平均律误差

以下为各平均律在各奇数限的误差，平均律对纯律音程的逼近方式为规则调律逼近(而非直接取整)。

2.3.7、2.3.9.11等子群的误差指的是，对于列举出来的数字互相之间形成的有理数误差中，最大的一组的误差是多少音分（如2.3.7包括3/2 7/2 7/3）。

平均律	3奇数限	5奇数限	2.3.7	7奇数限	9奇数限	2.3.9.11	2.3.5.9.11	11奇数限	2.3.5.9.13	2.3.5.7.9.13	13奇数限	15奇数限	17奇数限	19奇数限	21奇数限
1	498.04	884.36	498.04	884.36	1382.40	1547.41	1547.41	1547.41	1382.40	1382.40	1547.41	1547.41	1547.41	1547.41	1547.41
2	101.96	315.64	333.13	333.13	435.08	252.59	417.60	435.08	454.21	471.70	471.70	471.70	471.70	528.69	528.69
3	98.04	98.04	266.87	266.87	364.92	347.41	347.41	364.92	236.62	364.92	364.92	364.92	364.92	364.92	364.92
4	101.96	101.96	101.96	101.96	203.91	252.59	252.59	252.59	263.38	263.38	263.38	263.38	263.38	263.38	263.38
5	18.04	93.69	26.87	102.51	102.51	107.41	165.00	165.00	119.47	128.30	190.79	190.79	224.43	224.43	224.43
6	98.04	98.04	98.04	98.04	196.09	196.09	196.09	196.09	236.62	236.62	236.62	236.62	236.62	293.60	293.60
7	16.24	43.46	75.99	103.20	103.20	37.03	43.46	103.20	60.07	103.20	103.20	119.44	126.17	126.17	126.17
9	35.29	48.97	35.49	49.18	84.26	70.58	84.26	84.26	84.26	84.26	84.26	84.26	98.95	98.95	99.16
10	18.04	44.36	26.87	44.36	62.40	48.68	75.00	75.00	62.40	62.40	75.00	75.00	75.00	106.20	106.20
12	1.96	15.64	33.13	33.13	35.08	52.59	52.59	52.59	54.21	71.70	89.21	89.21	89.21	89.21	89.21
14	16.24	58.50	25.97	68.23	74.74	37.03	79.29	79.29	74.74	74.74	79.29	79.29	79.29	82.63	84.47
15	18.04	18.04	26.87	26.87	44.92	36.09	36.09	44.92	39.47	48.30	48.30	48.30	64.43	64.43	64.43
16	26.96	26.96	33.13	33.13	60.08	53.91	53.91	60.08	53.91	60.08	60.08	60.08	60.08	60.08	60.08
17	3.93	37.30	19.41	52.78	52.78	13.39	46.76	52.78	41.23	52.78	52.78	52.78	53.78	53.78	57.70
19	7.22	7.37	21.46	21.46	21.46	31.54	31.54	38.56	19.48	21.46	38.56	38.56	42.82	42.82	50.04
21	16.24	29.93	18.84	29.93	46.17	52.59	52.59	52.59	49.10	49.10	52.59	52.59	52.59	52.59	52.59
22	7.14	11.63	12.99	17.49	18.77	20.14	20.14	20.14	36.62	36.62	36.62	36.62	36.62	39.06	44.91
