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	Hekts	Approximate ratios
0	0	0	1/1
1	19	13
2	38	26	44/43, 45/44
3	57.1	39
4	76.1	52	23/22, 24/23
5	95.1	65	19/18
6	114.1	78	16/15, 31/29
7	133.1	91	41/38
8	152.2	104	12/11
9	171.2	117	21/19, 43/39
10	190.2	130	19/17
11	209.2	143	44/39
12	228.2	156
13	247.3	169	15/13
14	266.3	182	7/6
15	285.3	195	33/28
16	304.3	208	37/31
17	323.3	221	41/34
18	342.4	234	28/23, 39/32
19	361.4	247	16/13
20	380.4	260
21	399.4	273	34/27
22	418.4	286	14/11
23	437.4	299	9/7
24	456.5	312	13/10, 43/33
25	475.5	325
26	494.5	338
27	513.5	351	35/26, 43/32
28	532.5	364
29	551.6	377	11/8
30	570.6	390	32/23
31	589.6	403	38/27, 45/32
32	608.6	416	27/19
33	627.6	429	23/16
34	646.7	442	16/11
35	665.7	455
36	684.7	468
37	703.7	481	3/2
38	722.7	494	41/27
39	741.8	507	23/15, 43/28
40	760.8	520
41	779.8	533
42	798.8	546	27/17
43	817.8	559
44	836.9	572
45	855.9	585
46	874.9	598
47	893.9	611
48	912.9	624	22/13, 39/23
49	932	637	12/7
50	951	650	26/15, 45/26
51	970	663	7/4
52	989	676	23/13, 39/22
53	1008	689	34/19, 43/24
54	1027.1	702	38/21
55	1046.1	715
56	1065.1	728
57	1084.1	741	43/23
58	1103.1	754	17/9
59	1122.2	767	44/23
60	1141.2	780
61	1160.2	793	41/21, 43/22, 45/23
62	1179.2	806
63	1198.2	819	2/1
64	1217.3	832
65	1236.3	845
66	1255.3	858	33/16
67	1274.3	871
68	1293.3	884	19/9
69	1312.3	897	32/15
70	1331.4	910	41/19
71	1350.4	923	24/11
72	1369.4	936
73	1388.4	949
74	1407.4	962
75	1426.5	975	41/18
76	1445.5	988	30/13
77	1464.5	1001	7/3
78	1483.5	1014	33/14
79	1502.5	1027
80	1521.6	1040
81	1540.6	1053	39/16
82	1559.6	1066	32/13
83	1578.6	1079
84	1597.6	1092
85	1616.7	1105	28/11
86	1635.7	1118	18/7
87	1654.7	1131	13/5
88	1673.7	1144
89	1692.7	1157
90	1711.8	1170	43/16
91	1730.8	1183	19/7
92	1749.8	1196	11/4
93	1768.8	1209
94	1787.8	1222	45/16
95	1806.9	1235
96	1825.9	1248	23/8
97	1844.9	1261
98	1863.9	1274	44/15
99	1882.9	1287
100	1902	1300	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)