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269edo

Revision as of 22:48, 23 December 2024 by MisterShafXen (talk | contribs)

Template:EDO intro

← 268edo 269edo 270edo →
Prime factorization 269 (prime)
Step size 4.46097 ¢ 
Fifth 157\269 (700.372 ¢)
Semitones (A1:m2) 23:22 (102.6 ¢ : 98.14 ¢)
Dual sharp fifth 158\269 (704.833 ¢)
Dual flat fifth 157\269 (700.372 ¢)
Dual major 2nd 46\269 (205.204 ¢)
Consistency limit 3
Distinct consistency limit 3

269edo is inconsistent in the 5-odd-limit and the errors of both harmonics 3 and 5 are quite large. The patent val tempers out 6144/6125 in the 7-limit, 540/539 and 5632/5625 in the 11-limit and 364/363 and 676/675 in the 13-limit. The 269c val tempers out 225/224 and 4375/4374 in the 7-limit, and 269ce 385/384 in the 11-limit, so that it supports and provides an excellent tuning for catakleismic and marvel temperaments.


Steps Cents Approximate ratios Ups and downs notation
(Dual flat fifth 157\269) 		Ups and downs notation
(Dual sharp fifth 158\269)
0 0 1/1 D D
1 4.46 ^D, ^^E♭♭ ^D, ^14E♭♭
2 8.92 ^^D, ^3E♭♭ ^^D, v15E♭
3 13.38 ^3D, ^4E♭♭ ^3D, v14E♭
4 17.84 ^4D, ^5E♭♭ ^4D, v13E♭
5 22.3 76/75, 77/76 ^5D, ^6E♭♭ ^5D, v12E♭
6 26.77 65/64, 66/65 ^6D, ^7E♭♭ ^6D, v11E♭
7 31.23 57/56 ^7D, ^8E♭♭ ^7D, v10E♭
8 35.69 48/47, 49/48 ^8D, ^9E♭♭ ^8D, v9E♭
9 40.15 44/43 ^9D, ^10E♭♭ ^9D, v8E♭
10 44.61 ^10D, ^11E♭♭ ^10D, v7E♭
11 49.07 ^11D, v11E♭ ^11D, v6E♭
12 53.53 33/32 v11D♯, v10E♭ ^12D, v5E♭
13 57.99 30/29 v10D♯, v9E♭ ^13D, v4E♭
14 62.45 v9D♯, v8E♭ ^14D, v3E♭
15 66.91 80/77 v8D♯, v7E♭ ^15D, vvE♭
16 71.38 49/47 v7D♯, v6E♭ v14D♯, vE♭
17 75.84 47/45 v6D♯, v5E♭ v13D♯, E♭
18 80.3 v5D♯, v4E♭ v12D♯, ^E♭
19 84.76 v4D♯, v3E♭ v11D♯, ^^E♭
20 89.22 20/19 v3D♯, vvE♭ v10D♯, ^3E♭
21 93.68 vvD♯, vE♭ v9D♯, ^4E♭
22 98.14 vD♯, E♭ v8D♯, ^5E♭
23 102.6 35/33, 52/49, 87/82 D♯, ^E♭ v7D♯, ^6E♭
24 107.06 ^D♯, ^^E♭ v6D♯, ^7E♭
25 111.52 16/15 ^^D♯, ^3E♭ v5D♯, ^8E♭
26 115.99 31/29, 46/43 ^3D♯, ^4E♭ v4D♯, ^9E♭
27 120.45 74/69 ^4D♯, ^5E♭ v3D♯, ^10E♭
28 124.91 43/40 ^5D♯, ^6E♭ vvD♯, ^11E♭
29 129.37 ^6D♯, ^7E♭ vD♯, ^12E♭
30 133.83 ^7D♯, ^8E♭ D♯, ^13E♭
31 138.29 13/12 ^8D♯, ^9E♭ ^D♯, ^14E♭
32 142.75 38/35 ^9D♯, ^10E♭ ^^D♯, v15E
33 147.21 49/45 ^10D♯, ^11E♭ ^3D♯, v14E
