Lokismic temperaments: Difference between revisions

Revision as of 05:29, 27 November 2021

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

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

Template:Val list

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

Vals: Template:Val list

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

Vals: Template:Val list

Badness: 0.037612

@@ Line 10: / Line 10: @@
 * [[Hemimage temperaments #Bisupermajor|Bisupermajor]]
 * [[Landscape microtemperaments #Sextile|Sextile]]
+* [[Quindromeda family #Semiquindromeda|Semiquindromeda]]
 == Septisemitonic ==
@@ Line 51: / Line 52: @@
 Badness: 0.037612
-== Semiquindromeda ==
-{{see also|Quindromeda family}}
-The ''semiquindromeda'' temperament (410&amp;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]]

Lokismic temperaments: Difference between revisions

Revision as of 05:29, 27 November 2021

Septisemitonic

11-limit

13-limit

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