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:

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 sequence22, 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

Optimal tunings:

  • 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 sequence17, 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

Optimal tunings:

  • 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 sequence17c, 24, 34d, 41, 58, 99, 239, 338

Badness (Sintel): 8.77