50ed7/3

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50ed7/3

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Prime factorization	2 × 52
Step size	29.3374¢
Octave	41\50ed7/3 (1202.83¢)
Twelfth	65\50ed7/3 (1906.93¢) (→13\10ed7/3)
Consistency limit	12
Distinct consistency limit	8

50 equal divisions of 7/3 (abbreviated 50ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 50 equal parts of about 29.3 ¢ each. Each step represents a frequency ratio of (7/3)^1/50, or the 50th root of 7/3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	29.337
2	58.675	28/27, 29/28, 30/29, 31/30, 32/31
3	88.012	20/19, 21/20
4	117.35	15/14, 31/29
5	146.687	12/11, 25/23
6	176.025	21/19, 31/28
7	205.362	9/8
8	234.699	8/7, 31/27
9	264.037	7/6
10	293.374	19/16, 32/27
11	322.712	29/24
12	352.049	11/9, 27/22
13	381.386	5/4
14	410.724	19/15
15	440.061	9/7, 31/24
16	469.399	17/13, 21/16
17	498.736	4/3
18	528.074	19/14, 23/17
19	557.411	29/21
20	586.748	7/5
21	616.086	10/7
22	645.423	16/11, 29/20
23	674.761	28/19, 31/21
24	704.098	3/2
25	733.435	26/17, 29/19, 32/21
26	762.773	14/9, 31/20
27	792.11	19/12, 30/19
28	821.448	29/18
29	850.785	18/11, 31/19
30	880.123	5/3
31	909.46	27/16
32	938.797	31/18
33	968.135	7/4
34	997.472	16/9
35	1026.81	29/16
36	1056.147
37	1085.484	15/8, 28/15
38	1114.822	19/10, 21/11
39	1144.159	29/15, 31/16
40	1173.497
41	1202.834	2/1
42	1232.172
43	1261.509	29/14, 31/15
44	1290.846	19/9
45	1320.184	15/7
46	1349.521	24/11
47	1378.859	20/9, 31/14
48	1408.196	9/4
49	1437.533	23/10
50	1466.871	7/3

Harmonics

Approximation of harmonics in 50ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+2.8	+5.0	+5.7	+0.7	+7.8	+5.0	+8.5	+10.0	+3.6	+14.6	+10.6
	Relative (%)	+9.7	+17.0	+19.3	+2.5	+26.6	+17.0	+29.0	+33.9	+12.2	+49.8	+36.3
Steps (reduced)		41 (41)	65 (15)	82 (32)	95 (45)	106 (6)	115 (15)	123 (23)	130 (30)	136 (36)	142 (42)	147 (47)

Approximation of harmonics in 50ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-10.6	+7.8	+5.7	+11.3	-5.6	+12.8	+7.2	+6.4	+10.0	-11.9	-0.9
	Relative (%)	-36.1	+26.6	+19.5	+38.6	-19.1	+43.6	+24.5	+21.8	+33.9	-40.6	-2.9
Steps (reduced)		151 (1)	156 (6)	160 (10)	164 (14)	167 (17)	171 (21)	174 (24)	177 (27)	180 (30)	182 (32)	185 (35)