26edf

← 25edf

26edf

27edf →

Prime factorization	2 × 13
Step size	26.9983 ¢
Octave	44\26edf (1187.92 ¢) (→ 22\13edf)
Twelfth	70\26edf (1889.88 ¢) (→ 35\13edf)
Consistency limit	3
Distinct consistency limit	3

26EDF is the equal division of the just perfect fifth into 26 parts of 26.9983 cents each, corresponding to 44.4473 edo. It is nearly identical to every ninth step of 400edo.

Commas tempered by this tuning

7-limit: 50/49, 36/35, 126/125

11-limit: 56/55, 80/77, 99/98, 100/99, 128/121

17-limit: 52/51

Tempering out these commas results in the following equivalencies:

7/5~10/7

7/6~6/5

10/7~36/25

11/8~7/5

49/40~14/11

14/11~9/7

9/8~25/22

33/32~12/11

17/13~4/3

Harmonics

Approximation of harmonics in 26edf

Harmonic		2	3	4	5	6	7	8	9
Error	Absolute (¢)	-12.1	-12.1	+2.8	-5.5	+2.8	+6.0	-9.2	+2.8
	Relative (%)	-44.7	-44.7	+10.5	-20.3	+10.5	+22.1	-34.2	+10.5
Steps (reduced)		44 (18)	70 (18)	89 (11)	103 (25)	115 (11)	125 (21)	133 (3)	141 (11)

(contd.)

Harmonic		10	11	12	13	14	15	16	17
Error	Absolute (¢)	+9.4	+6.4	-9.2	-12.8	-6.1	+9.4	+5.7	+8.7
	Relative (%)	+34.9	+23.8	-34.2	-47.5	-22.7	+34.9	+21.1	+32.3
Steps (reduced)		148 (18)	154 (24)	159 (3)	164 (8)	169 (13)	174 (18)	178 (22)	182 (0)

Intervals

Intervals of 26edf

degree	cents value	corresponding JI intervals	comments
0		exact 1/1
1	26.9983	66/65, 65/64, 64/63
2	53.9965	33/32, 98/95
3	80.9948	22/21
4	107.9931	16/15
5	134.9913
6	161.9896
7	188.9879	135/121
8	215.9862	17/15
9	242.9844
10	269.9827	7/6
11	296.981	32/27, 19/16
12	323.9792		pseudo-6/5
13	350.9775	60/49, 49/40
14	377.9758		pseudo-5/4
15	404.974	24/19
16	431.9723
17	458.9706
18	485.9688	45/34	pseudo-4/3
19	512.9671	121/90
20	539.9654
21	566.9637
22	593.9619
23	620.9602	63/44
24	647.9585	16/11
25	674.9567
26	701.955	exact 3/2	just perfect fifth
27	728.9533	99/65, 195/128, 21/16
28	755.9515	99/64, 147/95
29	782.9498	11/7
30	809.9481	8/5
31	836.9463
32	863.9446
33	890.9429	405/242	pseudo-5/3
34	917.9412	17/10
35	944.9394
36	971.9377	7/4
37	998.936	16/9, 57/32
38	1025.9342		pseudo-9/5
39	1052.9325	90/49, 147/80
40	1079.9308		pseudo-15/8
41	1106.929
42	1133.9273
43	1160.9256
44	1187.9238	135/98	pseudo-2/1
45	1214.9221	121/60
46	1241.9204
47	1268.9187
48	1295.9169
49	1322.9152	189/88
50	1349.9135	24/11
51	1376.9117
52	1403.91	exact 9/4

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