135ed4

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135ed4

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Prime factorization	33 × 5
Step size	17.7778¢
Octave	68\135ed4 (1208.89¢)
Twelfth	107\135ed4 (1902.22¢) (semiconvergent)
Consistency limit	1
Distinct consistency limit	1

135 equal divisions of the 4th harmonic (abbreviated 135ed4) is a nonoctave tuning system that divides the interval of 4/1 into 135 equal parts of about 17.8 ¢ each. Each step represents a frequency ratio of 4^1/135, or the 135th root of 4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	17.778
2	35.556	47/46
3	53.333	34/33
4	71.111
5	88.889
6	106.667
7	124.444	29/27
8	142.222	51/47
9	160	45/41
10	177.778	41/37, 51/46
11	195.556	28/25, 47/42
12	213.333
13	231.111
14	248.889	15/13
15	266.667
16	284.444	33/28, 46/39
17	302.222
18	320
19	337.778	17/14, 45/37
20	355.556	43/35
21	373.333
22	391.111
23	408.889	19/15
24	426.667
25	444.444
26	462.222
27	480	33/25
28	497.778
29	515.556	31/23
30	533.333	34/25
31	551.111
32	568.889	25/18
33	586.667
34	604.444
35	622.222
36	640	42/29
37	657.778	19/13
38	675.556	31/21
39	693.333
40	711.111
41	728.889
42	746.667
43	764.444	14/9
44	782.222
45	800	27/17, 46/29
46	817.778
47	835.556	47/29
48	853.333	18/11
49	871.111
50	888.889
51	906.667
52	924.444	29/17
53	942.222
54	960	47/27
55	977.778	51/29
56	995.556
57	1013.333
58	1031.111
59	1048.889	11/6
60	1066.667
61	1084.444	43/23
62	1102.222	17/9
63	1120
64	1137.778	27/14
65	1155.556	37/19
66	1173.333
67	1191.111
68	1208.889
69	1226.667
70	1244.444	39/19
71	1262.222	29/14
72	1280
73	1297.778
74	1315.556
75	1333.333
76	1351.111
77	1368.889
78	1386.667
79	1404.444
80	1422.222	25/11
81	1440
82	1457.778
83	1475.556
84	1493.333	45/19
85	1511.111
86	1528.889
87	1546.667
88	1564.444	37/15, 42/17
89	1582.222
90	1600
91	1617.778	28/11
92	1635.556
93	1653.333	13/5
94	1671.111
95	1688.889
96	1706.667
97	1724.444	46/17
98	1742.222	41/15
99	1760	47/17
100	1777.778
101	1795.556
102	1813.333
103	1831.111
104	1848.889
105	1866.667
106	1884.444
107	1902.222	3/1
108	1920
109	1937.778
110	1955.556
111	1973.333
112	1991.111
113	2008.889
114	2026.667	29/9
115	2044.444
116	2062.222
117	2080
118	2097.778	47/14
119	2115.556
120	2133.333
121	2151.111	45/13
122	2168.889
123	2186.667	46/13
124	2204.444
125	2222.222
126	2240
127	2257.778
128	2275.556
129	2293.333
130	2311.111	19/5
131	2328.889
132	2346.667
133	2364.444
134	2382.222
135	2400

Harmonics

Approximation of harmonics in 135ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+8.89	+0.27	+0.00	+4.80	-8.62	-8.83	+8.89	+0.53	-4.09	+8.68	+0.27
	Relative (%)	+50.0	+1.5	+0.0	+27.0	-48.5	-49.6	+50.0	+3.0	-23.0	+48.8	+1.5
Steps (reduced)		68 (68)	107 (107)	135 (0)	157 (22)	174 (39)	189 (54)	203 (68)	214 (79)	224 (89)	234 (99)	242 (107)

Approximation of harmonics in 135ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+3.92	+0.06	+5.06	+0.00	+1.71	-8.35	+4.71	+4.80	-8.56	-0.21	-6.05
	Relative (%)	+22.0	+0.4	+28.5	+0.0	+9.6	-47.0	+26.5	+27.0	-48.1	-1.2	-34.0
Steps (reduced)		250 (115)	257 (122)	264 (129)	270 (0)	276 (6)	281 (11)	287 (17)	292 (22)	296 (26)	301 (31)	305 (35)