Relative errors of small EDOs

This article contains two lists. The first shows relative errors of the first 9 prime harmonics for EDOs up to 99. There is no point for showing higher primes because no EDO under 99 is consistent up to them. For other intervals, the relative error follows the additive rule, so they can be derived easily.

The second shows the TE simple badnesses aka relative errors in a certain JI subgroup for EDOs up to 99.

List of relative errors of prime harmonics for small EDOs

EDO	Relative Errors (Percent)
	3/1	5/1	7/1	11/1	13/1	17/1	19/1	23/1
1	41.50	-32.19	19.26	-45.94	29.96	-8.75	-24.79	47.64
2	-16.99	35.61	38.53	8.11	-40.09	-17.49	-49.59	-4.71
3	24.51	3.42	-42.21	-37.83	-10.13	-26.24	25.62	42.93
4	-33.99	-28.77	-22.94	16.23	19.82	-34.99	0.83	-9.42
5	7.52	39.04	-3.68	-29.72	49.78	-43.73	-23.96	38.22
6	49.02	6.84	15.59	24.34	-20.26	47.52	-48.76	-14.14
7	-9.47	-25.35	34.85	-21.60	9.69	38.78	26.45	33.51
8	32.03	42.46	-45.88	32.45	39.65	30.03	1.66	-18.85
9	-26.47	10.26	-26.62	-13.49	-30.40	21.28	-23.13	28.79
10	15.04	-21.93	-7.35	40.57	-0.44	12.54	-47.93	-23.56
11	-43.46	45.88	11.91	-5.37	29.52	3.79	27.28	24.08
12	-1.96	13.69	31.17	48.68	-40.53	-4.96	2.49	-28.27
13	39.55	-18.51	-49.56	2.74	-10.57	-13.70	-22.31	19.37
14	-18.95	49.30	-30.30	-43.20	19.38	-22.45	-47.10	-32.99
15	22.56	17.11	-11.03	10.85	49.34	-31.19	28.11	14.66
16	-35.94	-15.08	8.23	-35.09	-20.70	-39.94	3.32	-37.70
17	5.56	-47.28	27.50	18.97	9.25	-48.69	-21.48	9.94
18	47.07	20.53	46.76	-26.98	39.21	42.57	-46.27	-42.41
19	-11.43	-11.66	-33.97	27.08	-30.84	33.82	28.94	5.23
20	30.07	-43.86	-14.71	-18.86	-0.88	25.07	4.14	-47.12
21	-28.42	23.95	4.55	35.19	29.08	16.33	-20.65	0.52
22	13.08	-8.24	23.82	-10.75	-40.97	7.58	-45.44	48.16
23	-45.41	-40.43	43.08	43.31	-11.01	-1.16	29.77	-4.19
24	-3.91	27.37	-37.65	-2.64	18.94	-9.91	4.97	43.45
25	37.59	-4.82	-18.39	-48.58	48.90	-18.66	-19.82	-8.90
26	-20.90	-37.01	0.88	5.48	-21.14	-27.40	-44.61	38.74
27	20.60	30.79	20.14	-40.47	8.81	-36.15	30.60	-13.62
28	-37.90	-1.40	39.41	13.59	38.77	-44.90	5.80	34.03
29	3.61	-33.59	-41.33	-32.35	-31.28	46.36	-18.99	-18.33
30	45.11	34.22	-22.06	21.71	-1.32	37.61	-43.78	29.31
31	-13.38	2.02	-2.80	-24.24	28.64	28.87	31.42	-23.04
32	28.12	-30.17	16.46	29.82	-41.41	20.12	6.63	24.60
33	-30.38	37.64	35.73	-16.12	-11.45	11.37	-18.16	-27.75
34	11.13	5.44	-45.01	37.93	18.50	2.63	-42.95	19.89
35	-47.37	-26.75	-25.74	-8.01	48.46	-6.12	32.25	-32.47
36	-5.87	41.06	-6.48	46.05	-21.58	-14.87	7.46	15.18
37	35.64	8.87	12.79	0.10	8.37	-23.61	-17.33	-37.18
38	-22.86	-23.33	32.05	-45.84	38.33	-32.36	-42.12	10.46
39	18.65	44.48	-48.68	8.22	-31.71	-41.11	33.08	-41.89
40	-39.85	12.29	-29.42	-37.73	-1.76	-49.85	8.29	5.75
41	1.65	-19.91	-10.16	16.33	28.20	41.40	-16.50	-46.60
42	43.16	47.90	9.11	-29.61	-41.85	32.66	-41.30	1.04
43	-15.34	15.71	28.37	24.44	-11.89	23.91	33.91	48.68
44	26.16	-16.48	47.64	-21.50	18.07	15.16	9.12	-3.67
45	-32.33	-48.68	-33.10	32.56	48.02	6.42	-15.67	43.97
46	9.17	19.13	-13.83	-13.39	-22.02	-2.33	-40.47	-8.38
