User:Overthink/Sandbox: Difference between revisions

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{{#invoke: Interval_table | interval_table
| tuning=311edo
| additional=
| max_error=35
| debug={{lc:}}
}}
== EDO testing ==
== EDO testing ==
{{Infobox ET|71083ed31|debug=1|Consistency=56|Distinct consistency=56}}
{{Infobox ET|71083ed31|debug=1|Consistency=56|Distinct consistency=56}}

Revision as of 03:35, 1 December 2025

Tables

um yeah
Steps Cents Approximate ratios Ups and downs notation
0 0 1/1 D
1 3.86 ^D, ^8E♭♭
2 7.72 ^^D, ^9E♭♭
3 11.58 ^3D, ^10E♭♭
4 15.43 ^4D, ^11E♭♭
5 19.29 88/87, 91/90, 92/91, 93/92 ^5D, ^12E♭♭
6 23.15 75/74, 76/75, 77/76 ^6D, ^13E♭♭
7 27.01 64/63, 65/64, 66/65 ^7D, ^14E♭♭
8 30.87 56/55, 57/56 ^8D, v15E♭
9 34.73 50/49, 51/50 ^9D, v14E♭
10 38.59 45/44, 46/45 ^10D, v13E♭
11 42.44 41/40 ^11D, v12E♭
12 46.3 38/37 ^12D, v11E♭
13 50.16 35/34 ^13D, v10E♭
14 54.02 65/63 ^14D, v9E♭
15 57.88 91/88 ^15D, v8E♭
16 61.74 57/55, 85/82 v14D♯, v7E♭
17 65.59 27/26, 80/77 v13D♯, v6E♭
18 69.45 51/49, 77/74 v12D♯, v5E♭
19 73.31 24/23 v11D♯, v4E♭
20 77.17 23/22, 91/87 v10D♯, v3E♭
21 81.03 22/21 v9D♯, vvE♭
22 84.89 21/20 v8D♯, vE♭
23 88.75 20/19 v7D♯, E♭
24 92.6 58/55, 96/91 v6D♯, ^E♭
25 96.46 37/35, 55/52, 92/87 v5D♯, ^^E♭
26 100.32 v4D♯, ^3E♭
27 104.18 86/81 v3D♯, ^4E♭
28 108.04 33/31 vvD♯, ^5E♭
29 111.9 16/15 vD♯, ^6E♭
30 115.76 31/29, 77/72 D♯, ^7E♭
31 119.61 15/14 ^D♯, ^8E♭
32 123.47 29/27 ^^D♯, ^9E♭
33 127.33 ^3D♯, ^10E♭
34 131.19 41/38, 55/51 ^4D♯, ^11E♭
35 135.05 40/37, 93/86 ^5D♯, ^12E♭
36 138.91 13/12 ^6D♯, ^13E♭
37 142.77 38/35, 63/58 ^7D♯, ^14E♭
38 146.62 37/34 ^8D♯, v15E
39 150.48 12/11 ^9D♯, v14E
40 154.34 82/75 ^10D♯, v13E
41 158.2 ^11D♯, v12E
42 162.06 56/51 ^12D♯, v11E
43 165.92 ^13D♯, v10E
44 169.77 32/29, 75/68 ^14D♯, v9E
45 173.63 21/19, 94/85 ^15D♯, v8E
46 177.49 41/37, 72/65 v14D𝄪, v7E
47 181.35 v13D𝄪, v6E
48 185.21 69/62 v12D𝄪, v5E
49 189.07 29/26 v11D𝄪, v4E
50 192.93 19/17 v10D𝄪, v3E
51 196.78 28/25, 65/58 v9D𝄪, vvE
52 200.64 64/57 v8D𝄪, vE
53 204.5 9/8 E
54 208.36 44/39 ^E, ^8F♭
55 212.22 26/23 ^^E, ^9F♭
56 216.08 17/15 ^3E, ^10F♭
57 219.94 42/37, 92/81 ^4E, ^11F♭
58 223.79 33/29 ^5E, ^12F♭
59 227.65 65/57 ^6E, ^13F♭
60 231.51 8/7 ^7E, ^14F♭
61 235.37 55/48, 63/55 ^8E, v15F
62 239.23 31/27 ^9E, v14F
63 243.09 ^10E, v13F
64 246.95 ^11E, v12F
