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	Approximate Ratios
0	0	1/1
1	13.208
2	26.416
3	39.624	43/42, 44/43, 45/44, 46/45
4	52.832	34/33
5	66.04	27/26
6	79.248	22/21, 45/43
7	92.456	19/18, 39/37
8	105.664	50/47
9	118.872	15/14
10	132.08	27/25, 41/38, 55/51
11	145.288	25/23, 37/34
12	158.496	23/21, 34/31
13	171.704	21/19
14	184.912	49/44
15	198.12	37/33, 46/41
16	211.328	26/23, 35/31
17	224.536	33/29, 41/36, 49/43
18	237.744	31/27, 39/34, 47/41
19	250.952	52/45
20	264.16
21	277.368	27/23
22	290.576	13/11
23	303.784	31/26, 56/47
24	316.993	6/5
25	330.201	23/19, 52/43
26	343.409	50/41
27	356.617	43/35
28	369.825	26/21
29	383.033
30	396.241	39/31, 44/35, 49/39
31	409.449	19/15
32	422.657	37/29
33	435.865	9/7
34	449.073	35/27
35	462.281	47/36
36	475.489	25/19, 54/41
37	488.697
38	501.905
39	515.113	35/26
40	528.321	19/14
41	541.529	26/19, 41/30
42	554.737	51/37
43	567.945	25/18, 43/31
44	581.153	7/5
45	594.361	31/22, 55/39
46	607.569	27/19, 44/31
47	620.777
48	633.985	49/34
49	647.193
50	660.401	41/28
51	673.609	31/21
52	686.817	52/35, 55/37
53	700.025
54	713.233
55	726.441	35/23, 38/25
56	739.649	23/15
57	752.857	17/11
58	766.065	14/9
59	779.273
60	792.481	49/31
61	805.689	43/27
62	818.897
63	832.105	55/34
64	845.313	44/27
65	858.521	23/14
66	871.729	43/26
67	884.937	5/3
68	898.145	42/25, 47/28
69	911.353	22/13
70	924.561	29/17
71	937.769	43/25
72	950.978	26/15, 45/26
73	964.186
74	977.394	44/25, 51/29
75	990.602	39/22
76	1003.81	25/14
77	1017.018	9/5
78	1030.226	49/27
79	1043.434	42/23
80	1056.642	35/19, 46/25
81	1069.85
82	1083.058	43/23
83	1096.266	49/26
84	1109.474	55/29
85	1122.682	44/23
86	1135.89	27/14, 52/27
87	1149.098	33/17
88	1162.306	45/23, 47/24
89	1175.514
90	1188.722
91	1201.93
92	1215.138
93	1228.346
94	1241.554	41/20, 43/21
95	1254.762
96	1267.97	52/25
97	1281.178	44/21
98	1294.386	19/9
99	1307.594
100	1320.802	15/7
101	1334.01	54/25
102	1347.218	37/17
103	1360.426
104	1373.634	42/19
105	1386.842	49/22
106	1400.05
107	1413.258	43/19, 52/23
108	1426.466	41/18
109	1439.674
110	1452.882	44/19
111	1466.09	7/3
112	1479.298	47/20
113	1492.506	45/19
114	1505.714	31/13
115	1518.922
116	1532.13	46/19
117	1545.338
118	1558.546
119	1571.754
120	1584.963	5/2
121	1598.171
122	1611.379	33/13
123	1624.587	23/9
124	1637.795
125	1651.003
126	1664.211	34/13
127	1677.419	29/11
128	1690.627
129	1703.835
130	1717.043
131	1730.251	19/7
132	1743.459	52/19
133	1756.667
134	1769.875	25/9
135	1783.083	14/5
136	1796.291
137	1809.499	37/13, 54/19
138	1822.707	43/15
139	1835.915	26/9
140	1849.123
141	1862.331	44/15
142	1875.539
143	1888.747
144	1901.955	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)