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→Testing: huge table (23-limit)
Line 1: Line 1:
= Testing =
= Testing =
{{Collapsed huge table|311edo}}
= Scratchwork =
= Scratchwork =
{{Q-odd-limit intervals|5}}
{{Q-odd-limit intervals|5}}
= Whatever =
= Whatever =
{{Special:RecentChanges}}
{{Special:RecentChanges}}

Revision as of 06:51, 28 December 2025

Testing

Steps Cents Approximate Ratios Ups and Downs Notation
0 0 1/1 D
1 3.859 ^D, ^8E♭♭
2 7.717 ^^D, ^9E♭♭
3 11.576 ^3D, ^10E♭♭
4 15.434 ^4D, ^11E♭♭
5 19.293 ^5D, ^12E♭♭
6 23.151 ^6D, ^13E♭♭
7 27.01 ^7D, ^14E♭♭
8 30.868 ^8D, v15E♭
9 34.727 49/48, 50/49, 51/50, 52/51 ^9D, v14E♭
10 38.585 45/44, 46/45 ^10D, v13E♭
11 42.444 40/39 ^11D, v12E♭
12 46.302 39/38 ^12D, v11E♭
13 50.161 34/33, 35/34, 36/35 ^13D, v10E♭
14 54.019 33/32 ^14D, v9E♭
15 57.878 ^15D, v8E♭
16 61.736 28/27 v14D♯, v7E♭
17 65.595 27/26 v13D♯, v6E♭
18 69.453 25/24, 26/25, 51/49 v12D♯, v5E♭
19 73.312 24/23 v11D♯, v4E♭
20 77.17 23/22 v10D♯, v3E♭
21 81.029 22/21 v9D♯, vvE♭
22 84.887 21/20 v8D♯, vE♭
23 88.746 20/19 v7D♯, E♭
24 92.605 19/18 v6D♯, ^E♭
25 96.463 v5D♯, ^^E♭
26 100.322 18/17, 35/33 v4D♯, ^3E♭
27 104.18 17/16, 52/49 v3D♯, ^4E♭
28 108.039 49/46 vvD♯, ^5E♭
29 111.897 16/15 vD♯, ^6E♭
30 115.756 D♯, ^7E♭
31 119.614 15/14 ^D♯, ^8E♭
32 123.473 ^^D♯, ^9E♭
33 127.331 14/13 ^3D♯, ^10E♭
34 131.19 ^4D♯, ^11E♭
35 135.048 27/25 ^5D♯, ^12E♭
36 138.907 13/12 ^6D♯, ^13E♭
37 142.765 25/23, 38/35 ^7D♯, ^14E♭
38 146.624 49/45 ^8D♯, v15E
39 150.482 12/11 ^9D♯, v14E
40 154.341 35/32 ^10D♯, v13E
41 158.199 23/21 ^11D♯, v12E
42 162.058 ^12D♯, v11E
43 165.916 11/10 ^13D♯, v10E
44 169.775 54/49 ^14D♯, v9E
45 173.633 21/19 ^15D♯, v8E
46 177.492 51/46 v14D𝄪, v7E
47 181.35 10/9 v13D𝄪, v6E
48 185.209 49/44 v12D𝄪, v5E
49 189.068 39/35 v11D𝄪, v4E
50 192.926 19/17 v10D𝄪, v3E
51 196.785 28/25 v9D𝄪, vvE
52 200.643 v8D𝄪, vE
53 204.502 9/8 E
54 208.36 44/39 ^E, ^8F♭
55 212.219 26/23 ^^E, ^9F♭
56 216.077 17/15 ^3E, ^10F♭
57 219.936 25/22 ^4E, ^11F♭
58 223.794 ^5E, ^12F♭
59 227.653 ^6E, ^13F♭
60 231.511 8/7 ^7E, ^14F♭
61 235.37 ^8E, v15F
62 239.228 39/34 ^9E, v14F
63 243.087 23/20, 38/33 ^10E, v13F
64 246.945 15/13 ^11E, v12F
65 250.804 52/45 ^12E, v11F
66 254.662 22/19, 51/44 ^13E, v10F
