24th-octave temperaments: Difference between revisions

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24edo is otherwise known as the [[quartertone]] tuning, so 24th-octave [[temperament]]s include temperaments where the [[period]] is any [[interval]] which is considered a quartertone.

Temperaments discussed elswhere include:

* ''[[Hours]]'' → [[Compton family #Hours|Compton family]]

* ''[[Rabic]]'' → [[Rastmic rank-3 clan #Rabic|Rastmic rank-3 clan]]

* ''Hours'', → [[~~Compton family~~#~~Hours|Compton family~~]]

== Chromium (5-limit) ==

* ''Rabic''~~, → [[Alphaxenic rank three clan#Rabic|Alphaxenic rank three clan]]~~

: ''For extensions, see [[Landscape microtemperaments #Chromium]].''

~~== Chromium (5-limit) ==~~

The chromium temperament is defined by equating a stack of twenty-four [[250/243|porcupine commas]] with the octave.

~~{{Main|Chromium}}~~

The chromium temperament is defined by equating a stack of 24 [[~~256~~/243|porcupine commas]] with the octave~~. In 7-limit and higher, see [[Landscape microtemperaments#Chromium]]~~.

Subgroup: 2.3.5

[[Subgroup]]: 2.3.5

Comma list: {{monzo|-23 120 -72}}

[[Comma list]]: {{monzo| -23 120 -72 }}

: mapping generators: ~250/243, ~{{monzo| -8 42 -25 }}

: ~~mapping generators~~: ~~~256~~/243 = ~~1\24~~, ~~109418989131512359209~~/~~76293945312500000000~~ = 617.~~287~~

[[Optimal tuning]]s:

* [[WE]]: ~250/243 = 50.0000{{c}}, ~{{monzo| -8 42 -25 }} = 617.2852{{c}}

: [[error map]]: {{val| +0.007 -0.093 +0.120 }}

* [[CWE]]: ~250/243 = 50.0000{{c}}, ~{{monzo| -8 42 -25 }} = 617.2852{{c}}

: error map: {{val| 0.000 -0.099 +0.112 }}

~~[[Support]]ing [[ET]]s:~~ {{~~EDOs~~|72, 480, 552, 624, ~~696, 768~~, ~~1320~~}}~~, ...~~

{{Optimal ET sequence|legend=1| 72, …, 480, 552, 624, 1320, 1944 }}

Badness: ~~0.36784~~

[[Badness]] (Sintel): 169

@@ Line 1: / Line 1: @@
-{{Fractional-octave navigation|24}}
+{{Infobox fractional-octave|24}}
 edo is otherwise known as the [[quartertone]] tuning, so 24th-octave [[temperament]]s include temperaments where the [[period]] is any [[interval]] which is considered a quartertone.
 Temperaments discussed elswhere include:
+* ''[[Hours]]'' → [[Compton family #Hours|Compton family]]
+* ''[[Rabic]]'' → [[Rastmic rank-3 clan #Rabic|Rastmic rank-3 clan]]
-* ''Hours'', → [[Compton family#Hours|Compton family]]
+== Chromium (5-limit) ==
-* ''Rabic'', → [[Alphaxenic rank three clan#Rabic|Alphaxenic rank three clan]]
+{{Main| Chromium }}
+: ''For extensions, see [[Landscape microtemperaments #Chromium]].''
-== Chromium (5-limit) ==
+The chromium temperament is defined by equating a stack of twenty-four [[250/243|porcupine commas]] with the octave.
-{{Main|Chromium}}
-The chromium temperament is defined by equating a stack of 24 [[256/243|porcupine commas]] with the octave. In 7-limit and higher, see [[Landscape microtemperaments#Chromium]].
-Subgroup: 2.3.5
+[[Subgroup]]: 2.3.5
-Comma list: {{monzo|-23 120 -72}}
+[[Comma list]]: {{monzo| -23 120 -72 }}
-{{mapping|legend=1|24 37 54|0 3 5}}
+{{mapping|legend=1| 24 1 -6 | 0 3 5 }}
+: mapping generators: ~250/243, ~{{monzo| -8 42 -25 }}
-: mapping generators: ~256/243 = 1\24, 109418989131512359209/76293945312500000000 = 617.287
+[[Optimal tuning]]s:
+* [[WE]]: ~250/243 = 50.0000{{c}}, ~{{monzo| -8 42 -25 }} = 617.2852{{c}}
+: [[error map]]: {{val| +0.007 -0.093 +0.120 }}
+* [[CWE]]: ~250/243 = 50.0000{{c}}, ~{{monzo| -8 42 -25 }} = 617.2852{{c}}
+: error map: {{val| 0.000 -0.099 +0.112 }}
-[[Support]]ing [[ET]]s: {{EDOs|72, 480, 552, 624, 696, 768, 1320}}, ...
+{{Optimal ET sequence|legend=1| 72, …, 480, 552, 624, 1320, 1944 }}
-Badness: 0.36784
+[[Badness]] (Sintel): 169
 {{Navbox fractional-octave}}