20edo: Difference between revisions
20dedo as Ptolemy's intense diatonic. |
m source for Balzano and Zweifel modes |
||
| Line 8: | Line 8: | ||
== Theory == | == Theory == | ||
20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 [[cent]]s each. It contains smaller [[EDO|edo]]s [[2edo|2]], [[4edo|4]], [[5edo|5]], and [[10edo|10]] and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from [[5edo]]), 11, 13 & 15 (from [[10edo]]), 19 & 27 (from [[4edo]]), 29 and 31; as well as the other harmonics more loosely (though to some people, still functionally) approximated. Thus, 20-EDO does a reasonably convincing approximation of harmonics 4:7:11:13:15. | 20-tone equal temperament, or 20edo, divides the octave into exactly 20 equal steps of 60 [[cent]]s each. It contains smaller [[EDO|edo]]s [[2edo|2]], [[4edo|4]], [[5edo|5]], and [[10edo|10]] and is part of the 5n Family of equal divisions of the octave. 20 edo fairly approximates the harmonics 7 (from [[5edo]]), 11, 13 & 15 (from [[10edo]]), 19 & 27 (from [[4edo]]), 29 and 31; as well as the other harmonics more loosely (though to some people, still functionally) approximated. Thus, 20-EDO does a reasonably convincing approximation of harmonics 4:7:11:13:15. | ||
__FORCETOC__ | __FORCETOC__ | ||
| Line 222: | Line 220: | ||
|- | |- | ||
| 2 3 2 2 2 3 2 2 2 | | 2 3 2 2 2 3 2 2 2 | ||
| Balzano Nine-tone (<span style="">[[2L_7s|fair mavila]], [[score9]])</span> | | Balzano Nine-tone (<span style="">[[2L_7s|fair mavila]], [[score9]]) [https://www.jstor.org/stable/833490?seq=1]</span> | ||
|- | |- | ||
| 2 2 2 2 1 2 2 2 2 2 1 | | 2 2 2 2 1 2 2 2 2 2 1 | ||
| Line 459: | Line 457: | ||
[[Category:todo:unify_precision]] | [[Category:todo:unify_precision]] | ||
[[Category:twentuning]] | [[Category:twentuning]] | ||
<references /> | |||