8edo: Difference between revisions
introduction missing |
ET parameter name, cleanup |
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| Line 8: | Line 8: | ||
| Prime factorization = 2<sup>3</sup> | | Prime factorization = 2<sup>3</sup> | ||
| Step size = 150¢ | | Step size = 150¢ | ||
| Fifth | | Fifth = 5\8 = 750¢ | ||
| Major 2nd = 2\8 = 300¢ | | Major 2nd = 2\8 = 300¢ | ||
| Minor 2nd = -1\8 = -150¢ | | Minor 2nd = -1\8 = -150¢ | ||
| 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 | ||
|48. | | +48.0 | ||
|63.7 | | +63.7 | ||
| -68.8 | | -68.8 | ||
|48.7 | | +48.7 | ||
|59.5 | | +59.5 | ||
|45.0 | | +45.0 | ||
|2.5 | | +2.5 | ||
|- | |- | ||
![[Relative error|relative]] (%) | ! [[Relative error|relative]] (%) | ||
|0 | | 0 | ||
|32 | | +32 | ||
|42 | | +42 | ||
| -46 | | -46 | ||
|32 | | +32 | ||
|40 | | +40 | ||
|30 | | +30 | ||
|2 | | +2 | ||
|- | |- | ||
! colspan="2" |[[nearest edomapping]] | ! colspan="2" | [[nearest edomapping]] | ||
|8 | | 8 | ||
|5 | | 5 | ||
|3 | | 3 | ||
|6 | | 6 | ||
|4 | | 4 | ||
|6 | | 6 | ||
|1 | | 1 | ||
|2 | | 2 | ||
|- | |- | ||
! colspan="2" |[[fifthspan]] | ! colspan="2" | [[fifthspan]] | ||
|0 | | 0 | ||
| +1 | | +1 | ||
| -1 | | -1 | ||
| Line 68: | Line 68: | ||
| +2 | | +2 | ||
|} | |} | ||
8-edo forms an odd and even pitch set of two diminished seventh chords, which when used in combination yield dissonance. The system has been described as a "barbaric" harmonic system; even so, it does a good job representing the [[ | |||
8-edo forms an odd and even pitch set of two diminished seventh chords, which when used in combination yield dissonance. The system has been described as a "barbaric" harmonic system; even so, it does a good job representing the [[just intonation subgroup]]s 2.11/3.13/5, with good intervals of [[13/10]] and an excellent version of [[11/6]]. | |||
Another way of looking at 8-EDO is to treat a chord of 0-1-2-3-4 degrees (0-150-300-450-600 cents) as approximating harmonics 10:11:12:13:14 (~0-165-316-454-583 cents), which is not too implausible if you can buy that 12-EDO is a 5-limit temperament. This interpretation would imply that 121/120, 144/143, 169/168, and hence also 36/35 and 66/65, are tempered out. | Another way of looking at 8-EDO is to treat a chord of 0-1-2-3-4 degrees (0-150-300-450-600 cents) as approximating harmonics 10:11:12:13:14 (~0-165-316-454-583 cents), which is not too implausible if you can buy that 12-EDO is a 5-limit temperament. This interpretation would imply that 121/120, 144/143, 169/168, and hence also 36/35 and 66/65, are tempered out. | ||