47	-49.32	-13.06	5.43	40.67	7.93	-11.08	34.74	39.26
48	-7.82	-45.25	24.70	-5.27	37.89	-19.82	9.95	-13.10
49	33.68	22.55	43.96	48.79	-32.15	-28.57	-14.84	34.55
50	-24.81	-9.64	-36.77	2.84	-2.20	-37.31	-39.64	-17.81
51	16.69	-41.83	-17.51	-43.10	27.76	-46.06	35.57	29.83
52	-41.81	25.97	1.75	10.96	-42.29	45.19	10.78	-22.52
53	-0.30	-6.22	21.02	-34.99	-12.33	36.45	-14.02	25.12
54	41.20	-38.41	40.28	19.07	17.63	27.70	-38.81	-27.23
55	-17.29	29.40	-40.45	-26.87	47.58	18.95	36.40	20.41
56	24.21	-2.80	-21.19	27.18	-22.46	10.21	11.61	-31.95
57	-34.29	-34.99	-1.92	-18.76	7.49	1.46	-13.19	15.70
58	7.22	32.82	17.34	35.30	37.45	-7.28	-37.98	-36.66
59	48.72	0.62	36.61	-10.65	-32.59	-16.03	37.23	10.98
60	-9.78	-31.57	-44.13	43.41	-2.64	-24.78	12.43	-41.37
61	31.73	36.24	-24.87	-2.53	27.32	-33.52	-12.36	6.27
62	-26.77	4.05	-5.60	-48.48	-42.73	-42.27	-37.15	-46.08
63	14.74	-28.15	13.66	5.58	-12.77	48.98	38.06	1.56
64	-43.76	39.66	32.93	-40.36	17.19	40.24	13.26	49.20
65	-2.26	7.47	-47.81	13.69	47.14	31.49	-11.53	-3.15
66	39.25	-24.73	-28.54	-32.25	-22.90	22.75	-36.32	44.49
67	-19.25	43.08	-9.28	21.81	7.05	14.00	38.89	-7.87
68	22.25	10.89	9.99	-24.14	37.01	5.25	14.09	39.78
69	-36.24	-21.30	29.25	29.92	-33.03	-3.49	-10.70	-12.58
70	5.26	46.50	48.52	-16.02	-3.08	-12.24	-35.49	35.07
71	46.77	14.31	-32.22	38.04	26.88	-20.99	39.71	-17.29
72	-11.73	-17.88	-12.96	-7.91	-43.17	-29.73	14.92	30.35
73	29.77	49.92	6.31	46.15	-13.21	-38.48	-9.87	-22.00
74	-28.72	17.73	25.57	0.21	16.75	-47.23	-34.66	25.64
75	12.78	-14.46	44.84	-45.74	46.70	44.03	40.54	-26.71
76	-45.72	-46.65	-35.90	8.32	-23.34	35.28	15.75	20.93
77	-4.21	21.15	-16.63	-37.62	6.61	26.54	-9.04	-31.43
78	37.29	-11.04	2.63	16.43	36.57	17.79	-33.83	16.22
79	-21.20	-43.23	21.90	-29.51	-33.47	9.04	41.37	-36.14
80	20.30	24.58	41.16	24.55	-3.52	0.30	16.58	11.50
81	-38.20	-7.62	-39.57	-21.40	26.44	-8.45	-8.21	-40.85
82	3.31	-39.81	-20.31	32.66	-43.61	-17.20	-33.01	6.79
83	44.81	28.00	-1.05	-13.28	-13.65	-25.94	42.20	-45.56
84	-13.69	-4.20	18.22	40.77	16.31	-34.69	17.41	2.08
85	27.82	-36.39	37.48	-5.17	46.26	-43.43	-7.38	49.72
86	-30.68	31.42	-43.25	48.89	-23.78	47.82	-32.18	-2.63
87	10.83	-0.77	-23.99	2.94	6.17	39.07	43.03	45.01
88	-47.67	-32.97	-4.72	-43.00	36.13	30.33	18.24	-7.35
89	-6.17	34.84	14.54	11.06	-33.91	21.58	-6.55	40.30
90	35.34	2.65	33.81	-34.88	-3.96	12.83	-31.35	-12.06
91	-23.16	-29.55	-46.93	19.17	26.00	4.09	43.86	35.59
92	18.34	38.26	-27.67	-26.77	-44.05	-4.66	19.07	-16.77
93	-40.15	6.07	-8.40	27.29	-14.09	-13.40	-5.73	30.87
94	1.35	-26.12	10.86	-18.66	15.87	-22.15	-30.52	-21.48
95	42.86	41.68	30.13	35.40	45.82	-30.90	44.69	26.16
96	-15.64	9.49	49.39	-10.54	-24.22	-39.64	19.90	-26.19
97	25.86	-22.70	-31.34	43.51	5.73	-48.39	-4.90	21.45
98	-32.63	45.10	-12.08	-2.43	35.69	42.86	-29.69	-30.91
99	8.87	12.91	7.19	-48.37	-34.35	34.12	45.52	16.74

List of TE simple badnesses for small EDOs

Notes:

1. Patent val mapping is used throughout.
2. Each EDO is TE-optimally stretched.
3. Graham Breed's definition is used, scaled by 100.

