128edt

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128edt

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Prime factorization	27
Step size	14.859¢
Octave	81\128edt (1203.58¢)
Consistency limit	7
Distinct consistency limit	7

128 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 128edt or 128ed3), is a nonoctave tuning system that divides the interval of 3/1 into 128 equal parts of about 14.9 ¢ each. Each step represents a frequency ratio of 3^1/128, or the 128th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	14.859
2	29.718
3	44.577	38/37, 39/38
4	59.436
5	74.295	47/45
6	89.154
7	104.013	52/49
8	118.872	15/14
9	133.731
10	148.59	49/45
11	163.449
12	178.308	41/37, 51/46
13	193.167	19/17, 47/42
14	208.026	44/39
15	222.885	33/29
16	237.744	31/27, 39/34, 47/41
17	252.603	22/19
18	267.462	7/6
19	282.321
20	297.18	51/43
21	312.039
22	326.899
23	341.758
24	356.617
25	371.476	26/21
26	386.335	5/4
27	401.194	29/23
28	416.053
29	430.912
30	445.771	22/17
31	460.63	47/36
32	475.489
33	490.348
34	505.207
35	520.066
36	534.925	49/36
37	549.784
38	564.643	18/13, 43/31
39	579.502
40	594.361	31/22
41	609.22	27/19, 37/26
42	624.079	33/23
43	638.938
44	653.797	35/24
45	668.656
46	683.515	43/29, 46/31
47	698.374
48	713.233
49	728.092
50	742.951
51	757.81
52	772.669	25/16
53	787.528	41/26
54	802.387	27/17
55	817.246
56	832.105	21/13
57	846.964	31/19, 44/27
58	861.823	51/31
59	876.682
60	891.541
61	906.4
62	921.259	46/27
63	936.118
64	950.978	26/15, 45/26
65	965.837
66	980.696	37/21
67	995.555
68	1010.414
69	1025.273	38/21, 47/26
70	1040.132	31/17
71	1054.991
72	1069.85	13/7
73	1084.709	43/23
74	1099.568	17/9
75	1114.427
76	1129.286	48/25
77	1144.145
78	1159.004	41/21, 43/22
79	1173.863
80	1188.722
81	1203.581
82	1218.44
83	1233.299
84	1248.158	37/18
85	1263.017
86	1277.876	23/11
87	1292.735	19/9
88	1307.594
89	1322.453
90	1337.312	13/6
91	1352.171
92	1367.03
93	1381.889
94	1396.748
95	1411.607
96	1426.466	41/18
97	1441.325
98	1456.184	51/22
99	1471.043
100	1485.902
101	1500.761
102	1515.62	12/5
103	1530.479	46/19
104	1545.338
105	1560.197
106	1575.056
107	1589.916
108	1604.775	43/17
109	1619.634
110	1634.493	18/7
111	1649.352
112	1664.211	34/13
113	1679.07	29/11
114	1693.929
115	1708.788	51/19
116	1723.647	46/17
117	1738.506
118	1753.365
119	1768.224
120	1783.083	14/5
121	1797.942
122	1812.801
123	1827.66
124	1842.519
125	1857.378	38/13
126	1872.237
127	1887.096
128	1901.955	3/1

Harmonics

Approximation of harmonics in 128edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3.58	+0.00	+7.16	+7.18	+3.58	+4.17	-4.12	+0.00	-4.10	-5.65	+7.16
	Relative (%)	+24.1	+0.0	+48.2	+48.3	+24.1	+28.1	-27.7	+0.0	-27.6	-38.0	+48.2
Steps (reduced)		81 (81)	128 (0)	162 (34)	188 (60)	209 (81)	227 (99)	242 (114)	256 (0)	268 (12)	279 (23)	290 (34)

Approximation of harmonics in 128edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.32	-7.11	+7.18	-0.54	-1.48	+3.58	-0.87	-0.51	+4.17	-2.07	-4.73
	Relative (%)	+15.6	-47.8	+48.3	-3.6	-9.9	+24.1	-5.8	-3.5	+28.1	-13.9	-31.8
Steps (reduced)		299 (43)	307 (51)	316 (60)	323 (67)	330 (74)	337 (81)	343 (87)	349 (93)	355 (99)	360 (104)	365 (109)