Xenharmonic Wiki

245edo

Revision as of 23:14, 25 December 2024 by MisterShafXen (talk | contribs)
← 244edo 245edo 246edo →
Prime factorization 5 × 72
Step size 4.89796 ¢ 
Fifth 143\245 (700.408 ¢)
Semitones (A1:m2) 21:20 (102.9 ¢ : 97.96 ¢)
Consistency limit 5
Distinct consistency limit 5

Template:EDO intro

Theory

245edo is only consistent to the 5-odd-limit. The equal temperament tempers out [-17 21 -7⟩ and [19 10 -15⟩ in the 5-limit; 6144/6125 and 16875/16807 in the 7-limit; 441/440, 4000/3993, 6912/6875, 14700/14641, 30375/30184 and 54675/54208 in the 11-limit.

Intervals

Steps Cents Approximate ratios Ups and downs notation
0 0 1/1 D
1 4.9 ^D, ^^E♭♭
2 9.8 ^^D, ^3E♭♭
3 14.69 ^3D, ^4E♭♭
4 19.59 ^4D, ^5E♭♭
5 24.49 69/68 ^5D, ^6E♭♭
6 29.39 58/57 ^6D, ^7E♭♭
7 34.29 50/49 ^7D, ^8E♭♭
8 39.18 ^8D, ^9E♭♭
9 44.08 40/39 ^9D, ^10E♭♭
10 48.98 ^10D, v10E♭
11 53.88 33/32 v10D♯, v9E♭
12 58.78 30/29 v9D♯, v8E♭
13 63.67 v8D♯, v7E♭
14 68.57 26/25 v7D♯, v6E♭
15 73.47 24/23 v6D♯, v5E♭
16 78.37 45/43 v5D♯, v4E♭
17 83.27 v4D♯, v3E♭
18 88.16 20/19 v3D♯, vvE♭
19 93.06 vvD♯, vE♭
20 97.96 55/52 vD♯, E♭
21 102.86 52/49 D♯, ^E♭
22 107.76 33/31, 50/47 ^D♯, ^^E♭
23 112.65 ^^D♯, ^3E♭
24 117.55 46/43 ^3D♯, ^4E♭
25 122.45 44/41 ^4D♯, ^5E♭
26 127.35 ^5D♯, ^6E♭
27 132.24 41/38, 68/63 ^6D♯, ^7E♭
28 137.14 ^7D♯, ^8E♭
29 142.04 38/35 ^8D♯, ^9E♭
30 146.94 37/34 ^9D♯, ^10E♭
31 151.84 ^10D♯, v10E
32 156.73 23/21 v10D𝄪, v9E
33 161.63 v9D𝄪, v8E
34 166.53 v8D𝄪, v7E
35 171.43 v7D𝄪, v6E
36 176.33 31/28 v6D𝄪, v5E
37 181.22 v5D𝄪, v4E
38 186.12 49/44 v4D𝄪, v3E
39 191.02 48/43 v3D𝄪, vvE
40 195.92 28/25 vvD𝄪, vE
41 200.82 55/49, 64/57 E
42 205.71 ^E, ^^F♭
43 210.61 35/31 ^^E, ^3F♭
44 215.51 ^3E, ^4F♭
45 220.41 ^4E, ^5F♭
46 225.31 ^5E, ^6F♭
47 230.2 ^6E, ^7F♭
48 235.1 ^7E, ^8F♭
49 240 ^8E, ^9F♭
50 244.9 38/33 ^9E, ^10F♭
51 249.8 ^10E, v10F
52 254.69 v10E♯, v9F
53 259.59 43/37 v9E♯, v8F
54 264.49 v8E♯, v7F
55 269.39 v7E♯, v6F
56 274.29 41/35, 75/64 v6E♯, v5F
57 279.18 47/40, 74/63 v5E♯, v4F
58 284.08 33/28 v4E♯, v3F
59 288.98 13/11 v3E♯, vvF
60 293.88 77/65 vvE♯, vF
61 298.78 F
62 303.67 31/26, 56/47 ^F, ^^G♭♭
63 308.57 49/41 ^^F, ^3G♭♭
64 313.47 ^3F, ^4G♭♭
65 318.37 ^4F, ^5G♭♭
66 323.27 47/39 ^5F, ^6G♭♭
67 328.16 29/24 ^6F, ^7G♭♭
68 333.06 40/33 ^7F, ^8G♭♭
69 337.96 ^8F, ^9G♭♭
70 342.86 39/32, 50/41 ^9F, ^10G♭♭
71 347.76 ^10F, v10G♭
72 352.65 38/31 v10F♯, v9G♭
73 357.55 v9F♯, v8G♭
74 362.45 37/30 v8F♯, v7G♭
