Frameshift: Difference between revisions
Document both possible interpretations of the temperamemt |
Merge |
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See also the [[frameshift microtemperaments]], various other temperaments that temper the comma. | See also the [[frameshift microtemperaments]], various other temperaments that temper the comma. | ||
==Rank-2 frameshift?== | == Rank-4 temperaments == | ||
=== 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 | |||
== Rank-2 temperaments == | |||
Temperaments discussed elsewhere include: | |||
* ''[[Guiron]]'', {[[385/384]], [[441/440]], [[10976/10935]]} → [[Gamelismic clan #Guiron|Gamelismic clan]] | |||
* ''[[Quarterframe]]'', {[[3025/3024]], [[26214400/26198073]], [[29296875/29218112]]} → [[The Quartercache #Quarterframe|The Quartercache]] | |||
* ''[[Tritricot]]'', {[[4000/3993]], [[166698/166375]], [[200704/200475]]} → [[Tricot family #Tritricot|Tricot family]] | |||
* ''[[Auric]]'', {4000/3993, 15625/15552, 32805/32768} → [[159th-octave temperaments#Auric|159th-octave temperaments]] | |||
=== Rank-2 frameshift? === | |||
Subgroup: 2.3.11 | Subgroup: 2.3.11 | ||
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TE Error: 0.007983 cents/octave | TE Error: 0.007983 cents/octave | ||
== | === 159 & 400 === | ||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: [[200704/200475]], [[160083/160000]], [[166698/166375]] | |||
[[Mapping]]: [{{val|1 4 47 66 26}}, {{val|0 -6 -111 -157 -56}}] | |||
[[POTE generator]]: ~2707/2048 = 483.0025 | |||
{{Optimal ET sequence|legend=1|159, 241, 400, 559, 959}} | |||
[[ | [[Badness]]: | ||
=== 118 & 400 === | |||
Subgroup: 2.3.5.7.11 | |||
[[ | [[Comma list]]: [[5632/5625]], [[9801/9800]], [[200704/200475]] | ||
[[Mapping]]: [{{val|2 5 8 23 24}}, {{val|0 -6 -11 -57 -56}}] | |||
[[POTE generator]]: ~11585/8192 = 600, ~329/296 = 183.0023 | |||
{{Optimal ET sequence|legend=1|118, 282, 400, 518, 636, 754d, 918}} | |||
[[Badness]]: | |||
{{todo|inline=1|discuss title|expand}} | {{todo|inline=1|discuss title|expand}} | ||
[[Category:Temperaments]] | [[Category:Temperaments]] | ||
Revision as of 07:43, 17 September 2026
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-4 temperaments
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
Rank-2 temperaments
Temperaments discussed elsewhere include:
- Guiron, {385/384, 441/440, 10976/10935} → Gamelismic clan
- Quarterframe, {3025/3024, 26214400/26198073, 29296875/29218112} → The Quartercache
- Tritricot, {4000/3993, 166698/166375, 200704/200475} → Tricot family
- Auric, {4000/3993, 15625/15552, 32805/32768} → 159th-octave temperaments
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
159 & 400
Subgroup: 2.3.5.7.11
Comma list: 200704/200475, 160083/160000, 166698/166375
Mapping: [⟨1 4 47 66 26], ⟨0 -6 -111 -157 -56]]
POTE generator: ~2707/2048 = 483.0025
Optimal ET sequence: 159, 241, 400, 559, 959
118 & 400
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 9801/9800, 200704/200475
Mapping: [⟨2 5 8 23 24], ⟨0 -6 -11 -57 -56]]
POTE generator: ~11585/8192 = 600, ~329/296 = 183.0023
Optimal ET sequence: 118, 282, 400, 518, 636, 754d, 918
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Todo: discuss title, expand |