Diminished family: Difference between revisions
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{{Mapping|legend=1| 4 0 3 | 0 1 1 }} | {{Mapping|legend=1| 4 0 3 | 0 1 1 }} | ||
: mapping generators: ~6/5, ~3 | |||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
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Badness (Sintel): 1.26 | Badness (Sintel): 1.26 | ||
[[ | == Subgroup extensions == | ||
Diminished works on 17- and 19-limit subgroups very well, where the 1/4-octave period stands in for ~6/5, ~19/16, and ~20/17. | |||
=== Diminished (2.3.5.17 subgroup) === | |||
[[Subgroup]]: 2.3.5.17 | |||
[[Comma list]]: 51/50, 289/288 | |||
{{Mapping|legend=2| 4 0 3 10 | 0 1 1 1 }} | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~6/5 = 299.899{{c}}, ~3/2 = 698.251{{c}} (~17/16 = 98.453{{c}}) | |||
* [[CWE]]: ~6/5 = 300.000{{c}}, ~3/2 = 698.137{{c}} (~17/16 = 98.137{{c}}) | |||
{{Optimal ET sequence|legend=1| 4, 8, 12 }} | |||
[[Badness]] (Sintel): 0.509 | |||
=== Diminished (2.3.5.19 subgroup) === | |||
[[Subgroup]]: 2.3.5.19 | |||
[[Comma list]]: 96/95, 513/500 | |||
{{Mapping|legend=2| 4 0 3 17 | 0 1 1 0 }} | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~6/5 = 299.744{{c}}, ~3/2 = 698.206{{c}} (~20/19 = 98.718{{c}}) | |||
* [[CWE]]: ~6/5 = 300.000{{c}}, ~3/2 = 698.195{{c}} (~20/19 = 98.195{{c}}) | |||
{{Optimal ET sequence|legend=1| 4, 8, 12 }} | |||
[[Badness]] (Sintel): 0.681 | |||
[[Category:Diminished family| ]] <!-- main article --> | [[Category:Diminished family| ]] <!-- main article --> | ||
[[Category:Diminished| ]] <!-- key article --> | [[Category:Diminished| ]] <!-- key article --> | ||
[[Category: | [[Category:Temperament families]] | ||
[[Category:Catalogs of rank-2 temperaments]] | |||