156edt

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← 155edt

156edt

157edt →

Prime factorization

2² × 3 × 13

Step size

12.192 ¢

Octave

98\156edt (1194.82 ¢) (→ 49\78edt)

Consistency limit

3

Distinct consistency limit

3

156 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 156edt or 156ed3), is a nonoctave tuning system that divides the interval of 3/1 into 156 equal parts of about 12.2 ¢ each. Each step represents a frequency ratio of 3^1/156, or the 156th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	12.2	8.3
2	24.4	16.7
3	36.6	25
4	48.8	33.3
5	61	41.7	57/55
6	73.2	50
7	85.3	58.3	21/20, 41/39
8	97.5	66.7	18/17, 37/35
9	109.7	75	49/46
10	121.9	83.3
11	134.1	91.7
12	146.3	100
13	158.5	108.3	23/21
14	170.7	116.7
15	182.9	125	10/9
16	195.1	133.3
17	207.3	141.7
18	219.5	150
19	231.6	158.3
20	243.8	166.7	38/33
21	256	175
22	268.2	183.3	7/6
23	280.4	191.7	20/17
24	292.6	200	58/49
25	304.8	208.3
26	317	216.7
27	329.2	225
28	341.4	233.3
29	353.6	241.7
30	365.8	250	21/17
31	378	258.3	51/41
32	390.1	266.7
33	402.3	275	29/23
34	414.5	283.3	47/37
35	426.7	291.7	55/43
36	438.9	300	49/38
37	451.1	308.3
38	463.3	316.7	17/13
39	475.5	325	54/41
40	487.7	333.3	57/43
41	499.9	341.7
42	512.1	350	39/29
43	524.3	358.3	23/17
44	536.4	366.7
45	548.6	375
46	560.8	383.3
47	573	391.7
48	585.2	400
49	597.4	408.3
50	609.6	416.7	27/19
51	621.8	425	43/30
52	634	433.3	49/34
53	646.2	441.7	45/31
54	658.4	450	19/13
55	670.6	458.3
56	682.8	466.7	43/29
57	694.9	475
58	707.1	483.3
59	719.3	491.7	47/31
60	731.5	500	29/19
61	743.7	508.3
62	755.9	516.7
63	768.1	525
64	780.3	533.3
65	792.5	541.7
66	804.7	550	43/27
67	816.9	558.3
68	829.1	566.7	21/13, 50/31
69	841.2	575
70	853.4	583.3	18/11
71	865.6	591.7	33/20
72	877.8	600
73	890	608.3
74	902.2	616.7
75	914.4	625	39/23
76	926.6	633.3
77	938.8	641.7
78	951	650
79	963.2	658.3
80	975.4	666.7	58/33
81	987.6	675	23/13
82	999.7	683.3	41/23
83	1011.9	691.7
84	1024.1	700
85	1036.3	708.3	20/11
86	1048.5	716.7	11/6
87	1060.7	725
88	1072.9	733.3	13/7
89	1085.1	741.7
90	1097.3	750	49/26
91	1109.5	758.3	55/29
92	1121.7	766.7
93	1133.9	775
94	1146	783.3
95	1158.2	791.7	41/21
96	1170.4	800	57/29
97	1182.6	808.3
98	1194.8	816.7
99	1207	825
100	1219.2	833.3
101	1231.4	841.7	55/27
102	1243.6	850	39/19, 41/20
103	1255.8	858.3	31/15
104	1268	866.7
105	1280.2	875
106	1292.4	883.3	19/9
107	1304.5	891.7
108	1316.7	900
109	1328.9	908.3
110	1341.1	916.7
111	1353.3	925
112	1365.5	933.3
113	1377.7	941.7	51/23
114	1389.9	950	29/13
115	1402.1	958.3
116	1414.3	966.7	43/19
117	1426.5	975	41/18
118	1438.7	983.3	39/17
119	1450.9	991.7
120	1463	1000
121	1475.2	1008.3
122	1487.4	1016.7
123	1499.6	1025
124	1511.8	1033.3
125	1524	1041.7	41/17
126	1536.2	1050	17/7
127	1548.4	1058.3
128	1560.6	1066.7
129	1572.8	1075
130	1585	1083.3
131	1597.2	1091.7
132	1609.3	1100
133	1621.5	1108.3	51/20
134	1633.7	1116.7	18/7
135	1645.9	1125
136	1658.1	1133.3
137	1670.3	1141.7
138	1682.5	1150
139	1694.7	1158.3
140	1706.9	1166.7
141	1719.1	1175	27/10
142	1731.3	1183.3
143	1743.5	1191.7
144	1755.7	1200
145	1767.8	1208.3
146	1780	1216.7
147	1792.2	1225
148	1804.4	1233.3	17/6
149	1816.6	1241.7	20/7
150	1828.8	1250
151	1841	1258.3	55/19
152	1853.2	1266.7
153	1865.4	1275
154	1877.6	1283.3
155	1889.8	1291.7
156	1902	1300	3/1

Harmonics

Approximation of harmonics in 156edt
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-5.18	+0.00	+1.83	+5.66	-5.18	-3.83	-3.35	+0.00	+0.48	-6.03	+1.83
Error	Relative (%)	-42.5	+0.0	+15.0	+46.4	-42.5	-31.4	-27.5	+0.0	+3.9	-49.5	+15.0
Steps (reduced)		98 (98)	156 (0)	197 (41)	229 (73)	254 (98)	276 (120)	295 (139)	312 (0)	327 (15)	340 (28)	353 (41)

Approximation of harmonics in 156edt
Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	+3.18	+5.66	+3.66	-3.76	-5.18	-1.25	-4.71	-3.83	+0.98	-2.83
Error	Relative (%)	-21.6	+26.1	+46.4	+30.0	-30.9	-42.5	-10.2	-38.6	-31.4	+8.0	-23.2
Steps (reduced)		364 (52)	375 (63)	385 (73)	394 (82)	402 (90)	410 (98)	418 (106)	425 (113)	432 (120)	439 (127)	445 (133)