595/594: Difference between revisions
+some nonsuperparticular relations |
m It seems like a good idea to have a section for commatic relations for 17-limit+ commas cuz there really are many |
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'''595/594''', the '''dakotisma''', is a [[small comma|small]] [[17-limit]] [[comma]] measuring about 2.91 [[cent]]s. Named after [[Scott Dakota]], it is one of the simplest commas tempered out in [[311edo|311et]], a highly notable general-purpose equal temperament. | '''595/594''', the '''dakotisma''', is a [[small comma|small]] [[17-limit]] [[comma]] measuring about 2.91 [[cent]]s. Named after [[Scott Dakota]], it is one of the simplest commas tempered out in [[311edo|311et]], a highly notable general-purpose equal temperament. | ||
== Commatic relations == | |||
It identifies itself as the difference between the following superparticular pairs: | It identifies itself as the difference between the following superparticular pairs: | ||
Revision as of 03:18, 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
It identifies itself as the difference between the following superparticular pairs:
- (34/33)/(36/35)
- (85/84)/(99/98)
- (100/99)/(120/119)
- (136/135)/(176/175)
- (221/220)/(351/350)
- (289/288)/(561/560)
- (325/324)/(715/714)
- (364/363)/(936/935)
- (385/384)/(1089/1088)
- (441/440)/(1701/1700)
- (442/441)/(1716/1715)
- (540/539)/(5832/5831)
- (561/560)/(9801/9800)
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