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	17.5
2	34.9
3	52.4	34/33, 35/34
4	69.9	25/24
5	87.3	41/39
6	104.8	35/33
7	122.2	15/14, 29/27
8	139.7	38/35
9	157.2	23/21
10	174.6	21/19
11	192.1	19/17, 29/26
12	209.6	26/23
13	227
14	244.5	38/33
15	261.9
16	279.4	27/23
17	296.9
18	314.3	6/5
19	331.8	23/19
20	349.3	11/9
21	366.7	21/17, 26/21
22	384.2	5/4
23	401.6	29/23, 34/27
24	419.1	14/11, 37/29
25	436.6	9/7
26	454
27	471.5
28	489
29	506.4
30	523.9	23/17
31	541.3	26/19
32	558.8	29/21
33	576.3
34	593.7	38/27
35	611.2	27/19, 37/26
36	628.7	36/25
37	646.1
38	663.6	22/15
39	681
40	698.5
41	716
42	733.4	26/17, 29/19
43	750.9	17/11
44	768.4
45	785.8	41/26
46	803.3	27/17, 35/22
47	820.7	37/23
48	838.2
49	855.7
50	873.1
51	890.6
52	908.1
53	925.5	29/17
54	943
55	960.5
56	977.9	37/21
57	995.4
58	1012.8
59	1030.3
60	1047.8	11/6
61	1065.2
62	1082.7	28/15
63	1100.2	17/9
64	1117.6	21/11
65	1135.1	27/14
66	1152.5	35/18, 37/19
67	1170
68	1187.5
69	1204.9
70	1222.4
71	1239.9
72	1257.3
73	1274.8	23/11
74	1292.2	19/9
75	1309.7
76	1327.2
77	1344.6	37/17
78	1362.1	11/5
79	1379.6
80	1397
81	1414.5	34/15
82	1431.9
83	1449.4
84	1466.9	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)