Porcupine rank-3 family: Difference between revisions
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m FloraC moved page Porcupine rank three family to Porcupine rank-3 family: For obvious reasons |
Switch to Sintel's badness, WE & CWE tunings, per community consensus |
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| Line 11: | Line 11: | ||
: mapping generators: ~2, ~10/9, ~7 | : mapping generators: ~2, ~10/9, ~7 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1199.5444{{c}}, ~10/9 = 163.8881{{c}}, ~7/4 = 969.6868{{c}} | |||
: [[error map]]: {{val| -0.456 +5.469 -7.121 -0.050 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 164.0621{{c}}, ~7/4 = 969.4180{{c}} | |||
: error map: {{val| 0.000 +5.859 -6.624 +0.592 }} | |||
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~10/9 = 163.9504{{c}}, ~7/4 = 970.0552{{c}} --> | |||
{{Optimal ET sequence|legend=1| 7d, 8d, 14c, 15, 22, 37, 51, 73c }} | {{Optimal ET sequence|legend=1| 7d, 8d, 14c, 15, 22, 37, 51, 73c }} | ||
[[Badness]]: | [[Badness]] (Sintel): 2.36 | ||
== Sonic == | == Sonic == | ||
| Line 24: | Line 29: | ||
{{Mapping|legend=1| 1 2 3 0 4 | 0 -3 -5 0 -4 | 0 0 0 1 0 }} | {{Mapping|legend=1| 1 2 3 0 4 | 0 -3 -5 0 -4 | 0 0 0 1 0 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1200.3290{{c}}, ~11/10 = 164.1227{{c}}, ~7/4 = 968.1067{{c}} | |||
: [[error map]]: {{val| +0.329 +6.335 -5.940 -0.061 -6.492 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/10 = 163.9951{{c}}, ~7/4 = 968.2673{{c}} | |||
: error map: {{val| 0.000 +6.060 -6.289 -0.559 -7.298 }} | |||
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~11/10 = 164.0777{{c}}, ~7/4 = 967.8413{{c}} --> | |||
{{Optimal ET sequence|legend=1| 7d, 8d, 14c, 15, 22, 37, 51, 88b }} | {{Optimal ET sequence|legend=1| 7d, 8d, 14c, 15, 22, 37, 51, 88b }} | ||
[[Badness]]: 0. | [[Badness]] (Sintel): 0.629 | ||
== Tikal == | == Tikal == | ||
| Line 37: | Line 47: | ||
{{Mapping|legend=1| 1 2 3 0 0 | 0 -3 -5 0 5 | 0 0 0 1 1 }} | {{Mapping|legend=1| 1 2 3 0 0 | 0 -3 -5 0 5 | 0 0 0 1 1 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1195.9857{{c}}, ~11/10 = 160.9790{{c}}, ~7/4 = 967.7973{{c}} | |||
: [[error map]]: {{val| -4.014 +7.079 -3.252 -9.057 +13.346 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/10 = 162.1977{{c}}, ~7/4 = 964.6202{{c}} | |||
: error map: {{val| 0.000 +11.452 +2.698 -4.206 +24.291 }} | |||
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~10/9 = 161.5193{{c}}, ~7/4 = 971.0457{{c}} --> | |||
{{Optimal ET sequence|legend=1| 7d, 8d, 15, 30dee, 37ee, 52bee }} | {{Optimal ET sequence|legend=1| 7d, 8d, 15, 30dee, 37ee, 52bee }} | ||
[[Badness]]: | [[Badness]] (Sintel): 2.37 | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
Revision as of 12:17, 6 September 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 porcupine rank-3 family of temperaments tempers out the porcupine comma or maximal diesis, 250/243. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.
Rank-3 porcupine
Subgroup: 2.3.5.7
Mapping: [⟨1 2 3 0], ⟨0 -3 -5 0], ⟨0 0 0 1]]
- mapping generators: ~2, ~10/9, ~7
- WE: ~2 = 1199.5444 ¢, ~10/9 = 163.8881 ¢, ~7/4 = 969.6868 ¢
- error map: ⟨-0.456 +5.469 -7.121 -0.050]
- CWE: ~2 = 1200.0000 ¢, ~10/9 = 164.0621 ¢, ~7/4 = 969.4180 ¢
- error map: ⟨0.000 +5.859 -6.624 +0.592]
Optimal ET sequence: 7d, 8d, 14c, 15, 22, 37, 51, 73c
Badness (Sintel): 2.36
Sonic
Subgroup: 2.3.5.7.11
Comma list: 55/54, 100/99
Mapping: [⟨1 2 3 0 4], ⟨0 -3 -5 0 -4], ⟨0 0 0 1 0]]
- WE: ~2 = 1200.3290 ¢, ~11/10 = 164.1227 ¢, ~7/4 = 968.1067 ¢
- error map: ⟨+0.329 +6.335 -5.940 -0.061 -6.492]
- CWE: ~2 = 1200.0000 ¢, ~11/10 = 163.9951 ¢, ~7/4 = 968.2673 ¢
- error map: ⟨0.000 +6.060 -6.289 -0.559 -7.298]
Optimal ET sequence: 7d, 8d, 14c, 15, 22, 37, 51, 88b
Badness (Sintel): 0.629
Tikal
Subgroup: 2.3.5.7.11
Comma list: 56/55, 250/243
Mapping: [⟨1 2 3 0 0], ⟨0 -3 -5 0 5], ⟨0 0 0 1 1]]
- WE: ~2 = 1195.9857 ¢, ~11/10 = 160.9790 ¢, ~7/4 = 967.7973 ¢
- error map: ⟨-4.014 +7.079 -3.252 -9.057 +13.346]
- CWE: ~2 = 1200.0000 ¢, ~11/10 = 162.1977 ¢, ~7/4 = 964.6202 ¢
- error map: ⟨0.000 +11.452 +2.698 -4.206 +24.291]
Optimal ET sequence: 7d, 8d, 15, 30dee, 37ee, 52bee
Badness (Sintel): 2.37