Miscellaneous 7-limit temperaments: Difference between revisions

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Created page with "{{Technical data page}} 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 generator..."
 
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See also [[Miscellaneous 5-limit temperaments]].  
See also [[Miscellaneous 5-limit temperaments]].  
== Mirwomo ==
: ''For extensions, see [[Rastmic rank-3 clan #Mirwomo]].''
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 33075/32768
{{Mapping|legend=1| 1 1 0 6 | 0 2 0 -3 | 0 0 1 -1 }}
: mapping generators: ~2, ~128/105, ~5
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.8046{{c}}, ~11/9 = 350.3723{{c}}, ~5/4 = 384.1239{{c}}
: [[error map]]: {{val| +0.805 -0.406 -0.581 -0.848 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/9 = 350.1448{{c}}, ~5/4 = 383.8961{{c}}
: error map: {{val| 0.000 -1.665 -2.418 -3.157 }}
{{Optimal ET sequence|legend=1| 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|legend=1| 1 1 0 -1 | 0 2 0 13 | 0 0 1 0 }}
: mapping generators: ~2, ~896/729, ~5
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.7303{{c}}, ~896/729 = 351.4056{{c}}, ~5/4 = 386.8527{{c}}
: [[error map]]: {{val| -0.270 +0.586 -0.000 -0.284 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~896/729 = 351.4569{{c}}, ~5/4 = 386.6884{{c}}
: error map: {{val| 0.000 +0.959 +0.375 +0.114 }}
{{Optimal ET sequence|legend=1| 17c, 24, 34d, 41, 58, 99, 239, 338 }}
[[Badness]] (Sintel): 8.77


[[Category:Temperament collections]]
[[Category:Temperament collections]]

Revision as of 14:53, 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.

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