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The seventh harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~3.9 heptataves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with heptatave equivalence, this fact shapes one's musical approach dramatically.
The seventh harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~3.9 heptataves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with heptatave equivalence, this fact shapes one's musical approach dramatically.


Incidentally, one way to treat 7/1 as an equivalence is to eliminate the primes 2, 3, and 5 and use the 7:11:13:(49) 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 [[5/4]], here it takes seven [[13/7]] to get to [[11/7]] (tempering out the comma 63412811/62748517 in the 7.11.13 subgroup). This temperament yields 10, 13, 16, 19, 22, 25, and 47 note MOS. If 7/1 is too wide to be used as an equivalence, the next best option would be [[Ed11/7|equal divisions of 11/7]].
Incidentally, one way to treat 7/1 as an equivalence is to eliminate the primes 2, 3, and 5 and use the 7:11:13:(49) 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 [[5/4]], here it takes seven [[13/7]] to get to [[11/7]] ([[tempering out]] the [[comma]] 63412811/62748517 in the 7.11.13 [[subgroup]]). This temperament yields 10, 13, 16, 19, 22, 25, and 47 note [[MOS]]. If 7/1 is too wide to be used as an equivalence, the next best option would be [[Ed11/7|equal divisions of 11/7]].


== Individual pages for ED7s ==
== Table of similar ETs ==
* [[4ed7]]
* [[5ed7]]
* [[6ed7]]
* [[7ed7]] compare [[4edt]]
* [[8ed7]]
* [[9ed7]] compare [[5edt]]
* [[10ed7]]
* [[11ed7]] compare [[4edo]]
* [[12ed7]]
* [[13ed7]]
* [[14ed7]] compare [[5edo]]
* [[15ed7]]
* [[16ed7]] compare [[9edt]]
* [[17ed7]] compare [[6edo]]
* [[18ed7]] compare [[10edt]]
* [[19ed7]]
* [[20ed7]]
* [[21ed7]] compare [[12edt]]
* [[22ed7]]
* [[23ed7]] compare [[13edt]]
* [[24ed7]]
* [[25ed7]] compare [[9edo]]
* [[26ed7]]
* [[27ed7]]
* [[28ed7]] compare [[10edo]]
* [[29ed7]]
* [[30ed7]] compare [[17edt]]
* [[31ed7]] compare [[11edo]]
* [[32ed7]] compare [[18edt]]
* [[33ed7]]
* [[34ed7]] compare [[12edo]]
* [[35ed7]]
* [[36ed7]]
* [[37ed7]] compare [[21edt]]
* [[38ed7]]
* [[39ed7]] compare [[14edo]]
* [[40ed7]]
* [[41ed7]] compare [[23edt]]
* [[42ed7]] compare [[15edo]]
* [[43ed7]]
* [[44ed7]] compare [[25edt]]
* [[45ed7]] compare [[16edo]]
* [[46ed7]] compare [[26edt]]
* [[47ed7]]
* [[48ed7]] compare [[17edo]]
* [[49ed7]]
* [[50ed7]]
* [[51ed7]]
* [[52ed7]]
* [[53ed7]] compare [[30edt]]
* [[54ed7]]
* [[55ed7]] compare [[31edt]]
* [[56ed7]] compare [[20edo]]
* [[57ed7]] compare [[32edt]]
* [[58ed7]]
* [[59ed7]] compare [[21edo]]
* [[60ed7]] compare [[34edt]]
* [[61ed7]]
* [[62ed7]] compare [[22edo]]
* [[63ed7]]
* [[64ed7]] compare [[36edt]]
* [[65ed7]]
* [[66ed7]]
* [[67ed7]] compare [[38edt]]
* [[68ed7]]
* [[69ed7]] compare [[39edt]]
* [[70ed7]] compare [[25edo]]
* [[71ed7]] compare [[40edt]]
* [[72ed7]]
* [[73ed7]] compare [[26edo]]
* [[74ed7]]
* [[75ed7]]
* [[76ed7]] compare [[27edo]]
* [[77ed7]]
* [[78ed7]] compare [[44edt]]
* [[79ed7]]
* [[80ed7]] compare [[45edt]]
* [[81ed7]]
* [[82ed7]]
* [[83ed7]] compare [[47edt]]
* [[84ed7]] compare [[30edo]]
* [[85ed7]] compare [[48edt]]
* [[86ed7]]
* [[87ed7]] compare [[31edo]]
* [[88ed7]]
* [[89ed7]]
* [[90ed7]] compare [[32edo]]
* [[91ed7]]
* [[92ed7]] compare [[52edt]]
* [[93ed7]]
* [[94ed7]] compare [[53edt]]
* [[95ed7]]
* [[96ed7]] compare [[Carlos Gamma]]
* [[97ed7]]
* [[98ed7]] compare [[35edo]]
* [[99ed7]] compare [[56edt]]
* [[100ed7]]
* [[101ed7]]


