136edt

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

← 135edt

136edt

137edt →

Prime factorization	23 × 17
Step size	13.985¢
Octave	86\136edt (1202.71¢) (→43\68edt)
Consistency limit	4
Distinct consistency limit	4

136 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 136edt or 136ed3), is a nonoctave tuning system that divides the interval of 3/1 into 136 equal parts of about 14⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/136, or the 136th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	14	9.6
2	28	19.1
3	42	28.7	41/40, 42/41, 43/42
4	55.9	38.2	31/30
5	69.9	47.8	51/49
6	83.9	57.4	21/20, 43/41
7	97.9	66.9	18/17, 37/35
8	111.9	76.5
9	125.9	86	43/40
10	139.8	95.6	13/12, 51/47
11	153.8	105.1	47/43
12	167.8	114.7	43/39, 54/49
13	181.8	124.3	10/9
14	195.8	133.8	47/42
15	209.8	143.4	35/31, 44/39
16	223.8	152.9	33/29, 41/36
17	237.7	162.5	31/27, 39/34, 47/41
18	251.7	172.1
19	265.7	181.6	7/6
20	279.7	191.2	20/17, 47/40
21	293.7	200.7	45/38, 51/43
22	307.7	210.3	37/31, 43/36, 49/41
23	321.7	219.9	47/39
24	335.6	229.4	17/14
25	349.6	239	49/40
26	363.6	248.5	37/30
27	377.6	258.1	46/37, 51/41
28	391.6	267.6
29	405.6	277.2	43/34
30	419.5	286.8	51/40
31	433.5	296.3	9/7
32	447.5	305.9	22/17
33	461.5	315.4	30/23, 47/36
34	475.5	325	25/19, 54/41
35	489.5	334.6
36	503.5	344.1
37	517.4	353.7	31/23
38	531.4	363.2
39	545.4	372.8	37/27
40	559.4	382.4	29/21, 47/34
41	573.4	391.9	39/28, 46/33
42	587.4	401.5
43	601.4	411	17/12
44	615.3	420.6
45	629.3	430.1
46	643.3	439.7	29/20
47	657.3	449.3
48	671.3	458.8
49	685.3	468.4	49/33
50	699.2	477.9
51	713.2	487.5
52	727.2	497.1	35/23
53	741.2	506.6	23/15, 43/28
54	755.2	516.2	17/11
55	769.2	525.7
56	783.2	535.3	11/7
57	797.1	544.9	46/29
58	811.1	554.4
59	825.1	564	29/18
60	839.1	573.5	13/8
61	853.1	583.1	18/11
62	867.1	592.6	33/20
63	881.1	602.2
64	895	611.8	47/28
65	909	621.3	49/29
66	923	630.9	29/17, 46/27
67	937	640.4
68	951	650
69	965	659.6
70	978.9	669.1	37/21, 51/29
71	992.9	678.7
72	1006.9	688.2
73	1020.9	697.8
74	1034.9	707.4	20/11
75	1048.9	716.9	11/6
76	1062.9	726.5	24/13
77	1076.8	736	41/22, 54/29
78	1090.8	745.6
79	1104.8	755.1
80	1118.8	764.7	21/11
81	1132.8	774.3
82	1146.8	783.8	33/17
83	1160.8	793.4	43/22, 45/23
84	1174.7	802.9
85	1188.7	812.5
86	1202.7	822.1
87	1216.7	831.6
88	1230.7	841.2
89	1244.7	850.7
90	1258.6	860.3
91	1272.6	869.9
92	1286.6	879.4
93	1300.6	889	36/17
94	1314.6	898.5	47/22
95	1328.6	908.1	28/13
96	1342.6	917.6
97	1356.5	927.2	46/21
98	1370.5	936.8
99	1384.5	946.3
100	1398.5	955.9
101	1412.5	965.4
102	1426.5	975	41/18
103	1440.5	984.6	23/10
104	1454.4	994.1	51/22
105	1468.4	1003.7	7/3
106	1482.4	1013.2	40/17
107	1496.4	1022.8
108	1510.4	1032.4
109	1524.4	1041.9	41/17
110	1538.3	1051.5
111	1552.3	1061	49/20
112	1566.3	1070.6	42/17
113	1580.3	1080.1
114	1594.3	1089.7
115	1608.3	1099.3	38/15, 43/17
116	1622.3	1108.8	51/20
117	1636.2	1118.4	18/7
118	1650.2	1127.9
119	1664.2	1137.5	34/13
120	1678.2	1147.1	29/11
121	1692.2	1156.6
122	1706.2	1166.2
123	1720.2	1175.7	27/10
124	1734.1	1185.3	49/18
125	1748.1	1194.9
126	1762.1	1204.4	36/13, 47/17
127	1776.1	1214
128	1790.1	1223.5
129	1804.1	1233.1	17/6
130	1818	1242.6	20/7
131	1832	1252.2	49/17
132	1846	1261.8
133	1860	1271.3	41/14
134	1874	1280.9
135	1888	1290.4
136	1902	1300	3/1

Harmonics

Approximation of harmonics in 136edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+2.71	+0.00	+5.41	-3.31	+2.71	+1.55	-5.86	+0.00	-0.60	+2.22	+5.41
	Relative (%)	+19.4	+0.0	+38.7	-23.6	+19.4	+11.1	-41.9	+0.0	-4.3	+15.8	+38.7
Steps (reduced)		86 (86)	136 (0)	172 (36)	199 (63)	222 (86)	241 (105)	257 (121)	272 (0)	285 (13)	297 (25)	308 (36)

Approximation of harmonics in 136edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+6.69	+4.26	-3.31	-3.16	+3.77	+2.71	-6.99	+2.11	+1.55	+4.92	-2.11
	Relative (%)	+47.8	+30.4	-23.6	-22.6	+26.9	+19.4	-50.0	+15.1	+11.1	+35.2	-15.1
Steps (reduced)		318 (46)	327 (55)	335 (63)	343 (71)	351 (79)	358 (86)	364 (92)	371 (99)	377 (105)	383 (111)	388 (116)