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| The '''equal division of 7/3''' ('''ed7/3''') is a [[tuning]] obtained by dividing the [[7/3|septimal minor tenth (7/3)]] in a certain number of [[equal]] steps.
| | #REDIRECT [[User:Moremajorthanmajor/Ed7/3]] |
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| == Applications ==
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| Division of 7/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed7/3 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy.
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| The structural utility of 7/3 (or another tenth) is apparent by being the absolute widest range most generally used in popular songs{{citation needed}} (and even the range of a {{w|Dastg%C4%81h-e_M%C4%81hur|dastgah}}{{citation needed}}).
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| == Chords and harmonies ==
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| {{main|Pseudo-traditional harmonic functions of enneatonic scale_degrees}}
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| [[:Category:9-tone scales|Enneatonic scale]]s, especially those equivalent at 7/3, can sensibly take [[tetrad]]s as the fundamental complete sonorities of a pseudo-traditional functional harmony due to their seventh degree being as structurally important as it is. Many, though not all, of these scales have a perceptually important [[Pseudo-octave|pseudo (false) octave]], with various degrees of accuracy.
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| Incidentally, one way to treat 7/3 as an equivalence is the use of the 3:4:5:(7) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]]. Whereas in meantone it takes four [[3/2]] to get to [[5/1]], here it takes two [[28/15]] to get to [[7/2]] (tempering out the comma [[225/224]]). So, doing this yields 15-, 19-, and 34-note [[mos]] 2/1 apart. While the notes are rather farther apart, the scheme is uncannily similar to meantone. [[Joseph Ruhf]] named this scheme "macrobichromatic".
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| == Middletown ==
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| {{idiosyncratic terms}}
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| 7/3 provides a fairly trivial point to split the difference between the [[octave]] and the [[tritave]], which is why Ruhf has named the region of intervals between 6 and 7 degrees of [[5edo]] the "[[Middletown valley]]".
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| The proper [[Middletown family|Middletown temperament family]] is based on an [[enneatonic]] scale [[generator|generated]] by a third or a fifth optionally with a [[period]] of a [[Wolf interval|wolf]] fourth at most 560 [[cents]] wide) and, as is the twelfth (tritave), an alternative interval where {{w|Inversion (music) #Counterpoint|invertible counterpoint}} has classically occurred.
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| The branches of the Middletown family are named thus:
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| * 3&6: Tritetrachordal
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| * 4&5: Montrose (between 5\4edo and 4\3edo in particular, MOS generated by [pseudo] octaves belong to this branch)
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| * 2&7: Terra Rubra
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| The family of interlaced [[octatonic scale]]-based temperaments in the "Middletown valley" is called Vesuvius (i.e. the volcano east of Naples).
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| The Middlebury temperament falls in the "Middletown valley", but its enneatonic scales are "[[generator-remainder]]".
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| The temperaments neighboring Middletown proper are named thus:
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| * 5&6: Rosablanca
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| * 4&7: Saptimpun (10 1/2)
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| * 5&7: 8bittone (Old Middetown)
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| The [[pyrite]] tuning of [[edX]]s will turn out to divide a barely mistuned [[5/2]] of almost exactly 45\[[34edo]].
