2500/2499
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| Ratio | 2500/2499 |
| Factorization | 22 × 3-1 × 54 × 7-2 × 17-1 |
| Monzo | [2 -1 4 -2 0 0 -1⟩ |
| Size in cents | 0.69263216¢ |
| Name | sperasma |
| FJS name | [math]\text{ddd}{-3}^{5,5,5,5}_{7,7,17}[/math] |
| Special properties | square superparticular, reduced |
| Tenney height (log2 nd) | 22.5748 |
| Weil height (log2 max(n, d)) | 22.5754 |
| Wilson height (sopfr (nd)) | 58 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.401 bits |
| Comma size | unnoticeable |
| S-expression | S50 |
| open this interval in xen-calc | |
The sperasma is the 17-limit superparticular comma with a ratio of 2500/2499.
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.
Etymology
The sperasma was named by Aura in 2023. It comes from the Latin verb "spērāre" meaning "to hope" or "to fear"[1].