[[Category:Ed7| ]] <!-- main article -->
{| class="wikitable"
[[Category:Equal-step tuning]]
! ED7 !! Similar EDO !! Similar EDT !! Similar EDF
|-
| [[7ed7]] ||  || [[4edt]] ||
|-
| [[9ed7]] ||  || [[5edt]] ||
|-
| [[11ed7]] || [[4edo]] ||  ||
|-
| [[14ed7]] || [[5edo]] ||  ||
|-
| [[16ed7]] ||  || [[9edt]] ||
|-
| [[17ed7]] || [[6edo]] ||  ||
|-
| [[18ed7]] ||  || [[10edt]] ||
|-
| [[21ed7]] ||  || [[12edt]] ||
|-
| [[23ed7]] ||  || [[13edt]] ||
|-
| [[25ed7]] || [[9edo]] ||  ||
|-
| [[28ed7]] || [[10edo]] ||  ||
|-
| [[30ed7]] ||  || [[17edt]] ||
|-
| [[31ed7]] || [[11edo]] ||  ||
|-
| [[32ed7]] ||  || [[18edt]] ||
|-
| [[34ed7]] || [[12edo]] ||  ||
|-
| [[37ed7]] ||  || [[21edt]] ||
|-
| [[39ed7]] || [[14edo]] ||  ||
|-
| [[41ed7]] ||  || [[23edt]] ||
|-
| [[42ed7]] || [[15edo]] ||  ||
|-
| [[44ed7]] ||  || [[25edt]] ||
|-
| [[45ed7]] || [[16edo]] ||  ||
|-
| [[46ed7]] ||  || [[26edt]] ||
|-
| [[48ed7]] || [[17edo]] ||  ||
|-
| [[53ed7]] ||  || [[30edt]] ||
|-
| [[55ed7]] ||  || [[31edt]] ||
|-
| [[56ed7]] || [[20edo]] ||  ||
|-
| [[57ed7]] ||  || [[32edt]] ||
|-
| [[59ed7]] || [[21edo]] ||  ||
|-
| [[60ed7]] ||  || [[34edt]] ||
|-
| [[62ed7]] || [[22edo]] ||  ||
|-
| [[64ed7]] ||  || [[36edt]] ||
|-
| [[67ed7]] ||  || [[38edt]] ||
|-
| [[69ed7]] ||  || [[39edt]] ||
|-
| [[70ed7]] || [[25edo]] ||  ||
|-
| [[71ed7]] ||  || [[40edt]] ||
|-
| [[73ed7]] || [[26edo]] ||  ||
|-
| [[76ed7]] || [[27edo]] ||  ||
|-
| [[78ed7]] ||  || [[44edt]] ||
|-
| [[80ed7]] ||  || [[45edt]] ||
|-
| [[83ed7]] ||  || [[47edt]] ||
|-
| [[84ed7]] || [[30edo]] ||  ||
|-
| [[85ed7]] ||  || [[48edt]] ||
|-
| [[87ed7]] || [[31edo]] ||  ||
|-
| [[90ed7]] || [[32edo]] ||  ||
|-
| [[92ed7]] ||  || [[52edt]] ||
|-
| [[94ed7]] ||  || [[53edt]] ||
|-
| [[96ed7]] ||  ||  || [[20edf]] (& [[Carlos Gamma]])
|-
| [[98ed7]] || [[35edo]] ||  ||
|-
| [[99ed7]] ||  || [[56edt]] ||
|}
 