34 151.67 ^11D♯, v11E ^4D♯, v13E
35 156.13 v11D𝄪, v10E ^5D♯, v12E
36 160.59 34/31, 45/41 v10D𝄪, v9E ^6D♯, v11E
37 165.06 11/10 v9D𝄪, v8E ^7D♯, v10E
38 169.52 75/68 v8D𝄪, v7E ^8D♯, v9E
39 173.98 v7D𝄪, v6E ^9D♯, v8E
40 178.44 41/37, 51/46 v6D𝄪, v5E ^10D♯, v7E
41 182.9 v5D𝄪, v4E ^11D♯, v6E
42 187.36 v4D𝄪, v3E ^12D♯, v5E
43 191.82 19/17, 86/77 v3D𝄪, vvE ^13D♯, v4E
44 196.28 vvD𝄪, vE ^14D♯, v3E
45 200.74 64/57 E ^15D♯, vvE
46 205.2 ^E, ^^F♭ v14D𝄪, vE
47 209.67 35/31 ^^E, ^3F♭ E
48 214.13 43/38 ^3E, ^4F♭ ^E, ^14F♭
49 218.59 ^4E, ^5F♭ ^^E, v15F
50 223.05 33/29, 58/51 ^5E, ^6F♭ ^3E, v14F
51 227.51 65/57 ^6E, ^7F♭ ^4E, v13F
52 231.97 ^7E, ^8F♭ ^5E, v12F
53 236.43 47/41, 86/75 ^8E, ^9F♭ ^6E, v11F
54 240.89 ^9E, ^10F♭ ^7E, v10F
55 245.35 ^10E, ^11F♭ ^8E, v9F
56 249.81 52/45 ^11E, v11F ^9E, v8F
57 254.28 22/19 v11E♯, v10F ^10E, v7F
58 258.74 65/56 v10E♯, v9F ^11E, v6F
59 263.2 v9E♯, v8F ^12E, v5F
60 267.66 v8E♯, v7F ^13E, v4F
61 272.12 48/41 v7E♯, v6F ^14E, v3F
62 276.58 v6E♯, v5F ^15E, vvF
63 281.04 20/17 v5E♯, v4F v14E♯, vF
64 285.5 v4E♯, v3F F
65 289.96 v3E♯, vvF ^F, ^14G♭♭
66 294.42 vvE♯, vF ^^F, v15G♭
67 298.88 82/69 F ^3F, v14G♭
68 303.35 56/47 ^F, ^^G♭♭ ^4F, v13G♭
69 307.81 49/41 ^^F, ^3G♭♭ ^5F, v12G♭
70 312.27 ^3F, ^4G♭♭ ^6F, v11G♭
71 316.73 ^4F, ^5G♭♭ ^7F, v10G♭
72 321.19 ^5F, ^6G♭♭ ^8F, v9G♭
73 325.65 35/29 ^6F, ^7G♭♭ ^9F, v8G♭
74 330.11 23/19, 75/62 ^7F, ^8G♭♭ ^10F, v7G♭
75 334.57 57/47 ^8F, ^9G♭♭ ^11F, v6G♭
76 339.03 45/37 ^9F, ^10G♭♭ ^12F, v5G♭
77 343.49 ^10F, ^11G♭♭ ^13F, v4G♭
78 347.96 ^11F, v11G♭ ^14F, v3G♭
79 352.42 38/31 v11F♯, v10G♭ ^15F, vvG♭
80 356.88 43/35 v10F♯, v9G♭ v14F♯, vG♭
81 361.34 69/56 v9F♯, v8G♭ v13F♯, G♭
82 365.8 v8F♯, v7G♭ v12F♯, ^G♭
83 370.26 26/21 v7F♯, v6G♭ v11F♯, ^^G♭
84 374.72 77/62 v6F♯, v5G♭ v10F♯, ^3G♭
85 379.18 56/45 v5F♯, v4G♭ v9F♯, ^4G♭
86 383.64 v4F♯, v3G♭ v8F♯, ^5G♭
87 388.1 v3F♯, vvG♭ v7F♯, ^6G♭
88 392.57 64/51 vvF♯, vG♭ v6F♯, ^7G♭
89 397.03 vF♯, G♭ v5F♯, ^8G♭
90 401.49 29/23, 82/65 F♯, ^G♭ v4F♯, ^9G♭
91 405.95 43/34 ^F♯, ^^G♭ v3F♯, ^10G♭
92 410.41 ^^F♯, ^3G♭ vvF♯, ^11G♭
93 414.87 47/37 ^3F♯, ^4G♭ vF♯, ^12G♭
94 419.33 65/51 ^4F♯, ^5G♭ F♯, ^13G♭
95 423.79 ^5F♯, ^6G♭ ^F♯, ^14G♭
96 428.25 ^6F♯, ^7G♭ ^^F♯, v15G
97 432.71 ^7F♯, ^8G♭ ^3F♯, v14G
