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:  
Line 10: Line 11:
* [[Hemimage temperaments #Bisupermajor|Bisupermajor]]
* [[Hemimage temperaments #Bisupermajor|Bisupermajor]]
* [[Landscape microtemperaments #Sextile|Sextile]]
* [[Landscape microtemperaments #Sextile|Sextile]]
* [[Quindromeda family #Semiquindromeda|Semiquindromeda]]


== Septisemitonic ==
== Septisemitonic ==
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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
Line 35: Line 37:
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
Line 48: Line 50:
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]]
{{see also|Quindromeda family}}
[[Category:Pages with mostly numerical content]]
 
The ''semiquindromeda'' temperament (410&422) is an extension of the [[28ed5 #Regular temperaments|''quindromeda'' temperament]] with a half-octave period.
 
Subgroup: 2.3.5.7
 
[[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]]

Latest revision as of 00:26, 24 June 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

Lokismic rank two temperaments temper out the loki comma, 102760448/102515625 = [21 -8 -6 2⟩ (lokisma, Sasa-bizotrigu).

Temperaments dicussed elsewhere include:

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

Comma list: 102760448/102515625, 200120949/200000000

Mapping: [⟨2 5 0 -1], ⟨0 -13 33 47]]

POTE generator: ~21/20 = 84.446

Optimal ET sequence: 128, 142, 270

Badness: 0.166111

11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 131072/130977, 422576/421875

Mapping: [⟨2 5 0 -1 11], ⟨0 -13 33 47 -29]]

POTE generator: ~21/20 = 84.443

Optimal ET sequence: 128, 142, 270

Badness: 0.058273

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 3025/3024, 4096/4095, 405769/405000

Mapping: [⟨2 5 0 -1 11 15], ⟨0 -13 33 47 -29 -54]]

POTE generator: ~21/20 = 84.440

Optimal ET sequence: 128, 142, 270

Badness: 0.037612

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