24	1.96	15.64	18.83	32.51	32.51	3.91	17.60	32.51	17.60	32.51	32.51	32.51	32.51	32.51	34.47
26	9.65	17.08	10.05	17.49	19.70	21.82	21.82	21.82	19.29	19.70	21.82	29.26	29.26	29.26	29.26
27	9.16	13.69	9.16	13.69	18.31	36.30	36.30	36.30	18.31	18.31	36.30	40.83	40.83	40.83	40.83
29	1.49	15.39	18.60	18.60	20.09	16.37	16.89	20.09	16.89	20.09	20.09	20.09	36.28	36.28	36.28
31	5.18	5.96	5.18	5.96	11.14	10.36	11.14	11.14	21.45	21.45	21.45	21.45	21.54	22.53	22.53
34	3.93	3.93	19.81	19.81	23.74	13.39	13.39	29.27	7.85	23.74	29.27	29.27	29.27	29.27	29.27
36	1.96	15.64	2.16	15.85	17.60	19.26	19.26	19.26	20.88	20.88	22.54	22.54	22.54	22.54	22.54
41	0.48	6.31	3.46	6.31	6.79	4.78	10.61	10.61	14.08	14.08	14.08	14.08	17.94	17.94	17.94
43	4.28	8.66	12.20	12.20	16.48	15.38	15.38	16.48	12.95	16.48	16.48	16.48	16.48	18.02	18.02
46	2.39	4.99	6.00	8.60	8.60	8.28	8.48	8.60	10.74	10.74	10.74	13.13	13.13	17.94	17.94
50	5.96	5.96	8.83	8.83	11.91	12.59	12.59	12.59	11.91	11.91	12.59	12.59	12.59	12.59	15.46
53	0.07	1.41	4.83	6.17	6.17	7.92	7.92	12.68	2.79	7.55	12.68	12.68	16.17	16.17	16.17
58	1.49	6.79	3.59	6.79	6.79	7.30	7.30	7.30	7.75	7.75	7.75	8.28	9.79	16.14	16.14
62	5.18	5.96	5.18	5.96	11.14	10.36	11.14	11.14	11.14	11.14	11.14	11.14	11.14	11.14	11.14
65	0.42	1.80	8.83	10.20	10.20	3.36	3.36	11.35	9.54	17.53	17.53	17.53	17.53	17.53	17.95
68	3.93	3.93	3.93	3.93	7.85	12.11	12.11	12.11	7.85	7.85	12.11	12.11	12.11	12.11	12.11
72	1.96	2.98	2.16	2.98	3.91	3.91	3.91	3.91	7.19	7.19	7.19	7.19	7.19	9.68	9.68
77	0.66	3.95	2.59	5.89	5.89	5.86	9.16	9.16	4.61	5.89	9.16	9.16	10.00	10.00	10.00
80	3.04	3.69	6.17	6.17	6.17	6.09	6.09	6.17	6.62	6.70	6.70	7.26	7.26	7.26	9.75
87	1.49	1.60	4.80	4.80	6.30	2.99	3.09	6.30	3.09	6.30	6.30	6.30	8.70	9.24	9.24
94	0.17	3.51	1.39	4.72	4.72	2.73	3.68	4.72	5.36	5.36	5.36	5.36	5.36	5.92	5.92
99	1.08	1.57	1.08	1.57	2.15	8.01	8.01	8.01	6.31	6.31	8.01	8.50	10.00	11.38	11.38

