595/594: Difference between revisions
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This comma identifies itself as the difference between the following superparticular pairs: | 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: | |||
* [[154/153]] and [[245/243]] | |||
It factors into the following superparticular pairs: | It factors into the following superparticular pairs: | ||
* | * [[1156/1155]] and [[1225/1224]] | ||
* | * [[833/832]] and [[2080/2079]] | ||
* | * [[625/624]] and [[12376/12375]] | ||
not to mention some nonsuperparticular but useful relations: | |||
* | * [[1575/1573]] and [[2431/2430]] | ||
* | * [[1377/1375]] and [[4375/4374]] | ||
* | * [[1275/1274]] and [[4459/4455]] | ||
== Temperaments == | == Temperaments == | ||
Revision as of 05:09, 13 November 2022
| 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