The tuning system you describe sure sounds like it's got potential:
At 07:07 PM 5/6/98 -0400, you wrote: >From: "Triple Just" (Bill Flavell) >Subject: Triple-Just 12-Tone Tuning System
>... > This tuning system is based on the super-imposition of three just >tuning scales, the second being super-imposed on the F of the first >scale, and the third being super-imposed on the A of the first scale. >...
I added "Comments from Peanut Gallery" (i.e., comments from me):
> Pitch Frequency Interval Comments from Peanut Gallery ----- --------- -------- ============================ > C 1440 > 16/15 > B 1350 > 135/128 > A# 1280 <-call this "Bb" > 16/15 > A 1200 > 16/15 > G# 1125 > 25/24 > G 1080 > 9/8 <-correction: 27/25 > F# 1000 > 25/24 > F 960 > 16/15 > E 900 > 10/9 > D# 810 <-call this "D2" > 81/80 > D 800 <-call this "D1" > 16/15 > C# 750 > 25/24 > C 720
Here is the tuning system in two dimensions, a la Helmholtz/Ellis:
D2 810 G 1080 B 1350 C 720 E 900 G# 1125 F 960 A 1200 C# 750 Bb 1280 D1 800 F# 1000
I renamed the D# to D2, so as not to confuse it with the pitch of a typical D#. I presume you called it D# to indicate the key (button) on the keyboard the pitch is mapped to.
It can be thought of as an "A Duodene" (again using Helmholtz/Ellis terminology), but with the D#=843.75 removed and the D2=810 added in its place.
It looks useful that you have both "flavors" of D (D1=800 and D2=810) readily available on the keyboard. For example, a "ii V7 I" progression in C Major can be handled thusly: ii D minor D1, F, A V7 G Dom 7 G, B, D2, F I C Major C, E, G
> I'm going to be hosting an e-mail mailing list regarding this tuning >system, so if you'd like to subscribe, please let me know by private >e-mail.
Sounds good! Count me in!! Sign me up!!! Thanks, --Mark +------------------------------------------------------+ | Mark Nowitzky | | email: nowitzky@alum.mit.edu | | www: http://www.pacificnet.net/~nowitzky | | "If you haven't visited Mark Nowitzky's home | | page recently, you haven't missed much..." | +------------------------------------------------------+
>Based on your info, this may further interest you. If you haven't already heard >of it, I'd recommend Charles Lucy's "Lucy Tuning" which I find especially >"rational" based on _Pi_ used in the writings of John Harrison.
That strikes me as a deliciously ironic suggestion. Mr. Flavell is clearly interested in Just Intonation, and Lucy appears to believe that JI as a meaningless artifact of history (not to suggest for one bananosecond that I, or many other microtonalists, agree).