2500/2499
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Ratio | 2500/2499 |
Factorization | 2^{2} × 3^{-1} × 5^{4} × 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 (log_{2} nd) | 22.5748 |
Weil height (log_{2} 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]}.