139edt

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139edt

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Prime factorization	139 (prime)
Step size	13.6831¢
Octave	88\139edt (1204.12¢)
Consistency limit	2
Distinct consistency limit	2

139 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 139edt or 139ed3), is a nonoctave tuning system that divides the interval of 3/1 into 139 equal parts of about 13.7⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/139, or the 139th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	13.7	9.4
2	27.4	18.7
3	41	28.1	42/41, 43/42, 44/43
4	54.7	37.4
5	68.4	46.8	26/25, 51/49
6	82.1	56.1	22/21, 43/41
7	95.8	65.5	37/35
8	109.5	74.8	33/31
9	123.1	84.2	29/27, 44/41
10	136.8	93.5
11	150.5	102.9
12	164.2	112.2
13	177.9	121.6	41/37
14	191.6	130.9
15	205.2	140.3
16	218.9	149.6	42/37
17	232.6	159
18	246.3	168.3	15/13
19	260	177.7	43/37
20	273.7	187.1	41/35
21	287.3	196.4	46/39
22	301	205.8	44/37
23	314.7	215.1	6/5
24	328.4	224.5
25	342.1	233.8	28/23
26	355.8	243.2	27/22, 43/35
27	369.4	252.5
28	383.1	261.9
29	396.8	271.2	44/35
30	410.5	280.6	19/15
31	424.2	289.9	23/18
32	437.9	299.3
33	451.5	308.6
34	465.2	318
35	478.9	327.3	29/22
36	492.6	336.7
37	506.3	346
38	520	355.4
39	533.6	364.7
40	547.3	374.1
41	561	383.5	47/34
42	574.7	392.8	39/28
43	588.4	402.2
44	602.1	411.5
45	615.7	420.9
46	629.4	430.2
47	643.1	439.6
48	656.8	448.9	19/13
49	670.5	458.3	28/19
50	684.2	467.6	49/33
51	697.8	477
52	711.5	486.3
53	725.2	495.7	35/23, 38/25
54	738.9	505	23/15
55	752.6	514.4	17/11
56	766.3	523.7	14/9
57	779.9	533.1
58	793.6	542.4	49/31
59	807.3	551.8	43/27
60	821	561.2	45/28
61	834.7	570.5	34/21, 47/29
62	848.4	579.9
63	862	589.2	51/31
64	875.7	598.6
65	889.4	607.9
66	903.1	617.3
67	916.8	626.6
68	930.5	636
69	944.1	645.3
70	957.8	654.7
71	971.5	664
72	985.2	673.4
73	998.9	682.7
74	1012.6	692.1
75	1026.2	701.4
76	1039.9	710.8	31/17
77	1053.6	720.1
78	1067.3	729.5
79	1081	738.8	28/15
80	1094.7	748.2
81	1108.3	757.6
82	1122	766.9	44/23
83	1135.7	776.3	27/14
84	1149.4	785.6	33/17
85	1163.1	795	45/23
86	1176.7	804.3
87	1190.4	813.7
88	1204.1	823
89	1217.8	832.4
90	1231.5	841.7
91	1245.2	851.1	39/19
92	1258.8	860.4
93	1272.5	869.8
94	1286.2	879.1
95	1299.9	888.5
96	1313.6	897.8	47/22
97	1327.3	907.2	28/13
98	1340.9	916.5
99	1354.6	925.9
100	1368.3	935.3
101	1382	944.6
102	1395.7	954	47/21
103	1409.4	963.3
104	1423	972.7
105	1436.7	982
106	1450.4	991.4
107	1464.1	1000.7
108	1477.8	1010.1	54/23
109	1491.5	1019.4	45/19
110	1505.1	1028.8
111	1518.8	1038.1
112	1532.5	1047.5
113	1546.2	1056.8	22/9
114	1559.9	1066.2
115	1573.6	1075.5
116	1587.2	1084.9	5/2
117	1600.9	1094.2
118	1614.6	1103.6
119	1628.3	1112.9
120	1642	1122.3
121	1655.7	1131.7	13/5
122	1669.3	1141
123	1683	1150.4	37/14
124	1696.7	1159.7
125	1710.4	1169.1
126	1724.1	1178.4
127	1737.8	1187.8
128	1751.4	1197.1
129	1765.1	1206.5
130	1778.8	1215.8
131	1792.5	1225.2	31/11
132	1806.2	1234.5
133	1819.9	1243.9
134	1833.5	1253.2	49/17
135	1847.2	1262.6
136	1860.9	1271.9	41/14
137	1874.6	1281.3
138	1888.3	1290.6
139	1902	1300	3/1

Harmonics

Approximation of harmonics in 139edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+4.12	+0.00	-5.45	+5.04	+4.12	-2.78	-1.34	+0.00	-4.52	-5.33	-5.45
	Relative (%)	+30.1	+0.0	-39.8	+36.9	+30.1	-20.3	-9.8	+0.0	-33.1	-39.0	-39.8
Steps (reduced)		88 (88)	139 (0)	175 (36)	204 (65)	227 (88)	246 (107)	263 (124)	278 (0)	291 (13)	303 (25)	314 (36)

Approximation of harmonics in 139edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+6.49	+1.34	+5.04	+2.78	-6.40	+4.12	+6.29	-0.41	-2.78	-1.21	+3.93
	Relative (%)	+47.4	+9.8	+36.9	+20.3	-46.7	+30.1	+46.0	-3.0	-20.3	-8.9	+28.7
Steps (reduced)		325 (47)	334 (56)	343 (65)	351 (73)	358 (80)	366 (88)	373 (95)	379 (101)	385 (107)	391 (113)	397 (119)