218edt

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218edt

219edt →

Prime factorization	2 × 109
Step size	8.72456 ¢
Octave	138\218edt (1203.99 ¢) (→ 69\109edt)
Consistency limit	3
Distinct consistency limit	3

218 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 218edt or 218ed3), is a nonoctave tuning system that divides the interval of 3/1 into 218 equal parts of about 8.72 ¢ each. Each step represents a frequency ratio of 3^1/218, or the 218th root of 3.

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	8.72	5.96
2	17.45	11.93
3	26.17	17.89
4	34.9	23.85	50/49, 51/50
5	43.62	29.82
6	52.35	35.78	34/33
7	61.07	41.74	57/55
8	69.8	47.71	51/49
9	78.52	53.67	45/43
10	87.25	59.63	41/39
11	95.97	65.6
12	104.69	71.56
13	113.42	77.52
14	122.14	83.49
15	130.87	89.45	41/38, 55/51
16	139.59	95.41
17	148.32	101.38	49/45
18	157.04	107.34	23/21
19	165.77	113.3	11/10
20	174.49	119.27
21	183.22	125.23	10/9
22	191.94	131.19	19/17
23	200.66	137.16	55/49
24	209.39	143.12	35/31
25	218.11	149.08
26	226.84	155.05	49/43, 57/50, 65/57
27	235.56	161.01	47/41, 63/55
28	244.29	166.97	38/33
29	253.01	172.94
30	261.74	178.9	50/43, 57/49
31	270.46	184.86
32	279.19	190.83
33	287.91	196.79
34	296.64	202.75
35	305.36	208.72
36	314.08	214.68
37	322.81	220.64	47/39
38	331.53	226.61	23/19
39	340.26	232.57
40	348.98	238.53
41	357.71	244.5
42	366.43	250.46	21/17
43	375.16	256.42	41/33
44	383.88	262.39
45	392.61	268.35	69/55
46	401.33	274.31	29/23
47	410.05	280.28	19/15
48	418.78	286.24
49	427.5	292.2
50	436.23	298.17
51	444.95	304.13
52	453.68	310.09	13/10
53	462.4	316.06
54	471.13	322.02
55	479.85	327.98	62/47
56	488.58	333.94	57/43, 65/49
57	497.3	339.91
58	506.02	345.87
59	514.75	351.83
60	523.47	357.8	23/17
61	532.2	363.76
62	540.92	369.72	41/30
63	549.65	375.69
64	558.37	381.65	29/21, 69/50
65	567.1	387.61	43/31
66	575.82	393.58	46/33
67	584.55	399.54
68	593.27	405.5	69/49
69	601.99	411.47
70	610.72	417.43	37/26
71	619.44	423.39
72	628.17	429.36
73	636.89	435.32	13/9
74	645.62	441.28	45/31
75	654.34	447.25	54/37
76	663.07	453.21
77	671.79	459.17
78	680.52	465.14
79	689.24	471.1	70/47
80	697.97	477.06
81	706.69	483.03
82	715.41	488.99	62/41, 65/43
83	724.14	494.95	41/27
84	732.86	500.92	29/19
85	741.59	506.88
86	750.31	512.84
87	759.04	518.81
88	767.76	524.77
89	776.49	530.73	47/30
90	785.21	536.7
91	793.94	542.66
92	802.66	548.62	62/39
93	811.38	554.59
94	820.11	560.55
95	828.83	566.51
96	837.56	572.48	60/37
97	846.28	578.44
98	855.01	584.4
99	863.73	590.37
100	872.46	596.33
101	881.18	602.29
102	889.91	608.26
103	898.63	614.22
104	907.35	620.18	49/29
105	916.08	626.15
106	924.8	632.11	29/17
107	933.53	638.07
108	942.25	644.04	50/29
109	950.98	650
110	959.7	655.96	47/27
111	968.43	661.93
112	977.15	667.89	51/29, 58/33
113	985.88	673.85
114	994.6	679.82
115	1003.32	685.78
116	1012.05	691.74	70/39
117	1020.77	697.71
