4096/4095

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Interval information
Ratio 4096/4095
Monzo [12 -2 -1 -1 0 -1
Size in cents 0.42272
Name(s) schismina
Color name sathurugu comma
FJS name P15,7,13
open this interval in xen-calc

4096/4095, the schismina, is a 13-limit superparticular ratio of about 0.42 cents. It is the difference between the septimal comma (64/63) and the wilsorma (65/64), and between the septimal quartertone (36/35) and the tridecimal quartertone (1053/1024).

The name lends itself to the general interval size measure knowns as the mina. In Sagittal notation, 4096/4095 is the default comma represented by a mina or three tinas.

Temperaments

By tempering it out is defined the schisminic temperament, which enables the schisminic chords, the essentially tempered chords in the 21-odd-limit. You may find a list of good equal temperaments that support this temperament below.

Subgroup: 2.3.5.7.11.13

Mapping:
[1 0 0 0 0 12],
0 1 0 0 0 -2],
0 0 1 0 0 -1],
0 0 0 1 0 -1],
0 0 0 0 1 0]]

Mapping generators: ~2, ~3, ~5, ~7, ~11

Optimal GPV sequence22, 31, 41, 46, 53, 77, 84, 87, 118, 130, 183, 217, 224, 270, 494, 764, 935, 1012, 1236, 1506, 3236, 3323, 3817, 5323f, 9140cdef, 14463bcddeefff, 17786bccddeeefff

See also