Miscellaneous 5-limit temperaments: Difference between revisions
Document 5-limit jorgensen |
Move unidecmic, supersharp and lafa here |
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* [[Very low accuracy temperaments]] | * [[Very low accuracy temperaments]] | ||
* [[Very high accuracy temperaments]]. | * [[Very high accuracy temperaments]]. | ||
== Unidecmic == | |||
: ''For extensions, see [[Gamelismic clan #Unidec]].'' | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: 31381059609/31250000000 | |||
{{Mapping|legend=1| 2 -1 -3 | 0 6 11 }} | |||
: mapping generators: ~177147/125000, ~25000/19683 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~177147/125000 = 600.0124{{c}}, ~25000/19683 = 416.9619{{c}} | |||
: [[error map]]: {{val| +0.025 -0.196 +0.235 }} | |||
* [[CWE]]: ~177147/125000 = 600.0000{{c}}, ~25000/19683 = 416.9561{{c}} | |||
: error map: {{val| 0.000 -0.236 +0.172 }} | |||
{{Optimal ET sequence|legend=1| 26, 46, 72, 118, 2524, 2642, 2760 }} | |||
[[Badness]] (Sintel): 1.93 | |||
== Supersharp == | |||
: ''For extensions, see [[Trienstonic clan #Octokaidecal]].'' | |||
Supersharp tempers out [[800/729]], the difference between the [[27/20]] wolf fourth and the [[40/27]] wolf fifth, splitting the octave into two 27/20~40/27 semioctaves. It generally requires a very sharp fifth, even sharper than 3\5, as a generator. This means that five steps from the [[generator sequence #JI scales obtained from guided generator sequences|Zarlino generator sequence]] starting with 6/5 are tempered to one and a half octaves. The only reasonable 7-limit extension adds 28/27 and 50/49 to the comma list, taking advantage of the existing semioctave. | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: 800/729 | |||
{{Mapping|legend=1| 2 0 -5 | 0 1 3 }} | |||
: mapping generators: ~27/20, ~3 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~27/20 = 596.986{{c}}, ~3/2 = 725.434{{c}} (~10/9 = 128.448{{c}}) | |||
: [[error map]]: {{val| -6.029 +17.450 -13.027 }} | |||
* [[CWE]]: ~27/20 = 600.000{{c}}, ~3/2 = 726.548{{c}} (~10/9 = 126.548{{c}}) | |||
: error map: {{val| 0.000 +24.593 -6.670 }} | |||
{{Optimal ET sequence|legend=1| 8, 10, 18, 28b }} | |||
[[Badness]] (Sintel): 2.88 | |||
== Lafa == | |||
This temperament was named by [[Petr Pařízek]] in 2011, referring to the characteristic that stacking 12 generators makes 6/1 – "l" for 12, "f" for 6<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>. Its ploidacot is therefore beta-dodecacot. | |||
[[Subgroup]]: 2.3.5 | |||
[[Comma list]]: {{monzo| 77 -31 -12 }} | |||
{{Mapping|legend=1| 1 -1 9 | 0 12 -31 }} | |||
: mapping generators: ~2, ~{{monzo| -32 13 5 }} | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.9693{{c}}, ~{{monzo| -32 13 5 }} = 258.4963{{c}} | |||
: [[error map]]: {{val| -0.031 +0.031 +0.026 }} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~{{monzo| -32 13 5 }} = 258.5031{{c}} | |||
: error map: {{val| 0.000 +0.082 +0.091 }} | |||
{{Optimal ET sequence|legend=1| 65, 246, 311, 376, 441, 2711, 3152, 3593, 4034, 4475, 4916, 5357, 10273bc, 15630bbcc }} | |||
[[Badness]] (Sintel): 4.33 | |||
== Lafayette == | == Lafayette == | ||
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[[Badness]] (Sintel): 203 | [[Badness]] (Sintel): 203 | ||
== References == | |||
[[Category:Temperament collections]] | [[Category:Temperament collections]] | ||
[[Category:Pages with mostly numerical content]] | [[Category:Pages with mostly numerical content]] | ||