65 250.8 37/32, 52/45 ^12E, v11F
66 254.66 95/82 ^13E, v10F
67 258.52 36/31, 65/56 ^14E, v9F
68 262.38 57/49, 64/55 ^15E, v8F
69 266.24 7/6 v14E♯, v7F
70 270.1 76/65, 90/77 v13E♯, v6F
71 273.95 41/35, 75/64 v12E♯, v5F
72 277.81 27/23 v11E♯, v4F
73 281.67 20/17 v10E♯, v3F
74 285.53 46/39 v9E♯, vvF
75 289.39 13/11 v8E♯, vF
76 293.25 45/38, 77/65 F
77 297.11 19/16 ^F, ^8G♭♭
78 300.96 69/58 ^^F, ^9G♭♭
79 304.82 31/26 ^3F, ^10G♭♭
80 308.68 49/41, 92/77 ^4F, ^11G♭♭
81 312.54 ^5F, ^12G♭♭
82 316.4 ^6F, ^13G♭♭
83 320.26 77/64 ^7F, ^14G♭♭
84 324.12 41/34, 76/63 ^8F, v15G♭
85 327.97 29/24 ^9F, v14G♭
86 331.83 63/52 ^10F, v13G♭
87 335.69 17/14 ^11F, v12G♭
88 339.55 ^12F, v11G♭
89 343.41 50/41 ^13F, v10G♭
90 347.27 11/9 ^14F, v9G♭
91 351.13 49/40, 60/49 ^15F, v8G♭
92 354.98 27/22 v14F♯, v7G♭
93 358.84 16/13 v13F♯, v6G♭
94 362.7 37/30 v12F♯, v5G♭
95 366.56 v11F♯, v4G♭
96 370.42 v10F♯, v3G♭
97 374.28 36/29 v9F♯, vvG♭
98 378.14 51/41, 56/45 v8F♯, vG♭
99 381.99 96/77 v7F♯, G♭
100 385.85 5/4 v6F♯, ^G♭
101 389.71 v5F♯, ^^G♭
102 393.57 64/51 v4F♯, ^3G♭
103 397.43 39/31 v3F♯, ^4G♭
104 401.29 29/23 vvF♯, ^5G♭
105 405.14 91/72 vF♯, ^6G♭
106 409 19/15 F♯, ^7G♭
107 412.86 33/26 ^F♯, ^8G♭
108 416.72 ^^F♯, ^9G♭
109 420.58 51/40, 65/51, 88/69 ^3F♯, ^10G♭
110 424.44 23/18 ^4F♯, ^11G♭
111 428.3 ^5F♯, ^12G♭
112 432.15 77/60, 95/74 ^6F♯, ^13G♭
113 436.01 ^7F♯, ^14G♭
114 439.87 49/38, 58/45 ^8F♯, v15G
115 443.73 31/24, 84/65 ^9F♯, v14G
116 447.59 57/44 ^10F♯, v13G
117 451.45 74/57 ^11F♯, v12G
118 455.31 ^12F♯, v11G
119 459.16 ^13F♯, v10G
120 463.02 81/62 ^14F♯, v9G
121 466.88 55/42, 72/55 ^15F♯, v8G
122 470.74 21/16 v14F𝄪, v7G
123 474.6 25/19 v13F𝄪, v6G
124 478.46 29/22 v12F𝄪, v5G
125 482.32 37/28 v11F𝄪, v4G
126 486.17 49/37 v10F𝄪, v3G
127 490.03 69/52, 77/58 v9F𝄪, vvG
128 493.89 v8F𝄪, vG
129 497.75 4/3 G
130 501.61 ^G, ^8A♭♭
131 505.47 75/56 ^^G, ^9A♭♭
132 509.32 51/38 ^3G, ^10A♭♭
133 513.18 39/29, 74/55 ^4G, ^11A♭♭
134 517.04 31/23 ^5G, ^12A♭♭
135 520.9 50/37, 77/57 ^6G, ^13A♭♭
136 524.76 65/48, 88/65 ^7G, ^14A♭♭
137 528.62 19/14 ^8G, v15A♭
138 532.48 34/25 ^9G, v14A♭
139 536.33 15/11 ^10G, v13A♭
140 540.19 41/30, 56/41 ^11G, v12A♭
141 544.05 63/46 ^12G, v11A♭
142 547.91 70/51 ^13G, v10A♭
143 551.77 11/8 ^14G, v9A♭
144 555.63 51/37, 91/66 ^15G, v8A♭
145 559.49 76/55 v14G♯, v7A♭
146 563.34 18/13 v13G♯, v6A♭
147 567.2 68/49 v12G♯, v5A♭