67 258.521 ^14E, v9F
68 262.379 ^15E, v8F
69 266.238 7/6 v14E♯, v7F
70 270.096 v13E♯, v6F
71 273.955 v12E♯, v5F
72 277.814 27/23 v11E♯, v4F
73 281.672 20/17 v10E♯, v3F
74 285.531 33/28, 46/39 v9E♯, vvF
75 289.389 13/11 v8E♯, vF
76 293.248 32/27, 45/38 F
77 297.106 19/16 ^F, ^8G♭♭
78 300.965 25/21 ^^F, ^9G♭♭
79 304.823 ^3F, ^10G♭♭
80 308.682 ^4F, ^11G♭♭
81 312.54 ^5F, ^12G♭♭
82 316.399 6/5 ^6F, ^13G♭♭
83 320.257 ^7F, ^14G♭♭
84 324.116 ^8F, v15G♭
85 327.974 ^9F, v14G♭
86 331.833 23/19, 40/33 ^10F, v13G♭
87 335.691 17/14 ^11F, v12G♭
88 339.55 28/23 ^12F, v11G♭
89 343.408 39/32 ^13F, v10G♭
90 347.267 11/9 ^14F, v9G♭
91 351.125 49/40 ^15F, v8G♭
92 354.984 27/22 v14F♯, v7G♭
93 358.842 16/13 v13F♯, v6G♭
94 362.701 v12F♯, v5G♭
95 366.559 21/17 v11F♯, v4G♭
96 370.418 26/21 v10F♯, v3G♭
97 374.277 v9F♯, vvG♭
98 378.135 v8F♯, vG♭
99 381.994 v7F♯, G♭
100 385.852 5/4 v6F♯, ^G♭
101 389.711 v5F♯, ^^G♭
102 393.569 49/39 v4F♯, ^3G♭
103 397.428 34/27, 44/35 v3F♯, ^4G♭
104 401.286 vvF♯, ^5G♭
105 405.145 24/19 vF♯, ^6G♭
106 409.003 19/15 F♯, ^7G♭
107 412.862 33/26 ^F♯, ^8G♭
108 416.72 14/11 ^^F♯, ^9G♭
109 420.579 51/40 ^3F♯, ^10G♭
110 424.437 23/18 ^4F♯, ^11G♭
111 428.296 32/25, 50/39 ^5F♯, ^12G♭
112 432.154 ^6F♯, ^13G♭
113 436.013 9/7 ^7F♯, ^14G♭
114 439.871 49/38 ^8F♯, v15G
115 443.73 ^9F♯, v14G
116 447.588 22/17, 35/27 ^10F♯, v13G
117 451.447 ^11F♯, v12G
118 455.305 13/10 ^12F♯, v11G
119 459.164 30/23 ^13F♯, v10G
120 463.023 17/13 ^14F♯, v9G
121 466.881 ^15F♯, v8G
122 470.74 21/16 v14F𝄪, v7G
123 474.598 25/19, 46/35 v13F𝄪, v6G
124 478.457 v12F𝄪, v5G
125 482.315 33/25 v11F𝄪, v4G
126 486.174 45/34 v10F𝄪, v3G
127 490.032 v9F𝄪, vvG
128 493.891 v8F𝄪, vG
129 497.749 4/3 G
130 501.608 ^G, ^8A♭♭
131 505.466 ^^G, ^9A♭♭
132 509.325 51/38 ^3G, ^10A♭♭
133 513.183 35/26 ^4G, ^11A♭♭
134 517.042 ^5G, ^12A♭♭
135 520.9 27/20 ^6G, ^13A♭♭
136 524.759 23/17 ^7G, ^14A♭♭
137 528.617 19/14 ^8G, v15A♭
138 532.476 34/25, 49/36 ^9G, v14A♭
139 536.334 15/11 ^10G, v13A♭
140 540.193 ^11G, v12A♭
141 544.051 26/19 ^12G, v11A♭
142 547.91 48/35 ^13G, v10A♭
143 551.768 11/8 ^14G, v9A♭
144 555.627 ^15G, v8A♭
145 559.486 v14G♯, v7A♭
146 563.344 18/13 v13G♯, v6A♭
147 567.203 25/18 v12G♯, v5A♭
148 571.061 32/23 v11G♯, v4A♭
