Dimcomp family: Difference between revisions
m - redundant category |
+ optimal tunings |
||
| Line 10: | Line 10: | ||
: mapping generators: ~25/21, ~3, ~5 | : mapping generators: ~25/21, ~3, ~5 | ||
{{Optimal ET sequence|legend=1| | [[Optimal tuning]]s: | ||
* [[WE]]: ~25/21 = 300.0036{{c}}, ~3/2 = 702.0854{{c}}, ~5/4 = 385.6631{{c}} | |||
: [[error map]]: {{val| +0.014 +0.145 -0.622 +0.454 }} | |||
* [[CWE]]: ~25/21 = 300.0000{{c}}, ~3/2 = 702.0885{{c}}, ~5/4 = 385.6745{{c}} | |||
: error map: {{val| 0.000 +0.133 -0.639 +0.435 }} | |||
{{Optimal ET sequence|legend=1| 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }} | |||
[[Badness]] (Sintel): 3.45 | [[Badness]] (Sintel): 3.45 | ||
| Line 21: | Line 27: | ||
{{Mapping|legend=1| 4 0 0 -1 5 | 0 1 0 -1 -3 | 0 0 1 2 3 }} | {{Mapping|legend=1| 4 0 0 -1 5 | 0 1 0 -1 -3 | 0 0 1 2 3 }} | ||
{{Optimal ET sequence|legend=1| 68, 72, 140, 152, 224, 364, 436, 588 }} | [[Optimal tuning]]s: | ||
* [[WE]]: ~25/21 = 300.0093{{c}}, ~3/2 = 701.9976{{c}}, ~5/4 = 385.6591{{c}} | |||
: [[error map]]: {{val| +0.037 +0.080 -0.580 +0.597 -0.176 }} | |||
* [[CWE]]: ~25/21 = 300.0000{{c}}, ~3/2 = 702.0009{{c}}, ~5/4 = 385.6895{{c}} | |||
: error map: {{val| 0.000 +0.046 -0.624 +0.552 -0.252 }} | |||
{{Optimal ET sequence|legend=1| 12, …, 68, 72, 140, 152, 224, 364, 436, 588 }} | |||
[[Badness]] (Sintel): 0.751 | [[Badness]] (Sintel): 0.751 | ||
| Line 31: | Line 43: | ||
Mapping: {{mapping| 4 0 0 -1 5 -16 | 0 1 0 -1 -3 -1 | 0 0 1 2 3 4 }} | Mapping: {{mapping| 4 0 0 -1 5 -16 | 0 1 0 -1 -3 -1 | 0 0 1 2 3 4 }} | ||
Optimal tunings: | |||
* WE: ~25/21 = 300.0140{{c}}, ~3/2 = 701.9679{{c}}, ~5/4 = 385.5977{{c}} | |||
* CWE: ~25/21 = 300.0000{{c}}, ~3/2 = 701.9549{{c}}, ~5/4 = 385.6140{{c}} | |||
{{Optimal ET sequence|legend=0| 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c }} | {{Optimal ET sequence|legend=0| 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c }} | ||
| Line 42: | Line 58: | ||
{{Mapping|legend=1| 8 1 3 3 16 0 | 0 3 4 5 3 0 | 0 0 0 0 0 1 }} | {{Mapping|legend=1| 8 1 3 3 16 0 | 0 3 4 5 3 0 | 0 0 0 0 0 1 }} | ||
: mapping generators: ~12/11, ~7/5, ~13 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~12/11 = 150.0093{{c}}, ~7/5 = 583.9356{{c}}, ~13/8 = 840.6906{{c}} | |||
: [[error map]]: {{val| -0.055 -0.155 -0.592 +0.832 +0.380 -0.001 }} | |||
* [[CWE]]: ~12/11 = 150.0000{{c}}, ~7/5 = 583.9477{{c}}, ~13/8 = 840.6394{{c}} | |||
: error map: {{val| 0.000 -0.112 -0.523 +0.913 +0.525 +0.112 }} | |||
{{Optimal ET sequence|legend=1| 72, 144, 152f, 224, 824d }} | {{Optimal ET sequence|legend=1| 72, 144, 152f, 224, 824d }} | ||
Revision as of 08:36, 12 February 2026
- 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 dimcomp family of rank-3 temperaments tempers out the dimcomp comma (monzo: [-1 -4 8 -4⟩, ratio: 390625/388962).
Dimcomp
Subgroup: 2.3.5.7
Comma list: 390625/388962
Mapping: [⟨4 0 0 -1], ⟨0 1 0 -1], ⟨0 0 1 2]]
- mapping generators: ~25/21, ~3, ~5
- WE: ~25/21 = 300.0036 ¢, ~3/2 = 702.0854 ¢, ~5/4 = 385.6631 ¢
- error map: ⟨+0.014 +0.145 -0.622 +0.454]
- CWE: ~25/21 = 300.0000 ¢, ~3/2 = 702.0885 ¢, ~5/4 = 385.6745 ¢
- error map: ⟨0.000 +0.133 -0.639 +0.435]
Optimal ET sequence: 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952
Badness (Sintel): 3.45
Undecimal dimcomp
Subgroup: 2.3.5.7.11
Comma list: 1375/1372, 6250/6237
Mapping: [⟨4 0 0 -1 5], ⟨0 1 0 -1 -3], ⟨0 0 1 2 3]]
- WE: ~25/21 = 300.0093 ¢, ~3/2 = 701.9976 ¢, ~5/4 = 385.6591 ¢
- error map: ⟨+0.037 +0.080 -0.580 +0.597 -0.176]
- CWE: ~25/21 = 300.0000 ¢, ~3/2 = 702.0009 ¢, ~5/4 = 385.6895 ¢
- error map: ⟨0.000 +0.046 -0.624 +0.552 -0.252]
Optimal ET sequence: 12, …, 68, 72, 140, 152, 224, 364, 436, 588
Badness (Sintel): 0.751
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 1375/1372, 2080/2079
Mapping: [⟨4 0 0 -1 5 -16], ⟨0 1 0 -1 -3 -1], ⟨0 0 1 2 3 4]]
Optimal tunings:
- WE: ~25/21 = 300.0140 ¢, ~3/2 = 701.9679 ¢, ~5/4 = 385.5977 ¢
- CWE: ~25/21 = 300.0000 ¢, ~3/2 = 701.9549 ¢, ~5/4 = 385.6140 ¢
Optimal ET sequence: 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c
Badness (Sintel): 0.767
Octopod
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 1375/1372, 4000/3993
Mapping: [⟨8 1 3 3 16 0], ⟨0 3 4 5 3 0], ⟨0 0 0 0 0 1]]
- mapping generators: ~12/11, ~7/5, ~13
- WE: ~12/11 = 150.0093 ¢, ~7/5 = 583.9356 ¢, ~13/8 = 840.6906 ¢
- error map: ⟨-0.055 -0.155 -0.592 +0.832 +0.380 -0.001]
- CWE: ~12/11 = 150.0000 ¢, ~7/5 = 583.9477 ¢, ~13/8 = 840.6394 ¢
- error map: ⟨0.000 -0.112 -0.523 +0.913 +0.525 +0.112]
Optimal ET sequence: 72, 144, 152f, 224, 824d
Badness (Sintel): 1.16