148 571.06 57/41 v11G♯, v4A♭
149 574.92 46/33 v10G♯, v3A♭
150 578.78 81/58, 88/63, 95/68 v9G♯, vvA♭
151 582.64 7/5 v8G♯, vA♭
152 586.5 80/57, 87/62 v7G♯, A♭
153 590.35 45/32 v6G♯, ^A♭
154 594.21 31/22 v5G♯, ^^A♭
155 598.07 65/46 v4G♯, ^3A♭
156 601.93 92/65 v3G♯, ^4A♭
157 605.79 44/31 vvG♯, ^5A♭
158 609.65 64/45, 91/64 vG♯, ^6A♭
159 613.5 57/40 G♯, ^7A♭
160 617.36 10/7 ^G♯, ^8A♭
161 621.22 63/44 ^^G♯, ^9A♭
162 625.08 33/23 ^3G♯, ^10A♭
163 628.94 82/57 ^4G♯, ^11A♭
164 632.8 49/34 ^5G♯, ^12A♭
165 636.66 13/9 ^6G♯, ^13A♭
166 640.51 55/38 ^7G♯, ^14A♭
167 644.37 74/51 ^8G♯, v15A
168 648.23 16/11 ^9G♯, v14A
169 652.09 51/35 ^10G♯, v13A
170 655.95 92/63 ^11G♯, v12A
171 659.81 41/28, 60/41 ^12G♯, v11A
172 663.67 22/15, 91/62 ^13G♯, v10A
173 667.52 25/17 ^14G♯, v9A
174 671.38 28/19 ^15G♯, v8A
175 675.24 65/44, 96/65 v14G𝄪, v7A
176 679.1 37/25, 77/52 v13G𝄪, v6A
177 682.96 46/31 v12G𝄪, v5A
178 686.82 55/37, 58/39 v11G𝄪, v4A
179 690.68 76/51 v10G𝄪, v3A
180 694.53 v9G𝄪, vvA
181 698.39 v8G𝄪, vA
182 702.25 3/2 A
183 706.11 ^A, ^8B♭♭
184 709.97 ^^A, ^9B♭♭
185 713.83 74/49, 77/51 ^3A, ^10B♭♭
186 717.68 56/37 ^4A, ^11B♭♭
187 721.54 44/29, 91/60 ^5A, ^12B♭♭
188 725.4 38/25 ^6A, ^13B♭♭
189 729.26 32/21 ^7A, ^14B♭♭
190 733.12 55/36, 84/55 ^8A, v15B♭
191 736.98 75/49 ^9A, v14B♭
192 740.84 ^10A, v13B♭
193 744.69 ^11A, v12B♭
194 748.55 57/37 ^12A, v11B♭
195 752.41 88/57 ^13A, v10B♭
196 756.27 48/31, 65/42 ^14A, v9B♭
197 760.13 45/29, 76/49 ^15A, v8B♭
198 763.99 v14A♯, v7B♭
199 767.85 81/52 v13A♯, v6B♭
200 771.7 v12A♯, v5B♭
201 775.56 36/23 v11A♯, v4B♭
202 779.42 69/44, 80/51, 91/58 v10A♯, v3B♭
203 783.28 v9A♯, vvB♭
204 787.14 52/33 v8A♯, vB♭
205 791 30/19 v7A♯, B♭
206 794.86 v6A♯, ^B♭
207 798.71 46/29 v5A♯, ^^B♭
208 802.57 62/39 v4A♯, ^3B♭
209 806.43 51/32 v3A♯, ^4B♭
210 810.29 91/57 vvA♯, ^5B♭
211 814.15 8/5 vA♯, ^6B♭
212 818.01 77/48, 93/58 A♯, ^7B♭
213 821.86 45/28, 82/51 ^A♯, ^8B♭
214 825.72 29/18 ^^A♯, ^9B♭
215 829.58 ^3A♯, ^10B♭
216 833.44 ^4A♯, ^11B♭
217 837.3 60/37 ^5A♯, ^12B♭
218 841.16 13/8 ^6A♯, ^13B♭
219 845.02 44/27 ^7A♯, ^14B♭
220 848.87 49/30, 80/49 ^8A♯, v15B
221 852.73 18/11 ^9A♯, v14B
222 856.59 41/25 ^10A♯, v13B
223 860.45 ^11A♯, v12B
224 864.31 28/17 ^12A♯, v11B
225 868.17 ^13A♯, v10B
226 872.03 48/29, 91/55 ^14A♯, v9B
227 875.88 63/38, 68/41 ^15A♯, v8B
228 879.74 v14A𝄪, v7B
