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	14.968
2	29.936
3	44.904	38/37, 39/38
4	59.872	29/28, 30/29
5	74.84
6	89.808	39/37
7	104.776
8	119.745	15/14
9	134.713	27/25
10	149.681	12/11
11	164.649	11/10
12	179.617	41/37
13	194.585	19/17, 28/25
14	209.553	35/31
15	224.521	33/29
16	239.489	31/27, 39/34
17	254.457	29/25
18	269.425
19	284.393	33/28
20	299.361	25/21
21	314.329	6/5
22	329.298	23/19, 29/24
23	344.266
24	359.234
25	374.202	31/25, 36/29
26	389.17
27	404.138	43/34
28	419.106	14/11
29	434.074	9/7
30	449.042	35/27
31	464.01	17/13
32	478.978	29/22, 33/25
33	493.946
34	508.914
35	523.882	23/17, 42/31
36	538.851	15/11
37	553.819	11/8
38	568.787	25/18, 43/31
39	583.755	7/5
40	598.723
41	613.691
42	628.659
43	643.627	29/20, 42/29
44	658.595	19/13
45	673.563	31/21
46	688.531
47	703.499	3/2
48	718.467
49	733.435	26/17
50	748.404
51	763.372	14/9
52	778.34
53	793.308
54	808.276
55	823.244	29/18, 37/23
56	838.212
57	853.18	18/11
58	868.148	33/20, 38/23
59	883.116	5/3
60	898.084	42/25
61	913.052	39/23
62	928.02
63	942.988	31/18
64	957.957
65	972.925
66	987.893	23/13
67	1002.861	25/14, 41/23
68	1017.829	9/5
69	1032.797	20/11
70	1047.765	11/6
71	1062.733
72	1077.701
73	1092.669
74	1107.637
75	1122.605
76	1137.573	27/14
77	1152.541	35/18, 37/19
78	1167.509
79	1182.478
80	1197.446
81	1212.414
82	1227.382
83	1242.35	43/21
84	1257.318	31/15
85	1272.286	25/12
86	1287.254
87	1302.222
88	1317.19	15/7
89	1332.158	41/19
90	1347.126	37/17
91	1362.094
92	1377.062	31/14
93	1392.031	38/17
94	1406.999
95	1421.967	25/11
96	1436.935	39/17
97	1451.903
98	1466.871	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)