4096/4095

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). It is also a Mersenne comma.

Interval information

Ratio	4096/4095
Factorization	212 × 3-2 × 5-1 × 7-1 × 13-1
Monzo	[12 -2 -1 -1 0 -1⟩
Size in cents	0.4227162¢
Name	schismina
Color name	s3urg1, sathurugu 1sn, Sathurugu comma
FJS name	[math]\displaystyle{ \text{P1}_{5,7,13} }[/math]
Special properties	square superparticular, reduced, reduced subharmonic
Tenney norm (log2 nd)	23.9996
Weil norm (log2 max(n, d))	24
Wilson norm (sopfr(nd))	55
Comma size	unnoticeable
S-expression	S64
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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.

It is also the smallest superparticular ratio in the 2.3.5.7.13 subgroup.

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 ET sequence: 22, 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

• Unnoticeable comma
• List of superparticular intervals