238edo

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238edo

239edo →

Prime factorization	2 × 7 × 17
Step size	5.04202 ¢
Fifth	139\238 (700.84 ¢)
Semitones (A1:m2)	21:19 (105.9 ¢ : 95.8 ¢)
Consistency limit	3
Distinct consistency limit	3

Theory

Approximation of prime harmonics in 238edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-1.11	+1.92	-0.76	-1.74	+1.49	+0.93	-0.03	+1.98	-1.01	-0.50
	Relative (%)	+0.0	-22.1	+38.1	-15.0	-34.5	+29.5	+18.4	-0.7	+39.2	-19.9	-9.9
Steps (reduced)		238 (0)	377 (139)	553 (77)	668 (192)	823 (109)	881 (167)	973 (21)	1011 (59)	1077 (125)	1156 (204)	1179 (227)

Intervals

Steps	Cents	Approximate ratios	Ups and downs notation
0	0	1/1	D
1	5.04		^D, ^3E♭♭
2	10.08		^^D, ^4E♭♭
3	15.13		^3D, ^5E♭♭
4	20.17		^4D, ^6E♭♭
5	25.21	69/68, 70/69	^5D, ^7E♭♭
6	30.25	57/56, 58/57	^6D, ^8E♭♭
7	35.29	49/48	^7D, ^9E♭♭
8	40.34	43/42, 44/43	^8D, ^10E♭♭
9	45.38	38/37, 39/38	^9D, v10E♭
10	50.42	35/34	^10D, v9E♭
11	55.46	32/31	v10D♯, v8E♭
12	60.5	29/28	v9D♯, v7E♭
13	65.55		v8D♯, v6E♭
14	70.59		v7D♯, v5E♭
15	75.63	47/45	v6D♯, v4E♭
16	80.67	22/21	v5D♯, v3E♭
17	85.71	41/39	v4D♯, vvE♭
18	90.76	39/37	v3D♯, vE♭
19	95.8	37/35	vvD♯, E♭
20	100.84		vD♯, ^E♭
21	105.88		D♯, ^^E♭
22	110.92	16/15	^D♯, ^3E♭
23	115.97	31/29, 77/72	^^D♯, ^4E♭
24	121.01	74/69	^3D♯, ^5E♭
25	126.05		^4D♯, ^6E♭
26	131.09	41/38, 55/51, 69/64	^5D♯, ^7E♭
27	136.13		^6D♯, ^8E♭
28	141.18	51/47	^7D♯, ^9E♭
29	146.22	37/34, 62/57	^8D♯, ^10E♭
30	151.26	12/11	^9D♯, v10E
31	156.3		^10D♯, v9E
32	161.34	45/41, 56/51	v10D𝄪, v8E
33	166.39	76/69	v9D𝄪, v7E
34	171.43		v8D𝄪, v6E
35	176.47	31/28	v7D𝄪, v5E
36	181.51		v6D𝄪, v4E
37	186.55	39/35, 49/44	v5D𝄪, v3E
38	191.6		v4D𝄪, vvE
39	196.64		v3D𝄪, vE
40	201.68		E
41	206.72	62/55	^E, ^3F♭
42	211.76	26/23	^^E, ^4F♭
43	216.81	17/15	^3E, ^5F♭
44	221.85	58/51	^4E, ^6F♭
45	226.89	49/43	^5E, ^7F♭
46	231.93	8/7	^6E, ^8F♭
47	236.97	39/34, 47/41	^7E, ^9F♭
48	242.02	23/20	^8E, ^10F♭
49	247.06	15/13	^9E, v10F
50	252.1	37/32	^10E, v9F
51	257.14		v10E♯, v8F
52	262.18	57/49, 64/55	v9E♯, v7F
53	267.23	7/6	v8E♯, v6F
54	272.27	48/41, 55/47	v7E♯, v5F
55	277.31		v6E♯, v4F
56	282.35		v5E♯, v3F
57	287.39		v4E♯, vvF
58	292.44	45/38, 58/49	v3E♯, vF
59	297.48	19/16	F
60	302.52	56/47	^F, ^3G♭♭
61	307.56	43/36	^^F, ^4G♭♭
62	312.61		^3F, ^5G♭♭
63	317.65		^4F, ^6G♭♭
64	322.69	47/39	^5F, ^7G♭♭
