84ed7/3

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Prime factorization	22 × 3 × 7
Step size	17.4627¢
Octave	69\84ed7/3 (1204.93¢) (→23\28ed7/3)
Twelfth	109\84ed7/3 (1903.44¢)
Consistency limit	3
Distinct consistency limit	3

84 equal divisions of 7/3 (abbreviated 84ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 84 equal parts of about 17.5 ¢ each. Each step represents a frequency ratio of (7/3)^1/84, or the 84th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	17.463
2	34.925
3	52.388	34/33, 35/34
4	69.851	25/24
5	87.314	41/39
6	104.776	35/33
7	122.239	15/14, 29/27
8	139.702	38/35
9	157.165	23/21
10	174.627	21/19
11	192.09	19/17, 29/26
12	209.553	26/23
13	227.016
14	244.478	38/33
15	261.941
16	279.404	27/23
17	296.867
18	314.329	6/5
19	331.792	23/19
20	349.255	11/9
21	366.718	21/17, 26/21
22	384.18	5/4
23	401.643	29/23, 34/27
24	419.106	14/11, 37/29
25	436.569	9/7
26	454.031
27	471.494
28	488.957
29	506.42
30	523.882	23/17
31	541.345	26/19
32	558.808	29/21
33	576.271
34	593.733	38/27
35	611.196	27/19, 37/26
36	628.659	36/25
37	646.122
38	663.584	22/15
39	681.047
40	698.51
41	715.973
42	733.435	26/17, 29/19
43	750.898	17/11
44	768.361
45	785.824	41/26
46	803.286	27/17, 35/22
47	820.749	37/23
48	838.212
49	855.675
50	873.137
51	890.6
52	908.063
53	925.526	29/17
54	942.988
55	960.451
56	977.914	37/21
57	995.377
58	1012.839
59	1030.302
60	1047.765	11/6
61	1065.228
62	1082.69	28/15
63	1100.153	17/9
64	1117.616	21/11
65	1135.079	27/14
66	1152.541	35/18, 37/19
67	1170.004
68	1187.467
69	1204.93
70	1222.392
71	1239.855
72	1257.318
73	1274.781	23/11
74	1292.243	19/9
75	1309.706
76	1327.169
77	1344.632	37/17
78	1362.094	11/5
79	1379.557
80	1397.02
81	1414.483	34/15
82	1431.945
83	1449.408
84	1466.871	7/3

Harmonics

Approximation of harmonics in 84ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+4.93	+1.48	-7.60	+7.73	+6.41	+1.48	-2.67	+2.97	-4.81	+4.82	-6.12
	Relative (%)	+28.2	+8.5	-43.5	+44.2	+36.7	+8.5	-15.3	+17.0	-27.5	+27.6	-35.0
Steps (reduced)		69 (69)	109 (25)	137 (53)	160 (76)	178 (10)	193 (25)	206 (38)	218 (50)	228 (60)	238 (70)	246 (78)

Approximation of harmonics in 84ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-4.99	+6.41	-8.25	+2.26	+2.08	+7.90	+1.61	+0.12	+2.97	-7.72	+2.64
	Relative (%)	-28.6	+36.7	-47.3	+12.9	+11.9	+45.2	+9.2	+0.7	+17.0	-44.2	+15.1
Steps (reduced)		254 (2)	262 (10)	268 (16)	275 (23)	281 (29)	287 (35)	292 (40)	297 (45)	302 (50)	306 (54)	311 (59)