155ed6

← 154ed6

155ed6

156ed6 →

Prime factorization	5 × 31
Step size	20.0126¢
Octave	60\155ed6 (1200.76¢) (→12\31ed6)
Twelfth	95\155ed6 (1901.2¢) (→19\31ed6)
Consistency limit	10
Distinct consistency limit	10

155 equal divisions of the 6th harmonic (abbreviated 155ed6) is a nonoctave tuning system that divides the interval of 6/1 into 155 equal parts of about 20⁠ ⁠¢ each. Each step represents a frequency ratio of 6^1/155, or the 155th root of 6.

155ed6 is related to 60edo (tenth-tone tuning), but with the 6/1 rather than the 2/1 being just. This stretches the octave by about 0.8 ¢.

Lookalikes: 60edo, 139ed5, 95edt, 35edf

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	20
2	40	43/42, 44/43, 45/44
3	60	29/28, 30/29
4	80.1	22/21, 45/43
5	100.1	18/17
6	120.1	15/14
7	140.1	51/47
8	160.1	34/31, 45/41, 57/52
9	180.1	51/46
10	200.1	46/41, 55/49
11	220.1	25/22, 42/37
12	240.2	31/27, 54/47
13	260.2	36/31, 43/37, 50/43
14	280.2	20/17, 47/40
15	300.2	44/37
16	320.2
17	340.2	28/23, 45/37
18	360.2	16/13
19	380.2
20	400.3	29/23, 34/27
21	420.3	51/40
22	440.3	40/31, 58/45
23	460.3	30/23, 47/36
24	480.3	33/25
25	500.3
26	520.3	27/20, 50/37
27	540.3	41/30, 56/41
28	560.4	47/34
29	580.4
30	600.4	41/29, 58/41
31	620.4
32	640.4	42/29
33	660.4	41/28
34	680.4	40/27
35	700.4
36	720.5	44/29, 47/31, 50/33
37	740.5	23/15
38	760.5	45/29
39	780.5
40	800.5	27/17
41	820.5	45/28
42	840.5	13/8
43	860.5	23/14, 51/31
44	880.6
45	900.6	37/22
46	920.6
47	940.6	31/18
48	960.6	47/27, 54/31
49	980.6	37/21
50	1000.6	41/23, 57/32
51	1020.6
52	1040.7	31/17
53	1060.7	24/13
54	1080.7	28/15
55	1100.7	17/9
56	1120.7	21/11
57	1140.7	29/15, 56/29
58	1160.7	43/22, 45/23
59	1180.7
60	1200.8	2/1
61	1220.8
62	1240.8	43/21
63	1260.8	29/14
64	1280.8	44/21
65	1300.8
66	1320.8	15/7
67	1340.8
68	1360.9
69	1380.9
70	1400.9
71	1420.9	25/11
72	1440.9	23/10
73	1460.9
74	1480.9	40/17
75	1500.9	50/21
76	1521
77	1541	56/23
78	1561
79	1581
80	1601	58/23
81	1621	51/20
82	1641
83	1661	47/18
84	1681.1	37/14
85	1701.1
86	1721.1
87	1741.1	41/15
88	1761.1	47/17
89	1781.1	14/5
90	1801.1
91	1821.1
92	1841.2
93	1861.2	41/14
94	1881.2
95	1901.2	3/1
96	1921.2
97	1941.2	43/14, 46/15
98	1961.2
99	1981.2	22/7
100	2001.3	54/17
101	2021.3	45/14
102	2041.3	13/4
103	2061.3
104	2081.3
105	2101.3	37/11
106	2121.3
107	2141.3	31/9
108	2161.4
109	2181.4
110	2201.4
111	2221.4
112	2241.4
113	2261.4	48/13
114	2281.4	56/15
115	2301.5	34/9
116	2321.5
117	2341.5	58/15
118	2361.5	43/11
119	2381.5
120	2401.5
121	2421.5
122	2441.5	41/10
123	2461.6	29/7
124	2481.6
125	2501.6
126	2521.6
127	2541.6
128	2561.6
129	2581.6	40/9
130	2601.6
131	2621.7	50/11
132	2641.7	23/5
133	2661.7
134	2681.7
135	2701.7
136	2721.7
137	2741.7	39/8
138	2761.7
139	2781.8
140	2801.8
141	2821.8	51/10
142	2841.8	31/6
143	2861.8	47/9
144	2881.8	37/7
145	2901.8
146	2921.8
147	2941.9
148	2961.9
149	2981.9	28/5
150	3001.9	17/3
151	3021.9
152	3041.9	29/5
153	3061.9
154	3081.9
155	3102	6/1

Harmonics

Approximation of prime harmonics in 155ed6

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.76	-0.76	-4.56	-6.71	-8.71	+2.27	-1.87	+5.70	-4.86	-5.91	-1.29
	Relative (%)	+3.8	-3.8	-22.8	-33.5	-43.5	+11.4	-9.3	+28.5	-24.3	-29.5	-6.4
Steps (reduced)		60 (60)	95 (95)	139 (139)	168 (13)	207 (52)	222 (67)	245 (90)	255 (100)	271 (116)	291 (136)	297 (142)

Approximation of prime harmonics in 155ed6

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-7.41	-5.01	-7.42	-1.31	-9.18	+5.28	+7.61	+5.28	+4.96	-3.11	+0.23
	Relative (%)	-37.0	-25.1	-37.1	-6.5	-45.9	+26.4	+38.0	+26.4	+24.8	-15.5	+1.2
Steps (reduced)		312 (2)	321 (11)	325 (15)	333 (23)	343 (33)	353 (43)	356 (46)	364 (54)	369 (59)	371 (61)	378 (68)

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