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No-threes subgroup temperaments: Difference between revisions

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{{Mapping|legend=2| 1 1 3 | 0 3 1 }}
{{Mapping|legend=2| 1 1 3 | 0 3 1 }}
: mapping generators: ~2, ~11/8


[[Optimal tuning]] (CTE): ~2 = 1200.000{{c}}, ~11/8 = 529.846{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1203.0339{{c}}, ~11/8 = 528.4296{{c}}
: [[error map]]: {{val| +3.034 +2.009 -13.787 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/8 = 528.1575{{c}}
: error map: {{val| 0.000 -1.841 -23.160 }}


{{Optimal ET sequence|legend=1| 7, 9, 16, 25, 41e, 66ee }}
{{Optimal ET sequence|legend=1| 7, 9, 16, 25, 41e, 66ee }}
[[Badness]] (Sintel): 0.718


=== Wizz ===
=== Wizz ===
{{See also| Chromatic pairs #Wizz }}
{{See also| Chromatic pairs #Wizz }}


Wizz, the 6 & 16 temperament in the 2.5.11 subgroup, is related to [[wizard]].  
Wizz, the 6 & 16 temperament in the 2.5.11 subgroup, tempers out [[15625/15488]], and is related to [[wizard]].  


[[Subgroup]]: 2.5.11
[[Subgroup]]: 2.5.11


[[Comma list]]: [[15625/15488]]
[[Comma list]]: 15625/15488


{{Mapping|legend=2| 2 0 -7 | 0 1 3 }}
{{Mapping|legend=2| 2 0 -7 | 0 1 3 }}
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: mapping generators: ~125/88, ~5/4
: mapping generators: ~125/88, ~5/4


[[Optimal tuning]] ([[POTE]]): ~125/88 = 600.000{{c}}, ~5/4 = 383.768{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~125/88 = 600.1831{{c}}, ~5/4 = 383.8848{{c}}
: [[error map]]: {{val| +0.366 -1.697 +1.252 }}
* [[CWE]]: ~125/88 = 600.0000{{c}}, ~5/4 = 383.9977{{c}}
: error map: {{val| 0.000 -2.316 +0.675 }}


{{Optimal ET sequence|legend=1| 6, 16, 22, 28, 50, 122, 172, 222 }}
{{Optimal ET sequence|legend=1| 6, 16, 22, 28, 50, 122, 172, 222, 394c }}


[[Tp tuning #T2 tuning|RMS error]]: 0.3997
[[Badness]] (Sintel): 0.266


=== Insect ===
=== Insect ===
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: mapping generators, ~2, ~55/32
: mapping generators, ~2, ~55/32


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~55/32 = 928.032{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1201.1238{{c}}, ~55/32 = 928.5003{{c}}
: [[error map]]: {{val| +1.124 -0.813 -2.700 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~55/32 = 927.7384{{c}}
: error map: {{val| 0.000 -3.099 -6.975 }}


{{Optimal ET sequence|legend=1| 9, 13, 22, 97e, 119e, 141e, 163e, 304ceee }}
{{Optimal ET sequence|legend=1| 9, 13, 22, 97e, 119e, 141e, 163e, 304ceee }}
[[Badness]] (Sintel): 0.564


=== Sephiroth ===
=== Sephiroth ===
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Sephiroth is the no-7 [[restriction]] of [[muggles]].  
Sephiroth is the no-7 [[restriction]] of [[muggles]].  


[[Subgroup]]: 2.5.11.13.17
Subgroup: 2.5.11.13.17


[[Comma list]]: 65/64, 170/169, 221/220
Comma list: 65/64, 170/169, 221/220


{{Mapping|legend=2| 1 0 15 6 11 | 0 1 -5 -1 -3 }}
Subgroup-val mapping: {{mapping| 1 0 15 6 11 | 0 1 -5 -1 -3 }}


{{Mapping|legend=3| 1 0 2 0 5 4 5 | 0 0 1 0 -5 -1 -3 }}
Gencom mapping: {{mapping| 1 0 2 0 5 4 5 | 0 0 1 0 -5 -1 -3 }}
: mapping generators: ~2, ~5/4
: mapping generators: ~2, ~5/4


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~5/4 = 372.236{{c}}
Optimal tunings:
* WE: ~2 = 1203.6741{{c}}, ~5/4 = 373.3775{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 371.6773{{c}}


{{Optimal ET sequence|legend=1| 10, 13, 16, 29 }}
{{Optimal ET sequence|legend=0| 3, 10, 13, 16, 29g, 129ccceeffgggg }}


[[Tp tuning #T2 tuning|RMS error]]: 1.774 cents
Badness (Sintel): 0.299


=== Trader ===
=== Trader ===
[[Subgroup]]: 2.5.13
[[Subgroup]]: 2.5.13


[[Comma list]]: [[26/25]]
[[Comma list]]: 26/25


{{Mapping|legend=2| 1 2 3 | 0 1 2 }}
{{Mapping|legend=2| 1 2 3 | 0 1 2 }}
: mapping generators, ~2, ~5/4
: mapping generators, ~2, ~5/4


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~5/4 = 407.079{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1198.0216{{c}}, ~5/4 = 410.2152{{c}}
: [[error map]]: {{val| -1.978 +19.945 -26.033 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 408.9029{{c}}
: error map: {{val| 0.000 +22.589 -22.722 }}


{{Optimal ET sequence|legend=1| 3, 20c, 23c, 26c }}
{{Optimal ET sequence|legend=1| 3, 20c, 23c, 26c }}
[[Badness]] (Sintel): 0.138


=== Superquintal ===
=== Superquintal ===
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[[Comma list]]: 64000000/62748517
[[Comma list]]: 64000000/62748517


{{Mapping|legend=2| 1 5 6 | 0 -7 -6 }}
{{Mapping|legend=2| 1 -2 0 | 0 7 6 }}
: mapping generators, ~2, ~13/10
: mapping generators, ~2, ~20/13


[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~13/10 = 459.281{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.5925{{c}}, ~20/13 = 740.6286{{c}}
: [[error map]]: {{val| -0.408 -1.098 +3.244 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~20/13 = 740.8058{{c}}
: error map: {{val| 0.000 -0.673 +4.307 }}


{{Optimal ET sequence|legend=1| 8, 13, 21, 34, 81, 115 }}
{{Optimal ET sequence|legend=1| 8, 13, 21, 34, 81, 115 }}
[[Badness]] (Sintel): 1.93


== No-threes no-fives subgroup temperaments ==
== No-threes no-fives subgroup temperaments ==
Retrieved from "https://en.xen.wiki/w/No-threes_subgroup_temperaments"