2080/2079: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = ibnsinma, sinaisma | |||
| Color name = 3o1ury1, tholuruyo 1sn, <br>Tholuruyo comma | |||
| Comma = yes | |||
| Name = ibnsinma | |||
| Color name = | |||
| | |||
}} | }} | ||
'''2080/2079''', the '''ibnsinma''', is | '''2080/2079''', the '''ibnsinma''', otherwise known as the '''sinaisma''', is an [[unnoticeable comma|unnoticeable]] [[13-limit]] [[comma]] measuring about 0.83 [[cent]]s. It is the amount by which a stack consisting of [[11/10]] and [[14/13]] falls short of Pythagorean minor third, [[32/27]]. | ||
== Commatic relations == | |||
This comma identifies itself as the difference between eight pairs of 13-limit superparticular ratios: | |||
* [[64/63]] and [[66/65]] | * [[64/63]] and [[66/65]] | ||
* [[78/77]] and [[81/80]] | * [[78/77]] and [[81/80]] | ||
* [[100/99]] and [[105/104]] | * [[100/99]] and [[105/104]] | ||
* [[325/324]] and [[385/384]] | * [[325/324]] and [[385/384]] | ||
* [[364/363]] and [[441/440]] | * [[364/363]] and [[441/440]] | ||
| Line 22: | Line 16: | ||
* [[676/675]] and [[1001/1000]] | * [[676/675]] and [[1001/1000]] | ||
* [[1716/1715]] and [[9801/9800]] | * [[1716/1715]] and [[9801/9800]] | ||
Not to mention some nonsuperparticular but useful ratios: | |||
* [[896/891]] and [[196/195]] | |||
* [[5120/5103]] and [[352/351]] | |||
* [[352/351]] and [[847/845]] | |||
Or as a relation in the four formal commas defined by [[Functional Just System]]: | |||
* ((64/63)([[1053/1024]])) / ((81/80)([[33/32]])). | |||
It factors into the following superparticular intervals: | It factors into the following superparticular intervals: | ||
| Line 30: | Line 32: | ||
== Temperaments == | == Temperaments == | ||
[[Tempering out]] this comma in the 13-limit defines the rank-5 '''ibnsinmic''' or '''sinaismic''' temperament, which enables the [[ibnsinmic chords|ibnsinmic a.k.a. sinaismic chords]], the [[essentially tempered chord]]s in the [[21-odd-limit]]. Another consequence is that it makes [[13/11]] and [[80/63]] [[fifth complement]]s of each other, as well as [[40/33]] and [[26/21]]. You may find a list of good [[equal temperament]]s that [[support]] this temperament below. | |||
[[Subgroup]]: 2.3.5.7.11.13 | |||
[[Mapping]]: <br> | |||
{| class="right-all" | |||
|- | |||
| [⟨ || 1 || 0 || 0 || 0 || 0 || -5 || ], | |||
|- | |||
| ⟨ || 0 || 1 || 0 || 0 || 0 || 3 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 1 || 0 || 0 || -1 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 1 || 0 || 1 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 0 || 1 || 1 || ]] | |||
|} | |||
: mapping generators: ~2, ~3, ~5, ~7, ~11 | |||
[[Optimal tuning]]s: | |||
: [[WE]]: ~2 = 1199.9519{{c}}, ~3/2 = 702.0756{{c}}, ~5/4 = 386.3580{{c}}, ~7/4 = 968.9979{{c}}, ~11/8 = 551.5774{{c}} | |||
: [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0843{{c}}, ~5/4 = 386.3184{{c}}, ~7/4 = 968.9934{{c}}, ~11/8 = 551.5497{{c}} | |||
{{Optimal ET sequence|legend=1| 12f, 14cf, 15, 17c, 19, 22f, 26, 29, 31f, 39df, 41, 46, 53, 58, 72, 87, 111, 130, 183, 198, 224, 270, 494, 764, 935, 1075, 1205, 1699, 2280, 2774e, 3326de, 3596de, 3907bdee, 4401bdee, 4671bde }} * | |||
<nowiki>*</nowiki> [[optimal patent val]]: [[3044edo|3044]] | |||
[[Badness]] (Sintel): 0.149 | |||
== Etymology == | |||
This comma was named by [[Margo Schulter]] in 2012, when it went by ''ibn Sina's comma''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105620.html Yahoo! Tuning List | ''123201/123200 chalmersia, 194481/194480 scintillisma'']</ref>. It was contracted to ''avicennma'' and later changed to ''ibnsinma'' by [[Gene Ward Smith]], all essentially meaning the same. Note that ''avicennma'' refers to Avicenna's enharmonic diesis ([[525/512]]) today. In 2023, [[Flora Canou]] proposed ''sinaisma'' as another spelling, reflecting the fact that the [[interval region]] arising from the same source is called ''[[sinaic]]''. | |||
== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
== References == | |||
[[Category:Ibnsinmic]] | [[Category:Ibnsinmic]] | ||
[[Category: | [[Category:Commas named after polymaths]] | ||
Latest revision as of 08:00, 4 March 2026
| Interval information |
sinaisma
Tholuruyo comma
reduced
S78⋅S79⋅S80
2080/2079, the ibnsinma, otherwise known as the sinaisma, is an unnoticeable 13-limit comma measuring about 0.83 cents. It is the amount by which a stack consisting of 11/10 and 14/13 falls short of Pythagorean minor third, 32/27.
Commatic relations
This comma identifies itself as the difference between eight pairs of 13-limit superparticular ratios:
- 64/63 and 66/65
- 78/77 and 81/80
- 100/99 and 105/104
- 325/324 and 385/384
- 364/363 and 441/440
- 540/539 and 729/728
- 676/675 and 1001/1000
- 1716/1715 and 9801/9800
Not to mention some nonsuperparticular but useful ratios:
Or as a relation in the four formal commas defined by Functional Just System:
It factors into the following superparticular intervals:
In Sagittal notation, it is the default comma represented by two minas or six tinas.
Temperaments
Tempering out this comma in the 13-limit defines the rank-5 ibnsinmic or sinaismic temperament, which enables the ibnsinmic a.k.a. sinaismic chords, the essentially tempered chords in the 21-odd-limit. Another consequence is that it makes 13/11 and 80/63 fifth complements of each other, as well as 40/33 and 26/21. 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 | -5 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 3 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 1 | ]] |
- mapping generators: ~2, ~3, ~5, ~7, ~11
- WE: ~2 = 1199.9519 ¢, ~3/2 = 702.0756 ¢, ~5/4 = 386.3580 ¢, ~7/4 = 968.9979 ¢, ~11/8 = 551.5774 ¢
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.0843 ¢, ~5/4 = 386.3184 ¢, ~7/4 = 968.9934 ¢, ~11/8 = 551.5497 ¢
Optimal ET sequence: 12f, 14cf, 15, 17c, 19, 22f, 26, 29, 31f, 39df, 41, 46, 53, 58, 72, 87, 111, 130, 183, 198, 224, 270, 494, 764, 935, 1075, 1205, 1699, 2280, 2774e, 3326de, 3596de, 3907bdee, 4401bdee, 4671bde *
Badness (Sintel): 0.149
Etymology
This comma was named by Margo Schulter in 2012, when it went by ibn Sina's comma[1]. It was contracted to avicennma and later changed to ibnsinma by Gene Ward Smith, all essentially meaning the same. Note that avicennma refers to Avicenna's enharmonic diesis (525/512) today. In 2023, Flora Canou proposed sinaisma as another spelling, reflecting the fact that the interval region arising from the same source is called sinaic.