# 375/374

 Ratio 375/374 Factorization 2-1 × 3 × 53 × 11-1 × 17-1 Monzo [-1 1 3 0 -1 0 -1⟩ Size in cents 4.6227906¢ Names ursulisma,ursulic comma Color name 17u1uy3-2, sulutriyo negative 2nd FJS name $\text{dd}{-2}^{5,5,5}_{11,17}$ Special properties superparticular,reduced Tenney height (log2 nd) 17.0976 Weil height (log2 max(n, d)) 17.1015 Wilson height (sopfr (nd)) 48 Harmonic entropy(Shannon, $\sqrt{nd}$) ~1.39713 bits Comma size small open this interval in xen-calc

The ursulisma, or ursulic comma, is a 17-limit (also 2.3.5.11.17 subgroup) superparticular comma with a ratio of 375/374. It is the interval that separates 17/15 from 25/22, as well as separating 25/17 from 22/15.

## Commatic relations

This comma identifies itself as the difference between the following superparticular pairs:

It factors into the following superparticular pairs:

Not to mention some nonsuperparticular but useful relations:

## Temperaments

Tempering out this comma in the 17-limit leads to the rank-6 ursulismic temperament. Tempering it out in the 2.3.5.11.17 subgroup leads to the rank-4 ursulic temperament, enabling ursulismic chords. You may find a list of good equal temperaments that support these temperaments below.

### Ursulismic

Subgroup: 2.3.5.7.11.13.17

 [⟨ 1 0 0 0 0 0 -1 ], ⟨ 0 1 0 0 0 0 1 ], ⟨ 0 0 1 0 0 0 3 ], ⟨ 0 0 0 1 0 0 0 ], ⟨ 0 0 0 0 1 0 -1 ], ⟨ 0 0 0 0 0 1 0 ]]
mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.8093, ~5/4 = 385.3757, ~7/4, ~11/8 = 552.0120, ~13/8

Optimal ET sequence12f, 15g, 16, 19g, 22, 27eg, 29g, 31, 38df, 41g, 43, 49fg, 50, 53, 60e, 65d, 72, 103, 121, 152fg, 159, 171, 193, 224, 296, 395e, 467, 554g, 691eg

### Ursulic

Subgroup: 2.3.5.11.17

Sval mapping[1 0 0 0 -1], 0 1 0 0 1], 0 0 1 0 3], 0 0 0 1 -1]]

sval mapping generators: ~2, ~3, ~5, ~11

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.8093, ~5/4 = 385.3757, ~11/8 = 552.0120

Optimal ET sequence12, 15g, 19g, 22, 31, 34, 50, 53, 56, 60e, 65, 72, 137, 159, 296, 455, 489

## Etymology

The ursulisma was named by Aura and VIxen in 2023. It refers to 375 Ursula, the asteroid. After some naming attempts in the XA Discord Server that turned out dissatisfactory to the participants, VIxen came up with the idea to look up the list of minor planets in case everything else failed, and Aura was the first to put together the word ursulisma.