Catalog of rank-4 temperaments: Difference between revisions
+ elysic |
Added weak olympic extension to 19-limit; not the strong one; Optimal ET sequence is most likely wrong Tags: Reverted Visual edit |
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[[Badness]] (Sintel): 0.292 | [[Badness]] (Sintel): 0.292 | ||
=== Metaolympic === | |||
Metaolympic is a [[weak extension]] of olympic (tempering out [[5776/5775]]), 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 error. | |||
[[Subgroup]]: 2.3.5.7.11.13.17.19 | |||
[[Comma list]]: 2080/2079, 4096/4095, 4200/4199, 5776/5775 | |||
{{Mapping|legend=1| 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 tuning]]s: | |||
* [[WE]]: ~2 = 1199.954{{c}}, ~3/2 = 702.046{{c}}, ~5/4 = 386.264{{c}}, ~1197/640 = 1084.440{{c}} | |||
: [[error map]]: {{val|-0.046, 0.045, -0.141, 0.009, 0.227, -0.088, 0.192, -0.058}} | |||
* [[CWE]]: ~2 = 1200{{c}}, ~3/2 = 702.077{{c}}, ~5/4 = 386.266{{c}}, ~1197/640 = 1084.481{{c}} | |||
: error map: {{val|0.000, 0.122, -0.048, 0.137, 0.373, 0.090, 0.367, 0.118}} | |||
{{Optimal ET sequence|legend=1|46, 53, 84, 130, 183, 217, 224, 270, 354, 764, 935}} | |||
[[Badness]] (Sintel): 0.764 | |||
==== Subgroup: 2.3.5.7.11.13.19 ==== | |||
[[Subgroup]]: 2.3.5.7.11.13.19 | |||
[[Comma list]]: 2080/2079, 4096/4095, 5776/5775 | |||
{{Mapping|legend=1| 1 0 0 1 15 11 6| 0 1 0 0 -5 -2 -2| 0 0 1 0 0 -1 1| 0 0 0 2 -4 -2 -1}} | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.964{{c}}, ~3/2 = 702.064{{c}}, ~5/4 = 386.322{{c}}, ~1197/640 = 1084.468{{c}} | |||
: [[error map]]: {{val|-0.036, 0.073, -0.064, 0.073, 0.129, -0.166, -0.004}} | |||
* [[CWE]]: ~2 = 1200{{c}}, ~3/2 = 702.089{{c}}, ~5/4 = 386.326{{c}}, ~1197/640 = 1084.501{{c}} | |||
: error map: {{val|0.000, 0.134, 0.012, 0.175, 0.236, -0.032, 0.135}} | |||
{{Optimal ET sequence|legend=1|46, 53, 84, 130, 183, 217, 224, 270, 354, 764, 935}} | |||
[[Badness]] (Sintel): 0.618 | |||
== Alphaxenic (131769/131072) == | == Alphaxenic (131769/131072) == | ||