4096/4095

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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4096/4095, the schismina, is a 13-limit superparticular ratio of about 0.42 cents. It is the difference between:

• 64/63 and 65/64
• 27/26 and 8505/8192
• 36/35 and 1053/1024
• 35/32 and 128/117
• 39/32 and 128/105
• 45/32 and 128/91
• 13/8 and 512/315

It is also a Mersenne comma, and the smallest superparticular ratio in the 2.3.5.7.13 subgroup on which it is also a PIFE-like comma.

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 no-11 21-odd-limit. You may find a list of good equal temperaments that support this temperament below.

Subgroup: 2.3.5.7.13

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	],

mapping generators: ~2, ~3, ~5, ~7

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, 9140cdf, 14463bcddfff, 17786bccddfff

See also

• Unnoticeable comma
• List of superparticular intervals