13edf

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13edf

14edf →

Prime factorization	13 (prime)
Step size	53.9965 ¢
Octave	22\13edf (1187.92 ¢)
Twelfth	35\13edf (1889.88 ¢)
Consistency limit	4
Distinct consistency limit	4

13EDF is the equal division of the just perfect fifth into 13 parts of 53.9965 cents each, corresponding to 22.2236 edo. It is nearly identical to every ninth step of 200edo.

Harmonics

Approximation of prime harmonics in 13edf

Harmonic		2	3	5	7	11	13	17	19
Error	Absolute (¢)	-12.1	-12.1	+21.5	-21.0	+6.4	-12.8	+8.7	-21.8
	Relative (%)	-22.4	-22.4	+39.8	-39.0	+11.9	-23.7	+16.2	-40.4
Steps (reduced)		22 (9)	35 (9)	52 (0)	62 (10)	77 (12)	82 (4)	91 (0)	94 (3)

Approximation of prime harmonics in 13edf

Harmonic		23	29	31	37	41	43	47	53
Error	Absolute (¢)	+25.4	+2.0	-5.4	+12.3	-3.5	+22.1	-23.9	-15.9
	Relative (%)	+47.0	+3.8	-10.0	+22.7	-6.4	+40.9	-44.3	-29.5
Steps (reduced)		101 (10)	108 (4)	110 (6)	116 (12)	119 (2)	121 (4)	123 (6)	127 (10)

Intervals

Intervals of 13edf

degree	cents value	corresponding JI intervals	comments
0		exact 1/1
1	53.9965	33/32	pseudo-25/24
2	107.9931	17/16, 117/110, 16/15
3	161.9896	11/10
4	215.9862	17/15
5	269.9827	7/6
6	323.9792	77/64	pseudo-6/5
7	377.9758	56/45	pseudo-5/4
8	431.9723	9/7
9	485.9688	45/34	pseudo-4/3
10	539.9654	15/11
11	593.9619	55/39, 24/17
12	647.9585	16/11
13	701.9550	exact 3/2	just perfect fifth
14	755.9515	99/64
15	809.9481	51/32, 8/5
16	863.9446	33/20
17	917.9412	17/10
18	971.9377	7/4
19	1025.9342	29/16	pseudo-9/5
20	1079.9308	28/15	pseudo-15/8
21	1133.9273	52/27, 27/14
22	1187.9238	135/68	pseudo-octave
23	1241.9204	45/22
24	1295.9169	19/9, 36/17
25	1349.9135	24/11
26	1403.9100	exact 9/4	pythagorean major ninth

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