Fractional-octave temperaments: Difference between revisions

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-chromium
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* [[Porwell temperaments #Icositritonic|Icositritonic]] (1\23 period)
* [[Porwell temperaments #Icositritonic|Icositritonic]] (1\23 period)
* [[Compton family #Hours|Hours]] (1\24 period)
* [[Compton family #Hours|Hours]] (1\24 period)
* [[Landscape microtemperaments #Chromium|Chromium]] (1\24 period)
* [[26th-octave temperaments|Bosonic]] (1\26 period)
* [[26th-octave temperaments|Bosonic]] (1\26 period)
* [[Ragismic microtemperaments #Ennealimmal|Trinealimmal]], [[Tritrizo clan #Cobalt|cobalt]] (1\27 period)
* [[Ragismic microtemperaments #Ennealimmal|Trinealimmal]], [[Tritrizo clan #Cobalt|cobalt]] (1\27 period)
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Badness: 0.0269
Badness: 0.0269
== 24th-octave temperaments ==
===Chromium===
Defined as the 72 & 624 temperament, and named after 24th element for being period 24.
Subgroup: 2.3.5.7
Comma list: 250047/250000, 49589822592/49433168575
Mapping: [{{val|24 1 -6 18}}, {{val|0 3 5 4}}]
Mapping generators: ~250/243, ~10/7
Optimal tuning (CTE): ~10/7
Vals: 72, 552, 624, ...
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 46656/46585, 250047/250000
Mapping: [{{val|24 1 -6 18 46}}, {{val| 0 3 5 4 3}}]
Mapping generators: ~250/243, ~10/7
Optimal tuning (CTE): ~10/7
===13-limit===
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 34398/34375, 39366/39325
Mapping: [{{val|24 1 -6 18 46 -47 -13}}, {{val|0 3 5 4 3 11}}]
Mapping generators: ~250/243, ~10/7
Vals: 72, 552, 624, ...
===17-limit===
Subgroup: 2.3.5.7.11.13.17
Comma list: 936/935, 1716/1715, 2080/2079, 2500/2499, 11016/11011
Mapping: [{{val|24 1 -6 18 46 -47 -13}}, {{val|0 3 5 4 3 11 9}}]
Mapping generators: ~35/34, ~10/7
Vals: {{EDOs|72, 552, 624}}, ...


== 37th-octave temperaments ==
== 37th-octave temperaments ==