Passion family: Difference between revisions

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m Units. Misc. cleanup
Switch to Sintel's badness, WE & CWE tunings, per community consensus
Line 11: Line 11:
: mapping generators: ~2, ~16/15
: mapping generators: ~2, ~16/15


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~16/15 = 98.670{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1197.8074{{c}}, ~16/15 = 98.4898{{c}}
: [[error map]]: {{val| -2.193 +1.211 +3.260 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 98.7335{{c}}
: error map: {{val| 0.000 +4.378 +8.620 }}
<!-- * [[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, 231bccc }}


[[Badness]] (Smith): 0.168550
[[Badness]] (Sintel): 3.95


== Septimal passion ==
== Septimal passion ==
Line 24: Line 29:
{{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 = 1200.000{{c}}, ~16/15 = 98.153{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1197.0350{{c}}, ~21/20 = 97.9106{{c}}
: [[error map]]: {{val| -2.965 +2.562 -0.601 +4.351 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 98.1019{{c}}
: error map: {{val| 0.000 +7.535 +6.094 +12.193 }}
<!-- [[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]] (Smith): 0.062327
[[Badness]] (Sintel): 1.58


=== 11-limit ===
=== 11-limit ===
Line 37: Line 47:
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 = 1200.000{{c}}, ~16/15 = 98.019{{c}}
Optimal tunings:
* WE: ~2 = 1196.9304{{c}}, ~21/20 = 97.7686{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 97.9333{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~16/15 = 98.019{{c}} -->


Optimal ET sequence: {{Optimal ET sequence| 12, 37, 49 }}
{{Optimal ET sequence|legend=0| 12, 37, 49 }}


Badness (Smith): 0.040809
Badness (Sintel): 1.35


=== 13-limit ===
=== 13-limit ===
Line 50: Line 63:
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 = 1200.000{{c}}, ~16/15 = 97.910{{c}}
Optimal tunings:
* WE: ~2 = 1196.8712{{c}}, ~21/20 = 97.6548{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 97.8141{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~16/15 = 97.910{{c}} -->


Optimal ET sequence: {{Optimal ET sequence| 12f, 25f, 37, 49f }}
{{Optimal ET sequence|legend=0| 12f, 25f, 37, 49f }}


Badness (Smith): 0.030886
Badness (Sintel): 1.28


== Passionate ==
== Passionate ==
Line 63: Line 79:
{{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 = 1200.000{{c}}, ~16/15 = 98.817{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1197.9486{{c}}, ~16/15 = 98.6479{{c}}
: [[error map]]: {{val| -2.051 +0.703 +4.175 -0.623 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 98.7770{{c}}
: error map: {{val| 0.000 +4.160 +8.794 +4.269 }}
<!-- * [[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, 49d, 61, 73, 85c }}


[[Badness]] (Smith): 0.121293
[[Badness]] (Sintel): 3.07


=== 11-limit ===
=== 11-limit ===
Line 76: Line 97:
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 = 1200.000{{c}}, ~16/15 = 98.721{{c}}
Optimal tunings:
* WE: ~2 = 1197.8835{{c}}, ~16/15 = 98.5469{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/15 = 98.6733{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~16/15 = 98.721{{c}} -->


Optimal ET sequence: {{Optimal ET sequence| 12, 61, 73, 158bccee }}
{{Optimal ET sequence|legend=0| 12, 49de, 61, 73, 158bccee }}


Badness (Smith): 0.068322
Badness (Sintel): 2.26


==== 13-limit ====
==== 13-limit ====
Line 89: Line 113:
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 = 1200.000{{c}}, ~16/15 = 98.627{{c}}
Optimal tunings:
* WE: ~2 = 1197.8309{{c}}, ~16/15 = 98.4485{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/15 = 98.5760{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~16/15 = 98.627{{c}} -->


Optimal ET sequence: {{Optimal ET sequence| 12f, 61, 73f }}
{{Optimal ET sequence|legend=0| 12f, 49de, 61, 73f }}


