32nd-octave temperaments: Difference between revisions

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These are temperaments with period 1/32 of an octave.

These are temperaments with period 1/32 of an octave. 32edo is a wasteland as far as LCJI is concerned, but some of its multiples are good at harmonics, and thus can produce temperaments with period of 1/32 of an octave.

~~32edo is a wasteland as far as LCJI is concerned, but some of its multiples are good at harmonics, and thus can produce temperaments with period of 1/32 of an octave.~~

Temperaments discussed elsewhere include:

~~{{Todo~~|~~inline=1| cleanup | expand | comment=Complete the data. Work out the data for intermediate subgroups. }}~~

* ''Bezique,'' → [[Horwell temperaments#Bezique|Horwell temperaments]]

== Windrose ==

The temperament is called windrose because there are 32 cardinal directions commonly assigned to a compass rose. It is defined as the 608 & 1600 temperament. The [[maximal evenness]] pattern created inside the period 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]].

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[[Support|Supporting]] [[ET|ETs]]: {{EDOs|384bc, 608, 992, 1600, 2208, 2592}}

Badness (Sintel): 79.660

== Germanium ==

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[[Support]]ing [[ET]]s: {{EDOs|416, 768b, 1184, 1600, 2016, 2784}}, ...

=== Dam ===

Due to complexity, dam is not a remarkably interesting temperament on its own, but in higher limits, its 37-limit extension dike is worth considering (see below).

[[Subgroup]]: 2.3.5.7

Comma list: {{monzo|-54 3 20 1}}, {{monzo|-25 73 -4 -29}}

: mapping generators: ~2017815046875/1973822685184 = 1\32, ~16896102540283203125/15992037016835457024 = 95.247

Optimal tuning (CTE): ~16896102540283203125/15992037016835457024 = 95.247

Supporting ETs: {{EDOs|416d, 1600, 2016d}}, ...

=== Dike ===

==== 37-limit ====

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~~[[Category:32edo]]~~

~~[[Category:Temperament collections]]~~

~~[[Category:Rank 2]]~~

@@ Line 1: / Line 1: @@
-These are temperaments with period 1/32 of an octave.
+{{Technical data page}}
+{{Infobox fractional-octave|32}}
+These are temperaments with period 1/32 of an octave. 32edo is a wasteland as far as LCJI is concerned, but some of its multiples are good at harmonics, and thus can produce temperaments with period of 1/32 of an octave.
-edo is a wasteland as far as LCJI is concerned, but some of its multiples are good at harmonics, and thus can produce temperaments with period of 1/32 of an octave.
+Temperaments discussed elsewhere include:
-{{Todo|inline=1| cleanup | expand | comment=Complete the data. Work out the data for intermediate subgroups. }}
+* ''Bezique,'' → [[Horwell temperaments#Bezique|Horwell temperaments]]
 == Windrose ==
+{{Mathematical interest}}
 The temperament is called windrose because there are 32 cardinal directions commonly assigned to a compass rose. It is defined as the 608 & 1600 temperament. The [[maximal evenness]] pattern created inside the period 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]].
@@ Line 19: / Line 22: @@
 [[Support|Supporting]] [[ET|ETs]]: {{EDOs|384bc, 608, 992, 1600, 2208, 2592}}
+Badness (Sintel): 79.660
 == Germanium ==
@@ Line 76: / Line 81: @@
 [[Support]]ing [[ET]]s: {{EDOs|416, 768b, 1184, 1600, 2016, 2784}}, ...
+=== Dam ===
+Due to complexity, dam is not a remarkably interesting temperament on its own, but in higher limits, its 37-limit extension dike is worth considering (see below).
+[[Subgroup]]: 2.3.5.7
+Comma list: {{monzo|-54  3 20  1}}, {{monzo|-25 73 -4 -29}}
+{{mapping|legend=1|32 5 87 -27|0 18 -5 46}}
+: mapping generators: ~2017815046875/1973822685184 = 1\32, ~16896102540283203125/15992037016835457024 = 95.247
+Optimal tuning (CTE): ~16896102540283203125/15992037016835457024 = 95.247
+Supporting ETs: {{EDOs|416d, 1600, 2016d}}, ...
 === Dike ===
 ==== 37-limit ====
@@ Line 90: / Line 111: @@
 {{Optimal ET sequence|legend=1| 416dijk, 1600, 2016dijk }}
-[[Category:32edo]]
+{{Navbox fractional-octave}}
-[[Category:Temperament collections]]
-[[Category:Rank 2]]