# 11edf

 ← 10edf 11edf 12edf →
Prime factorization 11 (prime)
Step size 63.8141¢
Octave 19\11edf (1212.47¢)
Semitones (A1:m2) 1:2 (63.81¢ : 127.6¢)
Consistency limit 7
Distinct consistency limit 4

11EDF is the equal division of the just perfect fifth into 11 parts of 63.8141 cents each, corresponding to 18.8046 edo (similar to every fifth step of 94edo). It is similar to 19edo and nearly identical to Carlos Beta.

## Intervals

degree cents value corresponding
JI intervals
0 exact 1/1
1 63.8141 (28/27), (27/26)
2 127.6282 14/13
3 191.4423
4 255.2564
5 319.07045 6/5
6 382.8845 5/4
7 446.6986
8 510.5127
9 574.3268 39/28
10 638.1409 (13/9)
11 701.955 exact 3/2 just perfect fifth
12 765.7691 14/9, 81/52
13 828.5732 21/13
14 893.3973
15 956.2114
16 1020.0255 9/5
17 1084.8395 15/8
18 1148.6536
19 1211.4677
20 1276.2816 117/56
21 1340.0959 13/6
22 1403.91 exact 9/4

## Scale tree

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: 62.33766 cents (4\7/11 = 4\77) to 65.45 cents (3\5/11 = 3\55)

4\7 62.3377
27\47 62.66925
23\40 62.72
42\73 62.7646
19\33 62.8099
53\92 62.84585
34\59 62.86595
49\85 62.8877
15\26 62.9371
56\97 62.9803 The generator closest to a just 28/27 for EDOs less than 200
41\71 62.9962
67\116 63.0094
26\45 63.03 Flattone is in this region
63\109 63.0525
37\64 63.0681
48\83 63.0887
11\19 63.1579
51\88 63.2231
40\69 63.2411
69\119 63.2544
29\50 63.27
76\131 63.2893 Golden meantone (696.2145¢)
47\81 63.2997
65\112 63.3117
18\31 63.3431 Meantone is in this region
61\105 63.3766
43\74 63.3907
68\117 63.4033
25\43 63.42495
57\98 63.4508
32\55 63.45
39\67 63.5007
7\12 63.63
38\65 63.7762
31\53 63.8079 The fifth closest to a just 3/2 for EDOs less than 200
55\94 63.8298 Garibaldi / Cassandra
24\41 63.8581
65\111 63.8821
41\70 63.8951
58\99 63.91185
17\29 63.9499
61\104 63.8960
44\75 64.000
71\121 64.0120 Golden neogothic (704.0956¢)
27\46 64.0316 Neogothic is in this region
64\109 64.0534
37\63 64.0693
47\80 64.09
10\17 64.1711
43\73 64.2590
33\56 64.2857
56\95 64.3062
23\39 64.3357
59\100 64.36
36\61 64.3815
49\83 64.4031
13\22 64.4628 Archy is in this region
42\71 64.53265
29\49 64.5640
45\76 64.5933
16\27 64.64
35\59 64.71495
19\32 64.772
22\37 64.864
3\5 65.45

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.