Vuillafansisma
| Ratio | 25840/25839 |
| Factorization | 24 × 3-4 × 5 × 11-1 × 17 × 19 × 29-1 |
| Monzo | [4 -4 1 0 -1 0 1 1 0 -1⟩ |
| Size in cents | 0.066999518¢ |
| Name | vuillafansisma |
| Color name | 29u19o17o1uy2 twenunosoluyo 2nd |
| FJS name | [math]\text{m2}^{5,17,19}_{11,29}[/math] |
| Special properties | superparticular, reduced |
| Tenney height (log2 nd) | 29.3146 |
| Weil height (log2 max(n, d)) | 29.3146 |
| Wilson height (sopfr(nd)) | 101 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.19986 bits |
| Comma size | unnoticeable |
| open this interval in xen-calc | |
25840/25839, the vuillafansisma is a 29-limit superparticular comma of about 0.067 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 595/594 and 609/608
- 760/759 and 783/782
- 1216/1215 and 1276/1275
- 2080/2079 and 2262/2261
- 12376/12375 and 23751/23750
It can be factored into following superparticular commas:
- 27000/26999 and 601426/601425
- 28900/28899 and 244036/244035
- 30625/30624 and 165376/165375
- 30856/30855 and 158950/158949
Temperaments
Tempering out this comma in the full 29-limit leads to the rank-9 temperament vuillafansismic. Using the 2.3.5.11.17.19.29 subgroup leads to the rank-6 temperament vuillafansic.
Vuillafansismic
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 25840/25839
| [⟨ | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 7 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -4 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.961, ~5/4 = 386.311, ~7/4 = 968.826, ~11/8 = 551.325, ~13/8 = 840.528, ~17/16 = 104.946, ~19/16 = 297.503, ~23/16 = 628.274
Vuillafansic
Subgroup: 2.3.5.11.17.19.29
Comma list: 25840/25839
| [⟨ | 1 | 1 | 2 | 3 | 4 | 4 | 7 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | -4 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 1 | 1 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.961, ~5/4 = 386.311, ~11/8 = 551.325, ~17/16 = 104.946, ~19/16 = 297.503
Optimal ET sequence: 5eghj, 7ghjj, 7g, 10ej, 12eh, 12, 15g, 19egh, 22j, 22h, 24, 34h, 39gj, 41, 46hj, 50, 53g, 65, 87, 99e, 118, 183, 205, 270, 349gh, 354, 388, 422, 472, 487, 559, 653, 677, 836, 1323, 1395, 1513, 1783, 2000, 2836, 3395, 4231, 4619, 5178, 6014, 8014
Etymology
The vuillafansisma was named by Francium in 2024. It refers to the postal code of Vuillafans, France.