Ed8/3: Difference between revisions

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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.

== Equivalence ==

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.

Division of 8/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. The question of equivalence has not even been posed yet. Many, though not all, of these scales have a false [[octave]], with various degrees of accuracy. The eleventh is also the highest equivalence where composers do not need to go beyond the 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.

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]].

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

* Perfect Ionian through Pluperfect/Abundant Phrygian[9i]: Montréal

[[Category:Equal-step tuning]]

[[Category:Todo:cleanup]]

[[Category:Todo:improve layout]]

[[Category:Todo:improve readability]]

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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.
 == Equivalence ==
-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.
+Division of 8/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. The question of equivalence has not even been posed yet. Many, though not all, of these scales have a false [[octave]], with various degrees of accuracy. The eleventh is also the highest equivalence where composers do not need to go beyond the 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.
 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]].
@@ Line 26: / Line 26: @@
 * Locrian and Pluperfect/Abundant Phrygian[10i]/Lydian and Perfect Ionian[11i]: Scala Francisci
 * Perfect Ionian through Pluperfect/Abundant Phrygian[9i]: Montréal
 [[Category:Equal-step tuning]]
 [[Category:Todo:cleanup]]
 [[Category:Todo:improve layout]]
 [[Category:Todo:improve readability]]