with arrows connecting all possible combinations. That is, ET partials with JI tunings, JI partials with N-J N-E-T partials, etc., etc. Clearly when you multiply these combinations of timbre-and- tunings by the possible numbers of different intonations that can be employed simultaneously, the compositional space still unexplored is truly staggering.

Meantone, incidentally, can be considered a mishmash of ET and JI intervals smushed into the same tuning.

This suggests a 4th category of timbre & tuning:

Combined partials              Combined tunings

in which different classes of intervals/partials are smushed together as in meantone. Clearly, this is even more wildly heretical and opens up even vaster compositional vistas for the blasphemously microtonal apostate.

--mclaren