Passion family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings, per community consensus
- POTE tunings
Line 16: Line 16:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 98.7335{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 98.7335{{c}}
: error map: {{val| 0.000 +4.378 +8.620 }}
: 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, 231bccc }}
{{Optimal ET sequence|legend=1| 12, 49, 61, 73, 231bccc }}
Line 34: Line 33:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 98.1019{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 98.1019{{c}}
: error map: {{val| 0.000 +7.535 +6.094 +12.193 }}
: 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 }}
Line 50: Line 48:
* WE: ~2 = 1196.9304{{c}}, ~21/20 = 97.7686{{c}}
* WE: ~2 = 1196.9304{{c}}, ~21/20 = 97.7686{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 97.9333{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 97.9333{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~16/15 = 98.019{{c}} -->


{{Optimal ET sequence|legend=0| 12, 37, 49 }}
{{Optimal ET sequence|legend=0| 12, 37, 49 }}
Line 66: Line 63:
* WE: ~2 = 1196.8712{{c}}, ~21/20 = 97.6548{{c}}
* WE: ~2 = 1196.8712{{c}}, ~21/20 = 97.6548{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 97.8141{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 97.8141{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~16/15 = 97.910{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 25f, 37, 49f }}
{{Optimal ET sequence|legend=0| 12f, 25f, 37, 49f }}
Line 84: Line 80:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 98.7770{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 98.7770{{c}}
: error map: {{val| 0.000 +4.160 +8.794 +4.269 }}
: 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, 49d, 61, 73, 85c }}
{{Optimal ET sequence|legend=1| 12, 49d, 61, 73, 85c }}
Line 100: Line 95:
* WE: ~2 = 1197.8835{{c}}, ~16/15 = 98.5469{{c}}
* WE: ~2 = 1197.8835{{c}}, ~16/15 = 98.5469{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/15 = 98.6733{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/15 = 98.6733{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~16/15 = 98.721{{c}} -->


{{Optimal ET sequence|legend=0| 12, 49de, 61, 73, 158bccee }}
{{Optimal ET sequence|legend=0| 12, 49de, 61, 73, 158bccee }}
Line 116: Line 110:
* WE: ~2 = 1197.8309{{c}}, ~16/15 = 98.4485{{c}}
* WE: ~2 = 1197.8309{{c}}, ~16/15 = 98.4485{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/15 = 98.5760{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/15 = 98.5760{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~16/15 = 98.627{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 49de, 61, 73f }}
{{Optimal ET sequence|legend=0| 12f, 49de, 61, 73f }}
Line 132: Line 125:
* WE: ~2 = 1197.8306{{c}}, ~16/15 = 98.6124{{c}}
* WE: ~2 = 1197.8306{{c}}, ~16/15 = 98.6124{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/15 = 98.7468{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/15 = 98.7468{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~16/15 = 98.791{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 73, 85ce }}
{{Optimal ET sequence|legend=0| 12f, 73, 85ce }}
Line 150: Line 142:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 98.9690{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~16/15 = 98.9690{{c}}
: error map: {{val| 0.000 +3.200 +9.562 +33.236 }}
: 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 }}
{{Optimal ET sequence|legend=1| 1, 11, 12 }}
Line 170: Line 161:
* [[CWE]]: ~2 = 1200.0000{{c}}, ~48/35 = 550.8980{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~48/35 = 550.8980{{c}}
: error map: {{val| 0.000 +3.200 +9.562 +33.236 }}
: 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 }}
Line 186: Line 176:
* WE: ~2 = 1198.8053{{c}}, ~11/8 = 550.3522{{c}}
* WE: ~2 = 1198.8053{{c}}, ~11/8 = 550.3522{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 550.8760{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 550.8760{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~11/8 = 550.9007{{c}} -->


{{Optimal ET sequence|legend=0| 13d, 24, 37, 61 }}
{{Optimal ET sequence|legend=0| 13d, 24, 37, 61 }}
Line 202: Line 191:
* WE: ~2 = 1198.7706{{c}}, ~11/8 = 550.3418{{c}}
* WE: ~2 = 1198.7706{{c}}, ~11/8 = 550.3418{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 550.8892{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/8 = 550.8892{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~11/8 = 550.9062{{c}} -->


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

Revision as of 13:33, 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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