Friesachisma
| Ratio | 9361/9360 |
| Factorization | 2-4 × 3-2 × 5-1 × 11 × 13-1 × 23 × 37 |
| Monzo | [-4 -2 -1 0 1 -1 0 0 1 0 0 1⟩ |
| Size in cents | 0.18495102¢ |
| Name | friesachisma |
| Color name | 37o23o3u1og2 thisotwethothulogu 2nd |
| FJS name | [math]\text{m}{-2}^{11,23,37}_{5,13}[/math] |
| Special properties | superparticular, reduced |
| Tenney height (log2 nd) | 26.3847 |
| Weil height (log2 max(n, d)) | 26.3849 |
| Wilson height (sopfr(nd)) | 103 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.19854 bits |
| Comma size | unnoticeable |
| open this interval in xen-calc | |
9361/9360, the friesachisma, is a 37-limit superparticular comma of about 0.18 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
It can be factored into the following superparticular intervals:
- 9801/9800 and 208495/208494
- 10241/10240 and 108928/108927
- 10557/10556 and 82621/82620
- 10626/10625 and 78625/78624
- 10648/10647 and 77441/77440
- 10693/10692 and 75141/75140
- 11914/11913 and 43681/43680
- 12673/12672 and 35816/35815
- 14652/14651 and 25921/25920
- 16576/16575 and 21505/21504
- 18241/18240 and 19228/19227
Temperaments
Tempering out this comma leads to the rank-11 temperament friesachismic. Using the 2.3.5.11.13.23.37 subgroup leads to the rank-6 temperament friesachic.
Friesachismic
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37
Comma list: 9361/9360
| [⟨ | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | ]] |
Optimal tuning (CTE): ~2=1\1, ~3/2 = 701.965, ~5/4 = 386.325, ~7/4 = 968.826, ~11/8 = 551.293, ~13/8 = 840.556, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.232, ~29/16 = 1029.577, ~31/16 = 1145.036
Optimal ET sequence: 5cfik, 5egj, 5eghj, 6fhijl, 7dfghijjk, 8di, 9gijk, 10jk, 10k, 10, 10h, 12l, 12fk, 12fjk, 14cfjjkkl, 14cfjjl, 15gkl, 16j, 17cgk, 17cghk, 19egh, 21, 22i, 22fh, 24, 26ik, 29gjk, 29gk, 31fghjk, 31l, 34dhk, 38dfij, 39dfgijkl, 46, 50jk, 50k, 53, 53j, 58hik, 62, 65d, 68jl, 72hijk, 72ijk, 80, 80k, 94, 99efk, 103hl, 125f, 130j, 145jkl, 149, 152fgj, 159k, 181, 183k, 183, 198gl, 212ghj, 212gh, 217, 224, 239, 243e, 248h, 270, 311k, 311, 422l, 487, 525, 566gjl, 571, 597ik, 631, 639hj, 692ik, 718, 764j, 764hj, 814k, 814, 863efgjk, 882, 908, 1012, 1106, 1164fi, …
Friesachic
Subgroup: 2.3.5.11.13.23.37
Comma list: 9361/9360
| [⟨ | 1 | 1 | 2 | 3 | 3 | 4 | 4 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | 2 | ], |
| ⟨ | 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 = 701.965, ~5/4 = 386.325, ~11/8 = 551.293, ~13/8 = 840.556, ~23/16 = 628.232
Optimal ET sequence: 5e, 7fi, 7, 8i, 10, 12l, 12f, 14cfl, 15l, 19e, 22i, 22f, 24, 29, 34, 46, 50, 53, 65, 79l, 80, 87, 96, 118, 125f, 130, 152f, 159, 183, 224, 277, 357, 407, 684, 764, 988, 1012, 1171, 1448, 1696, 1855l, 2000, 2277, 2684, 5144, 6132, 7828l, 8816il, 9828il, 10512eil
Etymology
The friesachisma was named by Francium in 2024, referencing the postal code of Friesach, Austria.