149 574.92 39/28, 46/33 v10G♯, v3A♭
150 578.778 v9G♯, vvA♭
151 582.637 7/5 v8G♯, vA♭
152 586.495 v7G♯, A♭
153 590.354 38/27, 45/32 v6G♯, ^A♭
154 594.212 v5G♯, ^^A♭
155 598.071 24/17 v4G♯, ^3A♭
156 601.929 17/12 v3G♯, ^4A♭
157 605.788 vvG♯, ^5A♭
158 609.646 27/19 vG♯, ^6A♭
159 613.505 G♯, ^7A♭
160 617.363 10/7 ^G♯, ^8A♭
161 621.222 ^^G♯, ^9A♭
162 625.08 33/23 ^3G♯, ^10A♭
163 628.939 23/16 ^4G♯, ^11A♭
164 632.797 36/25, 49/34 ^5G♯, ^12A♭
165 636.656 13/9 ^6G♯, ^13A♭
166 640.514 ^7G♯, ^14A♭
167 644.373 ^8G♯, v15A
168 648.232 16/11 ^9G♯, v14A
169 652.09 35/24, 51/35 ^10G♯, v13A
170 655.949 19/13 ^11G♯, v12A
171 659.807 ^12G♯, v11A
172 663.666 22/15 ^13G♯, v10A
173 667.524 25/17 ^14G♯, v9A
174 671.383 28/19 ^15G♯, v8A
175 675.241 34/23 v14G𝄪, v7A
176 679.1 40/27 v13G𝄪, v6A
177 682.958 49/33 v12G𝄪, v5A
178 686.817 52/35 v11G𝄪, v4A
179 690.675 v10G𝄪, v3A
180 694.534 v9G𝄪, vvA
181 698.392 v8G𝄪, vA
182 702.251 3/2 A
183 706.109 ^A, ^8B♭♭
184 709.968 ^^A, ^9B♭♭
185 713.826 ^3A, ^10B♭♭
186 717.685 50/33 ^4A, ^11B♭♭
187 721.543 ^5A, ^12B♭♭
188 725.402 35/23, 38/25 ^6A, ^13B♭♭
189 729.26 32/21 ^7A, ^14B♭♭
190 733.119 ^8A, v15B♭
191 736.977 26/17, 49/32 ^9A, v14B♭
192 740.836 23/15 ^10A, v13B♭
193 744.695 20/13 ^11A, v12B♭
194 748.553 ^12A, v11B♭
195 752.412 17/11, 54/35 ^13A, v10B♭
196 756.27 ^14A, v9B♭
197 760.129 ^15A, v8B♭
198 763.987 14/9 v14A♯, v7B♭
199 767.846 v13A♯, v6B♭
200 771.704 25/16, 39/25 v12A♯, v5B♭
201 775.563 36/23 v11A♯, v4B♭
202 779.421 v10A♯, v3B♭
203 783.28 11/7 v9A♯, vvB♭
204 787.138 52/33 v8A♯, vB♭
205 790.997 30/19 v7A♯, B♭
206 794.855 19/12 v6A♯, ^B♭
207 798.714 v5A♯, ^^B♭
208 802.572 27/17, 35/22 v4A♯, ^3B♭
209 806.431 51/32 v3A♯, ^4B♭
210 810.289 vvA♯, ^5B♭
211 814.148 8/5 vA♯, ^6B♭
212 818.006 A♯, ^7B♭
213 821.865 45/28 ^A♯, ^8B♭
214 825.723 ^^A♯, ^9B♭
215 829.582 21/13 ^3A♯, ^10B♭
216 833.441 34/21 ^4A♯, ^11B♭
217 837.299 ^5A♯, ^12B♭
218 841.158 13/8 ^6A♯, ^13B♭
219 845.016 44/27 ^7A♯, ^14B♭
220 848.875 49/30 ^8A♯, v15B
221 852.733 18/11 ^9A♯, v14B
222 856.592 ^10A♯, v13B
223 860.45 23/14 ^11A♯, v12B
224 864.309 28/17 ^12A♯, v11B
225 868.167 33/20, 38/23 ^13A♯, v10B
226 872.026 ^14A♯, v9B
227 875.884 ^15A♯, v8B
228 879.743 v14A𝄪, v7B
229 883.601 5/3 v13A𝄪, v6B
