24th-octave temperaments: Difference between revisions

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

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]]

== Chromium (5-limit) ==

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~~]].

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

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

[[Subgroup]]: 2.3.5

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

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

~~Subgroup~~: 2.3.5

[[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 }}

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

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

~~{{mapping|legend=1|24 37 54|0 3 5}}~~

[[Badness]] (Sintel): 169

~~Badness: 0.36784~~

@@ Line 1: / Line 1: @@
-{{Fractional-octave navigation|24}}
+{{Infobox fractional-octave|24}}
-edo is otherwise known as the quartertone tuning, so 24th-octave temperaments include temperaments where the period is any interval which is considered a quartertone.
+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]]
 == Chromium (5-limit) ==
-{{Main|Chromium}}
+{{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]].
+: ''For extensions, see [[Landscape microtemperaments #Chromium]].''
+The chromium temperament is defined by equating a stack of twenty-four [[250/243|porcupine commas]] with the octave.
+[[Subgroup]]: 2.3.5
+[[Comma list]]: {{monzo| -23 120 -72 }}
+{{mapping|legend=1| 24 1 -6 | 0 3 5 }}
+: mapping generators: ~250/243, ~{{monzo| -8 42 -25 }}
-Subgroup: 2.3.5
+[[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 }}
-Comma list: {{monzo|-23 120 -72}}
+{{Optimal ET sequence|legend=1| 72, …, 480, 552, 624, 1320, 1944 }}
-{{mapping|legend=1|24 37 54|0 3 5}}
+[[Badness]] (Sintel): 169
-Badness: 0.36784
+{{Navbox fractional-octave}}