Ed5/4: Difference between revisions

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== Properties ==
== Properties ==
Division of 5/4 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. The question of equivalence is still in its infancy. The utility of 5/4 as a base though, is apparent by providing a novel consonance after 3, and being the [[octave reduction|octave-reduced]] basis for [[5-limit]] harmony. Many, if not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.
Division of 5/4 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed5/4 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy.
 
5/4 is particularly narrow as far as equivalences go and it is difficult to fit consonant chords in it, so we might consider using 5/4<sup>2</sup> = [[25/16]] as the equivalence instead.


ED5/4 tuning systems that accurately represent the intervals 10/9 and 9/8 include: [[17ed5/4]] (0.61 cent error), [[19ed5/4]] (0.59 cent error), and [[36ed5/4]] (0.02 cent error).
ED5/4 tuning systems that accurately represent the intervals 10/9 and 9/8 include: [[17ed5/4]] (0.61 cent error), [[19ed5/4]] (0.59 cent error), and [[36ed5/4]] (0.02 cent error).

Revision as of 01:16, 25 April 2025

The equal division of 5/4 (ed5/4) is a tuning obtained by dividing the just major third (5/4) in a certain number of equal steps.

Properties

Division of 5/4 into equal parts does not necessarily imply directly using this interval as an equivalence. Many, though not all, ed5/4 scales have a perceptually important false octave, with various degrees of accuracy.

ED5/4 tuning systems that accurately represent the intervals 10/9 and 9/8 include: 17ed5/4 (0.61 cent error), 19ed5/4 (0.59 cent error), and 36ed5/4 (0.02 cent error).

17ed5/4, 19ed5/4 and 36ed5/4 are to the division of the major third what 13ed4/3, 15ed4/3, and 28ed4/3 are to the division of the fourth, what 9ed3/2, 11ed3/2, and 20ed3/2 are to the division of the fifth, and what 5edo, 7edo, and 12edo are to the division of the octave.

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