229 883.6 v13A𝄪, v6B
230 887.46 v12A𝄪, v5B
231 891.32 77/46, 82/49, 87/52 v11A𝄪, v4B
232 895.18 52/31 v10A𝄪, v3B
233 899.04 v9A𝄪, vvB
234 902.89 32/19, 91/54 v8A𝄪, vB
235 906.75 76/45 B
236 910.61 22/13 ^B, ^8C♭
237 914.47 39/23, 95/56 ^^B, ^9C♭
238 918.33 17/10 ^3B, ^10C♭
239 922.19 46/27 ^4B, ^11C♭
240 926.05 70/41 ^5B, ^12C♭
241 929.9 65/38, 77/45 ^6B, ^13C♭
242 933.76 12/7 ^7B, ^14C♭
243 937.62 55/32 ^8B, v15C
244 941.48 31/18 ^9B, v14C
245 945.34 ^10B, v13C
246 949.2 45/26, 64/37 ^11B, v12C
247 953.05 85/49 ^12B, v11C
248 956.91 ^13B, v10C
249 960.77 54/31 ^14B, v9C
250 964.63 96/55 ^15B, v8C
251 968.49 7/4 v14B♯, v7C
252 972.35 v13B♯, v6C
253 976.21 58/33 v12B♯, v5C
254 980.06 37/21, 81/46 v11B♯, v4C
255 983.92 30/17 v10B♯, v3C
256 987.78 23/13 v9B♯, vvC
257 991.64 39/22 v8B♯, vC
258 995.5 16/9 C
259 999.36 57/32 ^C, ^8D♭♭
260 1003.22 25/14 ^^C, ^9D♭♭
261 1007.07 34/19, 93/52 ^3C, ^10D♭♭
262 1010.93 52/29 ^4C, ^11D♭♭
263 1014.79 ^5C, ^12D♭♭
264 1018.65 ^6C, ^13D♭♭
265 1022.51 65/36, 74/41 ^7C, ^14D♭♭
266 1026.37 38/21, 85/47 ^8C, v15D♭
267 1030.23 29/16 ^9C, v14D♭
268 1034.08 ^10C, v13D♭
269 1037.94 51/28 ^11C, v12D♭
270 1041.8 ^12C, v11D♭
271 1045.66 75/41 ^13C, v10D♭
272 1049.52 11/6 ^14C, v9D♭
273 1053.38 68/37 ^15C, v8D♭
274 1057.23 35/19 v14C♯, v7D♭
275 1061.09 24/13 v13C♯, v6D♭
276 1064.95 37/20 v12C♯, v5D♭
277 1068.81 76/41 v11C♯, v4D♭
278 1072.67 v10C♯, v3D♭
279 1076.53 54/29, 95/51 v9C♯, vvD♭
280 1080.39 28/15 v8C♯, vD♭
281 1084.24 58/31 v7C♯, D♭
282 1088.1 15/8 v6C♯, ^D♭
283 1091.96 62/33 v5C♯, ^^D♭
284 1095.82 81/43 v4C♯, ^3D♭
285 1099.68 v3C♯, ^4D♭
286 1103.54 70/37, 87/46 vvC♯, ^5D♭
287 1107.4 55/29, 91/48 vC♯, ^6D♭
288 1111.25 19/10 C♯, ^7D♭
289 1115.11 40/21 ^C♯, ^8D♭
290 1118.97 21/11 ^^C♯, ^9D♭
291 1122.83 44/23 ^3C♯, ^10D♭
292 1126.69 23/12 ^4C♯, ^11D♭
293 1130.55 ^5C♯, ^12D♭
294 1134.41 52/27, 77/40 ^6C♯, ^13D♭
295 1138.26 ^7C♯, ^14D♭
296 1142.12 ^8C♯, v15D
297 1145.98 95/49 ^9C♯, v14D
298 1149.84 68/35 ^10C♯, v13D
299 1153.7 37/19 ^11C♯, v12D
300 1157.56 80/41 ^12C♯, v11D
301 1161.41 45/23, 88/45 ^13C♯, v10D
302 1165.27 49/25 ^14C♯, v9D
303 1169.13 55/28 ^15C♯, v8D
304 1172.99 63/32, 65/33 v14C𝄪, v7D
305 1176.85 75/38 v13C𝄪, v6D
306 1180.71 87/44, 91/46 v12C𝄪, v5D
307 1184.57 v11C𝄪, v4D
308 1188.42 v10C𝄪, v3D
309 1192.28 v9C𝄪, vvD
310 1196.14 v8C𝄪, vD
311 1200 2/1 D