以下是误差用ie值的表示，数值越大，误差越小：

平均律	3奇数限	5奇数限	2.3.7	7奇数限	9奇数限	2.3.9.11	2.3.5.9.11	11奇数限	2.3.5.9.13	2.3.5.7.9.13	13奇数限	15奇数限	17奇数限	19奇数限	21奇数限
1	3.48	1.96	3.48	1.96	1.25	1.12	1.12	1.12	1.25	1.25	1.12	1.12	1.12	1.12	1.12
2	16.98	5.48	5.20	5.20	3.98	6.85	4.15	3.98	3.81	3.67	3.67	3.67	3.67	3.27	3.27
3	17.66	17.66	6.49	6.49	4.74	4.98	4.98	4.74	7.32	4.74	4.74	4.74	4.74	4.74	4.74
4	16.98	16.98	16.98	16.98	8.49	6.85	6.85	6.85	6.57	6.57	6.57	6.57	6.57	6.57	6.57
5	95.94	18.48	64.43	16.89	16.89	16.12	10.49	10.49	14.49	13.49	9.07	9.07	7.71	7.71	7.71
6	17.66	17.66	17.66	17.66	8.83	8.83	8.83	8.83	7.32	7.32	7.32	7.32	7.32	5.90	5.90
7	106.60	39.84	22.78	16.78	16.78	46.75	39.84	16.78	28.82	16.78	16.78	14.49	13.72	13.72	13.72
9	49.06	35.35	48.78	35.20	20.55	24.53	20.55	20.55	20.55	20.55	20.55	20.55	17.50	17.50	17.46
10	95.94	39.03	64.43	39.03	27.74	35.56	23.08	23.08	27.74	27.74	23.08	23.08	23.08	16.30	16.30
12	885.54	110.68	52.26	52.26	49.35	32.92	32.92	32.92	31.93	24.14	19.41	19.41	19.41	19.41	19.41
14	106.60	29.59	66.67	25.37	23.16	46.75	21.83	21.83	23.16	23.16	21.83	21.83	21.83	20.95	20.50
15	95.94	95.94	64.43	64.43	38.54	47.97	47.97	38.54	43.86	35.84	35.84	35.84	26.87	26.87	26.87
16	64.23	64.23	52.26	52.26	28.81	32.11	32.11	28.81	32.11	28.81	28.81	28.81	28.81	28.81	28.81
17	440.81	46.41	89.20	32.80	32.80	129.31	37.02	32.80	41.99	32.80	32.80	32.80	32.19	32.19	30.00
19	239.84	235.02	80.68	80.68	80.68	54.89	54.89	44.90	88.90	80.68	44.90	44.90	40.43	40.43	34.60
21	106.60	57.85	91.87	57.85	37.50	32.92	32.92	32.92	35.26	35.26	32.92	32.92	32.92	32.92	32.92
22	242.61	148.84	133.25	99.00	92.25	85.98	85.98	85.98	47.28	47.28	47.28	47.28	47.28	44.33	38.55
24	885.54	110.68	91.96	53.25	53.25	442.77	98.39	53.25	98.39	53.25	53.25	53.25	53.25	53.25	50.23
26	179.45	101.34	172.22	99.00	87.88	79.33	79.33	79.33	89.73	87.88	79.33	59.17	59.17	59.17	59.17
27	189.08	126.49	189.08	126.49	94.54	47.70	47.70	47.70	94.54	94.54	47.70	42.40	42.40	42.40	42.40
29	1159.35	112.47	93.10	93.10	86.18	105.73	102.52	86.18	102.52	86.18	86.18	86.18	47.71	47.71	47.71
31	334.16	290.29	334.16	290.29	155.34	167.08	155.34	155.34	80.72	80.72	80.72	80.72	80.39	76.85	76.85
34	440.81	440.81	87.38	87.38	72.93	129.31	129.31	59.14	220.41	72.93	59.14	59.14	59.14	59.14	59.14
36	885.54	110.68	801.78	109.26	98.39	89.89	89.89	89.89	82.91	82.91	76.80	76.80	76.80	76.80	76.80
41	3576.76	274.37	500.90	274.37	254.82	362.21	163.24	163.24	122.97	122.97	122.97	122.97	96.48	96.48	96.48
43	404.44	199.81	141.92	141.92	105.05	112.54	112.54	105.05	133.74	105.05	105.05	105.05	105.05	96.05	96.05
46	723.51	346.90	288.47	201.33	201.33	209.15	204.10	201.33	161.26	161.26	161.26	131.87	131.87	96.50	96.50
50	290.72	290.72	196.15	196.15	145.36	137.49	137.49	137.49	145.36	145.36	137.49	137.49	137.49	137.49	111.96
53	25381.53	1229.52	358.64	280.72	280.72	218.54	218.54	136.52	620.11	229.28	136.52	136.52	107.04	107.04	107.04
58	1159.35	254.98	482.52	254.98	254.98	237.07	237.07	237.07	223.44	223.44	223.44	209.01	176.83	107.26	107.26
62	334.16	290.29	334.16	290.29	155.34	167.08	155.34	155.34	155.34	155.34	155.34	155.34	155.34	155.34	155.34
65	4156.23	964.40	196.15	169.65	169.65	515.05	515.05	152.48	181.54	98.76	98.76	98.76	98.76	98.76	96.47
68	440.81	440.81	440.81	440.81	220.41	142.91	142.91	142.91	220.41	220.41	142.91	142.91	142.91	142.91	142.91
72	885.54	580.88	801.78	580.88	442.77	442.77	442.77	442.77	240.64	240.64	240.64	240.64	240.64	178.82	178.82
77	2637.87	437.96	667.88	293.99	293.99	295.26	189.00	189.00	375.60	293.99	189.00	189.00	173.14	173.14	173.14
80	568.55	469.64	280.40	280.40	280.40	284.27	284.27	280.40	261.61	258.33	258.33	238.50	238.50	238.50	177.62
87	1159.35	1081.96	360.53	360.53	275.01	579.68	559.66	275.01	559.66	275.01	275.01	275.01	199.04	187.28	187.28
94	10026.91	493.56	1248.31	366.64	366.64	634.83	470.40	366.64	322.96	322.96	322.96	322.96	322.96	292.36	292.36
99	1610.00	1106.17	1610.00	1106.17	805.00	216.03	216.03	216.03	274.16	274.16	216.03	203.58	173.14	152.12	152.12