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== Table of similar ETs ==
== Table of similar ETs ==
{| 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]] ||  ||  || [[Carlos Gamma]]
|-
| [[98ed7]] || [[35edo]] ||  ||
|-
| [[99ed7]] ||  || [[56edt]] ||
|}


== Individual pages for ED7s ==
== Individual pages for ED7s ==

Revision as of 06:33, 1 October 2024

Ed7 means Division of the Seventh Harmonic (7/1) into n equal parts.

Properties

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 equal divisions of 11/7.

Table of similar ETs

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 Carlos Gamma
98ed7 35edo
99ed7 56edt

Individual pages for ED7s

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