1225/1224
| Ratio | 1225/1224 |
| Factorization | 2-3 × 3-2 × 52 × 72 × 17-1 |
| Monzo | [-3 -2 2 2 0 0 -1⟩ |
| Size in cents | 1.4138294¢ |
| Name | noellisma |
| Color name | 17uzzyy1, subizoyo 1sn, Subizoyo comma |
| FJS name | [math]\text{A1}^{5,5,7,7}_{17}[/math] |
| Special properties | square superparticular, reduced |
| Tenney height (log2 nd) | 20.516 |
| Weil height (log2 max(n, d)) | 20.5171 |
| Wilson height (sopfr (nd)) | 53 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.40662 bits |
| Comma size | unnoticeable |
| S-expressions | S35, S49 × S50 |
| open this interval in xen-calc | |
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
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
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 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 = 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: 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.