Fractional-octave temperaments: Difference between revisions
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=== Protactinium === | === Protactinium === | ||
Protactinium is described as the 364 & 1547 temperament and named after the 91st element. | Protactinium is described as the 364 & 1547 temperament and named after the 91st element. | ||
Subgroup: 2.3.5.7 | |||
Comma list: {{monzo|47 -7 -7 -7}}, {{monzo|-2 -25 1 14}} | |||
Mapping: [{{val| 91 0 644 -33 1036}}, {{val| 0 1 -3 -2 -5}}] | |||
: mapping generators: ~1728/1715, ~3 | |||
Optimal tuning (CTE): ~3/2 = 701.991 | |||
[[Support]]ing [[ET]]s: {{EDOs|364, 819, 1183, 1547, 1911, 2730, 3094, 3913, 4277}} | |||
==== 11-limit ==== | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 234375/234256, 26214400/26198073, 514714375/514434888 | |||
Mapping: [{{val| 91 0 644 -33 1036}}, {{val| 0 1 -3 -2 -5}}] | |||
: mapping generators: ~1728/1715, ~3 | |||
Optimal tuning (CTE): ~3/2 = 702.015 | |||
[[Support]]ing [[ET]]s: {{EDOs|364, 819e, 1183, 1547, 1911, 2275, 2730e, 3458}} | |||
==== 13-limit ==== | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Mapping: [{{val| 91 0 644 -33 1036 481 }}, {{val| 0 1 -3 -2 -5 -1 }}] | Mapping: [{{val| 91 0 644 -33 1036 481 }}, {{val| 0 1 -3 -2 -5 -1 }}] | ||
: mapping generators: ~1728/1715, ~3 | |||
Optimal tuning (CTE): ~3/2 = 702.0195 | Optimal tuning (CTE): ~3/2 = 702.0195 | ||