Re: All, then best, 7-limit scales with 31 consonances (fwd)

I'm resending this, as it seems to have been a victim of list downage.

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "'Jever take'n try to give an ironclad leave to
-\-\-- o yourself from a three-rail billiard shot?"

NOTE: dehyphenate node to remove spamblock. <*>

---------- Forwarded message ----------
Date: Sat, 19 Dec 1998 14:05:02 -0600 (CST)
From: Paul Hahn <manynote@library.wustl.edu>
To: tuning@eartha.mills.edu
Subject: Re: All, then best, 7-limit scales with 31 consonances

On Mon, 30 Nov 1998, Paul Hahn wrote:
> There are only three [31-consonance 7-limit JI scales] whose
> smallest scale degree is not smaller than 25:24; they approximate 12TET
> reasonably well. This is the (IMHO) best one:
>
> 42:25------21:20-------21:16
> \'-. .-'/ \'-. .-'/ \'-.
> \ 6:5--/---\--3:2--/---\-15:8
> \ /|\ / \ /|\ / \ /|
> \ | / \ | / \ |
> / \|/ \ / \|/ \ / \|
> / 7:5---------7:4--------35:32
> /.-' '-.\ /.-' '-.\ /.-'
> 8:5---------1:1---------5:4

Incidentally, I just noticed that this scale differs by just one pitch
from a just version of Fokker's 12-pitch 7-limit scale that Dave Keenan
recently rediscovered. The one pitch that differs is 35:32, which needs
to be changed to 9:8. This reduces the number of 7-limit consonances in
the JI version to 30 again, but the 31TET or 1/4-comma meantone versions
have 38.

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "'Jever take'n try to give an ironclad leave to
-\-\-- o yourself from a three-rail billiard shot?"

NOTE: dehyphenate node to remove spamblock. <*>