4096/4095: Difference between revisions
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declared pife-like and also schisminic doesn't have prime 11 Tags: Reverted Visual edit |
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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 [[tina]]s. | 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. | ||
It is also the smallest superparticular ratio in the 2.3.5.7.13 subgroup. | It is also the smallest superparticular ratio in the 2.3.5.7.13 subgroup, and a [[PIFE comma|PIFE-like comma]]. | ||
== Temperaments == | == 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. | 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 | [[Subgroup]]: 2.3.5.7.13 | ||
[[Mapping]]: <br> | [[Mapping]]: <br> | ||
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|- | |- | ||
| ⟨ || 0 || 0 || 0 || 1 || 0 || -1 || ], | | ⟨ || 0 || 0 || 0 || 1 || 0 || -1 || ], | ||
|} | |} | ||
: mapping generators: ~2, ~3, ~5, ~7 | : mapping generators: ~2, ~3, ~5, ~7 | ||
{{Optimal ET sequence|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, | {{Optimal ET sequence|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, 9140cdf, 14463bcddfff, 17786bccddfff }} | ||
== See also == | == See also == | ||
Revision as of 11:59, 22 February 2026
| Interval information |
Sathurugu comma
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). It is also 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.
It is also the smallest superparticular ratio in the 2.3.5.7.13 subgroup, and a PIFE-like comma.
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
| [⟨ | 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