2500/2499

Interval information

Ratio	2500/2499
Factorization	22 × 3-1 × 54 × 7-2 × 17-1
Monzo	[2 -1 4 -2 0 0 -1⟩
Size in cents	0.6926322¢
Name	sperasma
FJS name	[math]\displaystyle{ \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
Comma size	unnoticeable
S-expression	S50
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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:

• 540/539 and 1377/1375
• 2025/2023 and 1701/1700

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".

See also

• Unnoticeable comma
• List of superparticular intervals