43edo: Difference between revisions
m Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot |
added the template, moved the primes-error table up to the top |
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{{Infobox ET | |||
| Step size = 27.907 | |||
| Fifth type = 25\43 = 697.674¢ | |||
| Major 2nd = 7\43 = 195¢ | |||
| Minor 2nd = 4\43 = 112¢ | |||
| Augmented 1sn = 3\43 = 84¢ | |||
}} | |||
== Theory == | == Theory == | ||
{| class="wikitable center-all" | |||
! colspan="2" | | |||
! prime 2 | |||
! prime 3 | |||
! prime 5 | |||
! prime 7 | |||
! prime 11 | |||
! prime 13 | |||
! prime 17 | |||
! prime 19 | |||
|- | |||
! rowspan="2" |Error | |||
! absolute (¢) | |||
| 0 | |||
| -4.28 | |||
| +4.4 | |||
| +7.9 | |||
| +6.8 | |||
| -3.3 | |||
| +6.7 | |||
| +9.5 | |||
|- | |||
![[Relative error|relative]] (%) | |||
| 0 | |||
| -15 | |||
| +16 | |||
| +28 | |||
| +24 | |||
| -12 | |||
| +24 | |||
| +34 | |||
|- | |||
! colspan="2" |[[nearest edomapping]] | |||
|43 | |||
|25 | |||
|14 | |||
|35 | |||
|20 | |||
|30 | |||
|4 | |||
|11 | |||
|} | |||
43edo is strongly associated with [[Meantone|meantone temperament]], particularly [[1/5-comma meantone]], being a good tuning system in the 5, 7, 11, and 13-limit. The version of 11-limit meantone is the one tempering out [[99/98]], [[176/175]] and [[441/440]] sometimes called Huygens. 43-equal has the first good 13-limit meantone available as an equal division of the octave. The baroque, French, ironically hearing and speech impaired acoustician [http://en.wikipedia.org/wiki/Joseph_Sauveur Joseph Sauveur] based his system on 43 equal tones to the octave, calling them "merides". Further information: http://tonalsoft.com/enc/m/meride.aspx | '''43edo''' divides the [[octave]] into 43 [[equal]] parts. It is strongly associated with [[Meantone|meantone temperament]], particularly [[1/5-comma meantone]], being a good tuning system in the 5, 7, 11, and 13-limit. The version of 11-limit meantone is the one tempering out [[99/98]], [[176/175]] and [[441/440]] sometimes called Huygens. 43-equal has the first good 13-limit meantone available as an equal division of the octave. The baroque, French, ironically hearing and speech impaired acoustician [http://en.wikipedia.org/wiki/Joseph_Sauveur Joseph Sauveur] based his system on 43 equal tones to the octave, calling them "merides". Further information: http://tonalsoft.com/enc/m/meride.aspx | ||
The composer [http://juhanpuhmmusic.ca Juhan Puhm] uses 43edo in some of his meantone suites for fortepiano and prefers it to [[31edo]]. | The composer [http://juhanpuhmmusic.ca Juhan Puhm] uses 43edo in some of his meantone suites for fortepiano and prefers it to [[31edo]]. | ||
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== Just approximation == | == Just approximation == | ||
=== Selected just intervals === | === Selected just intervals === | ||
==== 15-odd-limit mappings ==== | ==== 15-odd-limit mappings ==== | ||
The following table shows how [[15-odd-limit intervals]] are represented in 43edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''. | The following table shows how [[15-odd-limit intervals]] are represented in 43edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''. | ||