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	19.02
2	38.039	44/43, 45/44
3	57.059
4	76.078	23/22, 24/23
5	95.098	19/18
6	114.117	16/15, 31/29
7	133.137	41/38
8	152.156	12/11
9	171.176	21/19, 43/39
10	190.196	19/17
11	209.215	44/39
12	228.235
13	247.254	15/13
14	266.274	7/6
15	285.293	33/28
16	304.313	37/31
17	323.332	41/34
18	342.352	28/23, 39/32
19	361.371	16/13
20	380.391
21	399.411	34/27
22	418.43	14/11
23	437.45	9/7
24	456.469	13/10, 43/33
25	475.489
26	494.508
27	513.528	35/26, 43/32
28	532.547
29	551.567	11/8
30	570.587	32/23
31	589.606	38/27, 45/32
32	608.626	27/19
33	627.645	23/16
34	646.665	16/11
35	665.684
36	684.704
37	703.723	3/2
38	722.743	41/27
39	741.762	23/15, 43/28
40	760.782
41	779.802
42	798.821	27/17
43	817.841
44	836.86
45	855.88
46	874.899
47	893.919
48	912.938	22/13, 39/23
49	931.958	12/7
50	950.978	26/15, 45/26
51	969.997	7/4
52	989.017	23/13, 39/22
53	1008.036	34/19, 43/24
54	1027.056	38/21
55	1046.075
56	1065.095
57	1084.114	43/23
58	1103.134	17/9
59	1122.153	44/23
60	1141.173
61	1160.193	41/21, 43/22, 45/23
62	1179.212
63	1198.232	2/1
64	1217.251
65	1236.271
66	1255.29	33/16
67	1274.31
68	1293.329	19/9
69	1312.349	32/15
70	1331.369	41/19
71	1350.388	24/11
72	1369.408
73	1388.427
74	1407.447
75	1426.466	41/18
76	1445.486	30/13
77	1464.505	7/3
78	1483.525	33/14
79	1502.544
80	1521.564
81	1540.584	39/16
82	1559.603	32/13
83	1578.623
84	1597.642
85	1616.662	28/11
86	1635.681	18/7
87	1654.701	13/5
88	1673.72
89	1692.74
90	1711.76	43/16
91	1730.779	19/7
92	1749.799	11/4
93	1768.818
94	1787.838	45/16
95	1806.857
96	1825.877	23/8
97	1844.896
98	1863.916	44/15
99	1882.935
100	1901.955	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)