User:Xenllium/Xenllium's circulating scales: Difference between revisions
Created page with "Below are listed circulating scales introduced by Xenllium. == Xentwelve == '''Xentwelve''' is a 12-tone circulating scale based on 12edo|12 equal tempera..." |
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== Xentwelve == | == Xentwelve == | ||
'''Xentwelve''' is a 12-tone circulating scale based on [[12edo|12 equal temperament]]. In summary, it is close to [[1/3-comma meantone]] in the natural keys and [[Pythagorean tuning]] in the remote keys. The generator is a perfect fifth, which comes in three sizes, with eight pure fifths (at | '''Xentwelve''' is a 12-tone circulating scale based on [[12edo|12 equal temperament]]. In summary, it is close to [[1/3-comma meantone]] in the natural keys and [[Pythagorean tuning]] in the remote keys. The generator is a perfect fifth, which comes in three sizes, with eight pure fifths (at C–G, C♯–G♯, E♭–B♭, E–B, F–C, F♯–C♯, B♭–F and B–F♯, frequency ratio [[3/2]]), three 1/3-comma meantone fifths (at D–A, G–D and A–E, frequency ratio (10/3)^(1/3)), and one narrow schismic fifth (at G♯–D♯ (A♭–E♭), frequency ratio [[16384/10935]]). It derives two major thirds exact [[5/4]] (at C–E and G–B) and one minor third exact [[6/5]] (at E–G). | ||
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1200. | 1200. | ||
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{| class="wikitable center-all left-all" | |||
|+ Sizes and occurrences of fifth and fourth | |||
! colspan="4" | Fifth (7-step) | |||
! colspan="4" | Fourth (5-step) | |||
|- | |||
! Occurrences | |||
! Ratio | |||
! Cents | |||
! Error <br>from 3/2 | |||
! Occurrences | |||
! Ratio | |||
! Cents | |||
! Error <br>from 4/3 | |||
|- | |||
| D–A <br> G–D <br> A–E | |||
| <math>\sqrt{10/3}</math> | |||
| 694.78624 | |||
| −7.16876 | |||
| D–G <br> E–A <br> A–D | |||
| <math>\sqrt{12/5}</math> | |||
| 505.21376 | |||
| +7.16876 | |||
|- | |||
| G♯–D♯ <br> (A♭–E♭) | |||
| <math>16384/10935</math> | |||
| 700.00128 | |||
| −1.95372 | |||
| D♯–G♯ <br> (E♭–A♭) | |||
| <math>10935/8192</math> | |||
| 499.99872 | |||
| +1.95372 | |||
|- | |||
| C–G <br> C♯–G♯ <br> E♭–B♭ <br> E–B <br> F–C <br> F♯–C♯ <br> B♭–F <br> B–F♯ | |||
| <math>3/2</math> | |||
| 701.95500 | |||
| +0.00000 | |||
| C–F <br> C♯–F♯ <br> F–B♭ <br> F♯–B <br> G–C <br> G♯–C♯ <br> B♭–E♭ <br> B–E | |||
| <math>4/3</math> | |||
| 498.04500 | |||
| +0.00000 | |||
|} | |||
[[Category:12-tone scales]] | [[Category:12-tone scales]] | ||
[[Category:Tempered scales]] | [[Category:Tempered scales]] | ||