65	327.73	29/24	^6F, ^8G♭♭
66	332.77		^7F, ^9G♭♭
67	337.82	62/51	^8F, ^10G♭♭
68	342.86	39/32	^9F, v10G♭
69	347.9	11/9	^10F, v9G♭
70	352.94	38/31	v10F♯, v8G♭
71	357.98		v9F♯, v7G♭
72	363.03	37/30	v8F♯, v6G♭
73	368.07	47/38, 68/55	v7F♯, v5G♭
74	373.11		v6F♯, v4G♭
75	378.15	51/41, 56/45	v5F♯, v3G♭
76	383.19		v4F♯, vvG♭
77	388.24		v3F♯, vG♭
78	393.28	64/51, 69/55	vvF♯, G♭
79	398.32	39/31	vF♯, ^G♭
80	403.36		F♯, ^^G♭
81	408.4	19/15	^F♯, ^3G♭
82	413.45	47/37	^^F♯, ^4G♭
83	418.49		^3F♯, ^5G♭
84	423.53	60/47	^4F♯, ^6G♭
85	428.57	41/32	^5F♯, ^7G♭
86	433.61		^6F♯, ^8G♭
87	438.66	58/45	^7F♯, ^9G♭
88	443.7	31/24	^8F♯, ^10G♭
89	448.74	57/44	^9F♯, v10G
90	453.78	13/10	^10F♯, v9G
91	458.82	43/33	v10F𝄪, v8G
92	463.87	17/13	v9F𝄪, v7G
93	468.91		v8F𝄪, v6G
94	473.95	46/35	v7F𝄪, v5G
95	478.99	29/22, 62/47	v6F𝄪, v4G
96	484.03	41/31	v5F𝄪, v3G
97	489.08	69/52	v4F𝄪, vvG
98	494.12		v3F𝄪, vG
99	499.16		G
100	504.2		^G, ^3A♭♭
101	509.24	51/38, 55/41	^^G, ^4A♭♭
102	514.29	35/26, 74/55	^3G, ^5A♭♭
103	519.33		^4G, ^6A♭♭
104	524.37		^5G, ^7A♭♭
105	529.41	19/14	^6G, ^8A♭♭
106	534.45	49/36, 64/47	^7G, ^9A♭♭
107	539.5	56/41	^8G, ^10A♭♭
108	544.54		^9G, v10A♭
109	549.58		^10G, v9A♭
110	554.62	62/45	v10G♯, v8A♭
111	559.66	29/21, 47/34, 76/55	v9G♯, v7A♭
112	564.71		v8G♯, v6A♭
113	569.75	57/41	v7G♯, v5A♭
114	574.79		v6G♯, v4A♭
115	579.83		v5G♯, v3A♭
116	584.87		v4G♯, vvA♭
117	589.92	45/32, 52/37	v3G♯, vA♭
118	594.96	55/39	vvG♯, A♭
119	600	41/29, 58/41	vG♯, ^A♭
120	605.04	78/55	G♯, ^^A♭
121	610.08	37/26, 64/45	^G♯, ^3A♭
122	615.13	77/54	^^G♯, ^4A♭
123	620.17		^3G♯, ^5A♭
124	625.21		^4G♯, ^6A♭
125	630.25		^5G♯, ^7A♭
126	635.29		^6G♯, ^8A♭
127	640.34	42/29, 55/38, 68/47	^7G♯, ^9A♭
128	645.38	45/31	^8G♯, ^10A♭
129	650.42		^9G♯, v10A
130	655.46		^10G♯, v9A
131	660.5	41/28, 63/43	v10G𝄪, v8A
132	665.55	47/32, 69/47, 72/49	v9G𝄪, v7A
133	670.59	28/19	v8G𝄪, v6A
134	675.63		v7G𝄪, v5A
135	680.67		v6G𝄪, v4A
136	685.71	52/35, 55/37	v5G𝄪, v3A
137	690.76	76/51	v4G𝄪, vvA
138	695.8		v3G𝄪, vA
139	700.84		A
140	705.88		^A, ^3B♭♭
141	710.92		^^A, ^4B♭♭
142	715.97	62/41	^3A, ^5B♭♭
143	721.01	44/29, 47/31	^4A, ^6B♭♭
144	726.05	35/23	^5A, ^7B♭♭
145	731.09		^6A, ^8B♭♭
146	736.13	26/17	^7A, ^9B♭♭
147	741.18	66/43	^8A, ^10B♭♭
148	746.22	20/13	^9A, v10B♭
149	751.26		^10A, v9B♭
150	756.3	48/31	v10A♯, v8B♭
151	761.34	45/29	v9A♯, v7B♭
