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	17.4
2	34.9
3	52.3	34/33, 35/34
4	69.8	25/24
5	87.2	41/39
6	104.7
7	122.1	29/27
8	139.6
9	157	23/21
10	174.5	21/19, 31/28
11	191.9	19/17
12	209.4	35/31
13	226.8
14	244.3	38/33
15	261.7	43/37
16	279.2	27/23
17	296.6
18	314.1	6/5
19	331.5	23/19
20	349	11/9
21	366.4	21/17, 47/38
22	383.9
23	401.3	29/23, 34/27
24	418.8	14/11
25	436.2	9/7
26	453.7
27	471.1	46/35
28	488.6
29	506
30	523.5	23/17
31	540.9	26/19
32	558.4	29/21, 47/34
33	575.8	46/33
34	593.3	31/22, 38/27
35	610.7	37/26, 47/33
36	628.2
37	645.6	45/31
38	663.1	22/15
39	680.5	43/29
40	698
41	715.4
42	732.9	29/19
43	750.3
44	767.8
45	785.2
46	802.7	27/17, 35/22
47	820.1	45/28
48	837.6	47/29
49	855
50	872.5	43/26
51	889.9
52	907.4
53	924.8	29/17
54	942.3	31/18
55	959.7	47/27
56	977.2	44/25
57	994.6
58	1012
59	1029.5
60	1046.9
61	1064.4
62	1081.8	28/15, 43/23
63	1099.3	17/9
64	1116.7
65	1134.2
66	1151.6	35/18, 37/19
67	1169.1
68	1186.5
69	1204
70	1221.4
71	1238.9	43/21, 45/22, 47/23
72	1256.3	31/15
73	1273.8
74	1291.2
75	1308.7
76	1326.1
77	1343.6
78	1361
79	1378.5
80	1395.9	47/21
81	1413.4	43/19
82	1430.8
83	1448.3
84	1465.7	7/3
85	1483.2	33/14
86	1500.6
87	1518.1
88	1535.5	17/7
89	1553	27/11
90	1570.4
91	1587.9	5/2
92	1605.3	43/17
93	1622.8	23/9
94	1640.2
95	1657.7
96	1675.1
97	1692.6
98	1710
99	1727.5	19/7
100	1744.9
101	1762.4	47/17
102	1779.8
103	1797.3
104	1814.7
105	1832.2
106	1849.6
107	1867.1
108	1884.5
109	1902	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)