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'''Ed7''' means '''Division of the Seventh Harmonic ([[7/1]]) into n equal parts'''.
'''Equal divisions of the 7th harmonic''' ('''ed7''') are [[tuning]]s obtained by dividing the [[7/1|7th harmonic]] in a certain number of [[equal]] steps.  


== Properties ==
The seventh harmonic is particularly wide as far as equivalences go. There are (at absolute most) about 3.9 instances of the 7th harmonic in the human hearing range; imagine if that were the case with octaves. If one does indeed deal with equivalence of the 7th harmonic, 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 [[prime interval|primes]] [[2/1|2]], [[3/1|3]], and [[5/1|5]] and use the 7:11:13 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in meantone. Whereas in meantone it takes four [[3/2]] to get to [[5/4]], here it takes seven [[13/7]]'s 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 scale]]s. 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]].  


== Table of similar ETs ==
== Individual pages for ed7's ==  
 
{| class="wikitable"
! 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"
{| class="wikitable center-all"
|+ style=white-space:nowrap | 0…99
|+ style=white-space:nowrap | 0…99
Line 336: Line 231:
|}
|}


[[Category:Ed7| ]] <!-- main article -->
; 200 and above
[[Category:Equal-step tuning]]
* [[480ed7]]
 
== Table of similar equal tunings ==
{| class="wikitable"
! 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]] ||
|}
 
{{Todo|inline=1|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.}}
[[Category:Ed7's| ]] <!-- main article -->
Retrieved from "https://en.xen.wiki/w/Ed7"