98 437.17 ^8F♯, ^9G♭ ^4F♯, v13G
99 441.64 40/31 ^9F♯, ^10G♭ ^5F♯, v12G
100 446.1 22/17 ^10F♯, ^11G♭ ^6F♯, v11G
101 450.56 48/37 ^11F♯, v11G ^7F♯, v10G
102 455.02 v11F𝄪, v10G ^8F♯, v9G
103 459.48 30/23 v10F𝄪, v9G ^9F♯, v8G
104 463.94 v9F𝄪, v8G ^10F♯, v7G
105 468.4 38/29 v8F𝄪, v7G ^11F♯, v6G
106 472.86 46/35 v7F𝄪, v6G ^12F♯, v5G
107 477.32 v6F𝄪, v5G ^13F♯, v4G
108 481.78 37/28 v5F𝄪, v4G ^14F♯, v3G
109 486.25 49/37 v4F𝄪, v3G ^15F♯, vvG
110 490.71 77/58 v3F𝄪, vvG v14F𝄪, vG
111 495.17 vvF𝄪, vG G
112 499.63 G ^G, ^14A♭♭
113 504.09 87/65 ^G, ^^A♭♭ ^^G, v15A♭
114 508.55 ^^G, ^3A♭♭ ^3G, v14A♭
115 513.01 ^3G, ^4A♭♭ ^4G, v13A♭
116 517.47 31/23, 58/43 ^4G, ^5A♭♭ ^5G, v12A♭
117 521.93 ^5G, ^6A♭♭ ^6G, v11A♭
118 526.39 ^6G, ^7A♭♭ ^7G, v10A♭
119 530.86 87/64 ^7G, ^8A♭♭ ^8G, v9A♭
120 535.32 ^8G, ^9A♭♭ ^9G, v8A♭
121 539.78 56/41 ^9G, ^10A♭♭ ^10G, v7A♭
122 544.24 ^10G, ^11A♭♭ ^11G, v6A♭
123 548.7 70/51 ^11G, v11A♭ ^12G, v5A♭
124 553.16 v11G♯, v10A♭ ^13G, v4A♭
125 557.62 v10G♯, v9A♭ ^14G, v3A♭
126 562.08 65/47 v9G♯, v8A♭ ^15G, vvA♭
127 566.54 43/31 v8G♯, v7A♭ v14G♯, vA♭
128 571 32/23, 57/41 v7G♯, v6A♭ v13G♯, A♭
129 575.46 46/33 v6G♯, v5A♭ v12G♯, ^A♭
130 579.93 v5G♯, v4A♭ v11G♯, ^^A♭
131 584.39 v4G♯, v3A♭ v10G♯, ^3A♭
132 588.85 52/37 v3G♯, vvA♭ v9G♯, ^4A♭
133 593.31 31/22, 69/49 vvG♯, vA♭ v8G♯, ^5A♭
134 597.77 vG♯, A♭ v7G♯, ^6A♭
135 602.23 G♯, ^A♭ v6G♯, ^7A♭
136 606.69 44/31 ^G♯, ^^A♭ v5G♯, ^8A♭
137 611.15 37/26 ^^G♯, ^3A♭ v4G♯, ^9A♭
138 615.61 ^3G♯, ^4A♭ v3G♯, ^10A♭
139 620.07 ^4G♯, ^5A♭ vvG♯, ^11A♭
140 624.54 33/23 ^5G♯, ^6A♭ vG♯, ^12A♭
141 629 23/16, 82/57 ^6G♯, ^7A♭ G♯, ^13A♭
142 633.46 62/43 ^7G♯, ^8A♭ ^G♯, ^14A♭
143 637.92 ^8G♯, ^9A♭ ^^G♯, v15A
144 642.38 ^9G♯, ^10A♭ ^3G♯, v14A
145 646.84 ^10G♯, ^11A♭ ^4G♯, v13A
146 651.3 51/35 ^11G♯, v11A ^5G♯, v12A
147 655.76 v11G𝄪, v10A ^6G♯, v11A
148 660.22 41/28 v10G𝄪, v9A ^7G♯, v10A
149 664.68 69/47 v9G𝄪, v8A ^8G♯, v9A
150 669.14 v8G𝄪, v7A ^9G♯, v8A
151 673.61 v7G𝄪, v6A ^10G♯, v7A
152 678.07 v6G𝄪, v5A ^11G♯, v6A
153 682.53 43/29, 46/31 v5G𝄪, v4A ^12G♯, v5A
154 686.99 v4G𝄪, v3A ^13G♯, v4A
155 691.45 v3G𝄪, vvA ^14G♯, v3A
156 695.91 vvG𝄪, vA ^15G♯, vvA
157 700.37 A v14G𝄪, vA
158 704.83 ^A, ^^B♭♭ A
159 709.29 ^^A, ^3B♭♭ ^A, ^14B♭♭
160 713.75 74/49, 77/51 ^3A, ^4B♭♭ ^^A, v15B♭
