# 2500/2499

 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 Color name 17urry4-3, subiruyoyo negative 3rd FJS name $\text{ddd}{-3}^{5,5,5,5}_{7,7,17}$ 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, $\sqrt{nd}$) ~1.2043 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:

Not to mention some nonsuperparticular but useful relations:

It factors into the following superparticular pairs:

## 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 sequence19, 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

Sval 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 sequence19, 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].