Diminished family: Difference between revisions

The '''dimipent family''' tempers out the major diesis aka diminished comma, [[648/625]], the amount by which four [[6/5]] minor thirds exceed an [[octave]], and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as 12EDO.  

[[Mapping]]: [{{Val|4 0 3}}, {{Val|0 1 1}}]

[[POTE generator]]: ~3/2 = 699.507

{{Val list|legend=1| 4, 8, 12 }}

[[Mapping]]: [{{val|4 0 3 5}}, {{val|0 1 1 1}}]

{{Multival|legend=1|4 4 4 -3 -5 -2}}

[[POTE generator]]: ~3/2 = 699.523

{{Val list|legend=1| 4, 8d, 12 }}

[[Mapping]]: [{{val|4 0 3 8}}, {{val|0 2 2 1}}]

{{Multival|legend=1|8 8 4 -6 -16 -13}}

[[POTE generator]]: ~7/6 = 252.555

{{Val list|legend=1| 4, 20c, 24, 52d, 76cdd }}

[[Badness]]: 0.086378

Mapping: [{{val|4 0 3 8 -2}}, {{val|0 2 2 1 5}}]

POTE generator: ~7/6 = 251.658

Vals: {{Val list| 4e, 20ce, 24, 76cdde }}

Badness: 0.056576

Comma list: 49/48, 66/65, 77/75, 243/242

Mapping: [{{val|4 0 3 8 -2 -1}}, {{val|0 2 2 1 5 5}}]

POTE generator: ~7/6 = 252.225

Vals: {{Val list| 4ef, 20cef, 24, 52de, 76cdde }}

Badness: 0.039030

[[Mapping]]: [{{val|8 0 6 -3}}, {{val|0 1 1 2}}]

{{Multival|legend=1|8 8 16 -6 3 15}}

[[POTE generator]]: ~3/2 = 707.014

{{Vals|legend=1| 8d, 24, 32c, 56c }}

[[Badness]]: 0.107523

Vals: {{Val list| 8d, 24, 32c, 56c }}

Badness: 0.047598

Vals: {{Val list| 8d, 24, 32cf, 56cf }}

Badness: 0.030597