1225/1224: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = noellisma | | Name = noellisma | ||
| Color name = | | Color name = 17uzzyy1, subizoyo 1sn,<br>Subizoyo comma | ||
| | | Comma = yes | ||
}} | }} | ||
'''1225/1224''', the '''noellisma''', is a [[17-limit]] (also 2.3.5.7.17 subgroup) [[comma]] measuring about 1.41 [[cent]]s. It is the difference between [[35/34]] and [[36/35]], and between [[49/48]] and [[51/50]]. | '''1225/1224''', the '''noellisma''', is a [[17-limit]] (also 2.3.5.7.17 subgroup) [[comma]] measuring about 1.41 [[cent]]s. It is 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]] | * [[273/272]] and [[351/350]] | ||
* [[325/324]] and [[442/441]] | * [[325/324]] and [[442/441]] | ||
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* [[1089/1088]] and [[9801/9800]] | * [[1089/1088]] and [[9801/9800]] | ||
It factors into the following pairs: | It factors into the following superparticular pairs: | ||
* [[2401/2400]] and [[2500/2499]] | * [[2401/2400]] and [[2500/2499]] | ||
* [[2058/2057]] and [[3025/3024]] | * [[2058/2057]] and [[3025/3024]] | ||
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* [[1275/1274]] and [[31213/31212]] | * [[1275/1274]] and [[31213/31212]] | ||
== 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 | |||
{{Mapping|legend=2| 1 0 0 0 -3 | 0 1 0 0 -2 | 0 0 1 0 2 | 0 0 0 1 2 }} | |||
: sval mapping generators: ~2, ~3, ~5, ~7 | |||
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468 | |||
{{Optimal ET sequence|legend=1| 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 | |||
[[Mapping]]: <br> | |||
{| class="right-all" | |||
|- | |||
| [⟨ || 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 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468, ~11/8 = 551.3179, ~13/8 = 840.5277 | |||
== | {{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 }} | ||
== 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. | |||
== See also == | == See also == | ||
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* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Noellismic]] | [[Category:Noellismic]] | ||
[[Category:Commas referencing a famous use of a number]] | |||