Badness (Smith): 0.052302
Badness (Sintel): 2.16


==== Pash ====
==== Pash ====
Line 102: Line 129:
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 = 1200.000{{c}}, ~16/15 = 98.791{{c}}
Optimal tunings:
* WE: ~2 = 1197.8306{{c}}, ~16/15 = 98.6124{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/15 = 98.7468{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~16/15 = 98.791{{c}} -->


Optimal ET sequence: {{Optimal ET sequence| 12f, 61f, 73, 85ce }}
{{Optimal ET sequence|legend=0| 12f, 73, 85ce }}


Badness (Smith): 0.056386
Badness (Sintel): 2.33


== Passive ==
== Passive ==
Line 115: Line 145:
{{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 = 1200.000{{c}}, ~16/15 = 98.809{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1195.3551{{c}}, ~16/15 = 98.4266{{c}}
: [[error map]]: {{val| -4.645 -3.378 -1.897 +20.386 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 98.9690{{c}}
: error map: {{val| 0.000 +3.200 +9.562 +33.236 }}
<!-- * [[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 }}


[[Badness]] (Smith): 0.075055
[[Badness]] (Sintel): 1.90


== Freivald ==
== Freivald ==
Line 126: Line 161:
[[Comma list]]: 6144/6125, 6272/6075
[[Comma list]]: 6144/6125, 6272/6075


{{Mapping|legend=1| 1 7 -2 12 | 0 -10 8 -17 }}
{{Mapping|legend=1| 1 -3 6 -5 | 0 10 -8 17 }}


: mapping generator: ~2, ~35/24
: mapping generator: ~2, ~48/35


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~48/35 = 550.9374{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1198.4021{{c}}, ~48/35 = 550.2038{{c}}
: [[error map]]: {{val| -4.645 -3.378 -1.897 +20.386 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~48/35 = 550.8980{{c}}
: error map: {{val| 0.000 +3.200 +9.562 +33.236 }}
<!-- * [[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]] (Smith): 0.209095
[[Badness]] (Sintel): 5.29


=== 11-limit ===
=== 11-limit ===
Line 141: Line 181:
Comma list: 121/120, 176/175, 2744/2673
Comma list: 121/120, 176/175, 2744/2673


Mapping: {{mapping| 1 7 -2 12 4 | 0 -10 8 -17 -1 }}
Mapping: {{mapping| 1 -3 6 -5 3 | 0 10 -8 17 1 }}


Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~11/8 = 550.9007{{c}}
Optimal tunings:
* WE: ~2 = 1198.8053{{c}}, ~11/8 = 550.3522{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 550.8760{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~11/8 = 550.9007{{c}} -->


Optimal ET sequence: {{Optimal ET sequence| 13d, 24, 37, 61 }}
{{Optimal ET sequence|legend=0| 13d, 24, 37, 61 }}


Badness (Smith): 0.077504
Badness (Sintel): 2.56


=== 13-limit ===
=== 13-limit ===
Line 156: Line 199:
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 = 1200.0000{{c}}, ~11/8 = 550.9062{{c}}
Optimal tunings:
* WE: ~2 = 1198.7706{{c}}, ~11/8 = 550.3418{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 550.8892{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~11/8 = 550.9062{{c}} -->


Optimal ET sequence: {{Optimal ET sequence| 13d, 24, 37, 61 }}
{{Optimal ET sequence|legend=0| 13d, 24, 37, 61 }}


Badness (Smith): 0.045864
Badness (Sintel): 1.90


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

Revision as of 13:32, 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 tunings:

  • WE: ~2 = 1197.8074 ¢, ~16/15 = 98.4898 ¢
error map: ⟨-2.193 +1.211 +3.260]
  • CWE: ~2 = 1200.0000 ¢, ~16/15 = 98.7335 ¢
error map: ⟨0.000 +4.378 +8.620]

Optimal ET sequence: 12, 49, 61, 73, 231bccc

Badness (Sintel): 3.95

Septimal passion

Subgroup: 2.3.5.7

Comma list: 64/63, 3125/3087

Mapping: [⟨1 2 2 2], ⟨0 -5 4 10]]

Optimal tunings:

  • WE: ~2 = 1197.0350 ¢, ~21/20 = 97.9106 ¢
error map: ⟨-2.965 +2.562 -0.601 +4.351]
  • CWE: ~2 = 1200.0000 ¢, ~16/15 = 98.1019 ¢
error map: ⟨0.000 +7.535 +6.094 +12.193]

