# 14edf

 ← 13edf 14edf 15edf →
Prime factorization 2 × 7
Step size 50.1396¢
Octave 24\14edf (1203.35¢) (→12\7edf)
Semitones (A1:m2) 2:2 (100.3¢ : 100.3¢)
Consistency limit 6
Distinct consistency limit 4

Division of the just perfect fifth into 14 equal parts (14EDF) is related to 24 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 50.1396 cents. The patent val has a generally sharp tendency for harmonics up to 22, with the exception for 7, 14, and 21.

Lookalikes: 24edo, 38edt

Degree
0 0
1 50.1396
2 100.2793
3 150.4189
4 200.5586
5 250.6982
6 300.8379
7 350.9775
8 401.1171
9 451.2568
10 501.3964
11 551.536
12 601.6757
13 651.8154
14 701.955
15 752.0946
16 802.2343
17 852.3739
18 902.5136
19 952.6532
20 1002.7929
21 1052.9235
22 1103.0721
23 1153.2118
24 1203.3514
25 1253.4911
26 1303.6307
27 1353.7704
28 1403.91

## 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: 48.97959 cents (4\7/14 = 2\49) to 51.42857 cents (3\5/14 = 3\70)

4\7 48.9796
27\47 49.2401
23\40 49.2857
42\73 49.3151
19\33 49.35065
53\92 49.3789
34\59 49.3947
49\85 49.4118
15\26 49.45055
56\97 49.4845
41\71 49.4970
67\116 49.5074
26\45 49.5238 Flattone is in this region
63\109 49.5413
37\64 49.5535
48\83 49.5697
11\19 49.6241
51\88 49.6753
40\69 49.6894
69\119 49.6999
29\50 49.7143
76\131 49.7274 Golden meantone (696.2145¢)
47\81 49.73545
65\112 49.7449
18\31 49.7696 Meantone is in this region
61\105 49.7959
43\74 49.8070 The generator closest to a just 4/3 for EDOs less than 2800
68\117 49.81685
25\43 49.8339
57\98 49.8542
32\55 49.8701
39\67 49.8934
7\12 50.0000
38\65 50.1099
31\53 50.1348 The fifth closest to a just 3/2 for EDOs less than 200
55\94 50.1520 Garibaldi / Cassandra
24\41 50.1742
65\111 50.19305
41\70 50.2041
58\99 50.21645
17\29 50.2463
61\104 50.2747
44\75 50.2857
71\121 50.2952 Golden neogothic (704.0956¢)
27\46 50.3106 Neogothic is in this region
64\109 50.32765
37\63 50.3401
47\80 50.3571
10\17 50.4202
43\73 50.4892
33\56 50.5102
56\95 50.5263
23\39 50.54945
59\100 50.5714
36\61 50.5855
49\83 50.6024
13\22 50.64935 Archy is in this region
42\71 50.7042
29\49 50.7289
45\76 50.7519
16\27 50.79365
35\59 50.8475
19\32 50.8929
22\37 50.96525
3\5 51.4286

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.