8th-octave temperaments: Difference between revisions
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Review, + badness and optimal tunings |
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== Octatonic == | == Octatonic == | ||
[[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 | [[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 | [[Subgroup]]: 2.3.11 | ||
[[Comma list]]: | [[Comma list]]: 214990848/214358881 | ||
{{Mapping|legend= | {{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 06:56, 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.
An 8th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 8.
Temperaments discussed elsewhere include:
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
Subgroup-val mapping: [⟨8 0 15], ⟨0 1 1]]
- mapping generators: ~12/11, ~3
- WE: ~12/11 = 149.9917 ¢, ~3/2 = 701.9324 ¢
- error map: ⟨-0.066 -0.089 +0.424]
- CWE: ~12/11 = 150.0000 ¢, ~3/2 = 701.9147 ¢
- error map: ⟨0.000 -0.040 +0.597]
Optimal ET sequence: 8, 16, 24, 104, 128, 152, 176, 200, 1024e, 1224e, 1424e, 1624e
Badness (Sintel): 0.515