21st-octave temperaments

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