Catalog of rank-4 temperaments: Difference between revisions

Switch to Sintel's badness, WE & CWE tunings (5/5)
- tridecimal semicanousmic (not a very natural extension, feel free to revert if anyone thinks it's worth documenting)
Line 761: Line 761:


[[Badness]] (Sintel): 6.40
[[Badness]] (Sintel): 6.40
=== Tridecimal semicanousmic ===
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 14641/14580
Mapping: {{mapping| 1 0 -2 0 0 -3 | 0 1 2 0 2 3 | 0 0 4 0 1 -3 | 0 0 0 1 0 1 }}
Optimal tunings:
* WE: ~2 = 1199.9764{{c}}, ~3/2 = 702.4793{{c}}, ~11/9 = 345.3532{{c}}, ~7/4 = 968.9908{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.4828{{c}}, ~11/9 = 345.3583{{c}}, ~7/4 = 968.9886{{c}}
{{Optimal ET sequence|legend=0| 87, 111, 181, 198, 323, 410 }}
Badness (Sintel): 4.50
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Comma list: 715/714, 1089/1088, 14641/14580
Mapping: {{mapping| 1 0 -2 0 0 -3 -6 | 0 1 2 0 2 3 6 | 0 0 4 0 1 -3 2 | 0 0 0 1 0 1 0 }}
Optimal tunings:
* WE: ~2 = 1200.0035{{c}}, ~3/2 = 702.4119{{c}}, ~11/9 = 345.3672{{c}}, ~7/4 = 969.0257{{c}}
* CWE: ~2 = 1200.00.0{{c}}, ~3/2 = 702.4110{{c}}, ~11/9 = 345.3664{{c}}, ~7/4 = 969.0262{{c}}
{{Optimal ET sequence|legend=0| 87, 94, 111, 181, 198g, 212g, 292, 323, 410 }}
Badness (Sintel): 2.77
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 715/714, 1089/1088, 1216/1215, 1445/1444
Mapping: {{mapping| 1 0 -2 0 0 -3 -6 -8 | 0 1 2 0 2 3 6 7 | 0 0 4 0 1 -3 2 4 | 0 0 0 1 0 1 0 0 }}
Optimal tunings:
* WE: ~2 = 1200.0386{{c}}, ~3/2 = 702.3639{{c}}, ~18/11 = 345.3639{{c}}, ~7/4 = 969.0046{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.3508{{c}}, ~18/11 = 345.3556{{c}}, ~7/4 = 969.0100{{c}}
{{Optimal ET sequence|legend=0| 87, 94, 111, 181, 205, 212gh, 292h, 299, 323, 410, 622ef }}
Badness (Sintel): 2.13


== Semiporwellismic (16384/16335) ==
== Semiporwellismic (16384/16335) ==