Ed5/4: Difference between revisions

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'''~~Ed5~~/4''' ~~means~~ '''~~Division of~~ the ~~Just Major Third (~~[[5/4]]~~) into n~~ equal ~~parts'''~~.

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

== Division of ~~the just major third~~ into n equal parts ==

== 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 [[Pseudo-octave|false octave]], with various degrees of accuracy.

~~Division of~~ the 5:4 ~~into equal parts can be conceived of as to directly use this interval as an equivalence~~, ~~or not. 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 basis for~~ [[~~5-limit~~]] ~~harmony~~. ~~Many, if not all, of these scales have a perceptually important pseudo (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).

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~~.

[[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.

== Individual pages for ~~ED5~~/4s ==

== Individual pages for ed5/4's ==

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

[[Category:Major third]]

~~[[Category:Equal-step tuning]]~~

[[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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-'''Ed5/4''' means '''Division of the Just Major Third ([[5/4]]) into n equal parts'''.
+The '''equal division of 5/4''' ('''ed5/4''') is a [[tuning]] obtained by dividing the [[5/4|just major third (5/4)]] in a certain number of [[equal]] steps.
-== Division of the just major third into n equal parts ==
+== 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 [[Pseudo-octave|false octave]], with various degrees of accuracy.
-Division of the 5:4 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. 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 basis for [[5-limit]] harmony. Many, if not all, of these scales have a perceptually important pseudo (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).
-/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.
+[[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.
-== Individual pages for ED5/4s ==
+== Individual pages for ed5/4's ==
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+[[Category:Ed5/4's| ]]
+<!-- main article -->
 [[Category:Major third]]
-[[Category:Equal-step tuning]]
 [[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.}}