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 | [math]\text{m2}^{5,7,17}_{11}[/math] |
| 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, [math]\sqrt{n\cdot d}[/math]) |
~2.43482 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:
- 34/33 and 36/35
- 85/84 and 99/98
- 100/99 and 120/119
- 136/135 and 176/175
- 221/220 and 351/350
- 289/288 and 561/560
- 325/324 and 715/714
- 364/363 and 936/935
- 385/384 and 1089/1088
- 441/440 and 1701/1700
- 442/441 and 1716/1715
- 540/539 and 5832/5831
- 561/560 and 9801/9800
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 sequence: 12f, 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 sequence: 12, 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.