12-Tone Subsets

Here are some (anonymously-forwarded) comments and questions posed to me
directly, along with some of my opinions.


> My comment about using SysEx messages arose through forgetting that not
> all synthesizers have this facility, as you pointed out.

Perhaps we're both a little spoiled! No just kidding.



> Your remarks about the relative difficulty of retuning to 17- or 19ET on
> the one hand and 16ET on the other are interesting. I guess you are
> referring to the fact that in 16ET the 4-step intervals coincide with the
> minor thirds of 12ET but nothing matches the perfect fifth very closely,
> while in 17ET and 19ET the fifths do better. Have I understood this
> correctly?

That's certainly one way to put it. Another way is that several apparently
independent investigations of 16TET (Easley Blackwood and Ivor Darreg for
example) have concluded that the most useful way to work with 16TET is as four
interlaced diminished seventh chords rather than diatonic subset mode.
Blackwood went on to devise a diatonic-subset-based notation system from this
framework, but Ivor Darreg, Brian McLaren, and franky I as well, have found his
metaphore to diatonic structures difficult to relate to, and of little value.



> This all raises the question of why non-12 ETs are used. I gather from
> much of what I have been reading on the subject, that many use them in
> order to get closer approximations to various 'ideal' small-whole-number
> ratio intervals than are available in 12ET. Fair enough.

Finding more accurate approximations to just intonation is the most
traditional reason to pursue unusual tunings. Another, closely-related
motivation is to find all-new pitch relationships, whether they be just,
approximations to just, or based on some other underlying concept.

And speaking of Ivor Darreg, his main motivation was what he called "moods",
which, were I to try to define the concept, I would say that the mood of a
tuning is the collective effect of all of its available pitch relationships.

Another meaningful motivation is how the tuning works as a system, or perhaps
relative to a notation system, including what pitch relationships it casts as
more "basic". 17TET for example, on has a pretty good approximation to the 11:9
neutral third, and one probably could come up with a system for using 17TET that
way. Most people have approached it a very different way though, concentrating
on its way-sharp major third as a dissonance that must be resolved outward to a
fourth. That of course is a reversal of traditional harmonic principles, which
can lead to some surprising effects.




> in retuning for 16ET I wouldn't think of picking out a subset of size 12. I
> would simply tune two channels, each to 8ET, with one a 16ET step sharper
> than the other. Each channel would then have four unused note numbers.

That strikes me as reasonable. Most people just punt and map it linearly -
key for note, mismatching octave boundaries in the keyboard with octave
boundaries in the tuning. Some people (Brian McLaren and Jonathan Glasier for
example) have what I consider an amazing ability to ignore the black-white
structure of a traditional keyboard. I've never gotten the hang of that. Then
again, I never really got the hang of keyboard technique at all really; I'm
more of a woodwind and guitar kind of dude.



> I wonder how you carry out your retunings for 88CET. Here, I guess, would
> be a case where retuning on the fly or using pitch bends might be useful.

I use my Ensoniq ASR-10 for the majority of my 88CET work, and the ASR-10 has
provision for (realistically) four tuning tables per instrument. (Actually, it
can have up to eight per instrument, but only four of the eight can be switched
off between using the patch-select buttons.) I however use a purely static
tuning table based upon a circle of fifths wrapping within a 7:4. Under that
scheme, I remove the G#/Ab key from the system, which makes the black keys are
functionally meaningful auxiliaries, by which I mean that the notes along the
circle of fifths spans the white keys first and then the black keys, analogous
with the traditional circle. (The circle reads upward as C A F D B G E C# A# F#
D# B#=C, or downward toward the flats as B D F A C Eb Gb Bb Db Fb Ab Cb=B.)

As far as I know all others who have worked with 88CET have mapped it
linearly instead, and Johnny Klonaris found some curious analogies between
stacks of fifths in that notation system and what look on the keyboard like
open-position diminished triads in 12TET.


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