127edt

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127edt

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Prime factorization	127 (prime)
Step size	14.976¢
Octave	80\127edt (1198.08¢)
Consistency limit	11
Distinct consistency limit	11

127 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 127edt or 127ed3), is a nonoctave tuning system that divides the interval of 3/1 into 127 equal parts of about 15 ¢ each. Each step represents a frequency ratio of 3^1/127, or the 127th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	14.976
2	29.952
3	44.928	38/37
4	59.904	29/28, 30/29
5	74.88	24/23, 47/45
6	89.856	20/19
7	104.832
8	119.808	15/14
9	134.784	27/25, 40/37
10	149.76	12/11
11	164.736	11/10
12	179.712
13	194.688	28/25, 47/42
14	209.664	35/31
15	224.64	33/29, 41/36, 49/43
16	239.616	31/27
17	254.592	22/19
18	269.568
19	284.544	33/28
20	299.52	44/37
21	314.496	6/5
22	329.473	23/19, 29/24
23	344.449	50/41
24	359.425
25	374.401	36/29, 41/33
26	389.377
27	404.353	24/19
28	419.329	14/11
29	434.305	9/7
30	449.281	35/27, 48/37
31	464.257	17/13
32	479.233	29/22, 33/25
33	494.209
34	509.185	47/35
35	524.161	42/31
36	539.137	41/30
37	554.113
38	569.089	25/18
39	584.065	7/5
40	599.041	41/29
41	614.017	47/33
42	628.993	23/16
43	643.969	29/20, 45/31
44	658.945	41/28
45	673.921	31/21
46	688.897
47	703.873
48	718.849	47/31, 50/33
49	733.825	26/17, 29/19
50	748.801	37/24
51	763.777	14/9
52	778.753	47/30
53	793.729	19/12, 49/31
54	808.705
55	823.681	37/23
56	838.657
57	853.633	18/11
58	868.609	33/20, 38/23
59	883.585	5/3
60	898.561	37/22, 42/25
61	913.537
62	928.513	41/24
63	943.489	50/29
64	958.466	40/23, 47/27
65	973.442
66	988.418
67	1003.394	25/14
68	1018.37	9/5
69	1033.346	20/11, 49/27
70	1048.322	11/6
71	1063.298	37/20
72	1078.274	41/22
73	1093.25	47/25
74	1108.226	36/19
75	1123.202	44/23
76	1138.178	27/14
77	1153.154	37/19
78	1168.13	51/26
79	1183.106
80	1198.082
81	1213.058
82	1228.034
83	1243.01	41/20
84	1257.986	31/15
85	1272.962	48/23
86	1287.938	40/19
87	1302.914
88	1317.89	15/7
89	1332.866	41/19
90	1347.842
91	1362.818
92	1377.794	31/14
93	1392.77
94	1407.746
95	1422.722	25/11
96	1437.698	39/17
97	1452.674	37/16, 44/19
98	1467.65	7/3
99	1482.626	33/14
100	1497.602	19/8
101	1512.578
102	1527.554	29/12
103	1542.53
104	1557.506
105	1572.482
106	1587.459	5/2
107	1602.435
108	1617.411	28/11
109	1632.387
110	1647.363
111	1662.339	47/18
112	1677.315	29/11
113	1692.291
114	1707.267
115	1722.243
116	1737.219	30/11
117	1752.195	11/4
118	1767.171	25/9
119	1782.147	14/5
120	1797.123
121	1812.099
122	1827.075	23/8
123	1842.051	29/10
124	1857.027
125	1872.003
126	1886.979
127	1901.955	3/1

Harmonics

Approximation of harmonics in 127edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-1.92	+0.00	-3.84	-0.77	-1.92	+0.78	-5.75	+0.00	-2.69	-2.96	-3.84
	Relative (%)	-12.8	+0.0	-25.6	-5.2	-12.8	+5.2	-38.4	+0.0	-18.0	-19.8	-25.6
Steps (reduced)		80 (80)	127 (0)	160 (33)	186 (59)	207 (80)	225 (98)	240 (113)	254 (0)	266 (12)	277 (23)	287 (33)

Approximation of harmonics in 127edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+7.35	-1.14	-0.77	+7.30	+7.18	-1.92	-5.66	-4.61	+0.78	-4.88	-6.95
	Relative (%)	+49.1	-7.6	-5.2	+48.8	+47.9	-12.8	-37.8	-30.8	+5.2	-32.6	-46.4
Steps (reduced)		297 (43)	305 (51)	313 (59)	321 (67)	328 (74)	334 (80)	340 (86)	346 (92)	352 (98)	357 (103)	362 (108)