114edt

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

← 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

Division of the third harmonic into 114 equal parts (114EDT) is related to 72 edo, but with the 3/1 rather than the 2/1 being just. The octave is about 1.2347 cents stretched and the step size is about 16.6838 cents. It is consistent to the 18-integer-limit, and significantly improves on 72edo's approximation to 13.

Lookalikes: 72edo, 186ed6

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	16.7
2	33.4
3	50.1	34/33, 35/34, 36/35
4	66.7	26/25, 27/26
5	83.4	21/20, 43/41
6	100.1	18/17, 35/33
7	116.8	31/29, 46/43
8	133.5	27/25, 40/37
9	150.2	12/11
10	166.8	11/10
11	183.5	10/9
12	200.2	46/41
13	216.9	17/15
14	233.6
15	250.3	37/32
16	266.9	7/6
17	283.6	33/28
18	300.3	25/21, 44/37
19	317	6/5
20	333.7	40/33
21	350.4
22	367	21/17, 47/38
23	383.7
24	400.4	29/23, 34/27
25	417.1	14/11
26	433.8	9/7
27	450.5	35/27, 48/37
28	467.1
29	483.8	37/28, 41/31, 45/34
30	500.5
31	517.2	31/23
32	533.9	34/25
33	550.6	11/8
34	567.2	25/18, 43/31
35	583.9	7/5
36	600.6	41/29
37	617.3	10/7
38	634
39	650.7	16/11
40	667.4	25/17, 47/32
41	684	43/29, 46/31
42	700.7	3/2
43	717.4
44	734.1	26/17
45	750.8	37/24
46	767.5
47	784.1	11/7
48	800.8	27/17, 46/29
49	817.5
50	834.2	34/21
51	850.9	18/11
52	867.6	33/20
53	884.2	5/3
54	900.9	32/19, 37/22
55	917.6	17/10
56	934.3	12/7
57	951	26/15, 45/26
58	967.7	7/4
59	984.3	30/17
60	1001	41/23
61	1017.7	9/5
62	1034.4	20/11
63	1051.1	11/6
64	1067.8
65	1084.4	43/23
66	1101.1	17/9
67	1117.8	21/11
68	1134.5
69	1151.2	35/18
70	1167.9
71	1184.6
72	1201.2	2/1
73	1217.9
74	1234.6
75	1251.3	33/16, 35/17
76	1268
77	1284.7	21/10
78	1301.3
79	1318	15/7
80	1334.7
81	1351.4	24/11
82	1368.1
83	1384.8
84	1401.4
85	1418.1	34/15
86	1434.8
87	1451.5	37/16
88	1468.2	7/3
89	1484.9	33/14
90	1501.5
91	1518.2
92	1534.9	17/7
93	1551.6
94	1568.3	47/19
95	1585	5/2
96	1601.6
97	1618.3	28/11
98	1635	18/7
99	1651.7
100	1668.4
101	1685.1	45/17
102	1701.7
103	1718.4	27/10
104	1735.1	30/11
105	1751.8	11/4
106	1768.5	25/9
107	1785.2
108	1801.9	17/6
109	1818.5	20/7
110	1835.2	26/9
111	1851.9	35/12
112	1868.6
113	1885.3
114	1902	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)