152	766.39		v8A♯, v6B♭
153	771.43	64/41	v7A♯, v5B♭
154	776.47	47/30	v6A♯, v4B♭
155	781.51		v5A♯, v3B♭
156	786.55	74/47	v4A♯, vvB♭
157	791.6	30/19	v3A♯, vB♭
158	796.64		vvA♯, B♭
159	801.68	62/39	vA♯, ^B♭
160	806.72	51/32	A♯, ^^B♭
161	811.76		^A♯, ^3B♭
162	816.81		^^A♯, ^4B♭
163	821.85	45/28	^3A♯, ^5B♭
164	826.89		^4A♯, ^6B♭
165	831.93	55/34, 76/47	^5A♯, ^7B♭
166	836.97	60/37	^6A♯, ^8B♭
167	842.02		^7A♯, ^9B♭
168	847.06	31/19, 75/46	^8A♯, ^10B♭
169	852.1	18/11	^9A♯, v10B
170	857.14	64/39	^10A♯, v9B
171	862.18	51/31	v10A𝄪, v8B
172	867.23		v9A𝄪, v7B
173	872.27	48/29	v8A𝄪, v6B
174	877.31	78/47	v7A𝄪, v5B
175	882.35		v6A𝄪, v4B
176	887.39		v5A𝄪, v3B
177	892.44	72/43	v4A𝄪, vvB
178	897.48	47/28	v3A𝄪, vB
179	902.52	32/19	B
180	907.56	49/29, 76/45	^B, ^3C♭
181	912.61		^^B, ^4C♭
182	917.65		^3B, ^5C♭
183	922.69		^4B, ^6C♭
184	927.73	41/24	^5B, ^7C♭
185	932.77	12/7	^6B, ^8C♭
186	937.82	55/32	^7B, ^9C♭
187	942.86		^8B, ^10C♭
188	947.9	64/37	^9B, v10C
189	952.94	26/15	^10B, v9C
190	957.98	40/23	v10B♯, v8C
191	963.03	68/39	v9B♯, v7C
192	968.07	7/4	v8B♯, v6C
193	973.11		v7B♯, v5C
194	978.15	51/29	v6B♯, v4C
195	983.19	30/17	v5B♯, v3C
196	988.24	23/13	v4B♯, vvC
197	993.28	55/31	v3B♯, vC
198	998.32		C
199	1003.36		^C, ^3D♭♭
200	1008.4	77/43	^^C, ^4D♭♭
201	1013.45	70/39	^3C, ^5D♭♭
202	1018.49		^4C, ^6D♭♭
203	1023.53	56/31	^5C, ^7D♭♭
204	1028.57		^6C, ^8D♭♭
205	1033.61	69/38	^7C, ^9D♭♭
206	1038.66	51/28	^8C, ^10D♭♭
207	1043.7		^9C, v10D♭
208	1048.74	11/6	^10C, v9D♭
209	1053.78	57/31, 68/37	v10C♯, v8D♭
210	1058.82		v9C♯, v7D♭
211	1063.87		v8C♯, v6D♭
212	1068.91	76/41	v7C♯, v5D♭
213	1073.95		v6C♯, v4D♭
214	1078.99	69/37	v5C♯, v3D♭
215	1084.03	58/31	v4C♯, vvD♭
216	1089.08	15/8	v3C♯, vD♭
217	1094.12		vvC♯, D♭
218	1099.16		vC♯, ^D♭
219	1104.2	70/37	C♯, ^^D♭
220	1109.24	74/39	^C♯, ^3D♭
221	1114.29	78/41	^^C♯, ^4D♭
222	1119.33	21/11	^3C♯, ^5D♭
223	1124.37		^4C♯, ^6D♭
224	1129.41		^5C♯, ^7D♭
225	1134.45		^6C♯, ^8D♭
226	1139.5	56/29	^7C♯, ^9D♭
227	1144.54	31/16	^8C♯, ^10D♭
228	1149.58	68/35	^9C♯, v10D
229	1154.62	37/19, 76/39	^10C♯, v9D
230	1159.66	43/22	v10C𝄪, v8D
231	1164.71		v9C𝄪, v7D
232	1169.75	57/29	v8C𝄪, v6D
233	1174.79	69/35	v7C𝄪, v5D
234	1179.83		v6C𝄪, v4D
235	1184.87		v5C𝄪, v3D
236	1189.92		v4C𝄪, vvD
237	1194.96		v3C𝄪, vD
238	1200	2/1	D

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