100ed7/3

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100ed7/3

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Prime factorization	22 × 52
Step size	14.6687¢
Octave	82\100ed7/3 (1202.83¢) (→41\50ed7/3)
Twelfth	130\100ed7/3 (1906.93¢) (→13\10ed7/3)
Consistency limit	5
Distinct consistency limit	5

100 equal divisions of 7/3 (abbreviated 100ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 100 equal parts of about 14.7⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/100, or the 100th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	14.7
2	29.3
3	44	39/38, 40/39
4	58.7
5	73.3
6	88	20/19
7	102.7	35/33
8	117.3	15/14, 31/29
9	132
10	146.7	25/23, 37/34
11	161.4	34/31
12	176	41/37
13	190.7
14	205.4	9/8
15	220	25/22
16	234.7
17	249.4	15/13
18	264
19	278.7
20	293.4	32/27, 45/38
21	308	37/31
22	322.7	41/34
23	337.4
24	352
25	366.7
26	381.4
27	396.1	44/35
28	410.7	19/15, 33/26
29	425.4
30	440.1
31	454.7	13/10
32	469.4	21/16
33	484.1	41/31
34	498.7	4/3
35	513.4	35/26
36	528.1	19/14
37	542.7	26/19
38	557.4
39	572.1	39/28
40	586.7
41	601.4	41/29
42	616.1	10/7
43	630.8
44	645.4
45	660.1
46	674.8	34/23
47	689.4
48	704.1	3/2
49	718.8
50	733.4
51	748.1	20/13
52	762.8	14/9
53	777.4
54	792.1	30/19
55	806.8
56	821.4	37/23, 45/28
57	836.1
58	850.8
59	865.5	33/20
60	880.1
61	894.8
62	909.5	22/13
63	924.1	29/17
64	938.8	43/25
65	953.5	26/15, 33/19
66	968.1	7/4
67	982.8
68	997.5	16/9
69	1012.1
70	1026.8	38/21
71	1041.5	31/17
72	1056.1	35/19
73	1070.8	13/7
74	1085.5	43/23
75	1100.2
76	1114.8	40/21
77	1129.5
78	1144.2
79	1158.8	43/22
80	1173.5
81	1188.2
82	1202.8
83	1217.5
84	1232.2
85	1246.8	39/19
86	1261.5
87	1276.2	23/11
88	1290.8	40/19
89	1305.5
90	1320.2	15/7
91	1334.9
92	1349.5
93	1364.2	11/5
94	1378.9
95	1393.5
96	1408.2
97	1422.9	25/11
98	1437.5
99	1452.2	44/19
100	1466.9	7/3

Harmonics

Approximation of harmonics in 100ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+2.83	+4.98	+5.67	+0.74	-6.86	+4.98	-6.17	-4.71	+3.58	-0.07	-4.02
	Relative (%)	+19.3	+33.9	+38.6	+5.1	-46.7	+33.9	-42.0	-32.1	+24.4	-0.5	-27.4
Steps (reduced)		82 (82)	130 (30)	164 (64)	190 (90)	211 (11)	230 (30)	245 (45)	259 (59)	272 (72)	283 (83)	293 (93)

Approximation of harmonics in 100ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+4.09	-6.86	+5.72	-3.33	-5.61	-1.88	+7.20	+6.41	-4.71	+2.76	-0.85
	Relative (%)	+27.9	-46.7	+39.0	-22.7	-38.2	-12.8	+49.1	+43.7	-32.1	+18.8	-5.8
Steps (reduced)		303 (3)	311 (11)	320 (20)	327 (27)	334 (34)	341 (41)	348 (48)	354 (54)	359 (59)	365 (65)	370 (70)