EDO	TE simple badness × 100
	3 Limit	5 Limit	7 Limit	11 Limit	13 Limit	17 Limit	19 Limit	23 Limit
1	13.09	16.61	14.43	14.79	13.75	12.83	12.25	11.95
2	5.36	10.69	10.66	9.58	10.37	9.82	10.07	9.50
3	7.73	6.97	10.80	10.68	9.76	9.17	9.04	9.20
4	10.72	8.79	7.73	9.20	9.67	9.02	8.67	8.22
5	2.37	7.08	7.15	8.41	8.72	9.61	9.34	9.11
6	15.46	13.94	12.32	11.08	11.52	10.79	11.89	11.51
7	2.99	4.46	8.72	8.06	7.57	7.97	7.72	7.55
8	10.10	9.11	14.89	13.41	12.35	11.44	10.92	10.81
9	8.35	9.09	8.21	7.37	6.83	7.37	6.91	7.32
10	4.74	7.73	6.79	7.83	7.19	6.68	7.58	7.34
11	13.71	19.34	17.01	15.22	14.29	13.23	12.52	11.88
12	0.62	3.11	4.94	5.99	8.35	7.88	7.40	7.47
13	12.48	14.02	15.79	14.13	12.94	12.03	11.34	10.84
14	5.98	13.72	13.32	12.86	12.12	11.31	10.99	10.44
15	7.12	5.81	6.97	6.25	6.65	7.73	7.29	6.88
16	11.34	9.53	9.91	8.98	8.22	7.67	7.67	7.26
17	1.76	10.52	11.30	10.51	9.65	9.88	9.32	8.88
18	14.85	12.45	10.91	13.03	11.90	11.02	12.37	12.77
19	3.61	3.02	4.35	6.79	6.47	7.40	7.56	7.17
20	9.49	15.46	13.58	12.26	11.21	10.75	10.07	9.99
21	8.97	11.67	10.27	10.30	9.76	9.06	8.80	8.31
22	4.13	4.94	5.23	5.33	6.89	6.42	6.99	7.57
23	14.33	11.79	16.76	17.03	15.55	14.44	13.91	13.12
24	1.23	6.22	8.95	8.01	7.66	7.14	6.70	7.02
25	11.86	11.70	11.76	12.70	12.57	11.89	11.30	10.68
26	6.59	6.96	7.43	7.51	6.86	6.37	6.17	7.45
27	6.50	6.19	5.40	9.37	8.58	9.13	8.70	8.41
28	11.95	11.13	13.62	12.46	12.19	12.00	11.25	10.92
29	1.14	7.41	7.91	7.15	6.54	8.94	8.36	7.89
30	14.23	11.62	13.94	12.51	11.87	11.02	11.82	11.15
31	4.22	4.20	3.70	3.84	5.35	5.75	5.93	5.89
32	8.87	12.60	11.07	10.18	10.85	10.13	9.47	9.00
33	9.58	14.46	13.86	12.72	11.71	10.87	10.30	9.91
34	3.51	2.92	8.67	9.26	8.59	7.96	8.36	8.01
35	14.94	12.31	10.85	10.54	13.06	12.22	12.27	11.61
36	1.85	9.33	8.63	8.76	8.96	8.63	8.08	7.62
37	11.24	9.82	8.70	8.37	7.78	8.21	8.13	8.42
38	7.21	6.04	9.96	9.76	10.64	10.02	9.62	9.30
39	5.88	7.89	13.78	12.34	12.08	11.86	11.42	11.21
40	12.57	13.28	11.62	10.48	9.99	9.43	9.38	9.18
41	0.52	4.31	3.76	4.51	5.29	6.00	5.90	6.59
42	13.61	11.60	11.45	13.33	14.24	13.22	13.36	12.64
43	4.84	6.75	7.56	7.08	6.85	6.49	6.35	6.45
44	8.25	9.89	10.45	10.66	9.74	9.02	8.46	8.11
45	10.20	9.75	8.49	11.84	13.50	12.72	11.90	12.03
46	2.89	3.45	5.12	5.20	5.42	5.02	5.62	5.30
47	15.56	13.54	13.24	14.39	13.38	12.39	12.20	11.98
48	2.47	8.27	10.25	9.22	9.84	9.20	8.71	8.23
49	10.63	8.69	7.87	7.11	10.12	10.85	10.67	10.09
50	7.83	6.62	6.39	6.76	6.54	6.19	5.90	5.62