75 367.35 47/38 v7F♯, v6G♭
76 372.24 31/25 v6F♯, v5G♭
77 377.14 46/37 v5F♯, v4G♭
78 382.04 v4F♯, v3G♭
79 386.94 5/4 v3F♯, vvG♭
80 391.84 vvF♯, vG♭
81 396.73 39/31, 44/35 vF♯, G♭
82 401.63 29/23 F♯, ^G♭
83 406.53 43/34, 62/49 ^F♯, ^^G♭
84 411.43 52/41 ^^F♯, ^3G♭
85 416.33 ^3F♯, ^4G♭
86 421.22 37/29 ^4F♯, ^5G♭
87 426.12 ^5F♯, ^6G♭
88 431.02 ^6F♯, ^7G♭
89 435.92 ^7F♯, ^8G♭
90 440.82 40/31, 49/38 ^8F♯, ^9G♭
91 445.71 75/58 ^9F♯, ^10G♭
92 450.61 48/37 ^10F♯, v10G
93 455.51 v10F𝄪, v9G
94 460.41 30/23 v9F𝄪, v8G
95 465.31 v8F𝄪, v7G
96 470.2 21/16 v7F𝄪, v6G
97 475.1 25/19 v6F𝄪, v5G
98 480 33/25, 62/47 v5F𝄪, v4G
99 484.9 41/31, 45/34 v4F𝄪, v3G
100 489.8 65/49 v3F𝄪, vvG
101 494.69 vvF𝄪, vG
102 499.59 G
103 504.49 ^G, ^^A♭♭
104 509.39 55/41 ^^G, ^3A♭♭
105 514.29 35/26 ^3G, ^4A♭♭
106 519.18 ^4G, ^5A♭♭
107 524.08 23/17 ^5G, ^6A♭♭
108 528.98 19/14 ^6G, ^7A♭♭
109 533.88 64/47 ^7G, ^8A♭♭
110 538.78 ^8G, ^9A♭♭
111 543.67 26/19, 63/46 ^9G, ^10A♭♭
112 548.57 ^10G, v10A♭
113 553.47 v10G♯, v9A♭
114 558.37 29/21 v9G♯, v8A♭
115 563.27 v8G♯, v7A♭
116 568.16 v7G♯, v6A♭
117 573.06 39/28 v6G♯, v5A♭
118 577.96 v5G♯, v4A♭
119 582.86 7/5 v4G♯, v3A♭
120 587.76 66/47 v3G♯, vvA♭
121 592.65 vvG♯, vA♭
122 597.55 24/17 vG♯, A♭
123 602.45 17/12 G♯, ^A♭
124 607.35 ^G♯, ^^A♭
125 612.24 47/33 ^^G♯, ^3A♭
126 617.14 10/7 ^3G♯, ^4A♭
127 622.04 ^4G♯, ^5A♭
128 626.94 56/39 ^5G♯, ^6A♭
129 631.84 ^6G♯, ^7A♭
130 636.73 ^7G♯, ^8A♭
131 641.63 42/29 ^8G♯, ^9A♭
132 646.53 ^9G♯, ^10A♭
133 651.43 ^10G♯, v10A
134 656.33 19/13 v10G𝄪, v9A
135 661.22 63/43 v9G𝄪, v8A
136 666.12 47/32 v8G𝄪, v7A
137 671.02 28/19 v7G𝄪, v6A
138 675.92 34/23, 65/44 v6G𝄪, v5A
139 680.82 v5G𝄪, v4A
140 685.71 52/35 v4G𝄪, v3A
141 690.61 v3G𝄪, vvA
142 695.51 vvG𝄪, vA
143 700.41 A
144 705.31 ^A, ^^B♭♭
145 710.2 ^^A, ^3B♭♭
146 715.1 62/41, 68/45 ^3A, ^4B♭♭
147 720 47/31, 50/33 ^4A, ^5B♭♭
148 724.9 38/25 ^5A, ^6B♭♭
149 729.8 32/21 ^6A, ^7B♭♭
150 734.69 ^7A, ^8B♭♭
151 739.59 23/15 ^8A, ^9B♭♭
152 744.49 ^9A, ^10B♭♭
153 749.39 37/24 ^10A, v10B♭
154 754.29 v10A♯, v9B♭
155 759.18 31/20, 76/49 v9A♯, v8B♭
156 764.08 v8A♯, v7B♭
157 768.98 v7A♯, v6B♭
158 773.88 v6A♯, v5B♭
159 778.78 58/37 v5A♯, v4B♭
160 783.67 v4A♯, v3B♭
161 788.57 41/26 v3A♯, vvB♭
162 793.47 49/31, 68/43 vvA♯, vB♭
163 798.37 46/29, 65/41 vA♯, B♭
164 803.27 35/22, 62/39 A♯, ^B♭
165 808.16 ^A♯, ^^B♭
166 813.06 8/5 ^^A♯, ^3B♭
167 817.96 69/43 ^3A♯, ^4B♭
168 822.86 37/23 ^4A♯, ^5B♭
169 827.76 50/31 ^5A♯, ^6B♭
170 832.65 76/47 ^6A♯, ^7B♭
