Catalog of rank-4 temperaments: Difference between revisions
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[[Badness]] (Sintel): 0.292 | [[Badness]] (Sintel): 0.292 | ||
=== Metaolympic === | |||
Metaolympic is a [[weak extension]] of olympic, requiring the split of the prime 7 in half; or alternatively, the septimal comma or the garischisma. It is better without prime 17, but prime 17 can be added easily into the temperament by also tempering out 4200/4199, which also takes advantage of the split prime 7, at the cost of higher complexity. | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 2080/2079, 4096/4095, 35000/34969 | |||
Mapping: {{mapping| 1 0 0 1 15 11 -13 | 0 1 0 0 -5 -2 5 | 0 0 1 0 0 -1 2 | 0 0 0 2 -4 -2 5 }} | |||
: mapping generators: ~2, ~3, ~5, ~187/100 | |||
Optimal tunings: | |||
* WE: ~2 = 1199.9530{{c}}, ~3/2 = 702.0493{{c}}, ~5/4 = 386.2541{{c}}, ~187/100 = 1084.4393{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0798{{c}}, ~5/4 = 386.2658{{c}}, ~187/100 = 1084.4811{{c}} | |||
{{Optimal ET sequence|legend=0| 43, 53, 84, 94, 137, 176g, 217, 270, 311, 487, 571e, 581, 935, 1516e, 2234eg, 2815eg }} | |||
Badness (Sintel): 1.59 | |||
==== 19-limit ==== | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 2080/2079, 3250/3249, 4096/4095, 4200/4199 | |||
Mapping: {{mapping| 1 0 0 1 15 11 -13 6 | 0 1 0 0 -5 -2 5 -2 | 0 0 1 0 0 -1 2 1 | 0 0 0 2 -4 -2 5 -1 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.9539{{c}}, ~3/2 = 702.0464{{c}}, ~5/4 = 386.2644{{c}}, ~187/100 = 1084.4405{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0768{{c}}, ~5/4 = 386.2655{{c}}, ~187/100 = 1084.4813{{c}} | |||
{{Optimal ET sequence|legend=0| 43, 53, 84, 94, 137, 176g, 217, 270, 311, 487, 571e, 581, 935, 1516e, 2234eg, 2451eg }} | |||
Badness (Sintel): 0.764 | |||
== Alphaxenic (131769/131072) == | == Alphaxenic (131769/131072) == | ||