32nd-octave temperaments: Difference between revisions

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== Windrose ==

The temperament is called windrose because there are 32 cardinal directions commonly assigned to a compass rose. It is defined as a ~~224~~ & 1600 temperament.

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

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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.~~2541¢~~

POTE Generator: 17.2544¢

@@ Line 2: / Line 2: @@
 == Windrose ==
-The temperament is called windrose because there are 32 cardinal directions commonly assigned to a compass rose. It is defined as a 224 & 1600 temperament.
+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
@@ Line 15: / Line 27: @@
 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: 17.2541¢
+POTE Generator: 17.2544¢