Hindoo scale

Hindoo scale:

sa = 1

ri = 256/243, 16/15 = (81/80) x (256/243)

Ri = 10/9, 9/8 = (81/80) x (10/9)

ga = 32/27, 6/5 = (81/80) x (32/27)

Ga = 5/4, 81/64 = (81/80) x (5/4)

ma = 4/3, 20/27 = (81/80) x (4/3)

Ma = 64/45 , 45/32, 729/512 = (81/80) x (45/32)

pa = 40/27, 3/2 = (81/80) x (40/27)

dha = 128/81, 8/5 = (81/80) x (128/81)

Dha = 5/3, 27/16 = (81/80) x (5/3)

ni = 16/9, 9/5 = (81/80) x (16/9)

Ni = 15/8, 243/128 = (81/80) x (15/8)

Now for some reason they drop Ma and replace with tritone:

22 = 1 + 21 (<=> 256/243 x 243/128 = 2)

= 2 + 20 (<=> 16/15 x 15/8 = 2)

= 3 + 19 (<=> 10/9 x 9/5 = 2)

= 4 + 18 (<=> 9/8 x 16/9 = 2)

= 5 + 17 (<=> 32/27 x 27/16 = 2)

= 6 + 16 (<=> 6/5 x 5/3 = 2)

= 7 + 15 (<=> 5/4 x 8/5 = 2)

= 8 + 14 (<=> 81/64 x 128/81 = 2)

= 9 + 13 (<=> 4/3 x 3/2 = 2).

= 10 + 12 (<=> 27/20 x 40/27 = 2)

= 11 + 11 (<=> 2^(1/2) x 2^(1/2) =

So, it's true, the steps are way off from 22-tET. However, I notice
that there are three step sizes:

a=81/80
b=25/24
c=256/243

Also the difference between c/b is 2048/2025, the diaschisma.

So you get this scale: 1,c,a,b,a,c,a,b,a,c,a, and b,a together for
the 11th step, replaced by 2^1/2. Which for me is no big deal, since
the "tritone" isn't one of the Affine group intervals. (I call 11 of
22 the tritone). The Affine transform permutes the odd intervals,
except for 11. However, 11 is used in the "isomeric relation"

So I thought, cool, cuz I am concerned with odd intervals, the evens
merely adjust the odds by the syntonic comma and the odds are related
by the diaschisma!

If anyone is interested in my paper on musical set theory in 22-tET,
please see tuning-math Files-Paul Hj's Stuff - Isomeric Sets

PGH