144edt

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144edt

145edt →

Prime factorization	24 × 32
Step size	13.208¢
Octave	91\144edt (1201.93¢)
Consistency limit	10
Distinct consistency limit	10

144 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 144edt or 144ed3), is a nonoctave tuning system that divides the interval of 3/1 into 144 equal parts of about 13.2⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/144, or the 144th root of 3.

144edt is notable for being the first edt that is consistent to the no-twos 37-throdd limit, due to being highly accurate in the 3.5.7 subgroup while having a flat tendency for most higher primes up to 37; this record is not matched again until 316edt and not surpassed until 493edt (the latter essentially being a slight octave compression of 311edo).

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	13.2	9
2	26.4	18.1
3	39.6	27.1	43/42, 44/43, 45/44, 46/45
4	52.8	36.1	34/33
5	66	45.1	27/26
6	79.2	54.2	22/21, 45/43
7	92.5	63.2	19/18, 39/37
8	105.7	72.2	50/47
9	118.9	81.3	15/14
10	132.1	90.3	27/25, 41/38, 55/51
11	145.3	99.3	25/23, 37/34
12	158.5	108.3	23/21, 34/31
13	171.7	117.4	21/19
14	184.9	126.4	49/44
15	198.1	135.4	37/33, 46/41
16	211.3	144.4	26/23, 35/31
17	224.5	153.5	33/29, 41/36, 49/43
18	237.7	162.5	31/27, 39/34, 47/41
19	251	171.5	52/45
20	264.2	180.6
21	277.4	189.6	27/23
22	290.6	198.6	13/11
23	303.8	207.6	31/26, 56/47
24	317	216.7	6/5
25	330.2	225.7	23/19, 52/43
26	343.4	234.7	50/41
27	356.6	243.8	43/35
28	369.8	252.8	26/21
29	383	261.8
30	396.2	270.8	39/31, 44/35, 49/39
31	409.4	279.9	19/15
32	422.7	288.9	37/29
33	435.9	297.9	9/7
34	449.1	306.9	35/27
35	462.3	316	47/36
36	475.5	325	25/19, 54/41
37	488.7	334
38	501.9	343.1
39	515.1	352.1	35/26
40	528.3	361.1	19/14
41	541.5	370.1	26/19, 41/30
42	554.7	379.2	51/37
43	567.9	388.2	25/18, 43/31
44	581.2	397.2	7/5
45	594.4	406.3	31/22, 55/39
46	607.6	415.3	27/19, 44/31
47	620.8	424.3
48	634	433.3	49/34
49	647.2	442.4
50	660.4	451.4	41/28
51	673.6	460.4	31/21
52	686.8	469.4	52/35, 55/37
53	700	478.5
54	713.2	487.5
55	726.4	496.5	35/23, 38/25
56	739.6	505.6	23/15
57	752.9	514.6	17/11
58	766.1	523.6	14/9
59	779.3	532.6
60	792.5	541.7	49/31
61	805.7	550.7	43/27
62	818.9	559.7
63	832.1	568.8	55/34
64	845.3	577.8	44/27
65	858.5	586.8	23/14
66	871.7	595.8	43/26
67	884.9	604.9	5/3
68	898.1	613.9	42/25, 47/28
69	911.4	622.9	22/13
70	924.6	631.9	29/17
71	937.8	641	43/25
72	951	650	26/15, 45/26
73	964.2	659
74	977.4	668.1	44/25, 51/29
75	990.6	677.1	39/22
76	1003.8	686.1	25/14
77	1017	695.1	9/5
78	1030.2	704.2	49/27
79	1043.4	713.2	42/23
80	1056.6	722.2	35/19, 46/25
81	1069.8	731.3
82	1083.1	740.3	43/23
83	1096.3	749.3	49/26
84	1109.5	758.3	55/29
85	1122.7	767.4	44/23
86	1135.9	776.4	27/14, 52/27
87	1149.1	785.4	33/17
88	1162.3	794.4	45/23, 47/24
89	1175.5	803.5
90	1188.7	812.5
91	1201.9	821.5
92	1215.1	830.6
93	1228.3	839.6
94	1241.6	848.6	41/20, 43/21
95	1254.8	857.6
96	1268	866.7	52/25
97	1281.2	875.7	44/21
98	1294.4	884.7	19/9
99	1307.6	893.8
100	1320.8	902.8	15/7
101	1334	911.8	54/25
102	1347.2	920.8	37/17
103	1360.4	929.9
104	1373.6	938.9	42/19
105	1386.8	947.9	49/22
106	1400.1	956.9
107	1413.3	966	43/19, 52/23
108	1426.5	975	41/18
109	1439.7	984
110	1452.9	993.1	44/19
111	1466.1	1002.1	7/3
112	1479.3	1011.1	47/20
113	1492.5	1020.1	45/19
114	1505.7	1029.2	31/13
115	1518.9	1038.2
116	1532.1	1047.2	46/19
117	1545.3	1056.3
118	1558.5	1065.3
119	1571.8	1074.3
120	1585	1083.3	5/2
121	1598.2	1092.4
122	1611.4	1101.4	33/13
123	1624.6	1110.4	23/9
124	1637.8	1119.4
125	1651	1128.5
126	1664.2	1137.5	34/13
127	1677.4	1146.5	29/11
128	1690.6	1155.6
129	1703.8	1164.6
130	1717	1173.6
131	1730.3	1182.6	19/7
132	1743.5	1191.7	52/19
133	1756.7	1200.7
134	1769.9	1209.7	25/9
135	1783.1	1218.8	14/5
136	1796.3	1227.8
137	1809.5	1236.8	37/13, 54/19
138	1822.7	1245.8	43/15
139	1835.9	1254.9	26/9
140	1849.1	1263.9
141	1862.3	1272.9	44/15
142	1875.5	1281.9
143	1888.7	1291
144	1902	1300	3/1

Harmonics

Approximation of prime harmonics in 144edt

Harmonic		2	3	5	7	11	13	17	19	23
Error	Absolute (¢)	+1.93	+0.00	+0.58	-0.78	-4.00	-2.63	-4.78	+0.78	+0.22
	Relative (%)	+14.6	+0.0	+4.4	-5.9	-30.3	-19.9	-36.2	+5.9	+1.7
Steps (reduced)		91 (91)	144 (0)	211 (67)	255 (111)	314 (26)	336 (48)	371 (83)	386 (98)	411 (123)

Approximation of odd harmonics in 144edt

Harmonic		25	27	29	31	33	35	37	39	41	43	45
Error	Absolute (¢)	+1.16	+0.00	-4.84	-1.43	-4.00	-0.20	-3.95	-2.63	+3.24	+0.04	+0.58
	Relative (%)	+8.8	+0.0	-36.6	-10.8	-30.3	-1.5	-29.9	-19.9	+24.6	+0.3	+4.4
Steps (reduced)		422 (134)	432 (0)	441 (9)	450 (18)	458 (26)	466 (34)	473 (41)	480 (48)	487 (55)	493 (61)	499 (67)