171 837.55 60/37 ^7A♯, ^8B♭
172 842.45 ^8A♯, ^9B♭
173 847.35 31/19 ^9A♯, ^10B♭
174 852.24 ^10A♯, v10B
175 857.14 41/25, 64/39 v10A𝄪, v9B
176 862.04 v9A𝄪, v8B
177 866.94 33/20 v8A𝄪, v7B
178 871.84 48/29 v7A𝄪, v6B
179 876.73 78/47 v6A𝄪, v5B
180 881.63 v5A𝄪, v4B
181 886.53 v4A𝄪, v3B
182 891.43 v3A𝄪, vvB
183 896.33 47/28, 52/31 vvA𝄪, vB
184 901.22 B
185 906.12 ^B, ^^C♭
186 911.02 22/13 ^^B, ^3C♭
187 915.92 56/33 ^3B, ^4C♭
188 920.82 63/37, 80/47 ^4B, ^5C♭
189 925.71 70/41 ^5B, ^6C♭
190 930.61 ^6B, ^7C♭
191 935.51 ^7B, ^8C♭
192 940.41 74/43 ^8B, ^9C♭
193 945.31 ^9B, ^10C♭
194 950.2 ^10B, v10C
195 955.1 33/19 v10B♯, v9C
196 960 v9B♯, v8C
197 964.9 v8B♯, v7C
198 969.8 v7B♯, v6C
199 974.69 v6B♯, v5C
200 979.59 v5B♯, v4C
201 984.49 v4B♯, v3C
202 989.39 62/35 v3B♯, vvC
203 994.29 vvB♯, vC
204 999.18 57/32 C
205 1004.08 25/14 ^C, ^^D♭♭
206 1008.98 43/24 ^^C, ^3D♭♭
207 1013.88 ^3C, ^4D♭♭
208 1018.78 ^4C, ^5D♭♭
209 1023.67 56/31 ^5C, ^6D♭♭
210 1028.57 ^6C, ^7D♭♭
211 1033.47 ^7C, ^8D♭♭
212 1038.37 ^8C, ^9D♭♭
213 1043.27 42/23 ^9C, ^10D♭♭
214 1048.16 ^10C, v10D♭
215 1053.06 68/37 v10C♯, v9D♭
216 1057.96 35/19 v9C♯, v8D♭
217 1062.86 v8C♯, v7D♭
218 1067.76 63/34, 76/41 v7C♯, v6D♭
219 1072.65 v6C♯, v5D♭
220 1077.55 41/22 v5C♯, v4D♭
221 1082.45 43/23 v4C♯, v3D♭
222 1087.35 v3C♯, vvD♭
223 1092.24 47/25, 62/33 vvC♯, vD♭
224 1097.14 49/26 vC♯, D♭
225 1102.04 C♯, ^D♭
226 1106.94 ^C♯, ^^D♭
227 1111.84 19/10 ^^C♯, ^3D♭
228 1116.73 ^3C♯, ^4D♭
229 1121.63 ^4C♯, ^5D♭
230 1126.53 23/12 ^5C♯, ^6D♭
231 1131.43 25/13 ^6C♯, ^7D♭
232 1136.33 ^7C♯, ^8D♭
233 1141.22 29/15 ^8C♯, ^9D♭
234 1146.12 64/33 ^9C♯, ^10D♭
235 1151.02 ^10C♯, v10D
236 1155.92 39/20 v10C𝄪, v9D
237 1160.82 v9C𝄪, v8D
238 1165.71 49/25 v8C𝄪, v7D
239 1170.61 57/29 v7C𝄪, v6D
240 1175.51 v6C𝄪, v5D
241 1180.41 v5C𝄪, v4D
242 1185.31 v4C𝄪, v3D
243 1190.2 v3C𝄪, vvD
244 1195.1 vvC𝄪, vD
245 1200 2/1 D

Odd harmonics

Approximation of odd harmonics in 245edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -1.55 +0.63 +0.97 +1.80 +2.15 +1.92 -0.92 -2.10 +1.26 -0.58 -1.34
Relative (%) -31.6 +12.8 +19.8 +36.8 +43.9 +39.2 -18.8 -42.8 +25.8 -11.8 -27.3
Steps
(reduced) 		388
(143) 		569
(79) 		688
(198) 		777
(42) 		848
(113) 		907
(172) 		957
(222) 		1001
(21) 		1041
(61) 		1076
(96) 		1108
(128)

Subsets and supersets

Since 245 factors into 5 × 72, 245edo has subset edos 5, 7, 35, and 49.

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