== Individual pages for ED7s ==
{| class="wikitable center-all"
|+ style=white-space:nowrap | 0…99
| [[0ed7|0]]
| [[1ed7|1]]
| [[2ed7|2]]
| [[3ed7|3]]
| [[4ed7|4]]
| [[5ed7|5]]
| [[6ed7|6]]
| [[7ed7|7]]
| [[8ed7|8]]
| [[9ed7|9]]
|-
| [[10ed7|10]]
| [[11ed7|11]]
| [[12ed7|12]]
| [[13ed7|13]]
| [[14ed7|14]]
| [[15ed7|15]]
| [[16ed7|16]]
| [[17ed7|17]]
| [[18ed7|18]]
| [[19ed7|19]]
|-
| [[20ed7|20]]
| [[21ed7|21]]
| [[22ed7|22]]
| [[23ed7|23]]
| [[24ed7|24]]
| [[25ed7|25]]
| [[26ed7|26]]
| [[27ed7|27]]
| [[28ed7|28]]
| [[29ed7|29]]
|-
| [[30ed7|30]]
| [[31ed7|31]]
| [[32ed7|32]]
| [[33ed7|33]]
| [[34ed7|34]]
| [[35ed7|35]]
| [[36ed7|36]]
| [[37ed7|37]]
| [[38ed7|38]]
| [[39ed7|39]]
|-
| [[40ed7|40]]
| [[41ed7|41]]
| [[42ed7|42]]
| [[43ed7|43]]
| [[44ed7|44]]
| [[45ed7|45]]
| [[46ed7|46]]
| [[47ed7|47]]
| [[48ed7|48]]
| [[49ed7|49]]
|-
| [[50ed7|50]]
| [[51ed7|51]]
| [[52ed7|52]]
| [[53ed7|53]]
| [[54ed7|54]]
| [[55ed7|55]]
| [[56ed7|56]]
| [[57ed7|57]]
| [[58ed7|58]]
| [[59ed7|59]]
|-
| [[60ed7|60]]
| [[61ed7|61]]
| [[62ed7|62]]
| [[63ed7|63]]
| [[64ed7|64]]
| [[65ed7|65]]
| [[66ed7|66]]
| [[67ed7|67]]
| [[68ed7|68]]
| [[69ed7|69]]
|-
| [[70ed7|70]]
| [[71ed7|71]]
| [[72ed7|72]]
| [[73ed7|73]]
| [[74ed7|74]]
| [[75ed7|75]]
| [[76ed7|76]]
| [[77ed7|77]]
| [[78ed7|78]]
| [[79ed7|79]]
|-
| [[80ed7|80]]
| [[81ed7|81]]
| [[82ed7|82]]
| [[83ed7|83]]
| [[84ed7|84]]
| [[85ed7|85]]
| [[86ed7|86]]
| [[87ed7|87]]
| [[88ed7|88]]
| [[89ed7|89]]
|-
| [[90ed7|90]]
| [[91ed7|91]]
| [[92ed7|92]]
| [[93ed7|93]]
| [[94ed7|94]]
| [[95ed7|95]]
| [[96ed7|96]]
| [[97ed7|97]]
| [[98ed7|98]]
| [[99ed7|99]]
|}
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style=white-space:nowrap | 100…199
| [[100ed7|100]]
| [[101ed7|101]]
| [[102ed7|102]]
| [[103ed7|103]]
| [[104ed7|104]]
| [[105ed7|105]]
| [[106ed7|106]]
| [[107ed7|107]]
| [[108ed7|108]]
| [[109ed7|109]]
|-
| [[110ed7|110]]
| [[111ed7|111]]
| [[112ed7|112]]
| [[113ed7|113]]
| [[114ed7|114]]
| [[115ed7|115]]
| [[116ed7|116]]
| [[117ed7|117]]
| [[118ed7|118]]
| [[119ed7|119]]
|-
| [[120ed7|120]]
| [[121ed7|121]]
| [[122ed7|122]]
| [[123ed7|123]]
| [[124ed7|124]]
| [[125ed7|125]]
| [[126ed7|126]]
| [[127ed7|127]]
| [[128ed7|128]]
| [[129ed7|129]]
|-
| [[130ed7|130]]
| [[131ed7|131]]
| [[132ed7|132]]
| [[133ed7|133]]
| [[134ed7|134]]
| [[135ed7|135]]
| [[136ed7|136]]
| [[137ed7|137]]
| [[138ed7|138]]
| [[139ed7|139]]
|-
| [[140ed7|140]]
| [[141ed7|141]]
| [[142ed7|142]]
| [[143ed7|143]]
| [[144ed7|144]]
| [[145ed7|145]]
| [[146ed7|146]]
| [[147ed7|147]]
| [[148ed7|148]]
| [[149ed7|149]]
|-
| [[150ed7|150]]
| [[151ed7|151]]
| [[152ed7|152]]
| [[153ed7|153]]
| [[154ed7|154]]
| [[155ed7|155]]
| [[156ed7|156]]
| [[157ed7|157]]
| [[158ed7|158]]
| [[159ed7|159]]
|-
| [[160ed7|160]]
| [[161ed7|161]]
| [[162ed7|162]]
| [[163ed7|163]]
| [[164ed7|164]]
| [[165ed7|165]]
| [[166ed7|166]]
| [[167ed7|167]]
| [[168ed7|168]]
| [[169ed7|169]]
|-
| [[170ed7|170]]
| [[171ed7|171]]
| [[172ed7|172]]
| [[173ed7|173]]
| [[174ed7|174]]
| [[175ed7|175]]
| [[176ed7|176]]
| [[177ed7|177]]
| [[178ed7|178]]
| [[179ed7|179]]
|-
| [[180ed7|180]]
| [[181ed7|181]]
| [[182ed7|182]]
| [[183ed7|183]]
| [[184ed7|184]]
| [[185ed7|185]]
| [[186ed7|186]]
| [[187ed7|187]]
| [[188ed7|188]]
| [[189ed7|189]]
|-
| [[190ed7|190]]
| [[191ed7|191]]
| [[192ed7|192]]
| [[193ed7|193]]
| [[194ed7|194]]
| [[195ed7|195]]
| [[196ed7|196]]
| [[197ed7|197]]
| [[198ed7|198]]
| [[199ed7|199]]
|}
 
; 200 and above
* [[480ed7]]
 
[[Category:Ed7's| ]]
<!-- main article -->
{{todo|inline=1|cleanup|explain edonoi|text=Most people do not think 7/1 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.}}
Retrieved from "https://en.xen.wiki/w/Ed7"