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Passion family: Difference between revisions

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{{Technical data page}}
{{Technical data page}}
The '''passion family''' [[tempering out|tempers out]] the [[passion comma]], 262144/253125 = {{monzo| 18 -4 -5 }} in the 5-limit, which equates five instances of [[16/15]] with [[4/3]].  
The '''passion family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[passion comma]], 262144/253125 ({{monzo| 18 -4 -5 }}) in the [[5-limit]], which equates five instances of [[16/15]] with [[4/3]].  


== Passion ==
== Passion ==
Line 11: Line 11:
: mapping generators: ~2, ~16/15
: mapping generators: ~2, ~16/15


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/15 = 98.670
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~16/15 = 98.670{{c}}


{{Optimal ET sequence|legend=1| 12, 49, 61, 73 }}
{{Optimal ET sequence|legend=1| 12, 49, 61, 73 }}


[[Badness]]: 0.168550
[[Badness]] (Smith): 0.168550


== Septimal passion ==
== Septimal passion ==
Line 24: Line 24:
{{Mapping|legend=1| 1 2 2 2 | 0 -5 4 10 }}
{{Mapping|legend=1| 1 2 2 2 | 0 -5 4 10 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/15 = 98.153
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~16/15 = 98.153{{c}}


{{Optimal ET sequence|legend=1| 12, 37, 49, 110bcd }}
{{Optimal ET sequence|legend=1| 12, 37, 49, 110bcd }}


[[Badness]]: 0.062327
[[Badness]] (Smith): 0.062327


=== 11-limit ===
=== 11-limit ===
Line 37: Line 37:
Mapping: {{mapping| 1 2 2 2 2 | 0 -5 4 10 18 }}
Mapping: {{mapping| 1 2 2 2 2 | 0 -5 4 10 18 }}


Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.019
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~16/15 = 98.019{{c}}


Optimal ET sequence: {{Optimal ET sequence| 12, 37, 49 }}
Optimal ET sequence: {{Optimal ET sequence| 12, 37, 49 }}


Badness: 0.040809
Badness (Smith): 0.040809


=== 13-limit ===
=== 13-limit ===
Line 50: Line 50:
Mapping: {{mapping| 1 2 2 2 2 2 | 0 -5 4 10 18 21 }}
Mapping: {{mapping| 1 2 2 2 2 2 | 0 -5 4 10 18 21 }}


Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 97.910
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~16/15 = 97.910{{c}}


Optimal ET sequence: {{Optimal ET sequence| 12f, 25f, 37, 49f }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 25f, 37, 49f }}


Badness: 0.030886
Badness (Smith): 0.030886


== Passionate ==
== Passionate ==
Line 63: Line 63:
{{Mapping|legend=1| 1 2 2 1 | 0 -5 4 22 }}
{{Mapping|legend=1| 1 2 2 1 | 0 -5 4 22 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/15 = 98.817
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~16/15 = 98.817{{c}}


{{Optimal ET sequence|legend=1| 12, 61, 73, 85c }}
{{Optimal ET sequence|legend=1| 12, 61, 73, 85c }}


[[Badness]]: 0.121293
[[Badness]] (Smith): 0.121293


=== 11-limit ===
=== 11-limit ===
Line 76: Line 76:
Mapping: {{mapping| 1 2 2 1 1 | 0 -5 4 22 30 }}
Mapping: {{mapping| 1 2 2 1 1 | 0 -5 4 22 30 }}


Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.721
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~16/15 = 98.721{{c}}


Optimal ET sequence: {{Optimal ET sequence| 12, 61, 73, 158bccee }}
Optimal ET sequence: {{Optimal ET sequence| 12, 61, 73, 158bccee }}


Badness: 0.068322
Badness (Smith): 0.068322


==== 13-limit ====
==== 13-limit ====
Line 89: Line 89:
Mapping: {{mapping| 1 2 2 1 1 1 | 0 -5 4 22 30 33 }}
Mapping: {{mapping| 1 2 2 1 1 1 | 0 -5 4 22 30 33 }}


Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.627
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~16/15 = 98.627{{c}}


Optimal ET sequence: {{Optimal ET sequence| 12f, 61, 73f }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 61, 73f }}


Badness: 0.052302
Badness (Smith): 0.052302


==== Pash ====
==== Pash ====
Line 102: Line 102:
Mapping: {{mapping| 1 2 2 1 1 0 | 0 -5 4 22 30 45 }}
Mapping: {{mapping| 1 2 2 1 1 0 | 0 -5 4 22 30 45 }}


Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.791
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~16/15 = 98.791{{c}}


Optimal ET sequence: {{Optimal ET sequence| 12f, 61f, 73, 85ce }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 61f, 73, 85ce }}


Badness: 0.056386
Badness (Smith): 0.056386


== Passive ==
== Passive ==
Line 115: Line 115:
{{Mapping|legend=1| 1 2 2 3 | 0 -5 4 -2 }}
{{Mapping|legend=1| 1 2 2 3 | 0 -5 4 -2 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/15 = 98.809
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~16/15 = 98.809{{c}}


{{Optimal ET sequence|legend=1| 1, 11, 12, 49dd }}
{{Optimal ET sequence|legend=1| 1, 11, 12, 49dd }}


[[Badness]]: 0.075055
[[Badness]] (Smith): 0.075055


== Freivald ==
== Freivald ==
Line 130: Line 130:
: mapping generator: ~2, ~35/24
: mapping generator: ~2, ~35/24


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~48/35 = 550.9374
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~48/35 = 550.9374{{c}}


{{Optimal ET sequence|legend=1| 13d, 24, 37, 61, 98b }}
{{Optimal ET sequence|legend=1| 13d, 24, 37, 61, 98b }}


[[Badness]]: 0.209095
[[Badness]] (Smith): 0.209095


=== 11-limit ===
=== 11-limit ===
Line 143: Line 143:
Mapping: {{mapping| 1 7 -2 12 4 | 0 -10 8 -17 -1 }}
Mapping: {{mapping| 1 7 -2 12 4 | 0 -10 8 -17 -1 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 550.9007
Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~11/8 = 550.9007{{c}}


Optimal ET sequence: {{Optimal ET sequence| 13d, 24, 37, 61 }}
Optimal ET sequence: {{Optimal ET sequence| 13d, 24, 37, 61 }}


Badness: 0.077504
Badness (Smith): 0.077504


=== 13-limit ===
=== 13-limit ===
Line 156: Line 156:
Mapping: {{mapping| 1 7 -2 12 4 1 | 0 -10 8 -17 -1 5 }}
Mapping: {{mapping| 1 7 -2 12 4 1 | 0 -10 8 -17 -1 5 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 550.9062
Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~11/8 = 550.9062{{c}}


Optimal ET sequence: {{Optimal ET sequence| 13d, 24, 37, 61 }}
Optimal ET sequence: {{Optimal ET sequence| 13d, 24, 37, 61 }}


Badness: 0.045864
Badness (Smith): 0.045864


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