51	5.27	11.79	10.34	9.93	10.23	9.89	10.15	10.01
52	13.19	15.75	13.86	12.69	12.08	12.33	11.62	11.02
53	0.10	1.22	3.81	5.65	5.22	6.05	5.76	5.75
54	13.00	17.51	15.92	14.24	13.01	12.05	12.31	12.02
55	5.46	9.63	10.57	9.63	10.83	10.23	10.02	9.52
56	7.64	7.50	8.38	7.90	7.95	7.37	6.90	7.07
57	10.82	9.06	9.30	8.47	8.68	8.41	7.92	7.98
58	2.28	5.89	5.10	4.83	4.56	5.33	7.07	7.72
59	15.37	14.43	12.55	12.56	13.10	12.56	11.85	11.19
60	3.08	5.56	6.23	10.22	9.44	8.77	8.54	8.26
61	10.01	8.59	11.66	10.84	9.93	10.38	9.95	9.39
62	8.44	8.40	7.40	7.67	7.28	6.83	6.40	6.09
63	4.65	8.77	8.00	7.17	6.73	7.50	7.41	7.03
64	13.80	18.41	17.26	16.16	14.96	14.36	13.46	13.07
65	0.71	1.94	7.82	7.65	8.94	8.68	8.23	7.77
66	12.38	14.83	14.37	13.50	12.47	11.84	11.36	11.32
67	6.07	12.62	11.18	10.24	9.35	8.67	8.44	8.10
68	7.02	5.84	5.19	6.84	6.75	6.34	5.93	5.81
69	11.43	9.40	12.23	12.30	11.48	10.67	9.98	9.41
70	1.66	8.76	8.63	9.73	9.37	9.21	9.62	9.20
71	14.75	12.71	14.95	13.52	12.34	12.20	11.49	11.25
72	3.70	3.56	3.09	2.96	3.82	3.59	4.57	5.60
73	9.39	9.56	9.59	8.65	9.62	10.93	10.60	10.47
74	9.06	10.80	10.83	9.69	9.02	9.36	9.06	8.88
75	4.03	5.85	8.36	10.29	10.36	9.98	9.51	9.57
76	14.42	12.07	10.57	11.84	11.01	12.28	12.13	11.98
77	1.33	5.04	5.59	6.66	6.25	6.42	6.03	6.03
78	11.76	12.37	10.95	9.80	9.14	8.47	9.09	8.57
79	6.69	7.84	10.49	9.43	8.66	8.64	9.55	9.10
80	6.40	5.59	5.68	5.17	6.01	6.12	5.78	5.56
81	12.05	10.67	9.49	8.65	10.05	9.45	8.94	8.50
82	1.04	8.62	7.52	9.02	8.92	8.26	7.82	7.62
83	14.14	11.58	11.68	11.82	11.53	11.44	10.90	11.25
84	4.32	3.72	5.39	7.02	6.50	7.05	6.70	6.32
85	8.78	13.57	12.98	11.80	11.37	11.76	11.08	10.84
86	9.68	13.50	13.06	14.03	12.95	12.94	12.35	11.64
87	3.42	3.30	5.45	4.90	4.53	5.35	5.77	5.92
88	15.04	12.29	12.05	10.79	12.68	12.94	12.56	11.88
89	1.95	8.15	7.08	6.35	7.57	7.12	6.77	6.77
90	11.15	10.25	9.07	11.10	10.39	9.62	9.75	9.33
91	7.31	6.49	6.51	8.82	9.74	9.28	9.95	9.93
92	5.79	6.91	10.24	10.40	10.83	10.03	9.52	9.06
93	12.67	12.60	11.09	11.46	10.46	9.68	9.09	9.14
94	0.43	5.52	5.74	5.35	5.48	5.28	5.24	4.99
95	13.52	11.23	9.90	8.98	8.20	10.47	9.80	9.34
96	4.93	5.86	9.86	9.14	8.90	8.96	8.59	8.28
97	8.16	10.76	10.97	11.24	10.26	10.60	9.92	9.49
98	10.29	16.34	14.25	12.75	12.32	11.92	11.54	11.15
99	2.80	2.63	2.33	7.27	7.48	7.75	8.09	7.67

See also

• EDO
• Relative error
• Relative errors of small EDTs
• Relative errors of small EDFs
• Relative errors of small ED5s
• Relative errors of small ED6s