50edf

← 49edf

50edf

51edf →

Prime factorization	2 × 52
Step size	14.0391 ¢
Octave	85\50edf (1193.32 ¢) (→ 17\10edf)
Twelfth	135\50edf (1895.28 ¢) (→ 27\10edf)
Consistency limit	3
Distinct consistency limit	3

50EDF is the equal division of the just perfect fifth into 50 parts of 14.0391 cents each, corresponding to 85.4756 edo (similar to every second step of 171edo). It is related to the delta scale, but with the 3/2 rather than the classic diatonic semitone (16/15) being just.

Just intervals 5/4 and 6/5 fall exactly halfway between adjacent steps in 50EDF (just 5/4 between 27 and 28 degrees and just 6/5 between 22 and 23 degrees) respectively.

Lookalikes: Delta scale

Steps	Cents	Approximate ratios
0	0	1/1
1	14
2	28.1
3	42.1
4	56.2
5	70.2	26/25
6	84.2	22/21
7	98.3
8	112.3	31/29
9	126.4	14/13
10	140.4
11	154.4
12	168.5	21/19
13	182.5	10/9
14	196.5	19/17, 28/25
15	210.6
16	224.6
17	238.7
18	252.7	22/19
19	266.7
20	280.8
21	294.8
22	308.9	31/26
23	322.9
24	336.9	17/14
25	351
26	365	21/17, 26/21
27	379.1
28	393.1
29	407.1
30	421.2
31	435.2
32	449.3	22/17
33	463.3	17/13
34	477.3	29/22
35	491.4
36	505.4
37	519.4	27/20
38	533.5	19/14
39	547.5
40	561.6	29/21
41	575.6
42	589.6	31/22
43	603.7
44	617.7
45	631.8
46	645.8
47	659.8	19/13
48	673.9	31/21
49	687.9
50	702	3/2

Harmonics

Approximation of harmonics in 50edf

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-6.68	-6.68	+0.69	-6.57	+0.69	+0.56	-5.99	+0.69	+0.79	+4.26	-5.99
	Relative (%)	-47.6	-47.6	+4.9	-46.8	+4.9	+4.0	-42.7	+4.9	+5.6	+30.3	-42.7
Steps (reduced)		85 (35)	135 (35)	171 (21)	198 (48)	221 (21)	240 (40)	256 (6)	271 (21)	284 (34)	296 (46)	306 (6)

Approximation of harmonics in 50edf

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-4.17	-6.12	+0.79	+1.37	-5.31	-5.99	-1.32	-5.89	-6.12	-2.42	+4.86
	Relative (%)	-29.7	-43.6	+5.6	+9.8	-37.8	-42.7	-9.4	-41.9	-43.6	-17.2	+34.6
Steps (reduced)		316 (16)	325 (25)	334 (34)	342 (42)	349 (49)	356 (6)	363 (13)	369 (19)	375 (25)	381 (31)	387 (37)