Ed7

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			20edf (& Carlos Gamma)
98ed7	35edo
99ed7		56edt

Individual pages for ED7s

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