5edo: 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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| Line 4: | Line 4: | ||
| es = 5 EDO | | es = 5 EDO | ||
| ja = 5平均律 | | ja = 5平均律 | ||
}} | |||
{{Infobox ET | |||
| Step size = 240¢ | |||
| Fifth type = 3\5 = 720¢ | |||
| Major 2nd = 1\5 = 240¢ | |||
| Minor 2nd = 0\5 = 0¢ | |||
| Augmented 1sn = 1\5 = 240¢ | |||
}} | }} | ||
== 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 | |||
|18.04 | |||
|93.7 | |||
| -8.8 | |||
| -71.3 | |||
|119.5 | |||
| -105.0 | |||
| -57.5 | |||
|- | |||
![[Relative error|relative]] (%) | |||
|0 | |||
|8 | |||
|39 | |||
| -4 | |||
| -30 | |||
|50 | |||
| -44 | |||
| -24 | |||
|- | |||
! colspan="2" |[[nearest edomapping]] | |||
|5 | |||
|3 | |||
|2 | |||
|4 | |||
|2 | |||
|4 | |||
|0 | |||
|1 | |||
|- | |||
! colspan="2" |[[fifthspan]] | |||
|0 | |||
| +1 | |||
| -1 | |||
| -2 | |||
| -1 | |||
| -2 | |||
|0 | |||
| +2 | |||
|} | |||
'''5-edo''' divides the 1200-[[cent]] octave into 5 equal parts, making its smallest interval exactly 240 [[cent|cents]], or the fifth root of two. 5-edo is the 3rd [[prime numbers|prime]] edo, after [[2edo]] and [[3edo]]. Most importantly, 5-edo is the smallest [[EDO|edo]] containing xenharmonic intervals! (1edo 2edo 3edo 4edo are all subsets of 12edo.) | '''5-edo''' divides the 1200-[[cent]] octave into 5 equal parts, making its smallest interval exactly 240 [[cent|cents]], or the fifth root of two. 5-edo is the 3rd [[prime numbers|prime]] edo, after [[2edo]] and [[3edo]]. Most importantly, 5-edo is the smallest [[EDO|edo]] containing xenharmonic intervals! (1edo 2edo 3edo 4edo are all subsets of 12edo.) | ||