230 887.46 v12A𝄪, v5B
231 891.318 v11A𝄪, v4B
232 895.177 v10A𝄪, v3B
233 899.035 42/25 v9A𝄪, vvB
234 902.894 32/19 v8A𝄪, vB
235 906.752 27/16 B
236 910.611 22/13 ^B, ^8C♭
237 914.469 39/23 ^^B, ^9C♭
238 918.328 17/10 ^3B, ^10C♭
239 922.186 46/27 ^4B, ^11C♭
240 926.045 ^5B, ^12C♭
241 929.904 ^6B, ^13C♭
242 933.762 12/7 ^7B, ^14C♭
243 937.621 ^8B, v15C
244 941.479 ^9B, v14C
245 945.338 19/11 ^10B, v13C
246 949.196 45/26 ^11B, v12C
247 953.055 26/15 ^12B, v11C
248 956.913 33/19, 40/23 ^13B, v10C
249 960.772 ^14B, v9C
250 964.63 ^15B, v8C
251 968.489 7/4 v14B♯, v7C
252 972.347 v13B♯, v6C
253 976.206 v12B♯, v5C
254 980.064 44/25 v11B♯, v4C
255 983.923 30/17 v10B♯, v3C
256 987.781 23/13 v9B♯, vvC
257 991.64 39/22 v8B♯, vC
258 995.498 16/9 C
259 999.357 ^C, ^8D♭♭
260 1003.215 25/14 ^^C, ^9D♭♭
261 1007.074 34/19 ^3C, ^10D♭♭
262 1010.932 ^4C, ^11D♭♭
263 1014.791 ^5C, ^12D♭♭
264 1018.65 9/5 ^6C, ^13D♭♭
265 1022.508 ^7C, ^14D♭♭
266 1026.367 38/21 ^8C, v15D♭
267 1030.225 49/27 ^9C, v14D♭
268 1034.084 20/11 ^10C, v13D♭
269 1037.942 51/28 ^11C, v12D♭
270 1041.801 42/23 ^12C, v11D♭
271 1045.659 ^13C, v10D♭
272 1049.518 11/6 ^14C, v9D♭
273 1053.376 ^15C, v8D♭
274 1057.235 35/19, 46/25 v14C♯, v7D♭
275 1061.093 24/13 v13C♯, v6D♭
276 1064.952 50/27 v12C♯, v5D♭
277 1068.81 v11C♯, v4D♭
278 1072.669 13/7 v10C♯, v3D♭
279 1076.527 v9C♯, vvD♭
280 1080.386 28/15 v8C♯, vD♭
281 1084.244 v7C♯, D♭
282 1088.103 15/8 v6C♯, ^D♭
283 1091.961 v5C♯, ^^D♭
284 1095.82 32/17, 49/26 v4C♯, ^3D♭
285 1099.678 17/9 v3C♯, ^4D♭
286 1103.537 vvC♯, ^5D♭
287 1107.395 36/19 vC♯, ^6D♭
288 1111.254 19/10 C♯, ^7D♭
289 1115.113 40/21 ^C♯, ^8D♭
290 1118.971 21/11 ^^C♯, ^9D♭
291 1122.83 44/23 ^3C♯, ^10D♭
292 1126.688 23/12 ^4C♯, ^11D♭
293 1130.547 25/13, 48/25 ^5C♯, ^12D♭
294 1134.405 52/27 ^6C♯, ^13D♭
295 1138.264 27/14 ^7C♯, ^14D♭
296 1142.122 ^8C♯, v15D
297 1145.981 ^9C♯, v14D
298 1149.839 33/17, 35/18 ^10C♯, v13D
299 1153.698 ^11C♯, v12D
300 1157.556 39/20 ^12C♯, v11D
301 1161.415 45/23 ^13C♯, v10D
302 1165.273 49/25, 51/26 ^14C♯, v9D
303 1169.132 ^15C♯, v8D
304 1172.99 v14C𝄪, v7D
305 1176.849 v13C𝄪, v6D
306 1180.707 v12C𝄪, v5D
307 1184.566 v11C𝄪, v4D
308 1188.424 v10C𝄪, v3D
309 1192.283 v9C𝄪, vvD
310 1196.141 v8C𝄪, vD
311 1200 2/1 D