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

Badness (Sintel): 1.58

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 tunings:

  • WE: ~2 = 1196.9304 ¢, ~21/20 = 97.7686 ¢
  • CWE: ~2 = 1200.0000 ¢, ~21/20 = 97.9333 ¢

Optimal ET sequence: 12, 37, 49

Badness (Sintel): 1.35

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 tunings:

  • WE: ~2 = 1196.8712 ¢, ~21/20 = 97.6548 ¢
  • CWE: ~2 = 1200.0000 ¢, ~21/20 = 97.8141 ¢

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

Badness (Sintel): 1.28

Passionate

Subgroup: 2.3.5.7

Comma list: 126/125, 131072/127575

Mapping: [⟨1 2 2 1], ⟨0 -5 4 22]]

Optimal tunings:

  • WE: ~2 = 1197.9486 ¢, ~16/15 = 98.6479 ¢
error map: ⟨-2.051 +0.703 +4.175 -0.623]
  • CWE: ~2 = 1200.0000 ¢, ~16/15 = 98.7770 ¢
error map: ⟨0.000 +4.160 +8.794 +4.269]

Optimal ET sequence: 12, 49d, 61, 73, 85c

Badness (Sintel): 3.07

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 tunings:

  • WE: ~2 = 1197.8835 ¢, ~16/15 = 98.5469 ¢
  • CWE: ~2 = 1200.0000 ¢, ~16/15 = 98.6733 ¢

Optimal ET sequence: 12, 49de, 61, 73, 158bccee

Badness (Sintel): 2.26

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 tunings:

  • WE: ~2 = 1197.8309 ¢, ~16/15 = 98.4485 ¢
  • CWE: ~2 = 1200.0000 ¢, ~16/15 = 98.5760 ¢

Optimal ET sequence: 12f, 49de, 61, 73f

Badness (Sintel): 2.16

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 tunings:

  • WE: ~2 = 1197.8306 ¢, ~16/15 = 98.6124 ¢
  • CWE: ~2 = 1200.0000 ¢, ~16/15 = 98.7468 ¢

Optimal ET sequence: 12f, 73, 85ce

Badness (Sintel): 2.33

Passive

Subgroup: 2.3.5.7

Comma list: 225/224, 256/245

Mapping: [⟨1 2 2 3], ⟨0 -5 4 -2]]

Optimal tunings:

  • WE: ~2 = 1195.3551 ¢, ~16/15 = 98.4266 ¢
error map: ⟨-4.645 -3.378 -1.897 +20.386]
  • CWE: ~2 = 1200.0000 ¢, ~16/15 = 98.9690 ¢
error map: ⟨0.000 +3.200 +9.562 +33.236]

Optimal ET sequence: 1, 11, 12

Badness (Sintel): 1.90

Freivald

Subgroup: 2.3.5.7

Comma list: 6144/6125, 6272/6075

Mapping: [⟨1 -3 6 -5], ⟨0 10 -8 17]]

mapping generator: ~2, ~48/35

Optimal tunings:

  • WE: ~2 = 1198.4021 ¢, ~48/35 = 550.2038 ¢
error map: ⟨-4.645 -3.378 -1.897 +20.386]
  • CWE: ~2 = 1200.0000 ¢, ~48/35 = 550.8980 ¢
error map: ⟨0.000 +3.200 +9.562 +33.236]

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

Badness (Sintel): 5.29

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 -3 6 -5 3], ⟨0 10 -8 17 1]]

Optimal tunings:

  • WE: ~2 = 1198.8053 ¢, ~11/8 = 550.3522 ¢
  • CWE: ~2 = 1200.0000 ¢, ~11/8 = 550.8760 ¢

Optimal ET sequence: 13d, 24, 37, 61

Badness (Sintel): 2.56

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 tunings:

  • WE: ~2 = 1198.7706 ¢, ~11/8 = 550.3418 ¢
  • CWE: ~2 = 1200.0000 ¢, ~11/8 = 550.8892 ¢

Optimal ET sequence: 13d, 24, 37, 61

Badness (Sintel): 1.90

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