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| 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.
| | #REDIRECT [[User:Xenllium/Ed8/3]] |
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| == Equivalence ==
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| 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.
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| 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 [[Glossary#A|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.
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| 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]].
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| == Joseph Ruhf's approach ==
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| {{idiosyncratic terms}}
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| 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''.
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| === Temperament areas ===
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| Galveston Bay Temperament Area
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| * 2L 8s and 8L 2s, 5L 5s - Galveston Symmetric, Pentachordal Major, Macro-Blackwood
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| * 4L 6s and 6L 4s - Baytown
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| * '''3L 7s and 7L 3s - Bolivar'''
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| The similar decatonic scales in edIXs and edXs belong to the Chesapeake Bay Temperament Area:
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| * Double Neapolitan[10i]: Scala Mariae/Notre Dame
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| * Neapolitan/Middletown Valley Dorian[10i]: Annapolis
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| * Middletown Valley Mixolydian[10i]: Oriole
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| * Other similar decatonic ± 1 scales have the following names:
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| * Locrian and Pluperfect/Abundant Phrygian[10i]/Lydian and Perfect Ionian[11i]: Scala Francisci
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| * Perfect Ionian through Pluperfect/Abundant Phrygian[9i]: Montréal
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| [[Category:Ed8/3| ]] <!-- main article -->
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| [[Category:Edonoi]]
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| [[Category:Lists of scales]]
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| {{todo|inline=1|review|cleanup|improve layout}}
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