11edf

← 10edf

11edf

12edf →

Prime factorization	11 (prime)
Step size	63.8141¢
Octave	19\11edf (1212.47¢)
Twelfth	30\11edf (1914.42¢)
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	comments
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)

Fifth							Cents	Comments
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.