8th-octave temperaments: Difference between revisions

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Review, + badness and optimal tunings
- duplicate data (moved to no-5)
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* ''[[Octant]]'' → [[Schismatic family#Octant|Schismatic family]]
* ''[[Octant]]'' → [[Schismatic family#Octant|Schismatic family]]
* [[Octoid]] → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]
* [[Octoid]] → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]
 
* ''[[Octatonic (temperament)|Octatonic]]'' → [[No-fives subgroup temperaments #Octatonic|No-fives subgroup temperaments]]
== Octatonic ==
[[12/11]] is very close to 1 step of 8edo, and hence this temperament tempers out the [[undecimal octatonic comma]], the difference between a stack of eight 12/11's and the octave.
 
[[Subgroup]]: 2.3.11
 
[[Comma list]]: 214990848/214358881
 
{{Mapping|legend=2| 8 0 15 | 0 1 1 }}
: mapping generators: ~12/11, ~3
 
[[Optimal tuning]]s:
* [[WE]]: ~12/11 = 149.9917{{c}}, ~3/2 = 701.9324{{c}}
: [[error map]]: {{val| -0.066 -0.089 +0.424 }}
* [[CWE]]: ~12/11 = 150.0000{{c}}, ~3/2 = 701.9147{{c}}
: error map: {{val| 0.000 -0.040 +0.597 }}
 
{{Optimal ET sequence|legend=1| 8, 16, 24, 104, 128, 152, 176, 200, 1024e, 1224e, 1424e, 1624e }}
 
[[Badness]] (Sintel): 0.515


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

Revision as of 06:58, 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 
← 3rd • 4th • 5th • 6th • 7th • 8th-octave • 9th • 10th • 11th • 12th • 13th →
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