Frameshift: Difference between revisions
Created page with "The temperament generated by tempering out the frameshift comma. {{stub}} Category:Temperaments" |
Document both possible interpretations of the temperamemt |
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The temperament generated by tempering out the [[frameshift comma]]. | The temperament generated by tempering out the [[frameshift comma]]. | ||
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It still needs to be decided whether this name refers to the higher-rank 11-limit tuning implied by the comma, or whether this name applies to the the rank-2 2.3.11 subgroup tuning implied by the comma. | |||
Whichever it is, the other temperament will have to be given another name that relates to frameshift in some way. | |||
See also the [[frameshift microtemperaments]], various other temperaments that temper the comma. | |||
==Rank-2 frameshift?== | |||
Subgroup: 2.3.11 | |||
[[Comma list]]: [[frameshift comma|22876792454961/22866405883904]] | |||
[[Mapping]]: [{{val|1 1 -2}}, {{val|0 3 28}}] | |||
[[POTE generator]]: ~8/7 = 233.9749 | |||
Recommended [[EDO]]s: {{EDOs|159, 518, 359, 677, 318, 200, 836, 1036, 877, 1195}} | |||
Complexity: 3.456776 | |||
Adjusted Error: 0.027616 cents | |||
TE Error: 0.007983 cents/octave | |||
==Rank-4 frameshift?== | |||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: [[frameshift comma|22876792454961/22866405883904]] | |||
[[Mapping]]: [{{val|1 1 0 0 -2}}, {{val|0 3 0 0 28}}, {{val|0 0 1 0 0}}, {{val|0 0 0 1 0}}] | |||
[[POTE generator]]s: 1200.0000, 233.9749, 2786.2945, 3368.8027 | |||
Recommended [[EDO]]s: {{EDOs|1236, 836, 2190, 954, 2072, 1354, 400, 118, 3026, 1395}} | |||
Complexity: 0.063636 | |||
Adjusted Error: 0.021391 cents | |||
TE Error: 0.006183 cents/octave | |||
{{todo|inline=1|discuss title|expand}} | |||
[[Category:Temperaments]] | [[Category:Temperaments]] | ||
Latest revision as of 11:36, 27 October 2024
The temperament generated by tempering out the frameshift comma.
It still needs to be decided whether this name refers to the higher-rank 11-limit tuning implied by the comma, or whether this name applies to the the rank-2 2.3.11 subgroup tuning implied by the comma.
Whichever it is, the other temperament will have to be given another name that relates to frameshift in some way.
See also the frameshift microtemperaments, various other temperaments that temper the comma.
Rank-2 frameshift?
Subgroup: 2.3.11
Comma list: 22876792454961/22866405883904
Mapping: [⟨1 1 -2], ⟨0 3 28]]
POTE generator: ~8/7 = 233.9749
Recommended EDOs: 159, 518, 359, 677, 318, 200, 836, 1036, 877, 1195
Complexity: 3.456776
Adjusted Error: 0.027616 cents
TE Error: 0.007983 cents/octave
Rank-4 frameshift?
Subgroup: 2.3.5.7.11
Comma list: 22876792454961/22866405883904
Mapping: [⟨1 1 0 0 -2], ⟨0 3 0 0 28], ⟨0 0 1 0 0], ⟨0 0 0 1 0]]
POTE generators: 1200.0000, 233.9749, 2786.2945, 3368.8027
Recommended EDOs: 1236, 836, 2190, 954, 2072, 1354, 400, 118, 3026, 1395
Complexity: 0.063636
Adjusted Error: 0.021391 cents
TE Error: 0.006183 cents/octave
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Todo: discuss title, expand |