21st-octave temperaments: Difference between revisions
Created page with "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 ar..." |
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This page collectes temperaments with a period of 1/21 of an octave. | 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 {{EDOs|441, 1407, and 1848}} are. | Although 21edo itself is not remarkably accurate for low-complexity harmonics, some temperaments which are multiples of 21, such as {{EDOs|441, 1407, and 1848}} are. 441 and 1848 are also members of [[zeta]] edo list. | ||
== Akjayland == | == Akjayland == | ||
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[[Badness]]: 0.0309 | [[Badness]]: 0.0309 | ||
== Vasca == | |||
Vasca tempers out the {{Monzo|95 0 0 0 0 0 0 0 -21}} in the 23-limit, and sets a stack of 21 [[23/16]]<nowiki/>s equal with 11 octaves. derives from elements Vanadium (23) and Scandium (21), since this uses the 23rd harmonic, which itself is extremely well represented in 21edo. It is defined as a 525 & 357 temperament. | |||
Subgroup: 2.3.5.7.11.13.17.19.23 | |||
Comma list: 1496/1495, 2376/2375, 3060/3059, 17204/17199, 282625/282624, {{Monzo|95 0 0 0 0 0 0 0 -21}} | |||
Mapping: [{{Val|21 34 49 58 73 77 85 91 95}}, {{Val|0 -6 -2 8 -3 6 7 -15 0}}] | |||
POTE generator: 6.8162 | |||
Revision as of 11:24, 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
Main article: Landscape microtemperaments#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 tempers out the [95 0 0 0 0 0 0 0 -21⟩ in the 23-limit, and sets a stack of 21 23/16s equal with 11 octaves. derives from elements Vanadium (23) and Scandium (21), since this uses the 23rd harmonic, which itself is extremely well represented in 21edo. It is defined as a 525 & 357 temperament.
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