# 2058/2057

 Ratio 2058/2057 Factorization 2 × 3 × 73 × 11-2 × 17-1 Monzo [1 1 0 3 -2 0 -1⟩ Size in cents 0.84142604¢ Name xenisma Color name 17u1uuz32, sululutrizo 2nd FJS name $\text{M2}^{7,7,7}_{11,11,17}$ Special properties superparticular,reduced Tenney height (log2 nd) 22.0134 Weil height (log2 max(n, d)) 22.0141 Wilson height (sopfr (nd)) 65 Harmonic entropy(Shannon, $\sqrt{nd}$) ~1.20641 bits Comma size unnoticeable open this interval in xen-calc

2058/2057, the xenisma, is an unnoticeable 17-limit (also 2.3.7.11.17 subgroup) comma measuring about 0.84 cents. It is the amount by which a stack of two 14/11's exceed 34/21.

## 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 xenismic temperament, or in the 2.3.7.11.17 subgroup, the rank-4 xenic temperament. In either case it enables xenismic chords.

### Xenic

Subgroup: 2.3.7.11.17

Comma list: 2058/2057

Sval mapping[1 0 0 0 1], 0 1 0 0 1], 0 0 1 0 3], 0 0 0 1 -2]]

sval mapping generators: ~2, ~3, ~7, ~11
• CTE: ~2 = 1\1, ~3/2 = 701.9397, ~7/4 = 968.6818, ~11/8 = 551.4639
• CWE: ~2 = 1\1, ~3/2 = 701.9446, ~7/4 = 968.6908, ~11/8 = 551.4738

### Xenismic

Subgroup: 2.3.5.7.11.13.17

Comma list: 2058/2057

 [⟨ 1 0 0 0 0 0 1 ], ⟨ 0 1 0 0 0 0 1 ], ⟨ 0 0 1 0 0 0 0 ], ⟨ 0 0 0 1 0 0 3 ], ⟨ 0 0 0 0 1 0 -2 ], ⟨ 0 0 0 0 0 1 0 ]]
mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
• CTE: ~2 = 1\1, ~3/2 = 701.9397, ~5/4 = 386.3137, ~7/4 = 968.6818, ~11/8 = 551.4639, ~13/8 = 840.5277
• CWE: ~2 = 1\1, ~3/2 = 701.9445, ~5/4 = 386.3208, ~7/4 = 968.6908, ~11/8 = 551.4738, ~13/8 = 840.5389

Optimal ET sequence43, 46, 58, 72, 103, 121, 149, 161, 190g, 224, 270, 311, 354, 400, 460, 581, 742, 814, 935, 1084, 1323, 1395, 2137, 3072e, 3342eg, 4156eg*

## Etymology

The xenisma was named by Margo Schulter in 2000[1].