4096/4095: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = schismina | | Name = schismina | ||
| Color name = s3urg1, sathurugu 1sn,<br>Sathurugu comma | | Color name = s3urg1, sathurugu 1sn, <br>Sathurugu comma | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''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)]]. 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 [[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. | ||
== Temperaments == | == Temperaments == | ||
By tempering it out is defined the '''schisminic temperament''', which enables the | 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 | [[Subgroup]]: 2.3.5.7.11.13 | ||
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[[Category:Schisminic]] | [[Category:Schisminic]] | ||
[[Category:Mina]] | [[Category:Mina]] | ||
[[Category:Commas with unknown etymology]] | |||
Latest revision as of 03:29, 4 November 2024
| 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 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
| [⟨ | 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