595/594: Difference between revisions
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== 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. | |||
[[Category:Dakotismic]] | [[Category:Dakotismic]] | ||
Revision as of 10:39, 18 February 2023
| Interval information |
reduced
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, and enables the related essentially tempered chords. You may find a list of good equal temperaments that support this temperament below.
Subgroup: 2.3.5.7.11.13.17
Mapping:
[⟨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
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.