# 7edf

 ← 6edf 7edf 8edf →
Prime factorization 7 (prime)
Step size 100.279¢
Octave 12\7edf (1203.35¢)
(convergent)
Semitones (A1:m2) 1:1 (100.3¢ : 100.3¢)
Consistency limit 10
Distinct consistency limit 4

Division of the just perfect fifth into 7 equal parts (7EDF) is related to 12 edo, but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 100.2793 cents. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13.

Lookalikes: 12edo, 19ed3, 31ed6

## Intervals

# Cents 12edo notation
1 100.2793 C#, Db
2 200.5586 D
3 300.8379 D#, Eb
4 401.1171 E
5 501.3964 F
6 601.6757 F#, Gb
7 701.955 G
8 802.2343 G#, Ab
9 902.5136 A
10 1002.7929 A#, Bb
11 1103.0721 B
12 1203.3514 C
13 1303.6307 C#, Db
14 1403.91 D

## Scale tree

EDF scales can be approximated in EDOs by subdividing diatonic fifths. If 4\7 (four degrees of 7EDO) is at one extreme and 3\5 (three degrees of 5EDO) is at the other, all other possible 5L 2s scales exist in a continuum between them. You can chop this continuum up by taking "freshman sums" of the two edges - adding together the numerators, then adding together the denominators (i.e. adding them together as if you would be adding the complex numbers analogous real and imaginary parts). Thus, between 4\7 and 3\5 you have (4+3)\(7+5) = 7\12, seven degrees of 12EDO.

If we carry this freshman-summing out a little further, new, larger EDOs pop up in our continuum.

Generator range: 97.9592 cents (4\7/7 = 4\49) to 102.8571 cents (3\5/7 = 3\35)

4\7 97.959
27\47 98.480
23\40 98.571
42\73 98.630
19\33 98.701
53\92 98.758
34\59 98.789
49\85 98.8235
15\26 98.901
56\97 98.969 The generator closest to a just 18/17 for EDOs less than 1400
41\71 98.994
67\116 99.015
26\45 99.048 Flattone is in this region
63\109 99.083
37\64 99.107
48\83 99.139
11\19 99.248
51\88 99.351
40\69 99.379
69\119 99.400
29\50 99.429
76\131 99.455 Golden meantone (696.2145¢)
47\81 99.471
65\112 99.490
18\31 99.539 Meantone is in this region
61\105 99.592
43\74 99.613 The generator closest to a just 16/9 for EDOs less than 1400
68\117 99.634
25\43 99.668
57\98 99.7085
32\55 99.740
39\67 99.787
7\12 100.000
38\65 100.220
31\53 100.2695 The fifth closest to a just 3/2 for EDOs less than 200
55\94 100.304 Garibaldi / Cassandra
24\41 100.348
65\111 100.361
41\70 100.408
58\99 100.433
17\29 100.493
61\104 100.5495
44\75 100.571
71\121 100.590 Golden neogothic (704.0956¢)
27\46 100.621 Neogothic is in this region
64\109 100.655
37\63 100.680
47\80 100.714
10\17 100.840
43\73 100.9785
33\56 101.020
56\95 101.053
23\39 101.099
59\100 101.143
36\61 101.171
49\83 101.205
13\22 101.299 Archy is in this region
42\71 101.4085
29\49 101.458
45\76 101.504
16\27 101.587
35\59 101.695
19\32 101.786 The generator closest to a just 9/5 for EDOs less than 1400
22\37 101.9305
3\5 102.857

Tunings above 7\12 on this chart are called "negative tunings" (as they lessen the size of the fifth) and include meantone systems such as 1/3-comma (close to 11\19) and 1/4-comma (close to 18\31). As these tunings approach 4\7, the majors become flatter and the minors become sharper.

Tunings below 7\12 on this chart are called "positive tunings" and they include Pythagorean tuning itself (well approximated by 31\53) as well as superpyth tunings such as 10\17 and 13\22. As these tunings approach 3\5, the majors become sharper and the minors become flatter. Around 13\22 through 16\27, the thirds fall closer to 7-limit than 5-limit intervals: 7:6 and 9:7 as opposed to 6:5 and 5:4.