32nd-octave temperaments: Difference between revisions
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== Windrose == | == Windrose == | ||
The temperament is called windrose because there are 32 cardinal directions commonly assigned to a compass rose. It is defined as a | The temperament is called windrose because there are 32 cardinal directions commonly assigned to a compass rose. It is defined as a 608 & 1600 temperament. The maximal evenness pattern created inside the generator is a 12L 7s, if mapped to a keyboard, which has a 2:3 step ratio and thus offers elegant microtempering that plays with the just noticeable difference. Higher-dimensional versions of this are lower in badness than low-dimensional ones. | ||
=== 7-limit === | |||
Subgroup:2.3.5.7 | |||
Comma list: [38, 9, -8, -12⟩, [15, -28, 32, -16⟩ | |||
Mapping: 32 44 68 89, 0 16 15 2 | |||
POTE Generator: 15.7517¢ | |||
== Germanium == | |||
It is named after germanium, the 32nd element. This is the most just intonation-friendly 32st-octave temperament, | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Defined as a 2016dijk & 1600 temperament, since the warts on the val spell out the Dutch surname Van Dijk. | Defined as a 2016dijk & 1600 temperament, since the warts on the val spell out the Dutch surname Van Dijk. | ||
Subgroup: 2.3.5.7.11.13.17.19.23.29.31 | Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37 | ||
Comma list: | |||
Mapping: [{{monzo| 32 59 72 111 113 129 140 141 165 178 182}}, {{monzo|0 -18 5 -46 -5 -23 -20 -11 -44 -49 -51}}] | Mapping: [{{monzo| 32 59 72 111 113 129 140 141 165 178 182 169}}, {{monzo|0 -18 5 -46 -5 -23 -20 -11 -44 -49 -51 -5}}] | ||
POTE Generator: 17. | POTE Generator: 17.2544¢ | ||
Revision as of 21:34, 1 June 2022
These are temperaments with period 1/32 of an octave.
Windrose
The temperament is called windrose because there are 32 cardinal directions commonly assigned to a compass rose. It is defined as a 608 & 1600 temperament. The maximal evenness pattern created inside the generator is a 12L 7s, if mapped to a keyboard, which has a 2:3 step ratio and thus offers elegant microtempering that plays with the just noticeable difference. Higher-dimensional versions of this are lower in badness than low-dimensional ones.
7-limit
Subgroup:2.3.5.7
Comma list: [38, 9, -8, -12⟩, [15, -28, 32, -16⟩
Mapping: 32 44 68 89, 0 16 15 2
POTE Generator: 15.7517¢
Germanium
It is named after germanium, the 32nd element. This is the most just intonation-friendly 32st-octave temperament,
Subgroup: 2.3.5.7.11.13
Comma list:
Mapping: [[32 51 75 89 110 118⟩, [0 -2 -5 6 5 3⟩]
POTE Generator: 5.2381¢
Van Dijk
Defined as a 2016dijk & 1600 temperament, since the warts on the val spell out the Dutch surname Van Dijk.
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37
Comma list:
Mapping: [[32 59 72 111 113 129 140 141 165 178 182 169⟩, [0 -18 5 -46 -5 -23 -20 -11 -44 -49 -51 -5⟩]
POTE Generator: 17.2544¢