1225/1224: Difference between revisions
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'''1225/1224''', the '''noellisma''', is | '''1225/1224''', the '''noellisma''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] (also 2.3.5.7.17-[[subgroup]]) [[comma]] measuring about 1.41 [[cent]]s. It is the amount by which a stack of two [[7/6]] subminor thirds exceeds [[34/25]], and the amount by which a stack of two [[35/24]] subfifths exceeds [[17/8]], one octave above [[17/16]]. It is also the difference between [[35/34]] and [[36/35]], and between [[49/48]] and [[51/50]]. | ||
== Commatic relations == | == Commatic relations == | ||
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== Temperaments == | == Temperaments == | ||
Tempering out this comma in the 17-limit results in the rank-6 '''noellismic | [[Tempering out]] this comma in the 17-limit results in the rank-6 '''noellismic''' temperament, or in the 2.3.5.7.17 subgroup, the rank-4 '''noellic''' temperament. In either case [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below. | ||
=== Noellic === | === Noellic === | ||
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{{Mapping|legend=2| 1 0 0 0 -3 | 0 1 0 0 -2 | 0 0 1 0 2 | 0 0 0 1 2 }} | {{Mapping|legend=2| 1 0 0 0 -3 | 0 1 0 0 -2 | 0 0 1 0 2 | 0 0 0 1 2 }} | ||
: mapping generators: ~2, ~3, ~5, ~7 | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.0440{{c}}, ~5/4 = 386.1228{{c}}, ~7/4 = 968.5468{{c}} | |||
[[Optimal tuning]] ([[CTE]]): ~2 = | |||
{{Optimal ET sequence|legend=1| 19g, 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d }} | {{Optimal ET sequence|legend=1| 19g, 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d }} | ||
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| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]] | | ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]] | ||
|} | |} | ||
: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13 | : mapping generators: ~2, ~3, ~5, ~7, ~11, ~13 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.0440{{c}}, ~5/4 = 386.1228{{c}}, ~7/4 = 968.5468{{c}}, ~11/8 = 551.3179{{c}}, ~13/8 = 840.5277{{c}} | ||
{{Optimal ET sequence|legend=1| 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }} | {{Optimal ET sequence|legend=1| 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }} | ||
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== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Noellismic]] | [[Category:Noellismic]] | ||
[[Category:Commas referencing a famous use of a number]] | [[Category:Commas referencing a famous use of a number]] | ||
Revision as of 10:13, 25 March 2026
| Interval information |
Subizoyo comma
reduced
S49⋅S50
1225/1224, the noellisma, is an unnoticeable 17-limit (also 2.3.5.7.17-subgroup) comma measuring about 1.41 cents. It is the amount by which a stack of two 7/6 subminor thirds exceeds 34/25, and the amount by which a stack of two 35/24 subfifths exceeds 17/8, one octave above 17/16. It is also the difference between 35/34 and 36/35, and between 49/48 and 51/50.
Commatic relations
This comma is the difference between the following superparticular pairs:
- 273/272 and 351/350
- 325/324 and 442/441
- 375/374 and 540/539
- 385/384 and 561/560
- 595/594 and 1156/1155
- 625/624 and 1275/1274
- 715/714 and 1716/1715
- 833/832 and 2601/2600
- 1089/1088 and 9801/9800
It factors into the following superparticular pairs:
Temperaments
Tempering out this comma in the 17-limit results in the rank-6 noellismic temperament, or in the 2.3.5.7.17 subgroup, the rank-4 noellic temperament. In either case 18/17 is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below.
Noellic
Subgroup: 2.3.5.7.17
Subgroup-val mapping: [⟨1 0 0 0 -3], ⟨0 1 0 0 -2], ⟨0 0 1 0 2], ⟨0 0 0 1 2]]
- mapping generators: ~2, ~3, ~5, ~7
Optimal tuning (CTE): ~2 = 1200.0000 ¢, ~3/2 = 702.0440 ¢, ~5/4 = 386.1228 ¢, ~7/4 = 968.5468 ¢
Optimal ET sequence: 19g, 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d
Noellismic
Subgroup: 2.3.5.7.11.13.17
| [⟨ | 1 | 0 | 0 | 0 | 0 | 0 | -3 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | -2 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 0 | 2 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 0 | 2 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 1 | 0 | ]] |
- mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
Optimal tuning (CTE): ~2 = 1200.0000 ¢, ~3/2 = 702.0440 ¢, ~5/4 = 386.1228 ¢, ~7/4 = 968.5468 ¢, ~11/8 = 551.3179 ¢, ~13/8 = 840.5277 ¢
Optimal ET sequence: 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d
Etymology
The noellisma was named by Flora Canou in 2022. The name derives from Noel, for the numerator or the denominator, when written in decimal system, is reminiscent of the date of Christmas.