Aberschismic temperaments: Difference between revisions
Tag: Undo |
Move kwai back cuz mirkwai clan is a no-2 clan, which doesn't explain its structure very well |
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* [[Dominant (temperament)|Dominant]] (+36/35) → [[Meantone family #Dominant|Meantone family]] | * [[Dominant (temperament)|Dominant]] (+36/35) → [[Meantone family #Dominant|Meantone family]] | ||
* [[Garibaldi]] (+225/224) → [[Schismatic family #Garibaldi|Schismatic family]] | * [[Garibaldi]] (+225/224) → [[Schismatic family #Garibaldi|Schismatic family]] | ||
* [[Diaschismic]] (+126/125) → [[Diaschismic family #Septimal diaschismic|Diaschismic family]] | * [[Diaschismic]] (+126/125) → [[Diaschismic family #Septimal diaschismic|Diaschismic family]] | ||
* [[Hemififths]] (+2401/2400) → [[Breedsmic temperaments #Hemififths|Breedsmic temperaments]] | * [[Hemififths]] (+2401/2400) → [[Breedsmic temperaments #Hemififths|Breedsmic temperaments]] | ||
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* ''[[Alphaquarter]]'' (+29360128/29296875) → [[Escapade family #Alphaquarter|Escapade family]] | * ''[[Alphaquarter]]'' (+29360128/29296875) → [[Escapade family #Alphaquarter|Escapade family]] | ||
Considered below are septiquarter, ketchup, undecental, leapday, mystery, hemidromeda, countriton, artoneutral, quanic and jorgensen, in the order of increasing [[TE logflat badness]]. | Considered below are septiquarter, kwai, ketchup, undecental, leapday, mystery, hemidromeda, countriton, artoneutral, quanic and jorgensen, in the order of increasing [[TE logflat badness]]. | ||
== Septiquarter == | == Septiquarter == | ||
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Badness (Sintel): 1.44 | Badness (Sintel): 1.44 | ||
== Kwai == | |||
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Kwai]].'' | |||
Named by [[Gene Ward Smith]] in 2004 for its "bridgeability"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10766.html Yahoo! Tuning Group | ''Kwai'']</ref>, kwai is generated by a [[3/2|perfect fifth]], and can be described as {{nowrap| 41 & 70 }}. | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 5120/5103, 16875/16807 | |||
{{Mapping|legend=1| 1 0 -50 -40 | 0 1 33 27 }} | |||
: mapping generators: ~2, ~3 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.7337{{c}}, ~3/2 = 702.4600{{c}} | |||
: [[error map]]: {{val| -0.266 +0.239 -0.607 +1.055 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.6085{{c}} | |||
: error map: {{val| 0.000 +0.653 -0.234 +1.603 }} | |||
{{Optimal ET sequence|legend=1| 41, 111, 152, 345, 497d }} | |||
[[Badness]] (Sintel): 1.38 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 540/539, 1375/1372, 5120/5103 | |||
Mapping: {{mapping| 1 0 -50 -40 32 | 0 1 33 27 -18 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.6672{{c}}, ~3/2 = 702.4282{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6189{{c}} | |||
{{Optimal ET sequence|legend=0| 41, 111, 152, 497de, 649dde }} | |||
Badness (Sintel): 0.867 | |||
==== 13-limit ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 352/351, 540/539, 729/728, 1375/1372 | |||
Mapping: {{mapping| 1 0 -50 -40 32 27 | 0 1 33 27 -18 -21 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.4772{{c}}, ~3/2 = 702.3379{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6409{{c}} | |||
{{Optimal ET sequence|legend=0| 41, 111, 152f, 415dff }} | |||
Badness (Sintel): 1.01 | |||
===== 17-limit ===== | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 256/255, 352/351, 540/539, 715/714, 1089/1088 | |||
Mapping: {{mapping| 1 0 -50 -40 32 27 58 | 0 1 33 27 -18 -21 -34 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.3537{{c}}, ~3/2 = 702.2850{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6589{{c}} | |||
{{Optimal ET sequence|legend=0| 41, 70, 111, 152fg, 263dfg }} | |||
Badness (Sintel): 1.12 | |||
===== 19-limit ===== | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 256/255, 352/351, 400/399, 456/455, 715/714, 847/845 | |||
Mapping: {{mapping| 1 0 -50 -40 32 27 58 -56 | 0 1 33 27 -18 -21 -34 38 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.3401{{c}}, ~3/2 = 702.2705{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6548{{c}} | |||
{{Optimal ET sequence|legend=0| 41, 70h, 111, 152fg, 263dfgh }} | |||
Badness (Sintel): 1.03 | |||
==== Hemikwai ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 540/539, 676/675, 1375/1372, 5120/5103 | |||
Mapping: {{mapping| 1 0 -50 -40 32 -51 | 0 2 66 54 -36 69 }} | |||
: mapping generators: ~2, ~26/15 | |||
Optimal tunings: | |||
* WE: ~2 = 1199.6968{{c}}, ~26/15 = 951.0740{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.3123{{c}} | |||
{{Optimal ET sequence|legend=0| 82, 111, 193, 304d }} | |||
Badness (Sintel): 1.82 | |||
===== 17-limit ===== | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 442/441, 540/539, 676/675, 715/714, 5120/5103 | |||
Mapping: {{mapping| 1 0 -50 -40 32 -51 -30 | 0 2 66 54 -36 69 43 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.6861{{c}}, ~26/15 = 951.0654{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.3120{{c}} | |||
{{Optimal ET sequence|legend=0| 82, 111, 193, 304d }} | |||
Badness (Sintel): 1.31 | |||
===== 19-limit ===== | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 400/399, 442/441, 540/539, 676/675, 715/714, 1445/1444 | |||
Mapping: {{mapping| 1 0 -50 -40 32 -51 -30 -56 | 0 2 66 54 -36 69 43 76 }} | |||
Optimal tunings: | |||
* WE: ~2 = 1199.6718{{c}}, ~26/15 = 951.0526{{c}} | |||
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.3103{{c}} | |||
{{Optimal ET sequence|legend=0| 82, 111, 193, 304dh }} | |||
Badness (Sintel): 1.16 | |||
== Ketchup == | == Ketchup == | ||