Tetrameantone

The tetrameantone temperament is a nonoctave meantone temperament, tempering out the 81/80 in the 4.3.5 subgroup and repeating at the double octave 4/1. It is generated by 4/3 and, like in normal meantone temperament, 4 of them make a 8/5 plus an octave.

Interval chain

Generators	Cents (POTE)	Approximate ratios
-7	1273.671	25/12
-6	1777.432	45/16
-5	2281.193	15/4
-4	384.955	5/4
-3	888.716	5/3
-2	1392.477	9/4, 20/9
-1	1896.239	3/1
0	0.000	1/1
1	503.761	4/3
2	1007.523	16/9, 9/5
3	1511.284	12/5
4	2015.045	16/5
5	118.807	16/15
6	622.568	64/45
7	1126.329	48/25

Tetrameantone on tritave

Tritave-repeating tetrameantone (3.4.5 subgroup) is made by cutting off the 4/3 interval range of the tetratave scale. extension will start at 3.4.5.14 subgroup. If we want strict no-twos subgroup, will be 3.5.13.

Generators	Cents (15edt)	Approximate ratios 3.4.5.14	3.5.13
-7	253.594	7/6	15/13
-6	760.782	25/16, 63/40, 14/9	125/81
-5	1267.970	25/12, 21/10	27/13
-4	1775.158	45/16, 14/5	25/9
-3	380.391	5/4	81/65
-2	887.579	27/16, 5/3	5/3
-1	1394.767	9/4, 20/9	729/325
0	0.000	1/1	1/1
1	507.188	4/3, 27/20	325/243
2	1014.376	16/9, 9/5	9/5
3	1521.564	12/5	65/27
4	126.797	16/15, 15/14	27/25
5	633.985	36/25, 10/7	13/9
6	1141.173	48/25, 40/21, 27/14	243/125
7	1648.361	18/7	13/5

b15 & b4p

Subgroup: 3.5.13

Comma list: 531441/528125

Sval mapping: [⟨1 2 1], ⟨0 -2 5]]

Sval mapping generators: ~3, ~325/243

POTE generator: ~325/243 = 508.099