# 595/594

 Ratio 595/594 Factorization 2-1 × 3-3 × 5 × 7 × 11-1 × 17 Monzo [-1 -3 1 1 -1 0 1⟩ Size in cents 2.9120849¢ Name dakotisma Color name 17o1uzy2, soluzoyo 2nd FJS name $\text{m2}^{5,7,17}_{11}$ Special properties superparticular,reduced Tenney height (log2 nd) 18.4311 Weil height (log2 max(n, d)) 18.4335 Wilson height (sopfr (nd)) 51 Harmonic entropy(Shannon, $\sqrt{nd}$) ~1.27711 bits Comma size unnoticeable S-expression S34 × S35 open this interval in xen-calc

595/594, the dakotisma, is a small 17-limit comma measuring about 2.91 cents. Named after Scott Dakota, it is one of the simplest commas tempered out in 311et, a highly notable general-purpose equal temperament.

## Commatic relations

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

not to mention some nonsuperparticular but useful relations:

It factors into the following superparticular pairs:

not to mention some nonsuperparticular but useful relations:

## Temperaments

Tempering out this comma in the full 17-limit gives the rank-6 dakotismic temperament, or in the 2.3.5.7.11.17 subgroup, the rank-5 dakotic temperament, enabling dakotismic chords. You may find a list of good equal temperaments that support these temperaments below.

### Dakotismic

Subgroup: 2.3.5.7.11.13.17

 [⟨ 1 0 0 0 0 0 1 ], ⟨ 0 1 0 0 0 0 3 ], ⟨ 0 0 1 0 0 0 -1 ], ⟨ 0 0 0 1 0 0 -1 ], ⟨ 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 = 702.2950, ~5/4 = 386.0705, ~7/4 = 968.4704, ~11/8 = 551.8578, ~13/8 = 840.5277

Optimal ET sequence12f, 14cf, 15g, 19eg, 22, 26, 27eg, 34d, 38df, 41, 46, 58, 72, 121, 140, 171, 190g, 212g, 217, 289, 311, 668, 694g, 740g, 1051dg*

### Dakotic

Subgroup: 2.3.5.7.11.17

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.2950, ~5/4 = 386.0705, ~7/4 = 968.4704, ~11/8 = 551.8578

Optimal ET sequence12, 14c, 19eg, 22, 27eg, 31g, 34d, 38d, 41, 46, 58, 68, 72, 118, 171, 190g, 193, 212g, 217, 239, 311, 1051dg

## Etymology

The dakotisma was named by Praveen Venkataramana in 2022 in honor of Scott Dakota's pioneering study of this comma and of its role in 311et.