Triple-Just 12-Tone Tuning System (Digest 1407 Topic 4)

Hi Bill,

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
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| Mark Nowitzky |
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>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).