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	Hekts	Approximate ratios
0	0	0	1/1
1	14.9	10.2
2	29.7	20.3
3	44.6	30.5	38/37, 39/38
4	59.4	40.6
5	74.3	50.8	47/45
6	89.2	60.9
7	104	71.1	52/49
8	118.9	81.3	15/14
9	133.7	91.4
10	148.6	101.6	49/45
11	163.4	111.7
12	178.3	121.9	41/37, 51/46
13	193.2	132	19/17, 47/42
14	208	142.2	44/39
15	222.9	152.3	33/29
16	237.7	162.5	31/27, 39/34, 47/41
17	252.6	172.7	22/19
18	267.5	182.8	7/6
19	282.3	193
20	297.2	203.1	51/43
21	312	213.3
22	326.9	223.4
23	341.8	233.6
24	356.6	243.8
25	371.5	253.9	26/21
26	386.3	264.1	5/4
27	401.2	274.2	29/23
28	416.1	284.4
29	430.9	294.5
30	445.8	304.7	22/17
31	460.6	314.8	47/36
32	475.5	325
33	490.3	335.2
34	505.2	345.3
35	520.1	355.5
36	534.9	365.6	49/36
37	549.8	375.8
38	564.6	385.9	18/13, 43/31
39	579.5	396.1
40	594.4	406.3	31/22
41	609.2	416.4	27/19, 37/26
42	624.1	426.6	33/23
43	638.9	436.7
44	653.8	446.9	35/24
45	668.7	457
46	683.5	467.2	43/29, 46/31
47	698.4	477.3
48	713.2	487.5
49	728.1	497.7
50	743	507.8
51	757.8	518
52	772.7	528.1	25/16
53	787.5	538.3	41/26
54	802.4	548.4	27/17
55	817.2	558.6
56	832.1	568.8	21/13
57	847	578.9	31/19, 44/27
58	861.8	589.1	51/31
59	876.7	599.2
60	891.5	609.4
61	906.4	619.5
62	921.3	629.7	46/27
63	936.1	639.8
64	951	650	26/15, 45/26
65	965.8	660.2
66	980.7	670.3	37/21
67	995.6	680.5
68	1010.4	690.6
69	1025.3	700.8	38/21, 47/26
70	1040.1	710.9	31/17
71	1055	721.1
72	1069.8	731.3	13/7
73	1084.7	741.4	43/23
74	1099.6	751.6	17/9
75	1114.4	761.7
76	1129.3	771.9	48/25
77	1144.1	782
78	1159	792.2	41/21, 43/22
79	1173.9	802.3
80	1188.7	812.5
81	1203.6	822.7
82	1218.4	832.8
83	1233.3	843
84	1248.2	853.1	37/18
85	1263	863.3
86	1277.9	873.4	23/11
87	1292.7	883.6	19/9
88	1307.6	893.8
89	1322.5	903.9
90	1337.3	914.1	13/6
91	1352.2	924.2
92	1367	934.4
93	1381.9	944.5
94	1396.7	954.7
95	1411.6	964.8
96	1426.5	975	41/18
97	1441.3	985.2
98	1456.2	995.3	51/22
99	1471	1005.5
100	1485.9	1015.6
101	1500.8	1025.8
102	1515.6	1035.9	12/5
103	1530.5	1046.1	46/19
104	1545.3	1056.3
105	1560.2	1066.4
106	1575.1	1076.6
107	1589.9	1086.7
108	1604.8	1096.9	43/17
109	1619.6	1107
110	1634.5	1117.2	18/7
111	1649.4	1127.3
112	1664.2	1137.5	34/13
113	1679.1	1147.7	29/11
114	1693.9	1157.8
115	1708.8	1168	51/19
116	1723.6	1178.1	46/17
117	1738.5	1188.3
118	1753.4	1198.4
119	1768.2	1208.6
120	1783.1	1218.8	14/5
121	1797.9	1228.9
122	1812.8	1239.1
123	1827.7	1249.2
124	1842.5	1259.4
125	1857.4	1269.5	38/13
126	1872.2	1279.7
127	1887.1	1289.8
128	1902	1300	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)