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	Hekts	Approximate ratios
0	0	0	1/1
1	17.4	11.9
2	34.9	23.9
3	52.3	35.8	34/33, 35/34
4	69.8	47.7	25/24
5	87.2	59.6	41/39
6	104.7	71.6
7	122.1	83.5	29/27
8	139.6	95.4
9	157	107.3	23/21
10	174.5	119.3	21/19, 31/28
11	191.9	131.2	19/17
12	209.4	143.1	35/31
13	226.8	155
14	244.3	167	38/33
15	261.7	178.9	43/37
16	279.2	190.8	27/23
17	296.6	202.8
18	314.1	214.7	6/5
19	331.5	226.6	23/19
20	349	238.5	11/9
21	366.4	250.5	21/17, 47/38
22	383.9	262.4
23	401.3	274.3	29/23, 34/27
24	418.8	286.2	14/11
25	436.2	298.2	9/7
26	453.7	310.1
27	471.1	322	46/35
28	488.6	333.9
29	506	345.9
30	523.5	357.8	23/17
31	540.9	369.7	26/19
32	558.4	381.7	29/21, 47/34
33	575.8	393.6	46/33
34	593.3	405.5	31/22, 38/27
35	610.7	417.4	37/26, 47/33
36	628.2	429.4
37	645.6	441.3	45/31
38	663.1	453.2	22/15
39	680.5	465.1	43/29
40	698	477.1
41	715.4	489
42	732.9	500.9	29/19
43	750.3	512.8
44	767.8	524.8
45	785.2	536.7
46	802.7	548.6	27/17, 35/22
47	820.1	560.6	45/28
48	837.6	572.5	47/29
49	855	584.4
50	872.5	596.3	43/26
51	889.9	608.3
52	907.4	620.2
53	924.8	632.1	29/17
54	942.3	644	31/18
55	959.7	656	47/27
56	977.2	667.9	44/25
57	994.6	679.8
58	1012	691.7
59	1029.5	703.7
60	1046.9	715.6
61	1064.4	727.5
62	1081.8	739.4	28/15, 43/23
63	1099.3	751.4	17/9
64	1116.7	763.3
65	1134.2	775.2
66	1151.6	787.2	35/18, 37/19
67	1169.1	799.1
68	1186.5	811
69	1204	822.9
70	1221.4	834.9
71	1238.9	846.8	43/21, 45/22, 47/23
72	1256.3	858.7	31/15
73	1273.8	870.6
74	1291.2	882.6
75	1308.7	894.5
76	1326.1	906.4
77	1343.6	918.3
78	1361	930.3
79	1378.5	942.2
80	1395.9	954.1	47/21
81	1413.4	966.1	43/19
82	1430.8	978
83	1448.3	989.9
84	1465.7	1001.8	7/3
85	1483.2	1013.8	33/14
86	1500.6	1025.7
87	1518.1	1037.6
88	1535.5	1049.5	17/7
89	1553	1061.5	27/11
90	1570.4	1073.4
91	1587.9	1085.3	5/2
92	1605.3	1097.2	43/17
93	1622.8	1109.2	23/9
94	1640.2	1121.1
95	1657.7	1133
96	1675.1	1145
97	1692.6	1156.9
98	1710	1168.8
99	1727.5	1180.7	19/7
100	1744.9	1192.7
101	1762.4	1204.6	47/17
102	1779.8	1216.5
103	1797.3	1228.4
104	1814.7	1240.4
105	1832.2	1252.3
106	1849.6	1264.2
107	1867.1	1276.1
108	1884.5	1288.1
109	1902	1300	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)