148edt

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148edt

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Prime factorization	22 × 37
Step size	12.851¢
Octave	93\148edt (1195.15¢)
Consistency limit	2
Distinct consistency limit	2

148 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 148edt or 148ed3), is a nonoctave tuning system that divides the interval of 3/1 into 148 equal parts of about 12.9 ¢ each. Each step represents a frequency ratio of 3^1/148, or the 148th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	12.851
2	25.702
3	38.553
4	51.404	34/33, 35/34
5	64.255	27/26
6	77.106	23/22
7	89.957
8	102.808	35/33, 52/49
9	115.659	31/29
10	128.51
11	141.362	38/35, 51/47
12	154.213	47/43
13	167.064	54/49
14	179.915
15	192.766	19/17
16	205.617
17	218.468	42/37
18	231.319
19	244.17	38/33
20	257.021	29/25
21	269.872
22	282.723
23	295.574	51/43
24	308.425	49/41
25	321.276
26	334.127	57/47
27	346.978	11/9
28	359.829
29	372.68	31/25
30	385.531
31	398.382	34/27, 39/31
32	411.234	33/26, 52/41
33	424.085	23/18
34	436.936
35	449.787	35/27
36	462.638
37	475.489	25/19, 54/41
38	488.34	57/43
39	501.191
40	514.042	35/26, 39/29
41	526.893
42	539.744	41/30
43	552.595
44	565.446	43/31
45	578.297
46	591.148	38/27
47	603.999
48	616.85	10/7
49	629.701
50	642.552
51	655.403	54/37
52	668.254	25/17
53	681.106	43/29
54	693.957
55	706.808
56	719.659	47/31, 50/33
57	732.51	29/19
58	745.361
59	758.212
60	771.063	39/25
61	783.914	11/7
62	796.765
63	809.616
64	822.467	37/23
65	835.318	34/21, 47/29
66	848.169	31/19, 49/30
67	861.02	51/31
68	873.871
69	886.722
70	899.573	37/22
71	912.424
72	925.275	29/17
73	938.126	43/25
74	950.978	26/15, 45/26
75	963.829
76	976.68	51/29
77	989.531
78	1002.382
79	1015.233
80	1028.084	38/21
81	1040.935	31/17
82	1053.786	57/31
83	1066.637	50/27
84	1079.488
85	1092.339	47/25
86	1105.19
87	1118.041	21/11
88	1130.892	25/13
89	1143.743
90	1156.594
91	1169.445	57/29
92	1182.296
93	1195.147
94	1207.998
95	1220.849
96	1233.701	51/25
97	1246.552	37/18
98	1259.403
99	1272.254
100	1285.105	21/10
101	1297.956	55/26
102	1310.807	49/23
103	1323.658
104	1336.509
105	1349.36
106	1362.211
107	1375.062
108	1387.913	29/13
109	1400.764
110	1413.615	43/19, 52/23
111	1426.466	41/18, 57/25
112	1439.317
113	1452.168
114	1465.019
115	1477.87	54/23
116	1490.721	26/11
117	1503.573	31/13
118	1516.424
119	1529.275
120	1542.126
121	1554.977	27/11
122	1567.828	47/19
123	1580.679
124	1593.53
125	1606.381	43/17
126	1619.232
127	1632.083
128	1644.934
129	1657.785
130	1670.636
131	1683.487	37/14
132	1696.338
133	1709.189	51/19
134	1722.04
135	1734.891	49/18
136	1747.742
137	1760.593	47/17
138	1773.445
139	1786.296
140	1799.147
141	1811.998
142	1824.849
143	1837.7	26/9
144	1850.551
145	1863.402
146	1876.253
147	1889.104
148	1901.955	3/1

Harmonics

Approximation of harmonics in 148edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-4.85	+0.00	+3.15	+2.36	-4.85	-1.85	-1.71	+0.00	-2.49	-0.43	+3.15
	Relative (%)	-37.8	+0.0	+24.5	+18.4	-37.8	-14.4	-13.3	+0.0	-19.4	-3.3	+24.5
Steps (reduced)		93 (93)	148 (0)	187 (39)	217 (69)	241 (93)	262 (114)	280 (132)	296 (0)	310 (14)	323 (27)	335 (39)

Approximation of harmonics in 148edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.93	+6.15	+2.36	+6.29	+4.14	-4.85	+4.35	+5.51	-1.85	-5.28	-5.13
	Relative (%)	+46.2	+47.8	+18.4	+49.0	+32.3	-37.8	+33.9	+42.9	-14.4	-41.1	-39.9
Steps (reduced)		346 (50)	356 (60)	365 (69)	374 (78)	382 (86)	389 (93)	397 (101)	404 (108)	410 (114)	416 (120)	422 (126)