8th-octave temperaments: Difference between revisions

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Temperaments discussed elsewhere include:
Temperaments discussed elsewhere include:
* ''Octant'' → [[Schismatic family#Octant|Schismatic family]]
* ''[[Octant]]'' → [[Schismatic family #Octant|Schismatic family]]
 
* ''[[Octonion]]'' → [[Diminished family #Octonion|Diminished family]]
== Octatonic ==
* ''[[Twilight]]'' → [[Undim family #Twilight|Undim family]]
[[12/11]] is very close to 1 step of 8edo, and hence this temperament tempers out the octatonic comma, the difference between a stack of 8 12/11's and the octave. The octatonic temperament makes a [[consistent circle]].
* [[Octoid]] → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]
 
* ''[[Octatonic (temperament)|Octatonic]]'' → [[No-fives subgroup temperaments #Octatonic|No-fives subgroup temperaments]]
[[Subgroup]]: 2.3.11
 
[[Comma list]]: {{monzo|15 8 0 0 -8}}
 
{{Mapping|legend=1|8 0 15|0 1 1}}
 
: Mapping generators: ~12/11, ~3
 
[[Support]]ing [[ET]]s: {{EDOs|16, 24, 32, 48, 56, 72, 80, 120, 128, 152}}, ...
 
== Octoid ==
: ''For the 7-limit temperament, see [[Ragismic microtemperaments #Octoid]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 59604644775390625/59296646043258912
 
{{Mapping|legend=1| 8 1 3 | 0 3 4 }}
 
: Mapping generators: ~2125764/1953125, ~4374/3125
 
[[Optimal tuning]]s:
* [[WE]]: ~2125764/1953125 = 150.001{{c}}, ~4374/3125 = 584.027{{c}}
* [[CWE]]: ~2125764/1953125 = 150.000{{c}}, ~4374/3125 = 584.025{{c}}
 
{{Optimal ET sequence|legend=1| 8, 56bcc, 64c, 72, 152, 224, 376, 976 }}
 
[[Badness]] (Sintel): 6.687


{{Navbox fractional-octave}}
{{Navbox fractional-octave}}

Latest revision as of 07:04, 5 July 2026

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

← 7th-octave • 8th-octave • 9th-octave →

An 8th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 8.

Temperaments discussed elsewhere include:

View • Talk • EditFractional-octave temperaments 
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