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User:Inthar/311edo

< User:Inthar

Consistent patent val readings

TODO: separate into more-in-tune-than-out-of-tune and more-out-of-tune-than-in-tune

Steps Cents Consistent patent val readings
1 3.858521 449/448
2 7.717042 224/223, 225/224
3 11.575563 150/149
4 15.434084 338/335
5 19.292605 90/89
6 23.151125 70/69, 78/77, 77/76, 76/75, 75/74, 74/73, 73/72
7 27.009646 63/62, 64/63, 65/64, 66/65, 69/68
8 30.868167 55/54, 56/55, 57/56, 58/57
9 34.726688 49/48, 50/49, 51/50, 52/51
10 38.585209 45/44, 46/45
11 42.443730 40/39, 41/40, 42/41
12 46.302251 37/36, 38/37, 39/38
13 50.160772 34/33, 35/34, 36/35
14 54.019293 32/31, 33/32
15 57.877814 30/29, 31/30
16 61.736334 28/27, 29/28
17 65.594855 27/26
18 69.453376 25/24, 26/25
19 73.311897 24/23
20 77.170418 23/22
21 81.028939 22/21
22 84.887460 21/20
23 88.745981 20/19
24 92.604502 19/18, 39/37
25 96.463023 37/35
26 100.321543 18/17, 35/33
27 104.180064 17/16
28 108.038585 33/31
29 111.897106 16/15
30 115.755627 31/29
31 119.614148 15/14
32 123.472669 29/27
33 127.331190 14/13
34 131.189711 69/64
35 135.048232 27/25, 40/37
36 138.906752 13/12
37 142.765273 25/23
38 146.623794 37/34
39 150.482315 12/11
40 154.340836 35/32
41 158.199357 23/21, 34/31
42 162.057878 45/41, 56/51
43 165.916399 11/10
44 169.774920 32/29
45 173.633441 21/19
46 177.491961 31/28
47 181.350482 10/9
48 185.209003 49/44
49 189.067524 29/26, 39/35
50 192.926045 19/17
51 196.784566 28/25
52 200.643087 55/49
53 204.501608 9/8
54 208.360129 35/31
55 212.218650 26/23
56 216.077170 17/15
57 219.935691 25/22, 42/37
58 223.794212 33/29
59 227.652733 73/64
60 231.511254 8/7
61 235.369775 55/48
62 239.228296 31/27, 39/34
63 243.086817 23/20
64 246.945338 15/13, 128/111
65 250.803859 37/32
66 254.662379 22/19
67 258.520900 29/25, 36/31
68 262.379421 64/55
69 266.237942 7/6
70 270.096463 90/77
71 273.954984 34/29, 41/35, 48/41, 75/64
72 277.813505 27/23
73 281.672026 20/17
74 285.530547 33/28, 46/39
75 289.389068 13/11
76 293.247588 32/27
77 297.106109 19/16
78 300.964630 25/21
79 304.823151 31/26, 37/31
80 308.681672 49/41, 55/46
81 312.540193 109/91
82 316.398714 6/5
83 320.257235 77/64
84 324.115756 35/29
85 327.974277 29/24
86 331.832797 23/19, 40/33
87 335.691318 17/14
88 339.549839 28/23, 73/60
89 343.408360 39/32, 50/41, 128/105
90 347.266881 11/9
91 351.125402 38/31
92 354.983923 27/22
93 358.842444 16/13
94 362.700965 37/30
95 366.559486 21/17
96 370.418006 26/21
97 374.276527 36/29, 41/33
98 378.135048 46/37, 51/41, 56/45
99 381.993569 96/77
100 385.852090 5/4
101 389.710611 124/99
102 393.569132 49/39, 64/51
103 397.427653 39/31, 44/35
104 401.286174 29/23
105 405.144695 24/19
106 409.003215 19/15
107 412.861736 33/26
108 416.720257 14/11
109 420.578778 39/29
110 424.437299 23/18
111 428.295820 41/32, 32/25
112 432.154341 77/60
113 436.012862 9/7
114 439.871383 49/38
115 443.729904 31/24
116 447.588424 22/17
117 451.446945 83/64
118 455.305466 13/10
119 459.163987 30/23
120 463.022508 17/13, 49/32
121 466.881029 55/42, 38/29
122 470.739550 21/16
123 474.598071 25/19
124 478.456592 29/22
125 482.315113 33/25
126 486.173633 45/34, 49/37
127 490.032154 85/64
128 493.890675 278/209
129 497.749196 4/3
130 501.607717 322/241, 163/122
131 505.466238 75/56
132 509.324759 51/38
133 513.183280 35/26, 39/29
134 517.041801 31/23
135 520.900322 27/20
136 524.758842 23/17
137 528.617363 19/14
138 532.475884 34/25, 49/36, 87/64
139 536.334405 15/11
140 540.192926 41/30
