Girardisma
| Interval information |
fothunoloyoyo unison
reduced
10450/10449, the girardisma, is a 43-limit superparticular comma of about 0.17 cents.
Commatic relationships
This comma is the difference between the superparticular pair 1936/1935 and 2376/2375.
It can be factored into the following superparticular commas:
- 10648/10647 and 561925/561924
- 10880/10879 and 264385/264384
- 14535/14534 and 37180/37179
- 17545/17544 and 25840/25839
- 20125/20124 and 21736/21735
Temperaments
Tempering out this comma in the full 43-limit leads to the rank-13 temperament girardismic. Using the 2.3.5.11.19.43 subgroup leads to the rank-5 temperament girardic.
Girardismic
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41.43
Comma list: 10450/10449
| [⟨ | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 7 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -5 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 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 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 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 | 0 | 0 | 1 | 0 | 0 | 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 | 0 | 0 | 1 | 0 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.969, ~5/4 = 386.301, ~7/4 = 968.826, ~11/8 = 551.304, ~13/8 = 840.528, ~17/16 = 104.955, ~19/16 = 297.492, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036, ~37/32 = 251.344, ~41/32 = 429.062
Optimal ET sequence: 5fi, 5f, 5, 5g, 7dfghijjkllmmmn, 7dfghijjkllmn, 7dfghijjkmn, 7l, 8dhhimmn, 8dhhijjmmn, 10h, 12del, 12el, 12fijkmn, 14cfjjkklmmn, 14cfjjlmmn, 17cgn, 17cgkn, 19eghijjkklmnn, 19eghikklmnn, 22h, 24dn, 26eiknn, 26ik, 27egj, 27egij, 31fghjk, 34dhkn, 34dhjkmn, 34dhjklmn, 38dfijlm, 39dfgijkl, 39dfgijklmm, 45efghhijkmmnn, 46kln, 46ln, 53gikn, 53gkn, 53kn, 53ej, 58, 60eln, 72hijkllmn, 72hijkmn, 77m, 80, 80k, 87, 99efkmn, 111jln, 113l, 113, 118fikl, 121hhiklm, 125fm, 137n, 140kn, 144ghj, 145jkl, 152fjm, 152fgjm, 171, 183k, 183, 193, 217n, 217ln, 236dghin, 243eklmn, 270m, 270, 270i, 296, 311n, 373g, 388, 422, 422l, 525, 540, 566gjl, 639hjmn, 653, 711, 718, 764hj, 836, 863efgjk, 882, 908m, 954hjln, 1065, 1164fimn, 1178j, 1178, …
Girardic
Subgroup: 2.3.5.11.19.43
Comma list: 10450/10449
| [⟨ | 1 | 1 | 2 | 3 | 4 | 7 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | -5 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 2 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 1 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.969, ~5/4 = 386.301, ~11/8 = 551.304, ~19/16 = 297.492
Optimal ET sequence: 5, 7hn, 7, 12e, 14cn, 15, 19ehnn, 19h, 22h, 24n, 26, 27e, 31h, 34hn, 38, 41, 53n, 65, 118, 152, 217n, 270, 335, 460, 487, 566, 612, 677, 718, 836, 988, 1053, 1323, 1513, 1783, 2501, 2836, 4284, 4349, 4501, 6284, 7120, 8785, 9120
Etymology
The name girardisma was named by Francium in 2024. It refers to 10450 Girard, the asteroid. Which was in turn named after an American astronomer.