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Meantone family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings, per community consensus (4/)
Switch to Sintel's badness, WE & CWE tunings, per community consensus (5/5)
Line 2,683: Line 2,683:


{{Mapping|legend=2| 1 0 -4 9 | 0 1 4 -3 }}
{{Mapping|legend=2| 1 0 -4 9 | 0 1 4 -3 }}
: sval mapping generators: ~2, ~3


{{Mapping|legend=3| 1 0 -4 0 0 0 0 9 | 0 1 4 0 0 0 0 -3 }}
{{Mapping|legend=3| 1 0 -4 0 0 0 0 9 | 0 1 4 0 0 0 0 -3 }}


: [[gencom]]: [2 3; 81/80 96/95]
: mapping generators: ~2, ~3


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 697.681{{c}}
* [[WE]]: ~2 = 1199.5513{{c}}, ~3/2 = 697.6058{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 697.867{{c}}
: [[error map]]: {{val| -0.448 -4.798 +4.110 +6.977 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 697.8222{{c}}
: error map: {{val| 0.000 -4.133 +4.975 +9.020 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 697.681{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 697.867{{c}} -->


{{Optimal ET sequence|legend=1| 5, 7, 12, 31, 43 }}
{{Optimal ET sequence|legend=1| 5, 7, 12, 31, 43, 98h }}


[[Tp tuning #T2 tuning|RMS error]]: 1.378 cents
[[Badness]] (Sintel): 0.324


=== Hypnotone ===
=== Hypnotone ===
Line 2,707: Line 2,709:
{{Mapping|legend=2| 1 0 -4 -6 | 0 1 4 6 }}
{{Mapping|legend=2| 1 0 -4 -6 | 0 1 4 6 }}


: sval mapping generators: ~2, ~3
{{Mapping|legend=3| 1 0 -4 0 -6 | 0 1 4 0 6 }}
 
: mapping generators: ~2, ~3


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 694.700{{c}}
* [[WE]]: ~2 = 1202.0621{{c}}, ~3/2 = 694.5448{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 693.908{{c}}
: [[error map]]: {{val| +2.062 -5.348 -8.135 +15.951 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 693.9085{{c}}
: error map: {{val| 0.000 -8.047 -10.680 +12.133 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 694.700{{c}} -->


{{Optimal ET sequence|legend=1| 7, 12, 19, 26, 45 }}
{{Optimal ET sequence|legend=1| 7, 12, 19, 26, 45 }}


[[Badness]] (Smith): 0.0104
[[Badness]] (Sintel): 0.326


==== 2.3.5.11.13 subgroup ====
==== 2.3.5.11.13 subgroup ====
Line 2,722: Line 2,729:
Comma list: 45/44, 65/64, 81/80
Comma list: 45/44, 65/64, 81/80


Sval mapping: {{mapping| 1 0 -4 -6 10 | 0 1 4 6 -4 }}
Subgroup-val mapping: {{mapping| 1 0 -4 -6 10 | 0 1 4 6 -4 }}


: sval mapping generators: ~2, ~3
Gencom mapping: {{mapping| 1 0 -4 0 -6 10 | 0 1 4 0 6 -4 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 693.951{{c}}
* WE: ~2 = 1202.6916{{c}}, ~3/2 = 694.4181{{c}}
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 693.087{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 693.0870{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 693.951{{c}} -->


{{Optimal ET sequence|legend=0| 7, 12, 19, 26, 45f }}
{{Optimal ET sequence|legend=0| 7, 12, 19, 26, 45f }}


Badness (Smith): 0.0141
Badness (Sintel): 0.561


=== Dequarter ===
=== Dequarter ===
Line 2,741: Line 2,749:
{{Mapping|legend=2| 1 0 -4 5 | 0 1 4 -1 }}
{{Mapping|legend=2| 1 0 -4 5 | 0 1 4 -1 }}


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


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 696.039{{c}}
* [[WE]]: ~2 = 1206.5832{{c}}, ~3/2 = 695.8763{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 693.121{{c}}
: [[error map]]: {{val| +6.583 +0.504 -2.809 -20.862 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 693.1206{{c}}
: error map: {{val| 0.000 -8.834 -13.831 -44.439 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 696.039{{c}} -->


{{Optimal ET sequence|legend=1| 5, 7, 19e, 26e }}
{{Optimal ET sequence|legend=1| 5, 7, 19e, 26e }}


[[Badness]] (Smith): 0.0145
[[Badness]] (Sintel): 0.451


==== Dreamtone ====
==== Dreamtone ====
Line 2,756: Line 2,769:
Comma list: 33/32, 55/54, 975/968
Comma list: 33/32, 55/54, 975/968


Sval mapping: {{mapping| 1 0 -4 5 21 | 0 1 4 -1 -11 }}
Subgroup-val mapping: {{mapping| 1 0 -4 5 21 | 0 1 4 -1 -11 }}


: sval mapping generators: ~2, ~3
Gencom mapping: {{mapping| 1 0 -4 0 5 21 | 0 1 4 0 -1 -11 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 689.699{{c}}
* WE: ~2 = 1207.8248{{c}}, ~3/2 = 694.7806{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 690.183{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 690.1826{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 689.699{{c}} -->


{{Optimal ET sequence|legend=0| 7, 19eff, 26eff, 33ceeff, 40ceeff }}
{{Optimal ET sequence|legend=0| 7, 19eff, 26eff, 33ceeff, 40ceeff }}


Badness (Smith): 0.0353
Badness (Sintel): 1.40


[[Category:Temperament families]]
[[Category:Temperament families]]
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