21edo: Difference between revisions

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m Theory: the 23rd harmonic is notable
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==Theory==
==Theory==
{| class="wikitable center-all"
{{Primes in edo|21|columns=9}}
! colspan="2" | <!-- empty cell -->
! prime 2
! prime 3
! prime 5
! prime 7
! prime 11
! prime 13
! prime 17
! prime 19
|-
! rowspan="2" | Error
! absolute (¢)
| 0.0
| -16.2
| +13.7
| +2.6
| +20.1
| +16.6
| +9.3
| -11.8
|-
! [[Relative error|relative]] (%)
| 0
| -28
| +24
| +5
| +35
| +29
| +16
| -21
|-
! colspan="2" | [[nearest edomapping]]
| 21
| 12
| 7
| 17
| 10
| 15
| 2
| 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 &lt;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 &lt;26.