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| == Individual pages for ed7/3's ==
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| {| class="wikitable center-all"
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| |+ style=white-space:nowrap | 0…99
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| | [[0ed7/3|0]]
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| | [[1ed7/3|1]]
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| | [[2ed7/3|2]]
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| | [[3ed7/3|3]]
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| | [[4ed7/3|4]]
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| | [[5ed7/3|5]]
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| | [[6ed7/3|6]]
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| | [[7ed7/3|7]]
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| | [[8ed7/3|8]]
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| | [[9ed7/3|9]]
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| |-
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| | [[10ed7/3|10]]
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| | [[11ed7/3|11]]
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| | [[12ed7/3|12]]
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| | [[13ed7/3|13]]
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| | [[14ed7/3|14]]
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| | [[15ed7/3|15]]
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| | [[16ed7/3|16]]
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| | [[17ed7/3|17]]
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| | [[18ed7/3|18]]
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| | [[19ed7/3|19]]
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| |-
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| | [[20ed7/3|20]]
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| | [[21ed7/3|21]]
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| | [[22ed7/3|22]]
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| | [[23ed7/3|23]]
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| | [[24ed7/3|24]]
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| | [[25ed7/3|25]]
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| | [[26ed7/3|26]]
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| | [[27ed7/3|27]]
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| | [[28ed7/3|28]]
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| | [[29ed7/3|29]]
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| |-
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| | [[30ed7/3|30]]
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| | [[31ed7/3|31]]
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| | [[32ed7/3|32]]
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| | [[33ed7/3|33]]
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| | [[34ed7/3|34]]
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| | [[35ed7/3|35]]
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| | [[36ed7/3|36]]
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| | [[37ed7/3|37]]
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| | [[38ed7/3|38]]
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| | [[39ed7/3|39]]
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| |-
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| | [[40ed7/3|40]]
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| | [[41ed7/3|41]]
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| | [[42ed7/3|42]]
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| | [[43ed7/3|43]]
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| | [[44ed7/3|44]]
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| | [[45ed7/3|45]]
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| | [[46ed7/3|46]]
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| | [[47ed7/3|47]]
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| | [[48ed7/3|48]]
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| | [[49ed7/3|49]]
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| |-
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| | [[50ed7/3|50]]
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| | [[51ed7/3|51]]
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| | [[52ed7/3|52]]
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| | [[53ed7/3|53]]
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| | [[54ed7/3|54]]
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| | [[55ed7/3|55]]
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| | [[56ed7/3|56]]
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| | [[57ed7/3|57]]
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| | [[58ed7/3|58]]
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| | [[59ed7/3|59]]
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| |-
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| | [[60ed7/3|60]]
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| | [[61ed7/3|61]]
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| | [[62ed7/3|62]]
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| | [[63ed7/3|63]]
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| | [[64ed7/3|64]]
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| | [[65ed7/3|65]]
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| | [[66ed7/3|66]]
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| | [[67ed7/3|67]]
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| | [[68ed7/3|68]]
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| | [[69ed7/3|69]]
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| |-
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| | [[70ed7/3|70]]
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| | [[71ed7/3|71]]
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| | [[72ed7/3|72]]
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| | [[73ed7/3|73]]
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| | [[74ed7/3|74]]
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| | [[75ed7/3|75]]
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| | [[76ed7/3|76]]
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| | [[77ed7/3|77]]
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| | [[78ed7/3|78]]
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| | [[79ed7/3|79]]
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| |-
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| | [[80ed7/3|80]]
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| | [[81ed7/3|81]]
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| | [[82ed7/3|82]]
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| | [[83ed7/3|83]]
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| | [[84ed7/3|84]]
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| | [[85ed7/3|85]]
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| | [[86ed7/3|86]]
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| | [[87ed7/3|87]]
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| | [[88ed7/3|88]]
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| | [[89ed7/3|89]]
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| |-
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| | [[90ed7/3|90]]
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| | [[91ed7/3|91]]
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| | [[92ed7/3|92]]
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| | [[93ed7/3|93]]
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| | [[94ed7/3|94]]
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| | [[95ed7/3|95]]
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| | [[96ed7/3|96]]
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| | [[97ed7/3|97]]
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| | [[98ed7/3|98]]
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| | [[99ed7/3|99]]
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| |}
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| {| class="wikitable center-all mw-collapsible mw-collapsed"
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| |+ style=white-space:nowrap | 100…199
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| | [[100ed7/3|100]]
