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 height (log2 nd)	23.9996
Weil height (log2 max(n, d))	24
Wilson height (sopfr(nd))	55
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.20076 bits
Comma size	unnoticeable
S-expression	S64
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). It is a Mersenne 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 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