source file: m1554.txt
Date: Fri, 16 Oct 1998 10:45:16 -0500 (CDT)

Subject: Re: A meantone tuning with six 7-limit tetrads

From: Paul Hahn <Paul-Hahn@library.wustl.edu>

On Fri, 16 Oct 1998, Dave Keenan wrote:
> Hi, I'm new to this list. Greetings from Brisbane, Australia.

Welcome.

> Has anyone seen the following tuning before?
> [snip]
> 
> C  Db D  D# E  F  F# G  Ab A  A# B  C
>   3  2  2  3  3  2  3  3  2  2  3  3   (number of 31-TET steps between notes)

I've been working with various 9-out-of-31 scales lately.  One of the
most interesting is

3-4-3-3-5-3-4-3-3

which is a subset of Dave's scale.  It has 22 7-limit intervals (the
maximum possible with 9-out-of-31) and 3 complete tetrads.  If you
invert the lower pentachord, giving

3-3-4-3-5-3-4-3-3

, the result has only 21 7-limit intervals but 4 complete tetrads, the
maximum possible with 9-out-of-31 and the only way to do so.  (By
contrast, several 9-out-of-31 scales have 22 7-limit intervals, such as

3-5-2-5-3-3-4-3-3

, which I posted here some weeks ago.)

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
    O
   /\        "Foul?  What the hell for?"
  -\-\-- o   "Because you are chalking your cue with the 3-ball."

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