2500/2499
The sperasma is the 17-limit superparticular comma with a ratio of 2500/2499. Among other things, it equates a stack of two 25/21s with a 17/12.
| Interval information |
reduced
Commatic relations
This comma is the difference between the following superparticular pairs:
- 50/49 and 51/50
- 120/119 and 126/125
- 375/374 and 441/440
- 625/624 and 833/832
- 715/714 and 1001/1000
- 1225/1224 and 2401/2400
- 1275/1274 and 2601/2600
- 2080/2079 and 12376/12375
Not to mention some nonsuperparticular but useful relations:
It factors into the following superparticular pairs:
- 4375/4374 and 5832/5831
- 3025/3024 and 14400/14399
Temperaments
Tempering out this comma in the 17-limit results in the rank-6 sperasmic temperament, or in the the 2.3.5.7.17 subgroup, the rank-4 speric temperament. You may find a list of good equal temperaments that support these temperaments below.
Sperasmic
Subgroup: 2.3.5.7.11.13.17
| [⟨ | 1 | 0 | 0 | 0 | 0 | 0 | 2 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 0 | 4 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 0 | -2 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 1 | 0 | ]] |
- mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9677, ~5/4 = 386.2047, ~7/4 - 968.9056, ~11/8, ~13/8
Optimal ET sequence: 19, 24d, 27eg, 29g, 31, 41g, 43, 53g, 58g, 60e, 68, 72, 103, 111, 140, 171, 183, 239f, 243e, 270, 311, 354, 414, 422, 494, 581, 764, 935, 1075, 1106, 1178, 1672, 1942, 2113, 2253, 2535, 2805g, 3299d, 3713, 3983g, 4477
Speric
Subgroup: 2.3.5.7.17
Subgroup-val mapping: [⟨1 0 0 0 2], ⟨0 1 0 0 -1], ⟨0 0 1 0 4], ⟨0 0 0 1 -2]]
- sval mapping generators: ~2, ~3, ~5, ~7
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9677, ~5/4 = 386.2047, ~7/4 - 968.9056
Optimal ET sequence: 19, 27g, 31, 41g, 56, 60, 68, 72, 99, 171, 494, 525, 581, 593, 665, 764, 836, 935, 1771, 1942, 2706, 2877, 4477, 4648
Etymology
The sperasma was named by Aura in 2023. It comes from the Latin verb "spērāre" meaning "to hope" or "to fear"[1].