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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 ==
== 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 being used at the base of so much modern tonal 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 27/25). 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.
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 ==
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.
* 5 - [[5ed5/2]]
* 7 - [[7ed5/2]]
* 9 - [[9ed5/2]]
* 12 - [[12ed5/2]]
* 16 - [[16ed5/2]]
* 18 - [[18ed5/2]]
* 25 - [[25ed5/2]]
* 45 - [[45ed5/2]]


[[Category:Ed5/2| ]] <!-- main article -->
[[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.
[[Category:Equal-step tuning]]
 
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.}}
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