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Catalog of rank-4 temperaments: Difference between revisions

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→Symbiotic (19712/19683): extend to the 2.3.5.7.11.13.19 subgroup
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 702.213, ~5/4 = 386.314, ~7/4 = 968.736
* [[CTE]]: ~2 = 1200.000, ~3/2 = 702.213, ~5/4 = 386.314, ~7/4 = 968.736
* [[CWE]]: ~2 = 1\1, ~3/2 = 702.244, ~5/4 = 386.406, ~7/4 = 968.859
* [[CWE]]: ~2 = 1200.000, ~3/2 = 702.244, ~5/4 = 386.406, ~7/4 = 968.859


{{Optimal ET sequence|legend=1| 17c, 19e, 24, 34d, 41, 53, 58, 94, 99e, 118, 152, 270, 581, 733, 851, 1003, 1273, 1854, 2124b }}
{{Optimal ET sequence|legend=1| 17c, 19e, 24, 34d, 41, 53, 58, 94, 99e, 118, 152, 270, 581, 733, 851, 1003, 1273, 1854, 2124b }}


[[Badness]]: 0.120 × 10<sup>-6</sup>
[[Badness]] (Smith): 0.120 × 10<sup>-6</sup>


=== Tridecimal symbiotic ===
=== Tridecimal symbiotic ===
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~3/2 = 702.228, ~5/4 = 386.284, ~7/4 = 968.789
* [[CTE]]: ~2 = 1200.000, ~3/2 = 702.228, ~5/4 = 386.284, ~7/4 = 968.789
* [[CWE]]: ~2 = 1\1, ~3/2 = 702.254, ~5/4 = 386.401, ~7/4 = 968.898
* [[CWE]]: ~2 = 1200.000, ~3/2 = 702.254, ~5/4 = 386.401, ~7/4 = 968.898


{{Optimal ET sequence|legend=1| 17c, 34dff, 36ce, 41, 53, 58, 94, 111, 152f, 212, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 3127bf }}
{{Optimal ET sequence|legend=1| 17c, 34dff, 36ce, 41, 53, 58, 94, 111, 152f, 212, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 3127bf }}


[[Badness]]: 3.31 × 10<sup>-6</sup>
[[Badness]] (Smith): 3.31 × 10<sup>-6</sup>
 
=== 2.3.5.7.11.13.19 subgroup ===
Subgroup: 2.3.5.7.11.13.19
 
Comma list: 1216/1215, 1540/1539, 2080/2079
 
Mapping: {{mapping| 1 0 0 0 -8 -13 -6 | 0 1 0 0 9 12 5 | 0 0 1 0 0 -1 1 | 0 0 0 1 -1 0 0 }}
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~3/2 = 702.230, ~5/4 = 386.304, ~7/4 = 968.797
* CWE: ~2 = 1200.000, ~3/2 = 702.255, ~5/4 = 386.408, ~7/4 = 968.902
 
{{Optimal ET sequence|legend=0| 17ch, 24f, 34dffh, 36ceh, 41, 53, 58h, 94, 111, 152f, 212h, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 3127bfh }}
 
Badness (Smith): 4.37 × 10<sup>-6</sup>


== Olympic (131072/130977) ==
== Olympic (131072/130977) ==
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