1225/1224: Difference between revisions
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== Temperaments == | == 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. | 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. You may find a list of good equal temperaments that support this temperament below. | ||
[[Subgroup]]: 2.3.5.7.11.13.17 | |||
[[Mapping]]: | |||
<br>[{{val| 1 0 0 0 0 0 -3 }} | |||
<br>{{val| 0 1 0 0 0 0 -2 }} | |||
<br>{{val| 0 0 1 0 0 0 2 }} | |||
<br>{{val| 0 0 0 1 0 0 2 }} | |||
<br>{{val| 0 0 0 0 1 0 0 }} | |||
<br>{{val| 0 0 0 0 0 1 0 }} | |||
Mapping generators: ~2, ~3, ~5, ~7, ~11, ~13 | |||
{{Val list|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 == | == Etymology == | ||
Revision as of 18:46, 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. You may find a list of good equal temperaments that support this temperament below.
Subgroup: 2.3.5.7.11.13.17
Mapping:
[⟨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
Etymology
The name derives from Noel, for the numerator or the denominator, when written in decimal system, is reminiscent of the date of Christmas.