161 718.22 56/37 ^4A, ^5B♭♭ ^3A, v14B♭
162 722.68 ^5A, ^6B♭♭ ^4A, v13B♭
163 727.14 35/23 ^6A, ^7B♭♭ ^5A, v12B♭
164 731.6 29/19 ^7A, ^8B♭♭ ^6A, v11B♭
165 736.06 ^8A, ^9B♭♭ ^7A, v10B♭
166 740.52 23/15 ^9A, ^10B♭♭ ^8A, v9B♭
167 744.98 ^10A, ^11B♭♭ ^9A, v8B♭
168 749.44 37/24 ^11A, v11B♭ ^10A, v7B♭
169 753.9 17/11 v11A♯, v10B♭ ^11A, v6B♭
170 758.36 31/20 v10A♯, v9B♭ ^12A, v5B♭
171 762.83 87/56 v9A♯, v8B♭ ^13A, v4B♭
172 767.29 v8A♯, v7B♭ ^14A, v3B♭
173 771.75 v7A♯, v6B♭ ^15A, vvB♭
174 776.21 v6A♯, v5B♭ v14A♯, vB♭
175 780.67 v5A♯, v4B♭ v13A♯, B♭
176 785.13 74/47 v4A♯, v3B♭ v12A♯, ^B♭
177 789.59 v3A♯, vvB♭ v11A♯, ^^B♭
178 794.05 68/43 vvA♯, vB♭ v10A♯, ^3B♭
179 798.51 46/29, 65/41 vA♯, B♭ v9A♯, ^4B♭
180 802.97 A♯, ^B♭ v8A♯, ^5B♭
181 807.43 51/32 ^A♯, ^^B♭ v7A♯, ^6B♭
182 811.9 ^^A♯, ^3B♭ v6A♯, ^7B♭
183 816.36 ^3A♯, ^4B♭ v5A♯, ^8B♭
184 820.82 45/28 ^4A♯, ^5B♭ v4A♯, ^9B♭
185 825.28 ^5A♯, ^6B♭ v3A♯, ^10B♭
186 829.74 21/13 ^6A♯, ^7B♭ vvA♯, ^11B♭
187 834.2 ^7A♯, ^8B♭ vA♯, ^12B♭
188 838.66 ^8A♯, ^9B♭ A♯, ^13B♭
189 843.12 70/43 ^9A♯, ^10B♭ ^A♯, ^14B♭
190 847.58 31/19 ^10A♯, ^11B♭ ^^A♯, v15B
191 852.04 ^11A♯, v11B ^3A♯, v14B
192 856.51 v11A𝄪, v10B ^4A♯, v13B
193 860.97 74/45 v10A𝄪, v9B ^5A♯, v12B
194 865.43 v9A𝄪, v8B ^6A♯, v11B
195 869.89 38/23 v8A𝄪, v7B ^7A♯, v10B
196 874.35 58/35 v7A𝄪, v6B ^8A♯, v9B
197 878.81 v6A𝄪, v5B ^9A♯, v8B
198 883.27 v5A𝄪, v4B ^10A♯, v7B
199 887.73 v4A𝄪, v3B ^11A♯, v6B
200 892.19 77/46, 82/49 v3A𝄪, vvB ^12A♯, v5B
201 896.65 47/28 vvA𝄪, vB ^13A♯, v4B
202 901.12 69/41 B ^14A♯, v3B
203 905.58 ^B, ^^C♭ ^15A♯, vvB
204 910.04 ^^B, ^3C♭ v14A𝄪, vB
205 914.5 ^3B, ^4C♭ B
206 918.96 17/10 ^4B, ^5C♭ ^B, ^14C♭
207 923.42 75/44 ^5B, ^6C♭ ^^B, v15C
208 927.88 41/24 ^6B, ^7C♭ ^3B, v14C
209 932.34 ^7B, ^8C♭ ^4B, v13C
210 936.8 ^8B, ^9C♭ ^5B, v12C
211 941.26 ^9B, ^10C♭ ^6B, v11C
212 945.72 19/11 ^10B, ^11C♭ ^7B, v10C
213 950.19 45/26 ^11B, v11C ^8B, v9C
214 954.65 v11B♯, v10C ^9B, v8C
215 959.11 v10B♯, v9C ^10B, v7C
216 963.57 75/43, 82/47 v9B♯, v8C ^11B, v6C
217 968.03 v8B♯, v7C ^12B, v5C
218 972.49 v7B♯, v6C ^13B, v4C
219 976.95 51/29, 58/33 v6B♯, v5C ^14B, v3C
220 981.41 v5B♯, v4C ^15B, vvC
221 985.87 76/43 v4B♯, v3C v14B♯, vC
222 990.33 62/35 v3B♯, vvC C
