375/374
| Ratio | 375/374 |
| Factorization | 2-1 × 3 × 53 × 11-1 × 17-1 |
| Monzo | [-1 1 3 0 -1 0 -1⟩ |
| Size in cents | 4.6227906¢ |
| Names | ursulisma, ursulic comma |
| Color name | 17u1uy3-2, sulutriyo negative 2nd |
| FJS name | [math]\text{dd}{-2}^{5,5,5}_{11,17}[/math] |
| Special properties | superparticular, reduced |
| Tenney height (log2 nd) | 17.0976 |
| Weil height (log2 max(n, d)) | 17.1015 |
| Wilson height (sopfr (nd)) | 48 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.4907 bits |
| Comma size | small |
| open this interval in xen-calc | |
The ursulisma, or ursulic comma, is a 17-limit (also 2.3.5.11.17 subgroup) superparticular comma with a ratio of 375/374. It is the interval that separates 17/15 from 25/22, as well as separating 25/17 from 22/15.
Commatic relations
This comma identifies itself as the difference between the following superparticular pairs:
- 100/99 and 136/135
- 120/119 and 176/175
- 225/224 and 561/560
- 273/272 and 1001/1000
- 325/324 and 2431/2430
- 364/363 and 12376/12375
It factors into the following superparticular pairs:
Not to mention some nonsuperparticular but useful relations:
Temperaments
Tempering out this comma in the 17-limit leads to the rank-6 ursulismic temperament. Tempering it out in the 2.3.5.11.17 subgroup leads to the rank-4 ursulic temperament, enabling ursulismic chords. You may find a list of good equal temperaments that support these temperaments below.
Ursulismic
Subgroup: 2.3.5.7.11.13.17
| [⟨ | 1 | 0 | 0 | 0 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 0 | 3 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 1 | 0 | ]] |
- mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.8093, ~5/4 = 385.3757, ~7/4, ~11/8 = 552.0120, ~13/8
Optimal ET sequence: 12f, 15g, 16, 19g, 22, 27eg, 29g, 31, 38df, 41g, 43, 49fg, 50, 53, 60e, 65d, 72, 103, 121, 152fg, 159, 171, 193, 224, 296, 395e, 467, 554g, 691eg
Ursulic
Subgroup: 2.3.5.11.17
Sval mapping: [⟨1 0 0 0 -1], ⟨0 1 0 0 1], ⟨0 0 1 0 3], ⟨0 0 0 1 -1]]
- sval mapping generators: ~2, ~3, ~5, ~11
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.8093, ~5/4 = 385.3757, ~11/8 = 552.0120
Optimal ET sequence: 12, 15g, 19g, 22, 31, 34, 50, 53, 56, 60e, 65, 72, 137, 159, 296, 455, 489
Etymology
The ursulisma was named by Aura and VIxen in 2023. It refers to 375 Ursula, the asteroid. After some naming attempts in the XA Discord Server that turned out dissatisfactory to the participants, VIxen came up with the idea to look up the list of minor planets in case everything else failed, and Aura was the first to put together the word ursulisma.