Lokismic temperaments: Difference between revisions

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'''Lokismic''' rank-two temperaments temper out the [[Kalismic temperaments #Loki|loki]] comma, 102760448/102515625 = {{monzo|21 -8 -6 2}} (''lokisma'', sasazozo-atribigu).
{{Technical data page}}
'''Lokismic''' [[rank two temperaments]] temper out the [[Kalismic temperaments #Loki|loki]] comma, 102760448/102515625 = {{monzo|21 -8 -6 2}} (''lokisma'', Sasa-bizotrigu).


Temperaments dicussed elsewhere include:  
Temperaments dicussed elsewhere include:  
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* [[Hemimage temperaments #Bisupermajor|Bisupermajor]]
* [[Hemimage temperaments #Bisupermajor|Bisupermajor]]
* [[Landscape microtemperaments #Sextile|Sextile]]
* [[Landscape microtemperaments #Sextile|Sextile]]
* [[Quindromeda family #Semiquindromeda|Semiquindromeda]]


== Septisemitonic ==
== Septisemitonic ==
The ''septisemitonic'' temperament (128&142) has a half-octave period and uses a [[21/20]]-wide semitone (septimal semitone) as a generator.
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


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[[POTE generator]]: ~21/20 = 84.446
[[POTE generator]]: ~21/20 = 84.446


{{Val list|legend=1| 128, 142, 270 }}
{{Optimal ET sequence|legend=1| 128, 142, 270 }}


[[Badness]]: 0.166111
[[Badness]]: 0.166111
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POTE generator: ~21/20 = 84.443
POTE generator: ~21/20 = 84.443


Vals: {{Val list| 128, 142, 270 }}
{{Optimal ET sequence|legend=1| 128, 142, 270 }}


Badness: 0.058273
Badness: 0.058273
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POTE generator: ~21/20 = 84.440
POTE generator: ~21/20 = 84.440


Vals: {{Val list| 128, 142, 270 }}
{{Optimal ET sequence|legend=1| 128, 142, 270 }}


Badness: 0.037612
Badness: 0.037612


== Semiquindromeda ==
[[Category:Temperament collections]]
Subgroup: 2.3.5.7
[[Category:Pages with mostly numerical content]]
 
[[Comma list]]: 102760448/102515625, 1220703125/1219784832
 
[[Mapping]]: [{{val|2 4 0 -5}}, {{val|0 -5 28 64}}]
 
[[POTE generator]]: ~1323/1250 = 99.521
 
{{Val list|legend=1| 12, 398, 410, 422, 832, 1254d, 2086bd }}
 
[[Badness]]: 0.233140
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 5632/5625, 9801/9800, 85937500/85766121
 
Mapping: [{{val|2 4 0 -5 -10}}, {{val|0 -5 28 64 102}}]
 
POTE generator: ~1323/1250 = 99.525
 
Vals: {{Val list| 12, 410, 422 }}
 
Badness: 0.093926
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 1716/1715, 2080/2079, 5632/5625, 831875/830466
 
Mapping: [{{val|2 4 0 -5 -10 -13}}, {{val|0 -5 28 64 102 123}}]
 
POTE generator: ~1323/1250 = 99.523
 
Vals: {{Val list| 12f, 410, 422, 1254df, 1676bdff, 2098bcddff }}
 
Badness: 0.053361
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 1716/1715, 2080/2079, 2500/2499, 5632/5625, 15895/15876
 
Mapping: [{{val|2 4 0 -5 -10 -13 10}}, {{val|0 -5 28 64 102 123 -11}}]
 
POTE generator: ~18/17 = 99.522
 
Vals: {{Val list| 12f, 410, 422, 832, 1254df, 1676bdff }}
 
Badness: 0.034659
 
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 1216/1215, 1445/1444, 1716/1715, 2080/2079, 2376/2375, 2500/2499
 
Mapping: [{{val|2 4 0 -5 -10 -13 10 8}}, {{val|0 -5 28 64 102 123 -11 3}}]
 
POTE generator: ~18/17 = 99.523
 
Vals: {{Val list| 12f, 410, 422, 1254dfhh, 1676bdffhh }}
 
Badness: 0.025439
 
[[Category:Temperament]]
[[Category:Temperament collection]]
[[Category:Rank 2]]
[[Category:Rank 2]]