595/594: Difference between revisions

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:

154/153 and 245/243

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 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

Template:Val list*

* optimal patent val: 861

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.

@@ Line 36: / Line 36: @@
 == 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.
+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 this temperament below.
 [[Subgroup]]: 2.3.5.7.11.13.17

595/594: Difference between revisions

Revision as of 16:00, 18 February 2023

Commatic relations

Temperaments

Etymology

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