1225/1224: Difference between revisions
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'''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]]. | ||
In terms of commas, it is the difference between the following pairs: | == Commatic relations == | ||
In terms of commas, it 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 '''noellismic temperament''', where [[18/17]] is split into two equal parts, each representing 35/34~36/35. | |||
== Etymology == | |||
The name derives from ''Noel'', for the numerator or the denominator, when written in decimal system, is reminiscent of the date of Christmas. | 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 == | ||
Revision as of 07:02, 13 November 2022
| Interval information |
reduced
S49 × S50
1225/1224, the noellisma, is a 17-limit (also 2.3.5.7.17 subgroup) comma measuring about 1.41 cents. It is the difference between 35/34 and 36/35, and between 49/48 and 51/50.
Commatic relations
In terms of commas, it 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 noellismic temperament, where 18/17 is split into two equal parts, each representing 35/34~36/35.
Etymology
The name derives from Noel, for the numerator or the denominator, when written in decimal system, is reminiscent of the date of Christmas.