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No-fives subgroup temperaments: Difference between revisions

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=== Alphaxenean ===
=== Alphaxenean ===
Alphaxenean tempers out the [[Alpharabian comma]] and equates a stack of four undecimal quartertones with the [[9/8|Pythagorean whole tone]]. It also divides the [[2/1|octave]] into two.  
Alphaxenean tempers out the [[Alpharabian comma]] and equates a stack of four undecimal quartertones with the [[9/8|Pythagorean whole tone]]. It also divides the [[octave]] into two.  


[[Subgroup]]: 2.3.11
[[Subgroup]]: 2.3.11
Line 899: Line 899:


[[Badness]] (Sintel): 0.395
[[Badness]] (Sintel): 0.395
=== 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


=== Infraug ===
=== Infraug ===
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* CWE: ~2 = 1200.0000{{c}}, ~19/11 = 945.7779{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~19/11 = 945.7779{{c}}


{{Optimal ET sequence|legend=1| 14, 19, 33 }}
{{Optimal ET sequence|legend=0| 14, 19, 33 }}


Badness (Sintel): 1.59
Badness (Sintel): 1.59
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: [[error map]]: {{val| +3.129 -3.177 -4.349 }}
: [[error map]]: {{val| +3.129 -3.177 -4.349 }}
* [[CWE]]: ~2 = 1200.0000{{c}} ~3/2 = 693.6081{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}} ~3/2 = 693.6081{{c}}
: error map: {{val| 0.000 -8.347 +14.960 }}
: error map: {{val| 0.000 -8.347 -14.960 }}


{{Optimal ET sequence|legend=1| 5f, 7, 12, 19, 45f, 64f, 147bfff }}
{{Optimal ET sequence|legend=1| 5f, 7, 12, 19, 45f, 64f, 147bfff }}
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[[Badness]] (Sintel): 0.0294
[[Badness]] (Sintel): 0.0294
=== Deviaug ===
Deviaug tempers out [[6912/6859]] in the 2.3.19 subgroup, setting [[24/19]] to 1/3 of an octave.
[[Subgroup]]: 2.3.19
[[Comma list]]: 6912/6859
{{Mapping|legend=2| 3 0 8 | 0 1 1 }}
: mapping generators: ~24/19, ~3
[[Optimal tuning]]s:
* [[WE]]: ~24/19 = 399.8571{{c}}, ~3/2 = 701.9795{{c}}
: [[error map]]: {{val| -0.429 -0.404 +2.894 }}
* [[CWE]]: ~24/19 = 400.0000{{c}}, ~3/2 = 701.8810{{c}}
: error map: {{val| 0.000 -0.074 +4.368 }}
{{Optimal ET sequence|legend=1| 9, 12, 75, 87, 99, 111, 123h, 135h }}
[[Badness]] (Sintel): 0.237


=== Lipsett ===
=== Lipsett ===
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