User:FloraC/Flora's 12-note well temperament: Difference between revisions
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The commas in consideration are the [[Pythagorean comma]] ~ 23.4600¢, denoted ''p'', and the [[syntonic comma]] ~ 21.5063¢, denoted ''c''. | The commas in consideration are the [[Pythagorean comma]] ~ 23.4600¢, denoted ''p'', and the [[syntonic comma]] ~ 21.5063¢, denoted ''c''. | ||
The generator is a perfect fifth | The generator is a perfect fifth, which comes in three sizes, with four 1/5-comma meantone fifths, four 12edo fifths, and four counterpyth fifths. Specifically, | ||
* '' | * ''g''<sub>1</sub> = P5 - ''c''/5 ~ 697.6537¢ | ||
: at C–G, G–D, D–A, A–E. | : at C–G, G–D, D–A, A–E. | ||
* '' | * ''g''<sub>2</sub> = P5 - ''p''/12 = 700¢ = 7\12 | ||
: at Bb–F, F–C, E–B, B–F#. | : at Bb–F, F–C, E–B, B–F#. | ||
* '' | * ''g''<sub>3</sub> = P5 - ''p''/6 + ''c''/5 ~ 702.3463¢ | ||
: at F#–C#, C#–G#/Ab, G#/Ab–Eb, Eb–Bb. | : at F#–C#, C#–G#/Ab, G#/Ab–Eb, Eb–Bb. | ||
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{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
|+ Sizes and occurrences of | |+ Sizes and occurrences of minor third | ||
! rowspan="2" | Cents | ! rowspan="2" | Cents | ||
! colspan="2" | Error | ! colspan="2" | Error | ||
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| Bb–Db, D#–F# | | Bb–Db, D#–F# | ||
|} | |} | ||
[[Category:Pages with Scala files]] | |||
[[Category:12-tone scales]] | |||
[[Category:Tempered scales]] | |||