Miscellaneous 7-limit temperaments: Difference between revisions
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See also [[Miscellaneous 5-limit temperaments]]. | See also [[Miscellaneous 5-limit temperaments]]. | ||
== Uniwiz == | |||
: ''For extensions, see [[Keenanismic temperaments #Uniwiz]].'' | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 1500625/1492992 | |||
{{Mapping|legend=1| 2 1 0 7 | 0 2 0 3 | 0 0 1 -1 }} | |||
: mapping generators: ~1225/864, ~35/24, ~5 | |||
[[Optimal tuning]] ([[CTE]]): ~1225/864 = 600.0000{{c}}, ~35/24 = 651.1974{{c}}, ~5/4 = 385.6847{{c}} | |||
{{Optimal ET sequence|legend=1| 22, 46, 68, 72, 118, 140, 212, 330, 470, 542d, 872cdd, 1012cdd, 1414ccddd }} | |||
[[Badness]] (Smith): 0.7042 × 10<sup>-3</sup> | |||
== Mirwomo == | == Mirwomo == | ||
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{{Mapping|legend=1| 1 1 0 6 | 0 2 0 -3 | 0 0 1 -1 }} | {{Mapping|legend=1| 1 1 0 6 | 0 2 0 -3 | 0 0 1 -1 }} | ||
: mapping generators: ~2, ~128/105, ~5 | : mapping generators: ~2, ~128/105, ~5 | ||
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{{Mapping|legend=1| 1 1 0 -1 | 0 2 0 13 | 0 0 1 0 }} | {{Mapping|legend=1| 1 1 0 -1 | 0 2 0 13 | 0 0 1 0 }} | ||
: mapping generators: ~2, ~896/729, ~5 | : mapping generators: ~2, ~896/729, ~5 | ||
Revision as of 14:57, 27 November 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.
Below are listed some 7-limit rank-3 temperaments that do not belong to some other temperament collection, the majority of which are restrictions to the 7-limit of temperaments that emerge more fully in higher limits or subgroups; they are sorted by TE logflat badness. Most of these temperaments have low accuracy, high-complexity generators, or large number of generators for simple consonances. This is not an exhaustive list. Only expect to find a temperament here if you have not found it in:
- Individual temperament families and clans
- Very low accuracy temperaments
- Very high accuracy temperaments
See also Miscellaneous 5-limit temperaments.
Uniwiz
- For extensions, see Keenanismic temperaments #Uniwiz.
Subgroup: 2.3.5.7
Comma list: 1500625/1492992
Mapping: [⟨2 1 0 7], ⟨0 2 0 3], ⟨0 0 1 -1]]
- mapping generators: ~1225/864, ~35/24, ~5
Optimal tuning (CTE): ~1225/864 = 600.0000 ¢, ~35/24 = 651.1974 ¢, ~5/4 = 385.6847 ¢
Optimal ET sequence: 22, 46, 68, 72, 118, 140, 212, 330, 470, 542d, 872cdd, 1012cdd, 1414ccddd
Badness (Smith): 0.7042 × 10-3
Mirwomo
- For extensions, see Rastmic rank-3 clan #Mirwomo.
Subgroup: 2.3.5.7
Comma list: 33075/32768
Mapping: [⟨1 1 0 6], ⟨0 2 0 -3], ⟨0 0 1 -1]]
- mapping generators: ~2, ~128/105, ~5
- WE: ~2 = 1200.8046 ¢, ~11/9 = 350.3723 ¢, ~5/4 = 384.1239 ¢
- error map: ⟨+0.805 -0.406 -0.581 -0.848]
- CWE: ~2 = 1200.0000 ¢, ~11/9 = 350.1448 ¢, ~5/4 = 383.8961 ¢
- error map: ⟨0.000 -1.665 -2.418 -3.157]
Optimal ET sequence: 17, 21, 24, 31, 41, 72, 281d, 322cd, 353cd, 425bcdd, 497bcdd
Badness (Sintel): 3.40
Parahemif
- For extensions, see Rastmic rank-3 clan #Parahemif.
Subgroup: 2.3.5.7
Comma list: 1605632/1594323
Mapping: [⟨1 1 0 -1], ⟨0 2 0 13], ⟨0 0 1 0]]
- mapping generators: ~2, ~896/729, ~5
- WE: ~2 = 1199.7303 ¢, ~896/729 = 351.4056 ¢, ~5/4 = 386.8527 ¢
- error map: ⟨-0.270 +0.586 -0.000 -0.284]
- CWE: ~2 = 1200.0000 ¢, ~896/729 = 351.4569 ¢, ~5/4 = 386.6884 ¢
- error map: ⟨0.000 +0.959 +0.375 +0.114]
Optimal ET sequence: 17c, 24, 34d, 41, 58, 99, 239, 338
Badness (Sintel): 8.77