A 29-tone 7-limit scale with some averaged ratios

This is based on Pythagorean (14 fifths up and down), with schismas, septimal schismas and Beta 5s applied. The cents values are derived from the geometric means of ratios that map to the same pitch in extended Pythagorean, as in pairs like 81/80 and 64/30, and 45/32 and 7/5.

1/1
24.38520
87.34610
115.58705
10/9
9/8
8/7
32/27
6/5
5/4
410.69890
21/16
4/3
27/20
586.36795
613.63205
40/27
3/2
32/21
789.30110
8/5
5/3
27/16
7/4
16/9
9/5
1084.41295
1112.65390
1175.61480
2/1

~Danny~

A couple errors:

--- In tuning-math@yahoogroups.com, "Danny Wier" <dawiertx@s...> wrote:
> This is based on Pythagorean (14 fifths up and down), with schismas,
> septimal schismas and Beta 5s applied. The cents values are derived
from the
> geometric means of ratios that map to the same pitch in extended
> Pythagorean, as in pairs like 81/80 and 64/30, and 45/32 and 7/5.
>
> 87.34610

should be 88.32295 cents, because I prefer to use 135/128 instead of
256/243 in schismatic Pythagorean, and its inverse

> 1112.65390

should be 1111.67705.

But I still end up falling back on untempered 53-tone, since it itself
functions as a sort of compromise between 5-limit and 7-limit.

By the way: why are the intervals Beta 2 (aka septimal schisma) and
Beta 5 called Beta?

~Danny~