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).
-/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 ==
-* 2 - [[2ed5/4|Square Root of 5/4]]
+{| class="wikitable center-all"
-* 3 - [[3ed5/4|Cube Root of 5/4]]
+|+ style=white-space:nowrap | 0…49
-* 4 - [[4ed5/4|Fourth Root of 5/4]]
+| [[0ed5/4|0]]
-* 5 - [[5ed5/4|Fifth Root of 5/4]]
+| [[1ed5/4|1]]
-* 6 - [[6ed5/4|Sixth Root of 5/4]]
+| [[2ed5/4|2]]
-* 7 - [[7ed5/4|Seventh Root of 5/4]]
+| [[3ed5/4|3]]
-* 17 - [[17ed5/4|17th Root of 5/4]]
+| [[4ed5/4|4]]
-* 19 - [[19ed5/4|19th Root of 5/4]]
+| [[5ed5/4|5]]
-* 36 - [[36ed5/4|36th Root of 5/4]]
+| [[6ed5/4|6]]
+| [[7ed5/4|7]]
+| [[8ed5/4|8]]
+| [[9ed5/4|9]]
+|-
+| [[10ed5/4|10]]
+| [[11ed5/4|11]]
+| [[12ed5/4|12]]
+| [[13ed5/4|13]]
+| [[14ed5/4|14]]
+| [[15ed5/4|15]]
+| [[16ed5/4|16]]
+| [[17ed5/4|17]]
+| [[18ed5/4|18]]
+| [[19ed5/4|19]]
+|-
+| [[20ed5/4|20]]
+| [[21ed5/4|21]]
+| [[22ed5/4|22]]
+| [[23ed5/4|23]]
+| [[24ed5/4|24]]
+| [[25ed5/4|25]]
+| [[26ed5/4|26]]
+| [[27ed5/4|27]]
+| [[28ed5/4|28]]
+| [[29ed5/4|29]]
+|-
+| [[30ed5/4|30]]
+| [[31ed5/4|31]]
+| [[32ed5/4|32]]
+| [[33ed5/4|33]]
+| [[34ed5/4|34]]
+| [[35ed5/4|35]]
+| [[36ed5/4|36]]
+| [[37ed5/4|37]]
+| [[38ed5/4|38]]
+| [[39ed5/4|39]]
+|-
+| [[40ed5/4|40]]
+| [[41ed5/4|41]]
+| [[42ed5/4|42]]
+| [[43ed5/4|43]]
+| [[44ed5/4|44]]
+| [[45ed5/4|45]]
+| [[46ed5/4|46]]
+| [[47ed5/4|47]]
+| [[48ed5/4|48]]
+| [[49ed5/4|49]]
+|}
+[[Category:Ed5/4's| ]]
+<!-- main article -->
 [[Category:Major third]]
-[[Category:Equal-step tuning]]
+[[Category:Lists of scales]]
-[[Category:Lists]]
+{{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.}}