109edt

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109edt

110edt →

Prime factorization	109 (prime)
Step size	17.4491¢
Octave	69\109edt (1203.99¢)
Consistency limit	5
Distinct consistency limit	5

109 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 109edt or 109ed3), is a nonoctave tuning system that divides the interval of 3/1 into 109 equal parts of about 17.4 ¢ each. Each step represents a frequency ratio of 3^1/109, or the 109th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	17.449
2	34.898
3	52.347	34/33, 35/34
4	69.797	25/24
5	87.246	41/39
6	104.695
7	122.144	29/27
8	139.593
9	157.042	23/21
10	174.491	21/19, 31/28
11	191.94	19/17
12	209.39	35/31
13	226.839
14	244.288	38/33
15	261.737	43/37
16	279.186	27/23
17	296.635
18	314.084	6/5
19	331.533	23/19
20	348.983	11/9
21	366.432	21/17, 47/38
22	383.881
23	401.33	29/23, 34/27
24	418.779	14/11
25	436.228	9/7
26	453.677
27	471.126	46/35
28	488.576
29	506.025
30	523.474	23/17
31	540.923	26/19
32	558.372	29/21, 47/34
33	575.821	46/33
34	593.27	31/22, 38/27
35	610.719	37/26, 47/33
36	628.169
37	645.618	45/31
38	663.067	22/15
39	680.516	43/29
40	697.965
41	715.414
42	732.863	29/19
43	750.313
44	767.762
45	785.211
46	802.66	27/17, 35/22
47	820.109	45/28
48	837.558	47/29
49	855.007
50	872.456	43/26
51	889.906
52	907.355
53	924.804	29/17
54	942.253	31/18
55	959.702	47/27
56	977.151	44/25
57	994.6
58	1012.049
59	1029.499
60	1046.948
61	1064.397
62	1081.846	28/15, 43/23
63	1099.295	17/9
64	1116.744
65	1134.193
66	1151.642	35/18, 37/19
67	1169.092
68	1186.541
69	1203.99
70	1221.439
71	1238.888	43/21, 45/22, 47/23
72	1256.337	31/15
73	1273.786
74	1291.236
75	1308.685
76	1326.134
77	1343.583
78	1361.032
79	1378.481
80	1395.93	47/21
81	1413.379	43/19
82	1430.829
83	1448.278
84	1465.727	7/3
85	1483.176	33/14
86	1500.625
87	1518.074
88	1535.523	17/7
89	1552.972	27/11
90	1570.422
91	1587.871	5/2
92	1605.32	43/17
93	1622.769	23/9
94	1640.218
95	1657.667
96	1675.116
97	1692.565
98	1710.015
99	1727.464	19/7
100	1744.913
101	1762.362	47/17
102	1779.811
103	1797.26
104	1814.709
105	1832.158
106	1849.608
107	1867.057
108	1884.506
109	1901.955	3/1

Harmonics

Approximation of harmonics in 109edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3.99	+0.00	+7.98	+5.55	+3.99	-1.14	-5.48	+0.00	-7.91	+1.57	+7.98
	Relative (%)	+22.9	+0.0	+45.7	+31.8	+22.9	-6.6	-31.4	+0.0	-45.3	+9.0	+45.7
Steps (reduced)		69 (69)	109 (0)	138 (29)	160 (51)	178 (69)	193 (84)	206 (97)	218 (0)	228 (10)	238 (20)	247 (29)

Approximation of harmonics in 109edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-8.45	+2.85	+5.55	-1.49	-1.75	+3.99	-2.37	-3.92	-1.14	+5.56	-1.60
	Relative (%)	-48.4	+16.3	+31.8	-8.5	-10.0	+22.9	-13.6	-22.5	-6.6	+31.9	-9.1
Steps (reduced)		254 (36)	262 (44)	269 (51)	275 (57)	281 (63)	287 (69)	292 (74)	297 (79)	302 (84)	307 (89)	311 (93)