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| | [[101ed7/3|101]]
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| | [[102ed7/3|102]]
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| | [[103ed7/3|103]]
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| | [[104ed7/3|104]]
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| | [[105ed7/3|105]]
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| | [[106ed7/3|106]]
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| | [[107ed7/3|107]]
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| | [[108ed7/3|108]]
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| | [[109ed7/3|109]]
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| |-
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| | [[110ed7/3|110]]
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| | [[111ed7/3|111]]
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| | [[112ed7/3|112]]
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| | [[113ed7/3|113]]
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| | [[114ed7/3|114]]
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| | [[115ed7/3|115]]
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| | [[116ed7/3|116]]
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| | [[117ed7/3|117]]
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| | [[118ed7/3|118]]
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| | [[119ed7/3|119]]
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| |-
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| | [[120ed7/3|120]]
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| | [[121ed7/3|121]]
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| | [[122ed7/3|122]]
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| | [[123ed7/3|123]]
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| | [[124ed7/3|124]]
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| | [[125ed7/3|125]]
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| | [[126ed7/3|126]]
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| | [[127ed7/3|127]]
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| | [[128ed7/3|128]]
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| | [[129ed7/3|129]]
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| |-
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| | [[130ed7/3|130]]
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| | [[131ed7/3|131]]
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| | [[132ed7/3|132]]
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| | [[133ed7/3|133]]
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| | [[134ed7/3|134]]
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| | [[135ed7/3|135]]
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| | [[136ed7/3|136]]
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| | [[137ed7/3|137]]
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| | [[138ed7/3|138]]
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| | [[139ed7/3|139]]
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| |-
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| | [[140ed7/3|140]]
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| | [[141ed7/3|141]]
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| | [[142ed7/3|142]]
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| | [[143ed7/3|143]]
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| | [[144ed7/3|144]]
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| | [[145ed7/3|145]]
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| | [[146ed7/3|146]]
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| | [[147ed7/3|147]]
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| | [[148ed7/3|148]]
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| | [[149ed7/3|149]]
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| |-
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| | [[150ed7/3|150]]
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| | [[151ed7/3|151]]
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| | [[152ed7/3|152]]
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| | [[153ed7/3|153]]
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| | [[154ed7/3|154]]
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| | [[155ed7/3|155]]
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| | [[156ed7/3|156]]
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| | [[157ed7/3|157]]
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| | [[158ed7/3|158]]
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| | [[159ed7/3|159]]
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| |-
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| | [[160ed7/3|160]]
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| | [[161ed7/3|161]]
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| | [[162ed7/3|162]]
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| | [[163ed7/3|163]]
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| | [[164ed7/3|164]]
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| | [[165ed7/3|165]]
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| | [[166ed7/3|166]]
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| | [[167ed7/3|167]]
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| | [[168ed7/3|168]]
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| | [[169ed7/3|169]]
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| |-
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| | [[170ed7/3|170]]
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| | [[171ed7/3|171]]
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| | [[172ed7/3|172]]
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| | [[173ed7/3|173]]
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| | [[174ed7/3|174]]
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| | [[175ed7/3|175]]
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| | [[176ed7/3|176]]
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| | [[177ed7/3|177]]
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| | [[178ed7/3|178]]
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| | [[179ed7/3|179]]
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| |-
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| | [[180ed7/3|180]]
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| | [[181ed7/3|181]]
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| | [[182ed7/3|182]]
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| | [[183ed7/3|183]]
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| | [[184ed7/3|184]]
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| | [[185ed7/3|185]]
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| | [[186ed7/3|186]]
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| | [[187ed7/3|187]]
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| | [[188ed7/3|188]]
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| | [[189ed7/3|189]]
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| |-
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| | [[190ed7/3|190]]
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| | [[191ed7/3|191]]
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| | [[192ed7/3|192]]
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| | [[193ed7/3|193]]
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| | [[194ed7/3|194]]
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| | [[195ed7/3|195]]
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| | [[196ed7/3|196]]
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| | [[197ed7/3|197]]
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| | [[198ed7/3|198]]
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| | [[199ed7/3|199]]
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| |}
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| [[Category:Ed7/3| ]] <!-- main article -->
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| [[Category:Edonoi]]
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| [[Category:Lists of scales]]
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| {{todo|inline=1|review|cleanup|improve layout}}
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