EDO testing

← 71082ed31 71083ed31 71084ed31 →
Prime factorization 31 × 2293
Step size 0.0836351 ¢ 
Octave 14348\71083ed31 (1200 ¢)
Twelfth 22741\71083ed31 (1901.95 ¢)
Consistency limit 56
Distinct consistency limit 56

--Overthink (talk) 04:41, 29 September 2025 (UTC)

Scale tree and tuning spectrum of 5L 2s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
4\7 685.714 514.286 1:1 1.000 Equalized 5L 2s
15\26 692.308 507.692 4:3 1.333 Supersoft 5L 2s
11\19 694.737 505.263 3:2 1.500 Soft 5L 2s
18\31 696.774 503.226 5:3 1.667 Semisoft 5L 2s
7\12 700.000 500.000 2:1 2.000 Basic 5L 2s
Scales with tunings softer than this are proper
17\29 703.448 496.552 5:2 2.500 Semihard 5L 2s
10\17 705.882 494.118 3:1 3.000 Hard 5L 2s
13\22 709.091 490.909 4:1 4.000 Superhard 5L 2s
3\5 720.000 480.000 1:0 → ∞ Collapsed 5L 2s

Miscellaneous

~

~~

Overthink (talk)

Overthink (talk) 22:00, 22 November 2025 (UTC)

22:00, 22 November 2025 (UTC)

22:00, 22 November 2025 (UTC)~

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