98ed7/3

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98ed7/3

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Prime factorization	2 × 72
Step size	14.9681¢
Octave	80\98ed7/3 (1197.45¢) (→40\49ed7/3)
Twelfth	127\98ed7/3 (1900.94¢)
Consistency limit	6
Distinct consistency limit	6

98 equal divisions of 7/3 (abbreviated 98ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 98 equal parts of about 15⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/98, or the 98th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	15
2	29.9
3	44.9	38/37, 39/38
4	59.9	29/28, 30/29
5	74.8
6	89.8	39/37
7	104.8
8	119.7	15/14
9	134.7	27/25
10	149.7	12/11
11	164.6	11/10
12	179.6	41/37
13	194.6	19/17, 28/25
14	209.6	35/31
15	224.5	33/29
16	239.5	31/27, 39/34
17	254.5	29/25
18	269.4
19	284.4	33/28
20	299.4	25/21
21	314.3	6/5
22	329.3	23/19, 29/24
23	344.3
24	359.2
25	374.2	31/25, 36/29
26	389.2
27	404.1	43/34
28	419.1	14/11
29	434.1	9/7
30	449	35/27
31	464	17/13
32	479	29/22, 33/25
33	493.9
34	508.9
35	523.9	23/17, 42/31
36	538.9	15/11
37	553.8	11/8
38	568.8	25/18, 43/31
39	583.8	7/5
40	598.7
41	613.7
42	628.7
43	643.6	29/20, 42/29
44	658.6	19/13
45	673.6	31/21
46	688.5
47	703.5	3/2
48	718.5
49	733.4	26/17
50	748.4
51	763.4	14/9
52	778.3
53	793.3
54	808.3
55	823.2	29/18, 37/23
56	838.2
57	853.2	18/11
58	868.1	33/20, 38/23
59	883.1	5/3
60	898.1	42/25
61	913.1	39/23
62	928
63	943	31/18
64	958
65	972.9
66	987.9	23/13
67	1002.9	25/14, 41/23
68	1017.8	9/5
69	1032.8	20/11
70	1047.8	11/6
71	1062.7
72	1077.7
73	1092.7
74	1107.6
75	1122.6
76	1137.6	27/14
77	1152.5	35/18, 37/19
78	1167.5
79	1182.5
80	1197.4
81	1212.4
82	1227.4
83	1242.3	43/21
84	1257.3	31/15
85	1272.3	25/12
86	1287.3
87	1302.2
88	1317.2	15/7
89	1332.2	41/19
90	1347.1	37/17
91	1362.1
92	1377.1	31/14
93	1392	38/17
94	1407
95	1422	25/11
96	1436.9	39/17
97	1451.9
98	1466.9	7/3

Harmonics

Approximation of harmonics in 98ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.55	-1.01	-5.11	-2.25	-3.56	-1.01	+7.30	-2.02	-4.81	-5.16	-6.12
	Relative (%)	-17.1	-6.7	-34.1	-15.0	-23.8	-6.7	+48.8	-13.5	-32.1	-34.5	-40.9
Steps (reduced)		80 (80)	127 (29)	160 (62)	186 (88)	207 (11)	225 (29)	241 (45)	254 (58)	266 (70)	277 (81)	287 (91)

Approximation of harmonics in 98ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+4.99	-3.56	-3.26	+4.75	+4.57	-4.57	+6.60	-7.36	-2.02	+7.25	+5.14
	Relative (%)	+33.3	-23.8	-21.8	+31.7	+30.5	-30.6	+44.1	-49.2	-13.5	+48.4	+34.3
Steps (reduced)		297 (3)	305 (11)	313 (19)	321 (27)	328 (34)	334 (40)	341 (47)	346 (52)	352 (58)	358 (64)	363 (69)