145ed6

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145ed6

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Prime factorization	5 × 29
Step size	21.3928 ¢
Octave	56\145ed6 (1198 ¢)
Twelfth	89\145ed6 (1903.96 ¢)
Consistency limit	6
Distinct consistency limit	6

145 equal divisions of the 6th harmonic (abbreviated 145ed6) is a nonoctave tuning system that divides the interval of 6/1 into 145 equal parts of about 21.4 ¢ each. Each step represents a frequency ratio of 6^1/145, or the 145th root of 6.

145ED6 is close to 56edo, but with the 6/1 rather than the 2/1 being just. The octave is about 2 cents compressed and the step size is about 21.39 cents. This tuning provides a good alternative to 22edo for pajara, though with the second best mapping of 7, as in the 56d val.

If treated as a system with 6/1 as the equivalence, it does well as a 6.5.11.17.19 temperament.

Harmonics

Approximation of prime harmonics in 145ed6

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-2.00	+2.00	-5.25	-10.16	-1.12	+9.17	-6.01	-6.03	+5.50	+10.66	+2.16
	Relative (%)	-9.4	+9.4	-24.5	-47.5	-5.2	+42.9	-28.1	-28.2	+25.7	+49.8	+10.1
Steps (reduced)		56 (56)	89 (89)	130 (130)	157 (12)	194 (49)	208 (63)	229 (84)	238 (93)	254 (109)	273 (128)	278 (133)

Approximation of prime harmonics in 145ed6

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	-4.65	+10.17	-8.11	+9.04	-6.42	+0.45	+6.92	-5.76	+0.82	-4.49	+8.51
	Relative (%)	-21.7	+47.5	-37.9	+42.3	-30.0	+2.1	+32.3	-26.9	+3.8	-21.0	+39.8
Steps (reduced)		292 (2)	301 (11)	304 (14)	312 (22)	321 (31)	330 (40)	333 (43)	340 (50)	345 (55)	347 (57)	354 (64)

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	21.4
2	42.8
3	64.2	27/26
4	85.6	21/20, 41/39
5	107	33/31
6	128.4
7	149.7	12/11
8	171.1
9	192.5	19/17
10	213.9	43/38
11	235.3	47/41, 55/48
12	256.7	51/44
13	278.1	27/23
14	299.5	44/37
15	320.9
16	342.3
17	363.7	37/30
18	385.1	5/4
19	406.5	43/34
20	427.9	32/25
21	449.2	48/37
22	470.6	21/16
23	492
24	513.4	39/29
25	534.8
26	556.2	51/37
27	577.6
28	599	41/29
29	620.4
30	641.8
31	663.2	22/15
32	684.6	46/31
33	706
34	727.4
35	748.7	37/24
36	770.1
37	791.5	30/19
38	812.9	8/5
39	834.3	34/21
40	855.7
41	877.1
42	898.5	37/22, 42/25
43	919.9	17/10
44	941.3	31/18
45	962.7
46	984.1	30/17
47	1005.5
48	1026.9	38/21
49	1048.2	11/6
50	1069.6
51	1091
52	1112.4	19/10
53	1133.8	52/27
54	1155.2	37/19
55	1176.6
56	1198
57	1219.4
58	1240.8	43/21
59	1262.2
60	1283.6	21/10
61	1305	17/8
62	1326.4	43/20
63	1347.7	37/17
64	1369.1
65	1390.5	29/13
66	1411.9	52/23
67	1433.3
68	1454.7	44/19, 51/22
69	1476.1	54/23
70	1497.5	19/8
71	1518.9
72	1540.3
73	1561.7	37/15
74	1583.1
75	1604.5	48/19
76	1625.9	23/9
77	1647.2	44/17
78	1668.6
79	1690
80	1711.4	43/16
81	1732.8
82	1754.2
83	1775.6
84	1797	48/17
85	1818.4	20/7
86	1839.8	55/19
87	1861.2
88	1882.6
89	1904
90	1925.4
91	1946.7
92	1968.1
93	1989.5	41/13
94	2010.9
95	2032.3	55/17
96	2053.7	36/11
97	2075.1
98	2096.5
99	2117.9	17/5
100	2139.3
101	2160.7
102	2182.1
103	2203.5	25/7
104	2224.9	47/13
105	2246.2
106	2267.6
107	2289	15/4
108	2310.4	19/5
109	2331.8
110	2353.2
111	2374.6
112	2396
113	2417.4
114	2438.8	45/11
115	2460.2
116	2481.6
117	2503
118	2524.3	43/10
119	2545.7
120	2567.1
121	2588.5
122	2609.9
123	2631.3	32/7
124	2652.7	37/8
125	2674.1
126	2695.5
127	2716.9	24/5
128	2738.3
129	2759.7
130	2781.1
131	2802.5
132	2823.8	46/9
133	2845.2
134	2866.6
135	2888
136	2909.4
137	2930.8
138	2952.2	11/2
139	2973.6
140	2995
141	3016.4	40/7
142	3037.8	52/9
143	3059.2
144	3080.6
145	3102	6/1