Yahoo Tuning Groups Ultimate Backup tuning scales with three different step sizes

> From: "Luzius Lanrai" <luzius223@hotmail.com>
>
> Hello all,
>
> I have been investigateing into scales, that have exactly 3 different step
> sizes (between successive scale members), in different equal divisions, and
> also from ratio-based (n-limit) systems. Would anyone let me know what of
> these scales people are using, and what properties of structure are enjoyed
> about them?

Not quite understanding the question, I'll first throw out some well
known scales which have three step sizes (major, minor and augmented
seconds)

1 2 b3 4 5 b6 7 8 harmonic minor
1 b2 3 4 5 b6 7 8 etc
1 b2 3 #4 5 b6 7 8 etc

and there are other variations on this idea.

A potential tuning for the first that keeps things to 3 step sizes
(without going into your equivalence classes) is

9/8 28/27 9/8 9/8 28/27 243/196 28/27
1 9/8 7/6 4/3 3/2 14/9 27/14 2/1

>
> So my other questions are: what J.I. scales (any cardinality) of greater
> complexity might be used (or "do you use") to "approximate", in that meaning
> I just explained, a scale of three-step-sizes? So I look for J.I. scales

but a more traditional treatment would be

9/8 16/15 9/8 10/9 16/15 75/64 16/15
1 9/8 6/5 4/3 3/2 8/5 15/8 2/1

where the 9/8 and 10/9 fall into an equivalence class. Does the augmented
second fall into a compound equivalence class like in 12tet?

> And lastlly, a general question: have models been proposd, who describe, and
> explain a rationale for, this kind of equivalenceing of different J.I.
> intervals into classes?
>

I should think this is similar if not identical to some of the stuff
that gets talked about here all the time.

Where is it that you are going here, and do you have any suggested
scales that have interesting properties that you are dealing with?

Bob Valentine

scales with three different step sizes

🔗Robert C Valentine <bval@xxx.xxxxx.xxxx>

🔗Paul H. Erlich <PErlich@xxxxxxxxxxxxx.xxxx>