Meantone family: Difference between revisions

= Meantone (12&19, 2.3.5) =

[[Badness]]: 0.007381

[[Badness]]: 0.013707

Comma list: 81/80, 99/98, 126/125

Vals: {{Val list| 12, 19e, 31, 105, 136b, 167be, 198be }}

Badness: 0.017027

Vals: {{Val list| 12f, 19e, 31 }}

Badness: 0.018048

Vals: {{Val list| 12, 19ef, 31, 43, 74 }}

 

Vals: {{Val list| 12f, 31f, 43 }}

Badness: 0.026421

POTE generator: ~15/13 = 251.535

Vals: {{Val list| 19e, 43, 62, 167bef }}

Badness: 0.031433

Vals: {{Val list| 12e, 19, 31, 81 }}

Badness: 0.021543

=== Tridecimal Meanpop ===

Vals: {{Val list| 12ef, 19, 31, 50, 81, 131bd, 212bbddf }}

Badness: 0.020883

Vals: {{Val list| 12e, 19, 31f, 50ff, 81fff }}

Badness: 0.027666

Vals: {{Val list| 7d, 12, 19, 31e, 50ee }}

Badness: 0.021423

Vals: {{Val list| 12f, 19, 31e, 50ee }}

Badness: 0.021182

Vals: {{Val list| 7d, 12, 19 }}

Badness: 0.024763

Vals: {{Val list| 7d, 12, 19 }}

Badness: 0.025535

Vals: {{Val list| 7d, 12, 19 }}

Badness: 0.022302

Vals: {{Val list| 7d, 12, 19 }}

Badness: 0.020139

Vals: {{Val list| 7d, 12, 19 }}

Badness: 0.018168

Vals: {{Val list| 7d, 12, 19 }}

Badness: 0.017069

Vals: {{Val list| 7d, 12, 19 }}

Badness: 0.016129

Vals: {{Val list| 7d, 12, 19 }}

Badness: 0.015356

Vals: {{Val list| 7d, 12, 19 }}

Badness: 0.013906

Vals: {{Val list| 7d, 12, 19 }}

Badness: 0.013818

Vals: {{Val list| 7d, 12f, 19f, 31eff }}

Badness: 0.024243

Vals: {{Val list| 7d, 12e, 19e }}

Badness: 0.031539

Vals: {{Val list| 7d, 12e, 19e }}

Badness: 0.026288

Vals: {{Val list| 12, 26de, 38d, 50 }}

Badness: 0.038122

Mapping: [{{val| 2 0 -8 -26 -31 -40 }}, {{val| 0 1 4 10 12 15 }}]

Vals: {{Val list| 12f, 26deff, 38df, 50 }}

Badness: 0.028817

 

 

 

 

 

 

 

In flattone, 9 generator steps of 4/3 get to the interval class for 7, meaning that [[7/4]] is a diminished seventh interval (C-Bbb). Other intervals are [[7/6]], a diminished third (C-Ebb), and [[7/5]], a doubly diminshed fifth (C-Gbb). Good tunings for flattone are [[26edo|26EDO]], [[45edo|45EDO]] and [[64edo|64EDO]].

[[Badness]]: 0.038553

Vals: {{Val list| 7, 19, 26, 45, 71bc, 116bcde }}

Badness: 0.033839

Vals: {{Val list| 7, 19, 26, 45f, 71bcf, 116bcdef }}

Badness: 0.022260

The interval class for 7 is obtained from two fourths in succession, so that 7/4 is a minor seventh. The 7/6 interval is, like 6/5, now a minor third, and 7/5 is a diminished fifth. An excellent tuning for dominant is [[12edo|12EDO]], but it also works well with the Pythagorean tuning of pure [[3/2]] fifths, and with [[29edo|29EDO]], [[41edo|41EDO]], or [[53edo|53EDO]].

[[Badness]]: 0.020690

Vals: {{Val list| 5, 12, 17c, 29cde }}

Badness: 0.024180

Vals: {{Val list| 12f, 17c, 29cdef }}

Vals: {{Val list| 5, 12, 17c, 46cde }}

Vals: {{Val list| 5e, 7, 12, 19d, 43de }}

Badness: 0.021978

Vals: {{Val list| 5ef, 7, 12, 19d, 31def }}

Badness: 0.027039

Vals: {{Val list| 5ef, 7, 12, 19d, 31def }}

Badness: 0.024539

Vals: {{Val list| 5ef, 7, 12, 19d, 31def }}

Badness: 0.020398

Vals: {{Val list| 5e, 7, 12f, 19df }}

Vals: {{Val list| 5e, 12e, 17c, 46cd }}

Vals: {{Val list| 5e, 12e, 17c }}

Vals: {{Val list| 5, 7, 12e }}

Badness: 0.026141

Vals: {{Val list| 5, 7, 12ef, 19def }}

Badness: 0.023300

Vals: {{Val list| 5, 7, 12ef, 19def }}

Badness: 0.024535

Vals: {{Val list| 5, 7, 12ef, 19def }}

Badness: 0.021098

Sharptone is a low-accuracy temperament tempering out 21/20 and 28/27. In sharptone, a 7/4 is a major sixth, a 7/6 a whole tone, and a 7/5 a fourth. Genuinely septimal sounding harmony therefore cannot be expected, but it can be used to translate, more or less, 7-limit JI into 5-limit meantone. [[12edo|12EDO]] tuning does sharptone about as well as such a thing can be done, of course not in its patent val.

Vals: {{Val list| 5, 7d, 12de }}

Vals: {{Val list| 5de, 7 }}