223 994.8 vvB♯, vC ^C, ^14D♭♭
224 999.26 57/32 C ^^C, v15D♭
225 1003.72 ^C, ^^D♭♭ ^3C, v14D♭
226 1008.18 34/19, 77/43 ^^C, ^3D♭♭ ^4C, v13D♭
227 1012.64 ^3C, ^4D♭♭ ^5C, v12D♭
228 1017.1 ^4C, ^5D♭♭ ^6C, v11D♭
229 1021.56 74/41 ^5C, ^6D♭♭ ^7C, v10D♭
230 1026.02 ^6C, ^7D♭♭ ^8C, v9D♭
231 1030.48 ^7C, ^8D♭♭ ^9C, v8D♭
232 1034.94 20/11 ^8C, ^9D♭♭ ^10C, v7D♭
233 1039.41 31/17, 82/45 ^9C, ^10D♭♭ ^11C, v6D♭
234 1043.87 ^10C, ^11D♭♭ ^12C, v5D♭
235 1048.33 ^11C, v11D♭ ^13C, v4D♭
236 1052.79 v11C♯, v10D♭ ^14C, v3D♭
237 1057.25 35/19 v10C♯, v9D♭ ^15C, vvD♭
238 1061.71 24/13 v9C♯, v8D♭ v14C♯, vD♭
239 1066.17 87/47 v8C♯, v7D♭ v13C♯, D♭
240 1070.63 v7C♯, v6D♭ v12C♯, ^D♭
241 1075.09 80/43 v6C♯, v5D♭ v11C♯, ^^D♭
242 1079.55 69/37 v5C♯, v4D♭ v10C♯, ^3D♭
243 1084.01 43/23, 58/31 v4C♯, v3D♭ v9C♯, ^4D♭
244 1088.48 15/8 v3C♯, vvD♭ v8C♯, ^5D♭
245 1092.94 vvC♯, vD♭ v7C♯, ^6D♭
246 1097.4 49/26, 66/35 vC♯, D♭ v6C♯, ^7D♭
247 1101.86 C♯, ^D♭ v5C♯, ^8D♭
248 1106.32 ^C♯, ^^D♭ v4C♯, ^9D♭
249 1110.78 19/10 ^^C♯, ^3D♭ v3C♯, ^10D♭
250 1115.24 ^3C♯, ^4D♭ vvC♯, ^11D♭
251 1119.7 ^4C♯, ^5D♭ vC♯, ^12D♭
252 1124.16 ^5C♯, ^6D♭ C♯, ^13D♭
253 1128.62 ^6C♯, ^7D♭ ^C♯, ^14D♭
254 1133.09 77/40 ^7C♯, ^8D♭ ^^C♯, v15D
255 1137.55 ^8C♯, ^9D♭ ^3C♯, v14D
256 1142.01 29/15 ^9C♯, ^10D♭ ^4C♯, v13D
257 1146.47 64/33 ^10C♯, ^11D♭ ^5C♯, v12D
258 1150.93 ^11C♯, v11D ^6C♯, v11D
259 1155.39 v11C𝄪, v10D ^7C♯, v10D
260 1159.85 43/22 v10C𝄪, v9D ^8C♯, v9D
261 1164.31 47/24 v9C𝄪, v8D ^9C♯, v8D
262 1168.77 v8C𝄪, v7D ^10C♯, v7D
263 1173.23 65/33 v7C𝄪, v6D ^11C♯, v6D
264 1177.7 75/38 v6C𝄪, v5D ^12C♯, v5D
265 1182.16 v5C𝄪, v4D ^13C♯, v4D
266 1186.62 v4C𝄪, v3D ^14C♯, v3D
267 1191.08 v3C𝄪, vvD ^15C♯, vvD
268 1195.54 vvC𝄪, vD v14C𝄪, vD
269 1200 2/1 D D

Odd harmonics

Approximation of odd harmonics in 269edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -1.58 +1.79 -0.80 +1.29 +1.84 -1.87 +0.21 +2.11 +1.37 +2.08 +0.72
Relative (%) -35.5 +40.1 -17.8 +29.0 +41.3 -41.8 +4.6 +47.2 +30.7 +46.7 +16.2
Steps
(reduced) 		426
(157) 		625
(87) 		755
(217) 		853
(46) 		931
(124) 		995
(188) 		1051
(244) 		1100
(24) 		1143
(67) 		1182
(106) 		1217
(141)

Subsets and supersets

269edo is the 57th prime edo.

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