Scratchwork

The following tables show how 15-odd-limit intervals are represented in 5edo. Prime harmonics are in bold; inconsistent intervals are in italics.

15-odd-limit intervals in 5edo (direct approximation, even if inconsistent)
Interval and complement Error (abs, ¢) Error (rel, %)
1/1, 2/1 0.000 0.0
15/13, 26/15 7.741 3.2
7/4, 8/7 8.826 3.7
3/2, 4/3 18.045 7.5
13/10, 20/13 25.786 10.7
7/6, 12/7 26.871 11.2
9/8, 16/9 36.090 15.0
9/7, 14/9 44.916 18.7
13/11, 22/13 49.210 20.5
15/11, 22/15 56.951 23.7
9/5, 10/9 57.596 24.0
11/7, 14/11 62.492 26.0
11/8, 16/11 71.318 29.7
11/10, 20/11 74.996 31.2
5/3, 6/5 75.641 31.5
13/9, 18/13 83.382 34.7
11/6, 12/11 89.363 37.2
5/4, 8/5 93.686 39.0
13/12, 24/13 101.427 42.3
7/5, 10/7 102.512 42.7
11/9, 18/11 107.408 44.8
13/7, 14/13 111.702 46.5
15/8, 16/15 111.731 46.6
15/14, 28/15 119.443 49.8
13/8, 16/13 119.472 49.8
15-odd-limit intervals in 5edo (patent val mapping)
Interval and complement Error (abs, ¢) Error (rel, %)
1/1, 2/1 0.000 0.0
15/13, 26/15 7.741 3.2
7/4, 8/7 8.826 3.7
3/2, 4/3 18.045 7.5
13/10, 20/13 25.786 10.7
7/6, 12/7 26.871 11.2
9/8, 16/9 36.090 15.0
9/7, 14/9 44.916 18.7
9/5, 10/9 57.596 24.0
11/7, 14/11 62.492 26.0
11/8, 16/11 71.318 29.7
5/3, 6/5 75.641 31.5
13/9, 18/13 83.382 34.7
11/6, 12/11 89.363 37.2
5/4, 8/5 93.686 39.0
13/12, 24/13 101.427 42.3
7/5, 10/7 102.512 42.7
11/9, 18/11 107.408 44.8
15/8, 16/15 111.731 46.6
13/8, 16/13 119.472 49.8
15/14, 28/15 120.557 50.2
13/7, 14/13 128.298 53.5
11/10, 20/11 165.004 68.8
15/11, 22/15 183.049 76.3
13/11, 22/13 190.790 79.5

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13 June 2026

N    09:14  Heaven diffhist +52 Xenllium talk contribs (Redirected page to Very low accuracy temperaments#Heaven) Tags: New redirect Mobile edit Mobile web edit
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12 June 2026

