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	14.9
2	29.7
3	44.6	38/37, 39/38
4	59.4
5	74.3	47/45
6	89.2
7	104	52/49
8	118.9	15/14
9	133.7
10	148.6	49/45
11	163.4
12	178.3	41/37, 51/46
13	193.2	19/17, 47/42
14	208	44/39
15	222.9	33/29
16	237.7	31/27, 39/34, 47/41
17	252.6	22/19
18	267.5	7/6
19	282.3
20	297.2	51/43
21	312
22	326.9
23	341.8
24	356.6
25	371.5	26/21
26	386.3	5/4
27	401.2	29/23
28	416.1
29	430.9
30	445.8	22/17
31	460.6	47/36
32	475.5
33	490.3
34	505.2
35	520.1
36	534.9	49/36
37	549.8
38	564.6	18/13, 43/31
39	579.5
40	594.4	31/22
41	609.2	27/19, 37/26
42	624.1	33/23
43	638.9
44	653.8	35/24
45	668.7
46	683.5	43/29, 46/31
47	698.4
48	713.2
49	728.1
50	743
51	757.8
52	772.7	25/16
53	787.5	41/26
54	802.4	27/17
55	817.2
56	832.1	21/13
57	847	31/19, 44/27
58	861.8	51/31
59	876.7
60	891.5
61	906.4
62	921.3	46/27
63	936.1
64	951	26/15, 45/26
65	965.8
66	980.7	37/21
67	995.6
68	1010.4
69	1025.3	38/21, 47/26
70	1040.1	31/17
71	1055
72	1069.8	13/7
73	1084.7	43/23
74	1099.6	17/9
75	1114.4
76	1129.3	48/25
77	1144.1
78	1159	41/21, 43/22
79	1173.9
80	1188.7
81	1203.6
82	1218.4
83	1233.3
84	1248.2	37/18
85	1263
86	1277.9	23/11
87	1292.7	19/9
88	1307.6
89	1322.5
90	1337.3	13/6
91	1352.2
92	1367
93	1381.9
94	1396.7
95	1411.6
96	1426.5	41/18
97	1441.3
98	1456.2	51/22
99	1471
100	1485.9
101	1500.8
102	1515.6	12/5
103	1530.5	46/19
104	1545.3
105	1560.2
106	1575.1
107	1589.9
108	1604.8	43/17
109	1619.6
110	1634.5	18/7
111	1649.4
112	1664.2	34/13
113	1679.1	29/11
114	1693.9
115	1708.8	51/19
116	1723.6	46/17
117	1738.5
118	1753.4
119	1768.2
120	1783.1	14/5
121	1797.9
122	1812.8
123	1827.7
124	1842.5
125	1857.4	38/13
126	1872.2
127	1887.1
128	1902	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)