Ed5/4: Difference between revisions

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== 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).

[[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 [[9edf|9ed3/2]], [[11edf|11ed3/2,]] and [[20edf|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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[[Category:Ed5/4| ]]

[[Category:Ed5/4's| ]]

~~[[Category:Edonoi]]~~

[[Category:Major third]]

[[Category:Lists of scales]]

{{todo|inline=1|explain edonoi|text=Most people do not think 5/4 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.}}

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 == 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.
-/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).
 [[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 [[9edf|9ed3/2]], [[11edf|11ed3/2,]] and [[20edf|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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 |}
-[[Category:Ed5/4| ]] <!-- main article -->
+[[Category:Ed5/4's| ]]
-[[Category:Edonoi]]
+<!-- main article -->
 [[Category:Major third]]
 [[Category:Lists of scales]]
+{{todo|inline=1|explain edonoi|text=Most people do not think 5/4 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.}}