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	Hekts	Approximate ratios
0	0	0	1/1
1	12.9	8.8
2	25.7	17.6
3	38.6	26.4
4	51.4	35.1	34/33, 35/34
5	64.3	43.9	27/26
6	77.1	52.7	23/22
7	90	61.5
8	102.8	70.3	35/33, 52/49
9	115.7	79.1	31/29
10	128.5	87.8
11	141.4	96.6	38/35, 51/47
12	154.2	105.4	47/43
13	167.1	114.2	54/49
14	179.9	123
15	192.8	131.8	19/17
16	205.6	140.5
17	218.5	149.3	42/37
18	231.3	158.1
19	244.2	166.9	38/33
20	257	175.7	29/25
21	269.9	184.5
22	282.7	193.2
23	295.6	202	51/43
24	308.4	210.8	49/41
25	321.3	219.6
26	334.1	228.4	57/47
27	347	237.2	11/9
28	359.8	245.9
29	372.7	254.7	31/25
30	385.5	263.5
31	398.4	272.3	34/27, 39/31
32	411.2	281.1	33/26, 52/41
33	424.1	289.9	23/18
34	436.9	298.6
35	449.8	307.4	35/27
36	462.6	316.2
37	475.5	325	25/19, 54/41
38	488.3	333.8	57/43
39	501.2	342.6
40	514	351.4	35/26, 39/29
41	526.9	360.1
42	539.7	368.9	41/30
43	552.6	377.7
44	565.4	386.5	43/31
45	578.3	395.3
46	591.1	404.1	38/27
47	604	412.8
48	616.9	421.6	10/7
49	629.7	430.4
50	642.6	439.2
51	655.4	448	54/37
52	668.3	456.8	25/17
53	681.1	465.5	43/29
54	694	474.3
55	706.8	483.1
56	719.7	491.9	47/31, 50/33
57	732.5	500.7	29/19
58	745.4	509.5
59	758.2	518.2
60	771.1	527	39/25
61	783.9	535.8	11/7
62	796.8	544.6
63	809.6	553.4
64	822.5	562.2	37/23
65	835.3	570.9	34/21, 47/29
66	848.2	579.7	31/19, 49/30
67	861	588.5	51/31
68	873.9	597.3
69	886.7	606.1
70	899.6	614.9	37/22
71	912.4	623.6
72	925.3	632.4	29/17
73	938.1	641.2	43/25
74	951	650	26/15, 45/26
75	963.8	658.8
76	976.7	667.6	51/29
77	989.5	676.4
78	1002.4	685.1
79	1015.2	693.9
80	1028.1	702.7	38/21
81	1040.9	711.5	31/17
82	1053.8	720.3	57/31
83	1066.6	729.1	50/27
84	1079.5	737.8
85	1092.3	746.6	47/25
86	1105.2	755.4
87	1118	764.2	21/11
88	1130.9	773	25/13
89	1143.7	781.8
90	1156.6	790.5
91	1169.4	799.3	57/29
92	1182.3	808.1
93	1195.1	816.9
94	1208	825.7
95	1220.8	834.5
96	1233.7	843.2	51/25
97	1246.6	852	37/18
98	1259.4	860.8
99	1272.3	869.6
100	1285.1	878.4	21/10
101	1298	887.2	55/26
102	1310.8	895.9	49/23
103	1323.7	904.7
104	1336.5	913.5
105	1349.4	922.3
106	1362.2	931.1
107	1375.1	939.9
108	1387.9	948.6	29/13
109	1400.8	957.4
110	1413.6	966.2	43/19, 52/23
111	1426.5	975	41/18, 57/25
112	1439.3	983.8
113	1452.2	992.6
114	1465	1001.4
115	1477.9	1010.1	54/23
116	1490.7	1018.9	26/11
117	1503.6	1027.7	31/13
118	1516.4	1036.5
119	1529.3	1045.3
120	1542.1	1054.1
121	1555	1062.8	27/11
122	1567.8	1071.6	47/19
123	1580.7	1080.4
124	1593.5	1089.2
125	1606.4	1098	43/17
126	1619.2	1106.8
127	1632.1	1115.5
128	1644.9	1124.3
129	1657.8	1133.1
130	1670.6	1141.9
131	1683.5	1150.7	37/14
132	1696.3	1159.5
133	1709.2	1168.2	51/19
134	1722	1177
135	1734.9	1185.8	49/18
136	1747.7	1194.6
137	1760.6	1203.4	47/17
138	1773.4	1212.2
139	1786.3	1220.9
140	1799.1	1229.7
141	1812	1238.5
142	1824.8	1247.3
143	1837.7	1256.1	26/9
144	1850.6	1264.9
145	1863.4	1273.6
146	1876.3	1282.4
147	1889.1	1291.2
148	1902	1300	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)