229edt

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229edt

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Prime factorization	229 (prime)
Step size	8.30548 ¢
Octave	144\229edt (1195.99 ¢)
Consistency limit	3
Distinct consistency limit	3

229 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 229edt or 229ed3), is a nonoctave tuning system that divides the interval of 3/1 into 229 equal parts of about 8.31 ¢ each. Each step represents a frequency ratio of 3^1/229, or the 229th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	8.31	5.68
2	16.61	11.35
3	24.92	17.03
4	33.22	22.71
5	41.53	28.38	42/41, 43/42
6	49.83	34.06	35/34
7	58.14	39.74
8	66.44	45.41
9	74.75	51.09
10	83.05	56.77	43/41
11	91.36	62.45	39/37, 58/55
12	99.67	68.12
13	107.97	73.8	33/31
14	116.28	79.48	31/29, 46/43
15	124.58	85.15	29/27
16	132.89	90.83
17	141.19	96.51	51/47
18	149.5	102.18
19	157.8	107.86	23/21
20	166.11	113.54
21	174.42	119.21
22	182.72	124.89
23	191.03	130.57
24	199.33	136.24	46/41
25	207.64	141.92	62/55
26	215.94	147.6
27	224.25	153.28	33/29, 74/65
28	232.55	158.95
29	240.86	164.63
30	249.16	170.31
31	257.47	175.98
32	265.78	181.66
33	274.08	187.34	41/35
34	282.39	193.01
35	290.69	198.69
36	299	204.37
37	307.3	210.04
38	315.61	215.72	6/5
39	323.91	221.4	41/34, 47/39
40	332.22	227.07
41	340.52	232.75
42	348.83	238.43
43	357.14	244.1	43/35
44	365.44	249.78	21/17
45	373.75	255.46
46	382.05	261.14
47	390.36	266.81
48	398.66	272.49	34/27
49	406.97	278.17	43/34
50	415.27	283.84
51	423.58	289.52
52	431.88	295.2
53	440.19	300.87	58/45
54	448.5	306.55	35/27
55	456.8	312.23
56	465.11	317.9	17/13
57	473.41	323.58	46/35
58	481.72	329.26
59	490.02	334.93
60	498.33	340.61
61	506.63	346.29	63/47, 75/56
62	514.94	351.97	35/26
63	523.25	357.64	23/17
64	531.55	363.32
65	539.86	369
66	548.16	374.67
67	556.47	380.35	51/37
68	564.77	386.03
69	573.08	391.7
70	581.38	397.38
71	589.69	403.06
72	597.99	408.73	65/46
73	606.3	414.41
74	614.61	420.09
75	622.91	425.76
76	631.22	431.44	36/25
77	639.52	437.12	55/38
78	647.83	442.79
79	656.13	448.47	19/13
80	664.44	454.15	69/47
81	672.74	459.83
82	681.05	465.5	43/29
83	689.35	471.18
84	697.66	476.86
85	705.97	482.53
86	714.27	488.21	68/45
87	722.58	493.89	41/27
88	730.88	499.56
89	739.19	505.24
90	747.49	510.92	57/37
91	755.8	516.59	65/42
92	764.1	522.27	14/9
93	772.41	527.95
94	780.72	533.62
95	789.02	539.3	41/26
96	797.33	544.98	65/41
97	805.63	550.66	43/27
98	813.94	556.33
99	822.24	562.01	37/23, 45/28
100	830.55	567.69	21/13
101	838.85	573.36
102	847.16	579.04	31/19
103	855.46	584.72	77/47
104	863.77	590.39
105	872.08	596.07
106	880.38	601.75
107	888.69	607.42
108	896.99	613.1
109	905.3	618.78
110	913.6	624.45	39/23
111	921.91	630.13	46/27, 63/37
112	930.21	635.81	65/38
113	938.52	641.48
114	946.82	647.16	19/11
115	955.13	652.84	33/19
116	963.44	658.52
117	971.74	664.19
118	980.05	669.87	37/21
119	988.35	675.55	23/13
120	996.66	681.22
121	1004.96	686.9
