127ed4

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

← 125ed4

127ed4

129ed4 →

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	18.898
2	37.795	46/45, 47/46
3	56.693	31/30
4	75.591	47/45
5	94.488
6	113.386
7	132.283
8	151.181
9	170.079	43/39
10	188.976
11	207.874
12	226.772
13	245.669	38/33
14	264.567
15	283.465	33/28
16	302.362
17	321.26	47/39
18	340.157	45/37
19	359.055
20	377.953	46/37
21	396.85	39/31
22	415.748	14/11, 47/37
23	434.646
24	453.543	13/10
25	472.441
26	491.339
27	510.236	51/38
28	529.134	19/14
29	548.031
30	566.929	43/31
31	585.827
32	604.724
33	623.622	43/30
34	642.52
35	661.417
36	680.315	40/27
37	699.213
38	718.11
39	737.008	26/17
40	755.906
41	774.803
42	793.701
43	812.598
44	831.496	21/13
45	850.394
46	869.291	43/26
47	888.189
48	907.087	49/29
49	925.984
50	944.882	19/11, 50/29
51	963.78
52	982.677	30/17
53	1001.575	41/23
54	1020.472
55	1039.37	31/17, 51/28
56	1058.268
57	1077.165
58	1096.063
59	1114.961
60	1133.858
61	1152.756	37/19
62	1171.654
63	1190.551
64	1209.449
65	1228.346
66	1247.244
67	1266.142
68	1285.039	21/10
69	1303.937
70	1322.835
71	1341.732
72	1360.63
73	1379.528
74	1398.425
75	1417.323
76	1436.22	39/17
77	1455.118	51/22
78	1474.016
79	1492.913	45/19
80	1511.811
81	1530.709	46/19
82	1549.606
83	1568.504	47/19
84	1587.402
85	1606.299	43/17
86	1625.197
87	1644.094
88	1662.992
89	1681.89	37/14
90	1700.787
91	1719.685
92	1738.583	30/11
93	1757.48
94	1776.378
95	1795.276	31/11
96	1814.173
97	1833.071
98	1851.969
99	1870.866
100	1889.764
101	1908.661
102	1927.559
103	1946.457
104	1965.354	28/9
105	1984.252
106	2003.15
107	2022.047	45/14
108	2040.945
109	2059.843	23/7
110	2078.74
111	2097.638	47/14
112	2116.535
113	2135.433
114	2154.331
115	2173.228
116	2192.126	39/11
117	2211.024
118	2229.921
119	2248.819	11/3
120	2267.717
121	2286.614
122	2305.512
123	2324.409
124	2343.307
125	2362.205
126	2381.102
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)