8edo: Difference between revisions
m Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot |
made the template, made the primes-error table |
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| ja = 8平均律 | | ja = 8平均律 | ||
}} | }} | ||
{{Infobox ET | |||
| Prime factorization = 2<sup>3</sup> | |||
| Step size = 150¢ | |||
| Fifth type = 5\8 = 750¢ | |||
| Major 2nd = 2\8 = 300¢ | |||
| Minor 2nd = -1\8 = -150¢ | |||
| Augmented 1sn = 3\8 = 450¢ | |||
}} | |||
=Theory= | =Theory= | ||
{| class="wikitable" | |||
! colspan="2" | | |||
!prime 2 | |||
!prime 3 | |||
!prime 5 | |||
!prime 7 | |||
!prime 11 | |||
!prime 13 | |||
!prime 17 | |||
!prime 19 | |||
|- | |||
! rowspan="2" |error | |||
!absolute (¢) | |||
|0 | |||
|48.04 | |||
|63.7 | |||
| -68.8 | |||
|48.7 | |||
|59.5 | |||
|45.0 | |||
|2.5 | |||
|- | |||
![[Relative error|relative]] (%) | |||
|0 | |||
|32 | |||
|42 | |||
| -46 | |||
|32 | |||
|40 | |||
|30 | |||
|2 | |||
|- | |||
! colspan="2" |[[nearest edomapping]] | |||
|8 | |||
|5 | |||
|3 | |||
|6 | |||
|4 | |||
|6 | |||
|1 | |||
|2 | |||
|- | |||
! colspan="2" |[[fifthspan]] | |||
|0 | |||
| +1 | |||
| -1 | |||
| -2 | |||
| +4 | |||
| -2 | |||
| -3 | |||
| +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 [[Just_intonation_subgroups|just intonation subgroup]] 2.11/3.13/5, with good intervals of 13/10 and an excellent version of 11/6. | 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_subgroups|just intonation subgroup]] 2.11/3.13/5, with good intervals of 13/10 and an excellent version of 11/6. | ||