      23:55  Tubulong 2 changes history +7,796 [Naren (2×)]
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     19:52  Whitewood diffhist +18 FloraC talk contribs (Wording & misc. additions)
N    19:27  Dog comma diffhist +19 Hotcrystal0 talk contribs (Redirected page to 81/76) Tag: New redirect
      19:11  39edo 3 changes history +168 [Overthink (3×)]
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19:11 (cur | prev) +59 Overthink talk contribs (→As a tuning of other temperaments: link here)
     
19:09 (cur | prev) +22 Overthink talk contribs (→As a tuning of other temperaments: also this)
     
00:46 (cur | prev) +87 Overthink talk contribs (→Intervals: add these)
     14:13  97/84 diffhist +13 Godtone talk contribs (missing words)
N    11:09  2.3.5.7.11.13.19 subgroup 2 changes history +4,102 [Eufalesio (2×)]
     
11:09 (cur | prev) +1,580 Eufalesio talk contribs (Shameless near-copypaste from other articles, things missing TBA) Tag: Visual edit
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10:59 (cur | prev) +2,522 Eufalesio talk contribs (Birth) Tag: Visual edit
N    11:00  Yazalathana diffhist +39 Eufalesio talk contribs (Redirect) Tags: New redirect Visual edit
     10:47  2.11.13.17.19 subgroup diffhist +61 Eufalesio talk contribs (Please delete) Tag: Visual edit
N    09:30  1-3-5-7-9-13-15 pentatriandekany diffhist +1,296 Yourmusic Productions talk contribs (Create Page.)
     06:05  Map of rank-2 temperaments diffhist +214 Hkm talk contribs Tag: Visual edit
     06:04  Map of linear temperaments diffhist +165 Hkm talk contribs Tag: Visual edit
     05:59  MOS scale diffhist +131 Hkm talk contribs (→See also) Tag: Visual edit
     05:14  No-elevens subgroup temperaments diffhist +9 Hkm talk contribs (→Sensi (aka sensation): as per XA discussion in 2024) Tag: Visual edit
      05:12  Sensipent family 4 changes history 0 [Hkm (4×)]
     
05:12 (cur | prev) +9 Hkm talk contribs (Undo revision 232169 by Hkm (talk)) Tag: Undo
     
05:11 (cur | prev) +16 Hkm talk contribs (Undo revision 232170 by Hkm (talk)) Tag: Undo
     
03:53 (cur | prev) −16 Hkm talk contribs (→Sensi) Tags: Reverted Visual edit
     
03:52 (cur | prev) −9 Hkm talk contribs (→Septimal sensi) Tags: Reverted Visual edit
 m   00:48  94-comma diffhist 0 Overthink talk contribs (→Temperaments: caps)
     00:23  Wesley family 2 changes history +12 [Hkm (2×)]
     
00:23 (cur | prev) +2 Hkm talk contribs (→Roman) Tag: Visual edit
     
00:23 (cur | prev) +10 Hkm talk contribs (→Roman) Tag: Visual edit

11 June 2026

     23:26  Ivor Darreg diffhist −4 Naren talk contribs (Fix link to Darreg's Xenharmonic Bulletin No. 1)
     21:12  User:Hkm 2 changes history +18 [Hkm (2×)]
     
21:12 (cur | prev) −10 Hkm talk contribs Tag: Visual edit
     
21:11 (cur | prev) +28 Hkm talk contribs Tag: Visual edit
N    17:12  94-comma diffhist +1,181 Eufalesio talk contribs (Birth) Tag: Visual edit
      17:10  User:Eufalesio/Ultimate 2 changes history +597 [Eufalesio (2×)]
     
17:10 (cur | prev) +271 Eufalesio talk contribs (Hotfixes!) Tag: Visual edit
     
17:03 (cur | prev) +326 Eufalesio talk contribs (NOTATION!) Tag: Visual edit
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