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	Hekts	Approximate ratios
0	0	0	1/1
1	15	10.2
2	30	20.5
3	44.9	30.7	38/37
4	59.9	40.9	29/28, 30/29
5	74.9	51.2	24/23, 47/45
6	89.9	61.4	20/19
7	104.8	71.7
8	119.8	81.9	15/14
9	134.8	92.1	27/25, 40/37
10	149.8	102.4	12/11
11	164.7	112.6	11/10
12	179.7	122.8
13	194.7	133.1	28/25, 47/42
14	209.7	143.3	35/31
15	224.6	153.5	33/29, 41/36, 49/43
16	239.6	163.8	31/27
17	254.6	174	22/19
18	269.6	184.3
19	284.5	194.5	33/28
20	299.5	204.7	44/37
21	314.5	215	6/5
22	329.5	225.2	23/19, 29/24
23	344.4	235.4	50/41
24	359.4	245.7
25	374.4	255.9	36/29, 41/33
26	389.4	266.1
27	404.4	276.4	24/19
28	419.3	286.6	14/11
29	434.3	296.9	9/7
30	449.3	307.1	35/27, 48/37
31	464.3	317.3	17/13
32	479.2	327.6	29/22, 33/25
33	494.2	337.8
34	509.2	348	47/35
35	524.2	358.3	42/31
36	539.1	368.5	41/30
37	554.1	378.7
38	569.1	389	25/18
39	584.1	399.2	7/5
40	599	409.4	41/29
41	614	419.7	47/33
42	629	429.9	23/16
43	644	440.2	29/20, 45/31
44	658.9	450.4	41/28
45	673.9	460.6	31/21
46	688.9	470.9
47	703.9	481.1
48	718.8	491.3	47/31, 50/33
49	733.8	501.6	26/17, 29/19
50	748.8	511.8	37/24
51	763.8	522	14/9
52	778.8	532.3	47/30
53	793.7	542.5	19/12, 49/31
54	808.7	552.8
55	823.7	563	37/23
56	838.7	573.2
57	853.6	583.5	18/11
58	868.6	593.7	33/20, 38/23
59	883.6	603.9	5/3
60	898.6	614.2	37/22, 42/25
61	913.5	624.4
62	928.5	634.6	41/24
63	943.5	644.9	50/29
64	958.5	655.1	40/23, 47/27
65	973.4	665.4
66	988.4	675.6
67	1003.4	685.8	25/14
68	1018.4	696.1	9/5
69	1033.3	706.3	20/11, 49/27
70	1048.3	716.5	11/6
71	1063.3	726.8	37/20
72	1078.3	737	41/22
73	1093.2	747.2	47/25
74	1108.2	757.5	36/19
75	1123.2	767.7	44/23
76	1138.2	778	27/14
77	1153.2	788.2	37/19
78	1168.1	798.4	51/26
79	1183.1	808.7
80	1198.1	818.9
81	1213.1	829.1
82	1228	839.4
83	1243	849.6	41/20
84	1258	859.8	31/15
85	1273	870.1	48/23
86	1287.9	880.3	40/19
87	1302.9	890.6
88	1317.9	900.8	15/7
89	1332.9	911	41/19
90	1347.8	921.3
91	1362.8	931.5
92	1377.8	941.7	31/14
93	1392.8	952
94	1407.7	962.2
95	1422.7	972.4	25/11
96	1437.7	982.7	39/17
97	1452.7	992.9	37/16, 44/19
98	1467.7	1003.1	7/3
99	1482.6	1013.4	33/14
100	1497.6	1023.6	19/8
101	1512.6	1033.9
102	1527.6	1044.1	29/12
103	1542.5	1054.3
104	1557.5	1064.6
105	1572.5	1074.8
106	1587.5	1085	5/2
107	1602.4	1095.3
108	1617.4	1105.5	28/11
109	1632.4	1115.7
110	1647.4	1126
111	1662.3	1136.2	47/18
112	1677.3	1146.5	29/11
113	1692.3	1156.7
114	1707.3	1166.9
115	1722.2	1177.2
116	1737.2	1187.4	30/11
117	1752.2	1197.6	11/4
118	1767.2	1207.9	25/9
119	1782.1	1218.1	14/5
120	1797.1	1228.3
121	1812.1	1238.6
122	1827.1	1248.8	23/8
123	1842.1	1259.1	29/10
124	1857	1269.3
125	1872	1279.5
126	1887	1289.8
127	1902	1300	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)