Frameshift

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.

Todo: discuss title, cleanup

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

Badness:

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

Badness: