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 n⋅d) | 20.516 |
| Weil height (max(n, d)) | 1225 |
| Benedetti height (n⋅d) | 1499400 |
| 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
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
Optimal GPV 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 name derives from Noel, for the numerator or the denominator, when written in decimal system, is reminiscent of the date of Christmas.