Passion family: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
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The '''passion family''' tempers out 262144/253125 in the 5-limit, which equates five instances of [[16/15]] with [[4/3]].  
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]].  


== Passion ==
== Passion ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 262144/253125
[[Comma list]]: 262144/253125


[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -5 4 }}]
{{Mapping|legend=1| 1 2 2 | 0 -5 4 }}


Mapping generators: ~2, ~16/15
: mapping generators: ~2, ~16/15


[[POTE generator]]: ~16/15 = 98.670
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/15 = 98.670


{{Optimal ET sequence|legend=1| 12, 49, 61, 73 }}
{{Optimal ET sequence|legend=1| 12, 49, 61, 73 }}
Line 17: Line 17:


== Septimal passion ==
== Septimal passion ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 64/63, 3125/3087
[[Comma list]]: 64/63, 3125/3087


[[Mapping]]: [{{val| 1 2 2 2 }}, {{val| 0 -5 4 10 }}]
{{Mapping|legend=1| 1 2 2 2 | 0 -5 4 10 }}
 
Mapping generators: ~2, ~16/15


{{Multival|legend=1| 5 -4 -10 -18 -30 -12 }}
{{Multival|legend=1| 5 -4 -10 -18 -30 -12 }}


[[POTE generator]]: ~16/15 = 98.153
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/15 = 98.153


{{Optimal ET sequence|legend=1| 12, 37, 49, 110bcd }}
{{Optimal ET sequence|legend=1| 12, 37, 49, 110bcd }}
Line 38: Line 36:
Comma list: 64/63, 100/99, 1375/1372
Comma list: 64/63, 100/99, 1375/1372


Mapping: [{{val| 1 2 2 2 2 }}, {{val| 0 -5 4 10 18 }}]
Mapping: {{mapping| 1 2 2 2 2 | 0 -5 4 10 18 }}


POTE generator: ~16/15 = 98.019
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.019


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


Badness: 0.040809
Badness: 0.040809
Line 51: Line 49:
Comma list: 64/63, 100/99, 196/195, 275/273
Comma list: 64/63, 100/99, 196/195, 275/273


Mapping: [{{val| 1 2 2 2 2 2 }}, {{val| 0 -5 4 10 18 21 }}]
Mapping: {{mapping| 1 2 2 2 2 2 | 0 -5 4 10 18 21 }}


POTE generator: ~16/15 = 97.910
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 97.910


{{Optimal ET sequence|legend=1| 12f, 25f, 37, 49f }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 25f, 37, 49f }}


Badness: 0.030886
Badness: 0.030886


== Passionate ==
== Passionate ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 126/125, 131072/127575
[[Comma list]]: 126/125, 131072/127575


[[Mapping]]: [{{val|1 2 2 1}}, {{val|0 -5 4 22}}]
{{Mapping|legend=1| 1 2 2 1 | 0 -5 4 22 }}


{{Multival|legend=1|5 -4 -22 -18 -49 -40}}
{{Multival|legend=1| 5 -4 -22 -18 -49 -40 }}


[[POTE generator]]: ~16/15 = 98.817
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/15 = 98.817


{{Optimal ET sequence|legend=1| 12, 61, 73, 85c }}
{{Optimal ET sequence|legend=1| 12, 61, 73, 85c }}
Line 79: Line 77:
Comma list: 126/125, 176/175, 8192/8019
Comma list: 126/125, 176/175, 8192/8019


Mapping: [{{val|1 2 2 1 1}}, {{val|0 -5 4 22 30}}]
Mapping: {{mapping| 1 2 2 1 1 | 0 -5 4 22 30 }}


POTE generator: ~16/15 = 98.721
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.721


{{Optimal ET sequence|legend=1| 12, 61, 73, 158bccee }}
Optimal ET sequence: {{Optimal ET sequence| 12, 61, 73, 158bccee }}


Badness: 0.068322
Badness: 0.068322
Line 92: Line 90:
Comma list: 126/125, 176/175, 343/338, 364/363
Comma list: 126/125, 176/175, 343/338, 364/363


Mapping: [{{val|1 2 2 1 1 1}}, {{val|0 -5 4 22 30 33}}]
Mapping: {{mapping| 1 2 2 1 1 1 | 0 -5 4 22 30 33 }}


POTE generator: ~16/15 = 98.627
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.627


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


Badness: 0.052302
Badness: 0.052302
Line 105: Line 103:
Comma list: 126/125, 176/175, 196/195, 1352/1331
Comma list: 126/125, 176/175, 196/195, 1352/1331


Mapping: [{{val|1 2 2 1 1 0}}, {{val|0 -5 4 22 30 45}}]
Mapping: {{mapping| 1 2 2 1 1 0 | 0 -5 4 22 30 45 }}


POTE generator: ~16/15 = 98.791
Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.791


{{Optimal ET sequence|legend=1| 12f, 61f, 73, 85ce }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 61f, 73, 85ce }}


Badness: 0.056386
Badness: 0.056386


== Passive ==
== Passive ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 256/245
[[Comma list]]: 225/224, 256/245


[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -5 4 -2 }}]
{{Mapping|legend=1| 1 2 2 3 | 0 -5 4 -2 }}


[[POTE generator]]: ~16/15 = 98.809
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/15 = 98.809


{{Optimal ET sequence|legend=1| 1, 11, 12, 49dd }}
{{Optimal ET sequence|legend=1| 1, 11, 12, 49dd }}
Line 127: Line 125:


== Freivald ==
== Freivald ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 6144/6125, 6272/6075
[[Comma list]]: 6144/6125, 6272/6075


[[Mapping]]: [{{val| 1 7 -2 12 }}, {{val| 0 -10 8 -17 }}]
{{Mapping|legend=1| 1 7 -2 12 | 0 -10 8 -17 }}


Mapping generator: ~2, ~35/24
: mapping generator: ~2, ~35/24


[[POTE generator]]: ~48/35 = 550.9374
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~48/35 = 550.9374


{{Optimal ET sequence|legend=1| 13d, 24, 37, 61, 98b }}
{{Optimal ET sequence|legend=1| 13d, 24, 37, 61, 98b }}
Line 146: Line 144:
Comma list: 121/120, 176/175, 2744/2673
Comma list: 121/120, 176/175, 2744/2673


Mapping: [{{val| 1 7 -2 12 4 }}, {{val| 0 -10 8 -17 -1 }}]
Mapping: {{mapping| 1 7 -2 12 4 | 0 -10 8 -17 -1 }}


POTE generator: ~11/8 = 550.9007
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 550.9007


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


Badness: 0.077504
Badness: 0.077504
Line 159: Line 157:
Comma list: 91/90, 121/120, 176/175, 512/507
Comma list: 91/90, 121/120, 176/175, 512/507


Mapping: [{{val| 1 7 -2 12 4 1 }}, {{val| 0 -10 8 -17 -1 5 }}]
Mapping: {{mapping| 1 7 -2 12 4 1 | 0 -10 8 -17 -1 5 }}


POTE generator: ~11/8 = 550.9062
Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 550.9062


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


Badness: 0.045864
Badness: 0.045864
Line 169: Line 167:
[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Passion family| ]] <!-- main article -->
[[Category:Passion family| ]] <!-- main article -->
[[Category:Passion| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]

Revision as of 12:56, 9 February 2024

The passion family tempers out the passion comma, 262144/253125 = [18 -4 -5⟩ in the 5-limit, which equates five instances of 16/15 with 4/3.

Passion

Subgroup: 2.3.5

Comma list: 262144/253125

Mapping: [⟨1 2 2], ⟨0 -5 4]]

mapping generators: ~2, ~16/15

Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.670

Optimal ET sequence: 12, 49, 61, 73

Badness: 0.168550

Septimal passion

Subgroup: 2.3.5.7

Comma list: 64/63, 3125/3087

Mapping: [⟨1 2 2 2], ⟨0 -5 4 10]]

Wedgie: ⟨⟨ 5 -4 -10 -18 -30 -12 ]]

Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.153

Optimal ET sequence: 12, 37, 49, 110bcd

Badness: 0.062327

11-limit

Subgroup: 2.3.5.7.11

Comma list: 64/63, 100/99, 1375/1372

Mapping: [⟨1 2 2 2 2], ⟨0 -5 4 10 18]]

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

Optimal ET sequence: 12, 37, 49

Badness: 0.040809

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 64/63, 100/99, 196/195, 275/273

Mapping: [⟨1 2 2 2 2 2], ⟨0 -5 4 10 18 21]]

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

Optimal ET sequence: 12f, 25f, 37, 49f

Badness: 0.030886

Passionate

Subgroup: 2.3.5.7

Comma list: 126/125, 131072/127575

Mapping: [⟨1 2 2 1], ⟨0 -5 4 22]]

Wedgie: ⟨⟨ 5 -4 -22 -18 -49 -40 ]]

Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.817

Optimal ET sequence: 12, 61, 73, 85c

Badness: 0.121293

11-limit

Subgroup: 2.3.5.7.11

Comma list: 126/125, 176/175, 8192/8019

Mapping: [⟨1 2 2 1 1], ⟨0 -5 4 22 30]]

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

Optimal ET sequence: 12, 61, 73, 158bccee

Badness: 0.068322

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 176/175, 343/338, 364/363

Mapping: [⟨1 2 2 1 1 1], ⟨0 -5 4 22 30 33]]

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

Optimal ET sequence: 12f, 61, 73f

Badness: 0.052302

Pash

Subgroup: 2.3.5.7.11.13

Comma list: 126/125, 176/175, 196/195, 1352/1331

Mapping: [⟨1 2 2 1 1 0], ⟨0 -5 4 22 30 45]]

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

Optimal ET sequence: 12f, 61f, 73, 85ce

Badness: 0.056386

Passive

Subgroup: 2.3.5.7

Comma list: 225/224, 256/245

Mapping: [⟨1 2 2 3], ⟨0 -5 4 -2]]

Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 98.809

Optimal ET sequence: 1, 11, 12, 49dd

Badness: 0.075055

Freivald

Subgroup: 2.3.5.7

Comma list: 6144/6125, 6272/6075

Mapping: [⟨1 7 -2 12], ⟨0 -10 8 -17]]

mapping generator: ~2, ~35/24

Optimal tuning (POTE): ~2 = 1\1, ~48/35 = 550.9374

Optimal ET sequence: 13d, 24, 37, 61, 98b

Badness: 0.209095

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 176/175, 2744/2673

Mapping: [⟨1 7 -2 12 4], ⟨0 -10 8 -17 -1]]

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

Optimal ET sequence: 13d, 24, 37, 61

Badness: 0.077504

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 121/120, 176/175, 512/507

Mapping: [⟨1 7 -2 12 4 1], ⟨0 -10 8 -17 -1 5]]

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

Optimal ET sequence: 13d, 24, 37, 61

Badness: 0.045864

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