122	1013.27	692.58
123	1021.57	698.25	74/41
124	1029.88	703.93
125	1038.19	709.61
126	1046.49	715.28
127	1054.8	720.96	57/31
128	1063.1	726.64
129	1071.41	732.31	13/7
130	1079.71	737.99	28/15, 69/37
131	1088.02	743.67
132	1096.32	749.34
133	1104.63	755.02
134	1112.93	760.7
135	1121.24	766.38	65/34
136	1129.55	772.05
137	1137.85	777.73	27/14
138	1146.16	783.41
139	1154.46	789.08	37/19
140	1162.77	794.76
141	1171.07	800.44
142	1179.38	806.11
143	1187.68	811.79
144	1195.99	817.47
145	1204.29	823.14
146	1212.6	828.82
147	1220.91	834.5
148	1229.21	840.17
149	1237.52	845.85	47/23
150	1245.82	851.53	39/19
151	1254.13	857.21
152	1262.43	862.88
153	1270.74	868.56	25/12
154	1279.04	874.24
155	1287.35	879.91
156	1295.65	885.59	74/35
157	1303.96	891.27
158	1312.27	896.94
159	1320.57	902.62
160	1328.88	908.3
161	1337.18	913.97
162	1345.49	919.65	37/17
163	1353.79	925.33
164	1362.1	931
165	1370.4	936.68
166	1378.71	942.36	51/23
167	1387.02	948.03
168	1395.32	953.71	47/21, 56/25
169	1403.63	959.39
170	1411.93	965.07
171	1420.24	970.74
172	1428.54	976.42
173	1436.85	982.1	39/17
174	1445.15	987.77
175	1453.46	993.45
176	1461.76	999.13
177	1470.07	1004.8
178	1478.38	1010.48
179	1486.68	1016.16
180	1494.99	1021.83
181	1503.29	1027.51
182	1511.6	1033.19
183	1519.9	1038.86
184	1528.21	1044.54
185	1536.51	1050.22	17/7
186	1544.82	1055.9
187	1553.12	1061.57
188	1561.43	1067.25
189	1569.74	1072.93
190	1578.04	1078.6
191	1586.35	1084.28	5/2
192	1594.65	1089.96
193	1602.96	1095.63
194	1611.26	1101.31
195	1619.57	1106.99
196	1627.87	1112.66
197	1636.18	1118.34
198	1644.49	1124.02
199	1652.79	1129.69
200	1661.1	1135.37
201	1669.4	1141.05
202	1677.71	1146.72	29/11
203	1686.01	1152.4
204	1694.32	1158.08
205	1702.62	1163.76
206	1710.93	1169.43
207	1719.23	1175.11
208	1727.54	1180.79
209	1735.85	1186.46
210	1744.15	1192.14	63/23
211	1752.46	1197.82
212	1760.76	1203.49	47/17
213	1769.07	1209.17
214	1777.37	1214.85
215	1785.68	1220.52
216	1793.98	1226.2	31/11
217	1802.29	1231.88
218	1810.59	1237.55	37/13
219	1818.9	1243.23
220	1827.21	1248.91
221	1835.51	1254.59
222	1843.82	1260.26
223	1852.12	1265.94
224	1860.43	1271.62	41/14
225	1868.73	1277.29
226	1877.04	1282.97
227	1885.34	1288.65
228	1893.65	1294.32
229	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 229edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-4.01	+0.00	+0.28	-3.98	-4.01	+3.20	-3.73	+0.00	+0.32	+1.42	+0.28
	Relative (%)	-48.3	+0.0	+3.4	-47.9	-48.3	+38.5	-44.9	+0.0	+3.8	+17.1	+3.4
Steps (reduced)		144 (144)	229 (0)	289 (60)	335 (106)	373 (144)	406 (177)	433 (204)	458 (0)	480 (22)	500 (42)	518 (60)

Approximation of harmonics in 229edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.90	-0.81	-3.98	+0.57	+3.58	-4.01	+2.05	-3.69	+3.20	-2.59	+3.51
	Relative (%)	+35.0	-9.8	-47.9	+6.8	+43.1	-48.3	+24.7	-44.5	+38.5	-31.2	+42.3
Steps (reduced)		535 (77)	550 (92)	564 (106)	578 (120)	591 (133)	602 (144)	614 (156)	624 (166)	635 (177)	644 (186)	654 (196)