septimal and neutral tunings

> From: John Chalmers <jhchalmers@UCSD.Edu>
>
> The neutral diatonic mentioned in the last post and the Clampitt article
> has a JI tuning as the 18:22:27 tritriadic. 1/1 9/8 11/9 4/3 3/2 44/27
> 11/6 2/1. It has a rather Islamic sound and the 9/8 x 88/81 x 12/11
> tetrachord was known to Avicenna.
>
> --John

I actually had just produced this scale "on paper" as something to
investigate. I came up with a varient which puts the "large neutral
third" (27/22) in the position of the "major third" and the "small
neutral third" (11/9) in the "minor" position.

9/8 12/11 88/81 9/8 12/11 9/8 88/81
1/1 9/8 27/22 4/3 3/2 18/11 81/44

For some reason, the discussion of Harrisons septimal tuning

1/1 9/8 7/6 4/3 3/2 14/9 7/4

and the neutral thirds set off a light. "New algorithm to generate more
scales than I can deal with".

1) Drive the 3-limit stakes into the ground.
2) Pick a "third under test".
3) Boogie.

So another neutral type scale that comes out of this is
with the neutral third 49/40.

9/8 49/45 480/441 9/8 49/45 9/8 480/441
1/1 9/8 49/40 4/3 3/2 49/30 441/240

A more "rational" version of an 11/9 scale gives up some of the
niceness of Johns, or my counterproposal, but may be musically
useful too. Unfortunately, most of the fifths are flat, and it
doesn't obey the same "whole step half step" rules as the
others, but it has an interesting "11" oriented lydian mode.

10/9 11/10 12/11 9/8 10/9 11/10 12/11
1/1 10/9 11/9 4/3 3/2 5/3 11/6

Thats what happens when you forget to drive the "3-limit"
stakes into the ground.

Somebody give me "5", cuz I finally got my computer music
program up and can actually hear some of these things.

Bob Valentine