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]]

Revision as of 12:07, 22 August 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The passion family of temperaments 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 = 1200.000 ¢, ~16/15 = 98.670 ¢

Optimal ET sequence: 12, 49, 61, 73

Badness (Smith): 0.168550

Septimal passion

Subgroup: 2.3.5.7

Comma list: 64/63, 3125/3087

Mapping: [⟨1 2 2 2], ⟨0 -5 4 10]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~16/15 = 98.153 ¢

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

Badness (Smith): 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 = 1200.000 ¢, ~16/15 = 98.019 ¢

Optimal ET sequence: 12, 37, 49

Badness (Smith): 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 = 1200.000 ¢, ~16/15 = 97.910 ¢

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

Badness (Smith): 0.030886

Passionate

Subgroup: 2.3.5.7

Comma list: 126/125, 131072/127575

Mapping: [⟨1 2 2 1], ⟨0 -5 4 22]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~16/15 = 98.817 ¢

Optimal ET sequence: 12, 61, 73, 85c

Badness (Smith): 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 = 1200.000 ¢, ~16/15 = 98.721 ¢

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

Badness (Smith): 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 = 1200.000 ¢, ~16/15 = 98.627 ¢

Optimal ET sequence: 12f, 61, 73f

Badness (Smith): 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 = 1200.000 ¢, ~16/15 = 98.791 ¢

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

Badness (Smith): 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 = 1200.000 ¢, ~16/15 = 98.809 ¢

Optimal ET sequence: 1, 11, 12, 49dd

Badness (Smith): 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 = 1200.0000 ¢, ~48/35 = 550.9374 ¢

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

Badness (Smith): 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 = 1200.0000 ¢, ~11/8 = 550.9007 ¢

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

Badness (Smith): 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 = 1200.0000 ¢, ~11/8 = 550.9062 ¢

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

Badness (Smith): 0.045864

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