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'''Ed8/3''' means division of [[8/3]] into n equal parts.
The '''equal division of 8/3''' ('''ed8/3''') is a [[tuning]] obtained by dividing the [[8/3|Pythagorean perfect eleventh (8/3)]] in a certain number of [[equal]] steps.  


== Division of 8/3 into n equal parts ==
== Equivalence ==
Division of 8/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed8/3 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy.


Division of 8/3 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. Many, though not all, of these scales have a pseudo (false) octave, with various degrees of accuracy. The eleventh is also the highest equivalence where composers do not need to go beyond the pseudo (false) octave just to have a reasonably complete chordal harmony. However, the utility of 8:3 or another eleventh as a base is complicated by the fact that 8:3 is the avoid note in a major modality although this matters less in Mixolydian than it does in Ionian given that the former is the natural dominant scale anyway.
The eleventh is the highest [[period]] where composers do not need to go beyond the false octave just to have a reasonably complete chordal harmony. The structural utility of 8/3 or another eleventh as a period may be undermined, though, by the fact that 8/3 is the {{w|avoid note}} in a major modality. This matters less in Mixolydian than it does in Ionian given that the former is the natural dominant scale anyway.


Incidentally, one way to treat 8/3 as an equivalence is the use of the 3:4:5:6:(8) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes twelve octaves to get to 134217718/98415 (tempering out the schisma). So, doing this yields 7, 10 and 17 or 13, 16 or 19 note MOS. While the notes are rather farther apart, the scheme is uncannily similar to the [[Mohajira]] (within 8/3) ) temperaments. The terms for it are the "Macromohajira" Bolivarian mode (get your mind out of the ''other'' gutter, they don't have to do with ''[[wikipedia:Venezuela|that country that is there right now]]'', at least not particularly directly). Rather, they refer to a place that is slightly cleaner:
One approach to ed8/3 tunings is the use of the 3:4:5:6:(8) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]].


== Joseph Ruhf's approach ==
{{idiosyncratic terms}}
Whereas in meantone it takes four [[3/2]] to get to [[5/1]], here it takes twelve octaves to get to [[134217718/98415]] (tempering out the schisma). So, doing this yields 7-, 10- and 17- or 13-, 16- or 19-note [[mos scale]]s. While the notes are rather farther apart, the scheme is uncannily similar to the [[mohajira]] (within 8/3) temperaments. [[Joseph Ruhf]] calls this the ''Macromohajira Bolivarian mode''.
=== Temperament areas ===
Galveston Bay Temperament Area
Galveston Bay Temperament Area
 
* 2L 8s and 8L 2s, 5L 5s - Galveston Symmetric, Pentachordal Major, Macro-Blackwood
2L 8s and 8L 2s, 5L 5s - Galveston Symmetric, Pentachordal Major, Macro-Blackwood
* 4L 6s and 6L 4s - Baytown
 
* '''3L 7s and 7L 3s - Bolivar'''
4L 6s and 6L 4s - Baytown
 
'''3L 7s and 7L 3s - Bolivar'''


The similar decatonic scales in edIXs and edXs belong to the Chesapeake Bay Temperament Area:
The similar decatonic scales in edIXs and edXs belong to the Chesapeake Bay Temperament Area:
* Double Neapolitan[10i]: Scala Mariae/Notre Dame
* Neapolitan/Middletown Valley Dorian[10i]: Annapolis
* Middletown Valley Mixolydian[10i]: Oriole
* Other similar decatonic ± 1 scales have the following names:
* Locrian and Pluperfect/Abundant Phrygian[10i]/Lydian and Perfect Ionian[11i]: Scala Francisci
* Perfect Ionian through Pluperfect/Abundant Phrygian[9i]: Montréal


Double Neapolitan[10i]: Scala Mariae/Notre Dame
[[Category:Ed8/3's| ]]
 
<!-- main article -->
Neapolitan/Middletown Valley Dorian[10i]: Annapolis
[[Category:Lists of scales]]
 
Middletown Valley Mixolydian[10i]: Oriole
 
Other similar decatonic ± 1 scales have the following names:


Locrian and Pluperfect/Abundant Phrygian[10i]/Lydian and Perfect Ionian[11i]: Scala Francisci


Perfect Ionian through Pluperfect/Abundant Phrygian[9i]: Montréal
{{todo|inline=1|cleanup|explain edonoi|text=Most people do not think 8/3 sounds like an equivalence, so there must be some other reason why people are dividing it — some property ''other than'' equivalence that makes people want to divide it. Please add to this page an explanation of what that reason is... The page also needs a general overall cleanup.}}
[[Category:Equal-step tuning]]
[[Category:Todo:cleanup]]
[[Category:Todo:improve layout]]
[[Category:Todo:improve readability]]
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