14edf

← 13edf

14edf

15edf →

Prime factorization	2 × 7
Step size	50.1396¢
Octave	24\14edf (1203.35¢) (→12\7edf)
Twelfth	38\14edf (1905.31¢) (→19\7edf)
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

Intervals

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)

Fifth							Cents	Comments
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.