118	1029.5	703.67
119	1038.22	709.63
120	1046.95	715.6
121	1055.67	721.56
122	1064.4	727.52	37/20
123	1073.12	733.49
124	1081.85	739.45
125	1090.57	745.41
126	1099.3	751.38
127	1108.02	757.34	55/29
128	1116.74	763.3
129	1125.47	769.27
130	1134.19	775.23
131	1142.92	781.19
132	1151.64	787.16
133	1160.37	793.12
134	1169.09	799.08	57/29
135	1177.82	805.05
136	1186.54	811.01
137	1195.27	816.97
138	1203.99	822.94
139	1212.71	828.9
140	1221.44	834.86
141	1230.16	840.83
142	1238.89	846.79
143	1247.61	852.75	37/18
144	1256.34	858.72	31/15
145	1265.06	864.68	27/13
146	1273.79	870.64
147	1282.51	876.61	65/31
148	1291.24	882.57
149	1299.96	888.53
150	1308.68	894.5	49/23
151	1317.41	900.46
152	1326.13	906.42
153	1334.86	912.39
154	1343.58	918.35	50/23, 63/29
155	1352.31	924.31
156	1361.03	930.28
157	1369.76	936.24
158	1378.48	942.2	51/23
159	1387.21	948.17
160	1395.93	954.13
161	1404.65	960.09
162	1413.38	966.06	43/19
163	1422.1	972.02
164	1430.83	977.98
165	1439.55	983.94	62/27
166	1448.28	989.91	30/13
167	1457	995.87
168	1465.73	1001.83
169	1474.45	1007.8
170	1483.18	1013.76
171	1491.9	1019.72	45/19
172	1500.63	1025.69	69/29
173	1509.35	1031.65	55/23
174	1518.07	1037.61
175	1526.8	1043.58
176	1535.52	1049.54	17/7
177	1544.25	1055.5
178	1552.97	1061.47
179	1561.7	1067.43
180	1570.42	1073.39	57/23
181	1579.15	1079.36
182	1587.87	1085.32
183	1596.6	1091.28
184	1605.32	1097.25
185	1614.04	1103.21
186	1622.77	1109.17
187	1631.49	1115.14
188	1640.22	1121.1	49/19
189	1648.94	1127.06	70/27
190	1657.67	1133.03
191	1666.39	1138.99	55/21
192	1675.12	1144.95	50/19
193	1683.84	1150.92
194	1692.57	1156.88
195	1701.29	1162.84
196	1710.01	1168.81	51/19
197	1718.74	1174.77	27/10
198	1727.46	1180.73
199	1736.19	1186.7	30/11
200	1744.91	1192.66	63/23
201	1753.64	1198.62
202	1762.36	1204.59
203	1771.09	1210.55
204	1779.81	1216.51
205	1788.54	1222.48
206	1797.26	1228.44
207	1805.98	1234.4
208	1814.71	1240.37
209	1823.43	1246.33	43/15
210	1832.16	1252.29	49/17
211	1840.88	1258.26	55/19
212	1849.61	1264.22
213	1858.33	1270.18
214	1867.06	1276.15	50/17
215	1875.78	1282.11
216	1884.51	1288.07
217	1893.23	1294.04
218	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 218edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3.99	+0.00	-0.74	-3.18	+3.99	-1.14	+3.25	+0.00	+0.81	+1.57	-0.74
	Relative (%)	+45.7	+0.0	-8.5	-36.4	+45.7	-13.1	+37.2	+0.0	+9.3	+18.0	-8.5
Steps (reduced)		138 (138)	218 (0)	275 (57)	319 (101)	356 (138)	386 (168)	413 (195)	436 (0)	457 (21)	476 (40)	493 (57)

Approximation of harmonics in 218edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+0.28	+2.85	-3.18	-1.49	-1.75	+3.99	-2.37	-3.92	-1.14	-3.16	-1.60
	Relative (%)	+3.2	+32.6	-36.4	-17.1	-20.1	+45.7	-27.1	-45.0	-13.1	-36.2	-18.3
Steps (reduced)		509 (73)	524 (88)	537 (101)	550 (114)	562 (126)	574 (138)	584 (148)	594 (158)	604 (168)	613 (177)	622 (186)