21edo: Difference between revisions
m introduction missing |
ET parameter name, cleanup |
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}} | }} | ||
{{Infobox ET | {{Infobox ET | ||
| Prime factorization = 3 | | Prime factorization = 3 × 7 | ||
| Step size = 57.143 | | Step size = 57.143 | ||
| Fifth | | Fifth = 12\21 = 685.714¢ (→[[7edo|4\7]]) | ||
| Major 2nd = 3\21 = 171¢ | | Major 2nd = 3\21 = 171¢ | ||
| Minor 2nd = 3\21 = 171¢ | | Minor 2nd = 3\21 = 171¢ | ||
| Line 16: | Line 16: | ||
==Theory== | ==Theory== | ||
{| class="wikitable" | {| class="wikitable center-all" | ||
! colspan="2" | | ! colspan="2" | <!-- empty cell --> | ||
!prime 2 | ! prime 2 | ||
!prime 3 | ! prime 3 | ||
!prime 5 | ! prime 5 | ||
!prime 7 | ! prime 7 | ||
!prime 11 | ! prime 11 | ||
!prime 13 | ! prime 13 | ||
!prime 17 | ! prime 17 | ||
!prime 19 | ! prime 19 | ||
|- | |- | ||
! rowspan="2" |Error | ! rowspan="2" | Error | ||
!absolute (¢) | ! absolute (¢) | ||
|0 | | 0.0 | ||
| -16. | | -16.2 | ||
|13.7 | | +13.7 | ||
|2.6 | | +2.6 | ||
|20.1 | | +20.1 | ||
|16.6 | | +16.6 | ||
|9.3 | | +9.3 | ||
| -11.8 | | -11.8 | ||
|- | |- | ||
![[Relative error|relative]] (%) | ! [[Relative error|relative]] (%) | ||
|0 | | 0 | ||
| -28 | | -28 | ||
|24 | | +24 | ||
|5 | | +5 | ||
|35 | | +35 | ||
|29 | | +29 | ||
|16 | | +16 | ||
| -21 | | -21 | ||
|- | |- | ||
! colspan="2" |[[nearest edomapping]] | ! colspan="2" | [[nearest edomapping]] | ||
|21 | | 21 | ||
|12 | | 12 | ||
|7 | | 7 | ||
|17 | | 17 | ||
|10 | | 10 | ||
|15 | | 15 | ||
|2 | | 2 | ||
|5 | | 5 | ||
|} | |} | ||
21-edo provides both 7-edo as a subset and the familiar 400-cent major third, while also giving some higher-limit JI possibilities. The system can be treated as three intertwining 7-edo or "equi-heptatonic" scales, or as seven 3-edo ''augmented'' triads. The 7/4 at 968.826 cents is only off in 21-tone by 2.6 cents, which is better than any other EDO <26. | 21-edo provides both 7-edo as a subset and the familiar 400-cent major third, while also giving some higher-limit JI possibilities. The system can be treated as three intertwining 7-edo or "equi-heptatonic" scales, or as seven 3-edo ''augmented'' triads. The 7/4 at 968.826 cents is only off in 21-tone by 2.6 cents, which is better than any other EDO <26. | ||