Ed5/2: Difference between revisions

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-'''Ed5/2''' means '''Division of the classic major tenth ([[5/2]]) into n equal parts'''.
+The '''equal division of 5/2''' ('''ed5/2''') is a [[tuning]] obtained by dividing the [[5/2|classic major tenth (5/2)]] in a certain number of [[equal]] steps.
 == Properties ==
-Division of 5/2 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. The utility of 5:2, (or another tenth) as a base though, is apparent by, beside being the base of so much modern tonal harmony, 5:2 being the best option for “no-threes” harmony. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.
+Division of 5/2 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed5/2 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy.
-Incidentally, one way to treat 5/2 as an equivalence is the use of the 2:3:4:(5) chord as the fundamental complete sonority in a very similar way to the 3:4:5:(6) chord in meantone. Whereas in meantone it takes three 4/3 to get to 6/5, here it takes three 3/2 to get to 6/5 (tempering out the comma 3125/3048). So, doing this yields 5, 7, and 12 note MOS, just like meantone. While the notes are rather closer together, the scheme is exactly identical to meantone. "Macrodiatonic" might be a perfect term for it because it uses a scheme that turns out exactly identical to meantone, though severely stretched. These are also the MOS formerly known as Middletown because a tenth base stretches the meantone scheme to the point where it tempers out 64/63.
+The structural utility of 5/2 (or another tenth) is apparent by its being the base of so much common practice tonal harmony{{clarify}}, and by 5/2 being the best option for “no-threes” harmony excluding the octave{{clarify}}.
-== Individual pages for ED5/2s ==
-* [[5ed5/2]]
-* [[7ed5/2]]
-* [[9ed5/2]]
-* [[12ed5/2]]
-* [[16ed5/2]]
-* [[18ed5/2]]
-* [[25ed5/2]]
-* [[45ed5/2]]
-[[Category:Ed5/2| ]] <!-- main article -->
+One way to approach ed5/2 tunings is the use of the 2:3:4:(5) chord as the fundamental complete sonority in a very similar way to the 3:4:5:(6) chord in [[meantone]]. Whereas in meantone it takes three 4/3 to get to 6/5, here it takes three 3/2 to get to 6/5 (tempering out the comma 3125/3048). So, doing this yields 5-, 7-, and 12-note [[mos]], just like meantone. While the notes are rather closer together, the scheme shares the scale shape of meantone.
-[[Category:Equal-step tuning]]
+[[Joseph Ruhf]] proposes the term "[[Macrodiatonic and microdiatonic scales|Macrodiatonic]]"{{idiosyncratic}} for the above approach because it uses a scheme that turns out exactly identical to meantone, though severely stretched. These are also the [[MOS]] scales formerly known as Middletown{{idiosyncratic}} because a tenth base stretches the meantone scheme to the point where it tempers out 64/63.
+Another option is to treat ed5/2's as "no-threes" systems (like how [[edt]]s are usually treated as no-twos), using the 4:5:7:(10) chord as the fundamental complete sonority instead of 4:5:6:(8). Whereas in meantone it takes four [[4/3]] to get to [[6/5]], here it takes one [[10/7]] to get to [[7/5]] (tempering out the comma [[50/49]] in the no-threes 7-limit), producing a nonoctave version of [[jubilic]] temperament. Doing this yields 5-, 8-, 13-, and 21-note mos.
+== Individual pages for ed5/2's ==
+{| class="wikitable center-all"
+|+ style=white-space:nowrap | 0…99
+| [[0ed5/2|0]]
+| [[1ed5/2|1]]
+| [[2ed5/2|2]]
+| [[3ed5/2|3]]
+| [[4ed5/2|4]]
+| [[5ed5/2|5]]
+| [[6ed5/2|6]]
+| [[7ed5/2|7]]
+| [[8ed5/2|8]]
+| [[9ed5/2|9]]
+|-
+| [[10ed5/2|10]]
+| [[11ed5/2|11]]
+| [[12ed5/2|12]]
+| [[13ed5/2|13]]
+| [[14ed5/2|14]]
+| [[15ed5/2|15]]
+| [[16ed5/2|16]]
+| [[17ed5/2|17]]
+| [[18ed5/2|18]]
+| [[19ed5/2|19]]
+|-
+| [[20ed5/2|20]]
+| [[21ed5/2|21]]
+| [[22ed5/2|22]]
+| [[23ed5/2|23]]
+| [[24ed5/2|24]]
+| [[25ed5/2|25]]
+| [[26ed5/2|26]]
+| [[27ed5/2|27]]
+| [[28ed5/2|28]]
+| [[29ed5/2|29]]
+|-
+| [[30ed5/2|30]]
+| [[31ed5/2|31]]
+| [[32ed5/2|32]]
+| [[33ed5/2|33]]
+| [[34ed5/2|34]]
+| [[35ed5/2|35]]
+| [[36ed5/2|36]]
+| [[37ed5/2|37]]
+| [[38ed5/2|38]]
+| [[39ed5/2|39]]
+|-
+| [[40ed5/2|40]]
+| [[41ed5/2|41]]
+| [[42ed5/2|42]]
+| [[43ed5/2|43]]
+| [[44ed5/2|44]]
+| [[45ed5/2|45]]
+| [[46ed5/2|46]]
+| [[47ed5/2|47]]
+| [[48ed5/2|48]]
+| [[49ed5/2|49]]
+|-
+| [[50ed5/2|50]]
+| [[51ed5/2|51]]
+| [[52ed5/2|52]]
+| [[53ed5/2|53]]
+| [[54ed5/2|54]]
+| [[55ed5/2|55]]
+| [[56ed5/2|56]]
+| [[57ed5/2|57]]
+| [[58ed5/2|58]]
+| [[59ed5/2|59]]
+|-
+| [[60ed5/2|60]]
+| [[61ed5/2|61]]
+| [[62ed5/2|62]]
+| [[63ed5/2|63]]
+| [[64ed5/2|64]]
+| [[65ed5/2|65]]
+| [[66ed5/2|66]]
+| [[67ed5/2|67]]
+| [[68ed5/2|68]]
+| [[69ed5/2|69]]
+|-
+| [[70ed5/2|70]]
+| [[71ed5/2|71]]
+| [[72ed5/2|72]]
+| [[73ed5/2|73]]
+| [[74ed5/2|74]]
+| [[75ed5/2|75]]
+| [[76ed5/2|76]]
+| [[77ed5/2|77]]
+| [[78ed5/2|78]]
+| [[79ed5/2|79]]
+|-
+| [[80ed5/2|80]]
+| [[81ed5/2|81]]
+| [[82ed5/2|82]]
+| [[83ed5/2|83]]
+| [[84ed5/2|84]]
+| [[85ed5/2|85]]
+| [[86ed5/2|86]]
+| [[87ed5/2|87]]
+| [[88ed5/2|88]]
+| [[89ed5/2|89]]
+|-
+| [[90ed5/2|90]]
+| [[91ed5/2|91]]
+| [[92ed5/2|92]]
+| [[93ed5/2|93]]
+| [[94ed5/2|94]]
+| [[95ed5/2|95]]
+| [[96ed5/2|96]]
+| [[97ed5/2|97]]
+| [[98ed5/2|98]]
+| [[99ed5/2|99]]
+|}
+[[Category:Ed5/2's| ]]
+<!-- main article -->
+[[Category:Lists of scales]]
+{{todo|inline=1|cleanup|explain edonoi|text=Most people do not think 5/2 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... The page also needs a general overall cleanup.}}