1225/1224
| Interval information |
Subizoyo comma
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, or in the 2.3.5.7.17 subgroup, the 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.
Noellismic
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
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
Noellic
Subgroup: 2.3.5.7.17
Sval mapping:
[⟨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 GPV sequence: Template:Val list
Etymology
The name derives from Noel, for the numerator or the denominator, when written in decimal system, is reminiscent of the date of Christmas.