4096/4095: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = | | Name = minisma, minic comma | ||
| Color name = s3urg1, sathurugu 1sn, <br>Sathurugu comma | | Color name = s3urg1, sathurugu 1sn, <br>Sathurugu comma | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''4096/4095''', the ''' | '''4096/4095''', the '''minisma''' or '''minic comma''', also described as the ''tridecimal schisma'' or ''tridecimal schismina''<ref>[https://sagittal.org/sagittal.pdf Sagittal – A Microtonal Notation System] by [[George Secor|George D. Secor]] and [[Dave Keenan|David C. Keenan]]</ref>, is an [[unnoticeable comma|unnoticeable]] [[13-limit]] [[superparticular]] [[comma]] 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 also a [[Mersenne comma]]. | ||
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. | |||
== Temperaments == | == Temperaments == | ||
By tempering | By tempering out this comma in the full 13-limit is defined the '''minismic''' temperament, which enables the [[minismic 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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| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || ]] | | ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || ]] | ||
|} | |} | ||
: mapping generators: ~2, ~3, ~5, ~7, ~11 | : mapping generators: ~2, ~3, ~5, ~7, ~11 | ||
{{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, 9140cdef, 14463bcddeefff, 17786bccddeeefff }} | {{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, 9140cdef, 14463bcddeefff, 17786bccddeeefff }} | ||
== Etymology == | |||
The names ''minisma'' and ''minic comma'' were given by [[Flora Canou]] in 2026 after the general interval size measure knowns as the ''[[mina]]'', because 4096/4095 is the default comma represented by a mina (or three [[tina]]s) in [[Sagittal notation]]. ''Mina'' is a clipping of ''schismina'', which describes a range of commas in Sagittal notation, and in turn comes from ''schisma'' (the interval region) + -in (diminutive suffix). [[Eufalesio]] proposed ''trinyblisma'', for the denominator is the largest integer that can be written in 3 {{w|nibble|nybbles}} (1.5 bytes). | |||
== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category: | == References == | ||
<references/> | |||
[[Category:Minismic]] | |||
[[Category:Mina]] | [[Category:Mina]] | ||
[[Category:Commas | [[Category:Commas named after their interval size]] | ||
Revision as of 09:23, 3 March 2026
| Interval information |
minic comma
Sathurugu comma
reduced,
reduced subharmonic
4096/4095, the minisma or minic comma, also described as the tridecimal schisma or tridecimal schismina[1], is an unnoticeable 13-limit superparticular comma 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.
It is also the smallest superparticular ratio in the 2.3.5.7.13 subgroup.
Temperaments
By tempering out this comma in the full 13-limit is defined the minismic temperament, which enables the minismic 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
Etymology
The names minisma and minic comma were given by Flora Canou in 2026 after the general interval size measure knowns as the mina, because 4096/4095 is the default comma represented by a mina (or three tinas) in Sagittal notation. Mina is a clipping of schismina, which describes a range of commas in Sagittal notation, and in turn comes from schisma (the interval region) + -in (diminutive suffix). Eufalesio proposed trinyblisma, for the denominator is the largest integer that can be written in 3 nybbles (1.5 bytes).