127ed4

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127ed4

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Prime factorization	127 (prime)
Step size	18.8976 ¢
Octave	64\127ed4 (1209.45 ¢)
Twelfth	101\127ed4 (1908.66 ¢)
Consistency limit	1
Distinct consistency limit	1

127 equal divisions of the 4th harmonic (abbreviated 127ed4) is a nonoctave tuning system that divides the interval of 4/1 into 127 equal parts of about 18.9 ¢ each. Each step represents a frequency ratio of 4^1/127, or the 127th root of 4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	18.9
2	37.8	46/45, 47/46
3	56.7	31/30
4	75.6	47/45
5	94.5
6	113.4
7	132.3
8	151.2
9	170.1	43/39
10	189
11	207.9
12	226.8
13	245.7	38/33
14	264.6
15	283.5	33/28
16	302.4
17	321.3	47/39
18	340.2	45/37
19	359.1
20	378	46/37
21	396.9	39/31
22	415.7	14/11, 47/37
23	434.6
24	453.5	13/10
25	472.4
26	491.3
27	510.2	51/38
28	529.1	19/14
29	548
30	566.9	43/31
31	585.8
32	604.7
33	623.6	43/30
34	642.5
35	661.4
36	680.3	40/27
37	699.2
38	718.1
39	737	26/17
40	755.9
41	774.8
42	793.7
43	812.6
44	831.5	21/13
45	850.4
46	869.3	43/26
47	888.2
48	907.1	49/29
49	926
50	944.9	19/11, 50/29
51	963.8
52	982.7	30/17
53	1001.6	41/23
54	1020.5
55	1039.4	31/17, 51/28
56	1058.3
57	1077.2
58	1096.1
59	1115
60	1133.9
61	1152.8	37/19
62	1171.7
63	1190.6
64	1209.4
65	1228.3
66	1247.2
67	1266.1
68	1285	21/10
69	1303.9
70	1322.8
71	1341.7
72	1360.6
73	1379.5
74	1398.4
75	1417.3
76	1436.2	39/17
77	1455.1	51/22
78	1474
79	1492.9	45/19
80	1511.8
81	1530.7	46/19
82	1549.6
83	1568.5	47/19
84	1587.4
85	1606.3	43/17
86	1625.2
87	1644.1
88	1663
89	1681.9	37/14
90	1700.8
91	1719.7
92	1738.6	30/11
93	1757.5
94	1776.4
95	1795.3	31/11
96	1814.2
97	1833.1
98	1852
99	1870.9
100	1889.8
101	1908.7
102	1927.6
103	1946.5
104	1965.4	28/9
105	1984.3
106	2003.1
107	2022	45/14
108	2040.9
109	2059.8	23/7
110	2078.7
111	2097.6	47/14
112	2116.5
113	2135.4
114	2154.3
115	2173.2
116	2192.1	39/11
117	2211
118	2229.9
119	2248.8	11/3
120	2267.7
121	2286.6
122	2305.5
123	2324.4
124	2343.3
125	2362.2
126	2381.1
127	2400

Harmonics

Approximation of harmonics in 127ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+9.45	+6.71	+0.00	-8.36	-2.74	-5.05	+9.45	-5.48	+1.09	+6.16	+6.71
	Relative (%)	+50.0	+35.5	+0.0	-44.2	-14.5	-26.7	+50.0	-29.0	+5.8	+32.6	+35.5
Steps (reduced)		64 (64)	101 (101)	127 (0)	147 (20)	164 (37)	178 (51)	191 (64)	201 (74)	211 (84)	220 (93)	228 (101)

Approximation of harmonics in 127ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+0.42	+4.40	-1.65	+0.00	+8.43	+3.96	+4.85	-8.36	+1.66	-3.29	-4.65
	Relative (%)	+2.2	+23.3	-8.8	+0.0	+44.6	+21.0	+25.7	-44.2	+8.8	-17.4	-24.6
Steps (reduced)		235 (108)	242 (115)	248 (121)	254 (0)	260 (6)	265 (11)	270 (16)	274 (20)	279 (25)	283 (29)	287 (33)