Ed8/3: Difference between revisions

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== 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 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.

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 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]].

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]].

== Regular temperament approaches ==

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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 == 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 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.
+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 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]].
+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]].
 == Regular temperament approaches ==
+{{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''.