Meantone family: Difference between revisions

Vals: {{Val list| 14cf, 19, 33cdff, 52cdff }}

[[Comma list]]: 81/80, 392/375

[[Mapping]]: [{{val| 1 1 0 -1 }}, {{val| 0 2 8 13 }}]

[[POTE generator]]: ~25/21 = 350.586

{{Val list|legend=1| 7d, 17c, 24, 65cc, 89ccd }}

[[Badness]]: 0.077734

Vals: {{Val list| 7d, 17c, 24, 65cc, 89ccd }}

Badness: 0.036207

Vals: {{Val list| 7d, 17c, 24, 41c, 65cc }}

Badness: 0.028738

[[Mapping]]: [{{val| 2 5 12 7 }}, {{val| 0 -4 -16 -3 }}]

Mapping generators: ~2401/1728, ~7/6

[[POTE generator]]: ~7/6 = 275.794

{{Val list|legend=1| 26, 48c, 74, 174bd, 248bbd }}

[[Badness]]: 0.258825

Mapping: [{{val| 2 5 12 7 6 }}, {{val| 0 -4 -16 -3 2 }}]

Mapping generators: ~363/256, ~7/6

Vals: {{Val list| 26, 48c, 74, 248bbd, 322bbdd }}

Badness: 0.101499

Mapping: [{{val| 2 5 12 7 6 12 }}, {{val| 0 -4 -16 -3 2 -10 }}]

Mapping generators: ~55/39, ~7/6

Vals: {{Val list| 26, 48c, 74, 174bd, 248bbd, 322bbdd }}

Badness: 0.053482

Mothra splits the fifth into three 8/7 generators. It uses [[1029/1024]], the gamelisma, to accomplish this deed and also tempers out [[1728/1715]], the orwell comma. Using [[31edo|31EDO]] with a generator of 6/31 is an excellent tuning choice. Once again something other than a MOS should be used as a scale to get the most out of mothra. In the 2.3.7 subgroup, mothra is identical to [[slendric]].

[[Badness]]: 0.037146

Vals: {{Val list| 5, 26, 31, 88, 150be, 181bee }}

Badness: 0.025642

Vals: {{Val list| 5, 26, 31, 57, 88 }}

Badness: 0.023954

Vals: {{Val list| 5e, 26, 57e, 83bce }}

Badness: 0.055706

POTE generator: ~8/7 = 231.293

Vals: {{Val list| 5e, 26, 57e, 83bce }}

Badness: 0.034124

Vals: {{Val list| 31, 129, 160be, 191bce, 222bce, 253bcee }}

Vals: {{Val list| 31, 36, 67, 98 }}

Badness: 0.036857

Squares splits the interval of an eleventh, or 8/3, into four supermajor third ([[9/7]]) intervals, and uses it for a generator. [[31edo|31EDO]], with a generator of 11/31, makes for a good squares tuning, with 8, 11, and 14 note MOS available. Squares tempers out [[2401/2400]], the breedsma, as well as [[2430/2401]].

[[Badness]]: 0.045993

Vals: {{Val list| 14c, 17c, 31 }}

Badness: 0.021636

Vals: {{Val list| 14c, 17c, 31, 79cf }}

Badness: 0.025514

Vals: {{Val list| 14cf, 31, 45ef, 76e }}

Badness: 0.024522

Vals: {{Val list| 14cf, 31, 76e }}

 

Vals: {{Val list| 14ce, 17ce, 31, 107b, 138b, 169be, 200be }}

Badness: 0.056826

Liese splits the twelfth interval of 3/1 into three generators of 10/7, using the comma 1029/1000. It also tempers out 686/675, the senga. [[74edo|74EDO]] makes for a good liese tuning, though [[19edo|19EDO]] can be used. The tuning is well-supplied with MOS: 7, 9, 11, 13, 15, 17, 19, 36, 55.

[[Badness]]: 0.046706

Vals: {{Val list| 17c, 19, 36, 91cee }}

Badness: 0.040721

Vals: {{Val list| 17c, 19, 36, 91ceef }}

Badness: 0.027304

Mapping: [{{val| 1 0 -4 -3 -5 }}, {{val| 0 3 12 11 16 }}]

Vals: {{Val list| 17c, 19e, 36e }}

 

 

=== 13-limit ===

 

 

Mapping: [{{val| 1 0 -4 -3 -5 0 }}, {{val| 0 3 12 11 16 7 }}]

 

 

 

Vals: {{Val list| 17c, 19e, 36e }}

Badness: 0.026922

Mapping: [{{val| 1 0 -4 -3 -6 }}, {{val| 0 3 12 11 18 }}]

Vals: {{Val list| 17cee, 19 }}

Badness: 0.054829

Mapping: [{{val| 1 0 -4 -3 -6 0 }}, {{val| 0 3 12 11 18 7 }}]

Vals: {{Val list| 17cee, 19 }}

Badness: 0.036144

{{Multival|legend=1| 5 20 7 20 -3 -40 }}

[[Badness]]: 0.108656

Vals: {{Val list| 17c, 26, 43, 69 }}

Badness: 0.047914

Vals: {{Val list| 17c, 26, 43, 69 }}

Badness: 0.029285

Vals: {{Val list| 17cg, 26, 43, 69 }}

Badness: 0.020878

Mapping: [{{val| 1 1 0 2 3 3 2 1 }}, {{val| 0 5 20 7 4 6 18 28 }}]

Vals: {{Val list| 17cgh, 26, 43, 69 }}

Badness: 0.018229