100edt

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100edt

101edt →

Prime factorization	22 × 52
Step size	19.0196¢
Octave	63\100edt (1198.23¢)
Consistency limit	8
Distinct consistency limit	8

100 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 100edt or 100ed3), is a nonoctave tuning system that divides the interval of 3/1 into 100 equal parts of about 19⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/100, or the 100th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	19
2	38	44/43, 45/44
3	57.1
4	76.1	23/22, 24/23
5	95.1	19/18
6	114.1	16/15, 31/29
7	133.1	41/38
8	152.2	12/11
9	171.2	21/19, 43/39
10	190.2	19/17
11	209.2	44/39
12	228.2
13	247.3	15/13
14	266.3	7/6
15	285.3	33/28
16	304.3	37/31
17	323.3	41/34
18	342.4	28/23, 39/32
19	361.4	16/13
20	380.4
21	399.4	34/27
22	418.4	14/11
23	437.4	9/7
24	456.5	13/10, 43/33
25	475.5
26	494.5
27	513.5	35/26, 43/32
28	532.5
29	551.6	11/8
30	570.6	32/23
31	589.6	38/27, 45/32
32	608.6	27/19
33	627.6	23/16
34	646.7	16/11
35	665.7
36	684.7
37	703.7	3/2
38	722.7	41/27
39	741.8	23/15, 43/28
40	760.8
41	779.8
42	798.8	27/17
43	817.8
44	836.9
45	855.9
46	874.9
47	893.9
48	912.9	22/13, 39/23
49	932	12/7
50	951	26/15, 45/26
51	970	7/4
52	989	23/13, 39/22
53	1008	34/19, 43/24
54	1027.1	38/21
55	1046.1
56	1065.1
57	1084.1	43/23
58	1103.1	17/9
59	1122.2	44/23
60	1141.2
61	1160.2	41/21, 43/22, 45/23
62	1179.2
63	1198.2	2/1
64	1217.3
65	1236.3
66	1255.3	33/16
67	1274.3
68	1293.3	19/9
69	1312.3	32/15
70	1331.4	41/19
71	1350.4	24/11
72	1369.4
73	1388.4
74	1407.4
75	1426.5	41/18
76	1445.5	30/13
77	1464.5	7/3
78	1483.5	33/14
79	1502.5
80	1521.6
81	1540.6	39/16
82	1559.6	32/13
83	1578.6
84	1597.6
85	1616.7	28/11
86	1635.7	18/7
87	1654.7	13/5
88	1673.7
89	1692.7
90	1711.8	43/16
91	1730.8	19/7
92	1749.8	11/4
93	1768.8
94	1787.8	45/16
95	1806.9
96	1825.9	23/8
97	1844.9
98	1863.9	44/15
99	1882.9
100	1902	3/1

Harmonics

Approximation of harmonics in 100edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-1.77	+0.00	-3.54	-9.46	-1.77	-2.37	-5.31	+0.00	+7.79	-5.06	-3.54
	Relative (%)	-9.3	+0.0	-18.6	-49.7	-9.3	-12.4	-27.9	+0.0	+41.0	-26.6	-18.6
Steps (reduced)		63 (63)	100 (0)	126 (26)	146 (46)	163 (63)	177 (77)	189 (89)	200 (0)	210 (10)	218 (18)	226 (26)

Approximation of harmonics in 100edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-8.97	-4.13	-9.46	-7.07	+2.09	-1.77	-0.27	+6.02	-2.37	-6.82	-7.70
	Relative (%)	-47.2	-21.7	-49.7	-37.2	+11.0	-9.3	-1.4	+31.7	-12.4	-35.9	-40.5
Steps (reduced)		233 (33)	240 (40)	246 (46)	252 (52)	258 (58)	263 (63)	268 (68)	273 (73)	277 (77)	281 (81)	285 (85)