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	sathurugu comma
FJS name	[math]\displaystyle{ \text{P1}_{5,7,13} }[/math]
Special properties	square superparticular, reduced, reduced subharmonic
Tenney height (log2 nd)	23.9996
Weil height (log2 max(n, d))	24
Wilson height (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 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

See also

• Unnoticeable comma
• List of superparticular intervals