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
Color name	17urry4-3, subiruyoyo negative 3rd
FJS name	[math]\displaystyle{ \text{ddd}{-3}^{5,5,5,5}_{7,7,17} }[/math]
Special properties	square superparticular, reduced
Tenney norm (log2 nd)	22.5748
Weil norm (log2 max(n, d))	22.5754
Wilson norm (sopfr(nd))	58
Comma size	unnoticeable
S-expression	S50
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2500/2499, the sperasma, is an unnoticeable 17-limit superparticular comma with a size of about 0.693 cents. Among other things, it is the difference between the small septimal sixth-tone of 50/49 and the large septendecimal sixth-tone of 51/50. It also represents the little gap between 17/12 and a stack of two 25/21's.

Commatic relations

This comma is the difference between the following superparticular pairs:

• 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. You may find a list of good equal temperaments that support these temperaments below.

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]]

mapping generators: ~2, ~3, ~5, ~7

Optimal tunings:

• WE: ~2 = 1199.9902 ¢, ~3/2 = 701.9772 ¢, ~5/4 = 386.2274 ¢, ~7/4 = 968.9230 ¢
• CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.9754 ¢, ~5/4 = 386.2178 ¢, ~7/4 = 968.9184 ¢

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

Badness (Sintel): 0.122

Sperasmic

Subgroup: 2.3.5.7.11.13.17

Mapping:

[⟨	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 tunings:

• WE: ~2 = 1199.9902 ¢, ~3/2 = 701.9772 ¢, ~5/4 = 386.2274 ¢, ~7/4 = 968.9230 ¢, ~11/8 = 551.3474 ¢, ~13/8 = 840.5571 ¢
• CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.9754 ¢, ~5/4 = 386.2178 ¢, ~7/4 = 968.9184 ¢, ~11/8 = 551.3352 ¢, ~13/8 = 840.5461 ¢

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

Badness (Sintel): 1.13

Etymology

The sperasma was named by Aura in 2023. It comes from the Latin verb "spērāre" meaning "to hope" or "to fear".

See also

• List of superparticular intervals