4096/4095: Difference between revisions
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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 [[64/63|septimal comma (64/63)]] and the [[65/64|wilsorma (65/64)]], and between the [[36/35|septimal quartertone (36/35)]] and the [[1053/1024|tridecimal quartertone (1053/1024)]]. | '''4096/4095''', the '''schismina''', is a [[13-limit]] [[superparticular]] [[ratio]] of about 0.42 cents. It is the difference between the [[64/63|septimal comma (64/63)]] and the [[65/64|wilsorma (65/64)]], and between the [[36/35|septimal quartertone (36/35)]] and the [[1053/1024|tridecimal quartertone (1053/1024)]]. | ||
By tempering it out is defined the '''schisminic temperament''', which enables the '''schisminic chords''', the essentially tempered chords in the 21-odd-limit. | 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 [[tina]]s. | ||
== 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]]: <br> | |||
[{{val| 1 0 0 0 0 12 }}, <br> | |||
{{val| 0 1 0 0 0 -2 }}, <br> | |||
{{val| 0 0 1 0 0 -1 }}, <br> | |||
{{val| 0 0 0 1 0 -1 }}, <br> | |||
{{val| 0 0 0 0 1 0 }}] | |||
Mapping generators: ~2, ~3, ~5, ~7, ~11 | |||
{{Val list|legend=1| 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 == | == See also == | ||
Revision as of 17:22, 28 March 2022
| Interval information |
reduced,
reduced subharmonic
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