9504/9503
| Interval information |
fothusuthulo negative 2nd
reduced
(Shannon, [math]\sqrt{nd}[/math])
9504/9503, the lionelisma, is a 43-limit superparticular comma of about 0.18 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 216/215 and 221/220
- 560/559 and 595/594
- 1548/1547 and 1849/1848
- 1936/1935 and 2431/2430
- 2925/2924 and 4225/4224
It can be factored into the following superparticular intervals:
- 9801/9800 and 313600/313599
- 10450/10449 and 104976/104975
- 10626/10625 and 90000/89999
- 10648/10647 and 88452/88451
- 10830/10829 and 77616/77615
- 10880/10879 and 75141/75140
- 11340/11339 and 58696/58695
- 11935/11934 and 46656/46655
- 14080/14079 and 29241/29240
- 14400/14399 and 27951/27950
- 14535/14534 and 27456/27455
- 14652/14651 and 27048/27047
- 17545/17544 and 20736/20735
- 18792/18791 and 19228/19227
Temperaments
Tempering out this comma in the full 43-limit leads to the rank-13 temperament lionelismic. Using the 2.3.11.13.17.43 subgroup leads to the rank-5 temperament lionelic.
Lionelic
Subgroup: 2.3.11.13.17.43
Comma list: 9504/9503
| [⟨ | 1 | 1 | 3 | 3 | 4 | 4 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 3 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | -1 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.940, ~11/8 = 551.295, ~13/8 = 840.554, ~17/16 = 104.988
Optimal ET sequence: 5, 5eg, 7g, 8n, 10n, 12e, 16n, 17g, 24, 34n, 46, 58, 70, 94, 113, 157, 159, 181, 183, 277, 328, 390, 511, 605, 718, 788, 1506, 1783, 1966, 2207, 2925, 2995, 3713, 3896, 4684, 6103n, 6891n, 10604fgn
Badness (Sintel): 0.021
Etymology
This comma was named by Francium in 2025. It refers to 9504 Lionel, the asteroid, which in turn was named after Sir Lionel, a legendary knight of the Round Table.