155edt

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155edt

156edt →

Prime factorization	5 × 31
Step size	12.2707 ¢
Octave	98\155edt (1202.53 ¢)
Consistency limit	6
Distinct consistency limit	6

155 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 155edt or 155ed3), is a nonoctave tuning system that divides the interval of 3/1 into 155 equal parts of about 12.3 ¢ each. Each step represents a frequency ratio of 3^1/155, or the 155th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	12.3	8.4
2	24.5	16.8
3	36.8	25.2	46/45, 47/46, 49/48
4	49.1	33.5	35/34, 36/35
5	61.4	41.9	57/55
6	73.6	50.3
7	85.9	58.7	21/20, 41/39
8	98.2	67.1	18/17
9	110.4	75.5
10	122.7	83.9	29/27, 44/41
11	135	92.3
12	147.2	100.6
13	159.5	109
14	171.8	117.4
15	184.1	125.8
16	196.3	134.2
17	208.6	142.6	44/39
18	220.9	151	25/22
19	233.1	159.4
20	245.4	167.7	38/33
21	257.7	176.1	29/25
22	270	184.5
23	282.2	192.9	20/17
24	294.5	201.3	51/43
25	306.8	209.7	37/31, 43/36
26	319	218.1
27	331.3	226.5	23/19
28	343.6	234.8	50/41
29	355.8	243.2	27/22, 43/35
30	368.1	251.6	47/38
31	380.4	260
32	392.7	268.4
33	404.9	276.8
34	417.2	285.2
35	429.5	293.5	50/39
36	441.7	301.9
37	454	310.3	13/10
38	466.3	318.7
39	478.6	327.1	29/22
40	490.8	335.5
41	503.1	343.9
42	515.4	352.3	31/23, 35/26
43	527.6	360.6
44	539.9	369	41/30
45	552.2	377.4
46	564.5	385.8	18/13
47	576.7	394.2
48	589	402.6
49	601.3	411	58/41
50	613.5	419.4	47/33
51	625.8	427.7	33/23
52	638.1	436.1	13/9
53	650.3	444.5	51/35
54	662.6	452.9	22/15
55	674.9	461.3
56	687.2	469.7	55/37, 58/39
57	699.4	478.1
58	711.7	486.5
59	724	494.8	38/25, 41/27
60	736.2	503.2	26/17, 49/32
61	748.5	511.6	57/37
62	760.8	520	45/29
63	773.1	528.4
64	785.3	536.8
65	797.6	545.2	46/29
66	809.9	553.5
67	822.1	561.9	37/23
68	834.4	570.3	34/21
69	846.7	578.7	31/19, 44/27
70	858.9	587.1
71	871.2	595.5	43/26
72	883.5	603.9	5/3
73	895.8	612.3
74	908	620.6
75	920.3	629
76	932.6	637.4	12/7
77	944.8	645.8	19/11
78	957.1	654.2	33/19
79	969.4	662.6	7/4
80	981.7	671
81	993.9	679.4	55/31
82	1006.2	687.7
83	1018.5	696.1	9/5
84	1030.7	704.5
85	1043	712.9
86	1055.3	721.3	46/25, 57/31
87	1067.5	729.7	50/27
88	1079.8	738.1
89	1092.1	746.5	47/25
90	1104.4	754.8
91	1116.6	763.2	40/21
92	1128.9	771.6
93	1141.2	780	29/15
94	1153.4	788.4	37/19
95	1165.7	796.8	51/26
96	1178	805.2
97	1190.3	813.5
98	1202.5	821.9
99	1214.8	830.3
100	1227.1	838.7
101	1239.3	847.1	43/21, 45/22
102	1251.6	855.5	35/17
103	1263.9	863.9	27/13
104	1276.2	872.3	23/11
105	1288.4	880.6
106	1300.7	889
107	1313	897.4	47/22
108	1325.2	905.8	43/20
109	1337.5	914.2	13/6
110	1349.8	922.6
111	1362	931
112	1374.3	939.4
113	1386.6	947.7
114	1398.9	956.1
115	1411.1	964.5
116	1423.4	972.9
117	1435.7	981.3
118	1447.9	989.7	30/13
119	1460.2	998.1
120	1472.5	1006.5
121	1484.8	1014.8
122	1497	1023.2
123	1509.3	1031.6	55/23
124	1521.6	1040
125	1533.8	1048.4
126	1546.1	1056.8	22/9
127	1558.4	1065.2
128	1570.6	1073.5	52/21, 57/23
129	1582.9	1081.9
130	1595.2	1090.3
131	1607.5	1098.7	43/17
132	1619.7	1107.1	51/20
133	1632	1115.5
134	1644.3	1123.9
135	1656.5	1132.3
136	1668.8	1140.6
137	1681.1	1149
138	1693.4	1157.4
139	1705.6	1165.8
140	1717.9	1174.2
141	1730.2	1182.6
142	1742.4	1191
143	1754.7	1199.4
144	1767	1207.7
145	1779.2	1216.1
146	1791.5	1224.5
147	1803.8	1232.9	17/6
148	1816.1	1241.3	20/7
149	1828.3	1249.7
150	1840.6	1258.1	55/19
151	1852.9	1266.5	35/12
152	1865.1	1274.8
153	1877.4	1283.2
154	1889.7	1291.6
155	1902	1300	3/1

Harmonics

Approximation of harmonics in 155edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+2.53	+0.00	+5.05	-0.87	+2.53	+5.61	-4.69	+0.00	+1.66	-3.83	+5.05
	Relative (%)	+20.6	+0.0	+41.2	-7.1	+20.6	+45.7	-38.2	+0.0	+13.5	-31.2	+41.2
Steps (reduced)		98 (98)	155 (0)	196 (41)	227 (72)	253 (98)	275 (120)	293 (138)	310 (0)	325 (15)	338 (28)	351 (41)

Approximation of harmonics in 155edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+1.46	-4.13	-0.87	-2.17	+3.32	+2.53	-5.18	+4.18	+5.61	-1.30	-4.63
	Relative (%)	+11.9	-33.7	-7.1	-17.6	+27.0	+20.6	-42.2	+34.1	+45.7	-10.6	-37.8
Steps (reduced)		362 (52)	372 (62)	382 (72)	391 (81)	400 (90)	408 (98)	415 (105)	423 (113)	430 (120)	436 (126)	442 (132)