114edt

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← 113edt

114edt

115edt →

Prime factorization	2 × 3 × 19
Step size	16.6838¢
Octave	72\114edt (1201.23¢) (→12\19edt)
Consistency limit	17
Distinct consistency limit	11

114 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 114edt or 114ed3), is a nonoctave tuning system that divides the interval of 3/1 into 114 equal parts of about 16.7 ¢ each. Each step represents a frequency ratio of 3^1/114, or the 114th root of 3.

114EDT is related to 72 edo, but with the 3/1 rather than the 2/1 being just, resulting in octaves being stretched by about 1.2347 cents stretched. It is consistent to the 18-integer-limit, and significantly improves on 72edo's approximation to 13.

Lookalikes: 72edo, 186ed6

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	16.7	11.4
2	33.4	22.8
3	50.1	34.2	34/33, 35/34, 36/35
4	66.7	45.6	26/25, 27/26
5	83.4	57	21/20, 43/41
6	100.1	68.4	18/17, 35/33
7	116.8	79.8	31/29, 46/43
8	133.5	91.2	27/25, 40/37
9	150.2	102.6	12/11
10	166.8	114	11/10
11	183.5	125.4	10/9
12	200.2	136.8	46/41
13	216.9	148.2	17/15
14	233.6	159.6
15	250.3	171.1	37/32
16	266.9	182.5	7/6
17	283.6	193.9	33/28
18	300.3	205.3	25/21, 44/37
19	317	216.7	6/5
20	333.7	228.1	40/33
21	350.4	239.5
22	367	250.9	21/17, 47/38
23	383.7	262.3
24	400.4	273.7	29/23, 34/27
25	417.1	285.1	14/11
26	433.8	296.5	9/7
27	450.5	307.9	35/27, 48/37
28	467.1	319.3
29	483.8	330.7	37/28, 41/31, 45/34
30	500.5	342.1
31	517.2	353.5	31/23
32	533.9	364.9	34/25
33	550.6	376.3	11/8
34	567.2	387.7	25/18, 43/31
35	583.9	399.1	7/5
36	600.6	410.5	41/29
37	617.3	421.9	10/7
38	634	433.3
39	650.7	444.7	16/11
40	667.4	456.1	25/17, 47/32
41	684	467.5	43/29, 46/31
42	700.7	478.9	3/2
43	717.4	490.4
44	734.1	501.8	26/17
45	750.8	513.2	37/24
46	767.5	524.6
47	784.1	536	11/7
48	800.8	547.4	27/17, 46/29
49	817.5	558.8
50	834.2	570.2	34/21
51	850.9	581.6	18/11
52	867.6	593	33/20
53	884.2	604.4	5/3
54	900.9	615.8	32/19, 37/22
55	917.6	627.2	17/10
56	934.3	638.6	12/7
57	951	650	26/15, 45/26
58	967.7	661.4	7/4
59	984.3	672.8	30/17
60	1001	684.2	41/23
61	1017.7	695.6	9/5
62	1034.4	707	20/11
63	1051.1	718.4	11/6
64	1067.8	729.8
65	1084.4	741.2	43/23
66	1101.1	752.6	17/9
67	1117.8	764	21/11
68	1134.5	775.4
69	1151.2	786.8	35/18
70	1167.9	798.2
71	1184.6	809.6
72	1201.2	821.1	2/1
73	1217.9	832.5
74	1234.6	843.9
75	1251.3	855.3	33/16, 35/17
76	1268	866.7
77	1284.7	878.1	21/10
78	1301.3	889.5
79	1318	900.9	15/7
80	1334.7	912.3
81	1351.4	923.7	24/11
82	1368.1	935.1
83	1384.8	946.5
84	1401.4	957.9
85	1418.1	969.3	34/15
86	1434.8	980.7
87	1451.5	992.1	37/16
88	1468.2	1003.5	7/3
89	1484.9	1014.9	33/14
90	1501.5	1026.3
91	1518.2	1037.7
92	1534.9	1049.1	17/7
93	1551.6	1060.5
94	1568.3	1071.9	47/19
95	1585	1083.3	5/2
96	1601.6	1094.7
97	1618.3	1106.1	28/11
98	1635	1117.5	18/7
99	1651.7	1128.9
100	1668.4	1140.4
101	1685.1	1151.8	45/17
102	1701.7	1163.2
103	1718.4	1174.6	27/10
104	1735.1	1186	30/11
105	1751.8	1197.4	11/4
106	1768.5	1208.8	25/9
107	1785.2	1220.2
108	1801.9	1231.6	17/6
109	1818.5	1243	20/7
110	1835.2	1254.4	26/9
111	1851.9	1265.8	35/12
112	1868.6	1277.2
113	1885.3	1288.6
114	1902	1300	3/1

Harmonics

Approximation of harmonics in 114edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.23	+0.00	+2.47	-0.12	+1.23	+1.30	+3.70	+0.00	+1.12	+2.95	+2.47
	Relative (%)	+7.4	+0.0	+14.8	-0.7	+7.4	+7.8	+22.2	+0.0	+6.7	+17.7	+14.8
Steps (reduced)		72 (72)	114 (0)	144 (30)	167 (53)	186 (72)	202 (88)	216 (102)	228 (0)	239 (11)	249 (21)	258 (30)

Approximation of harmonics in 114edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	+2.54	-0.12	+4.94	+0.09	+1.23	+7.73	+2.35	+1.30	+4.19	-6.03
	Relative (%)	-15.8	+15.2	-0.7	+29.6	+0.5	+7.4	+46.4	+14.1	+7.8	+25.1	-36.2
Steps (reduced)		266 (38)	274 (46)	281 (53)	288 (60)	294 (66)	300 (72)	306 (78)	311 (83)	316 (88)	321 (93)	325 (97)