21st-octave temperaments: Difference between revisions
This "vasca" is an extension of akjayland |
Cleanup and +categories |
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=== Vasca === | === Vasca === | ||
Vasca tempers out the {{monzo| 95 0 0 0 0 0 0 0 -21 }} | Vasca can be described as the 357 & 525 temperament, extended as high as the 23-limit. It tempers out the {{monzo| 95 0 0 0 0 0 0 0 -21 }}, and sets a stack of 21 [[23/16]]'s equal with 11 octaves. The name derives from elements vanadium (23) and scandium (21), since this uses the 23rd harmonic, which itself is extremely well represented in 21edo. | ||
==== 23-limit ==== | |||
Subgroup: 2.3.5.7.11.13.17.19.23 | Subgroup: 2.3.5.7.11.13.17.19.23 | ||
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POTE generator: 6.8162 | POTE generator: 6.8162 | ||
[[Category:21edo]] | |||
[[Category:Temperament collections]] | |||
[[Category:Rank 2]] | |||
Revision as of 12:48, 20 May 2022
This page collectes temperaments with a period of 1/21 of an octave.
Although 21edo itself is not remarkably accurate for low-complexity harmonics, some temperaments which are multiples of 21, such as 441, 1407, and 1848 are. 441 and 1848 are also members of zeta edo list.
Akjayland
Subgroup: 2.3.5.7
Comma list: 250047/250000, [43 -1 -13 -4⟩
Mapping: [⟨21 1 38 102], ⟨0 3 1 -4]]
Mapping generators: ~1323/1280, ~131072/91875
POTE generator: ~131072/91875 = 614.9361
Optimal GPV sequence: Template:Val list
Badness: 0.0309
Vasca
Vasca can be described as the 357 & 525 temperament, extended as high as the 23-limit. It tempers out the [95 0 0 0 0 0 0 0 -21⟩, and sets a stack of 21 23/16's equal with 11 octaves. The name derives from elements vanadium (23) and scandium (21), since this uses the 23rd harmonic, which itself is extremely well represented in 21edo.
23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 1496/1495, 2376/2375, 3060/3059, 17204/17199, 282625/282624, [95 0 0 0 0 0 0 0 -21⟩
Mapping: [⟨21 34 49 58 73 77 85 91 95], ⟨0 -6 -2 8 -3 6 7 -15 0]]
POTE generator: 6.8162