21st-octave temperaments: Difference between revisions

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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 }} in the 23-limit, and sets a stack of 21 [[23/16]]'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 357 & 525 temperament.  
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