141 544.051447 26/19, 37/27
142 547.909968 48/35
143 551.768489 11/8
144 555.627010 29/21, 40/29, 51/37
145 559.485531 105/76
146 563.344051 18/13
147 567.202572 25/18, 68/49
148 571.061093 89/64, 32/23
149 574.919614 39/28, 46/33
150 578.778135 88/63
151 582.636656 7/5
152 586.495177 87/62
153 590.353698 45/32, 128/91
154 594.212219 31/22, 148/105
155 598.070740 24/17, 41/29
156 601.929260 17/12, 58/41
157 605.787781 44/31, 105/74
158 609.646302 64/45, 91/64
159 613.504823 124/87
160 617.363344 10/7
161 621.221865 63/44
162 625.080386 33/23, 56/39
163 628.938907 23/16, 128/89
164 632.797428 36/25, 49/34
165 636.655949 13/9
166 640.514469 152/105
167 644.372990 29/20, 42/29, 74/51
168 648.231511 16/11, 93/64
169 652.090032 35/24
170 655.948553 19/13, 54/37
171 659.807074 60/41
172 663.665595 22/15
173 667.524116 25/17, 72/49, 128/87
174 671.382637 28/19
175 675.241158 34/23
176 679.099678 40/27
177 682.958199 46/31
178 686.816720 52/35, 58/39
179 690.675241 76/51
180 694.533762 112/75
181 698.392283 241/161, 244/163
182 702.250804 3/2
183 706.109325 209/139
184 709.967846 128/85
185 713.826367 68/45, 74/49
186 717.684887 50/33
187 721.543408 97/64
188 725.401929 38/25
189 729.260450 32/21
190 733.118971 84/55
191 736.977492 49/32, 26/17
192 740.836013 23/15
193 744.694534 20/13
194 748.553055 128/83
195 752.411576 17/11
196 756.270096 99/64
197 760.128617 48/31
198 763.987138 14/9
199 767.845659 120/77
200 771.704180 25/16
201 775.562701 36/23
202 779.421222 58/39
203 783.279743 11/7
204 787.138264 52/33
205 790.996785 30/19
206 794.855305 19/12
207 798.713826 46/29
208 802.572347 35/22, 62/39
209 806.430868 51/32, 78/49
210 810.289389 99/62
211 814.147910 8/5
212 818.006431 77/48
213 821.864952 37/23, 82/51, 45/28
214 825.723473 29/18, 66/41
215 829.581994 21/13
216 833.440514 34/21, 55/34, 89/55, 144/89
217 837.299035 60/37
218 841.157556 13/8
219 845.016077 44/27
220 848.874598 31/19
221 852.733119 18/11
222 856.591640 41/25, 64/39, 105/64
223 860.450161 23/14, 120/73
224 864.308682 28/17
225 868.167203 32/20, 38/23
226 872.025723 48/29
227 875.884244 58/35
228 879.742765 123/74, 128/77
229 883.601286 5/3
230 887.459807 182/109
231 891.318328 82/49, 92/55
232 895.176849 52/31, 62/37
233 899.035370 42/25
234 902.893891 32/19, 219/130
235 906.752412 27/16
236 910.610932 22/13
237 914.469453 39/23, 56/33
238 918.327974 17/10
239 922.186495 109/64
240 926.045016 29/17, 70/41, 41/24, 128/75
241 929.903537 65/38, 77/45
242 933.762058 12/7
243 937.620579 55/32
244 941.479100 50/29, 31/18
245 945.337621 19/11
246 949.196141 64/37
247 953.054662 26/15, 111/64
248 956.913183 40/23
249 960.771704 54/31, 68/39
250 964.630225 96/55
251 968.488746 7/4
252 972.347267 128/73
253 976.205788 58/33
254 980.064309 37/21, 44/25
255 983.922830 30/17, 113/64
256 987.781350 23/13
257 991.639871 62/35
258 995.498392 16/9
259 999.356913 98/55, 57/32
260 1003.215434 25/14
261 1007.073955 34/19
262 1010.932476 52/29, 70/39
263 1014.790997 88/49, 115/64
264 1018.649518 9/5
265 1022.508039 56/31
266 1026.366559 38/21
267 1030.225080 29/16
268 1034.083601 20/11
269 1037.942122 51/28, 82/45
270 1041.800643 31/17, 42/23
271 1045.659164 64/35, 117/64
272 1049.517685 11/6
273 1053.376206 68/37
274 1057.234727 46/25
275 1061.093248 24/13
276 1064.951768 37/20, 50/27
277 1068.810289 128/69
278 1072.668810 13/7, 119/64
279 1076.527331 54/29
280 1080.385852 28/15
281 1084.244373 58/31
282 1088.102894 15/8
283 1091.961415 62/33
284 1095.819936 32/17
285 1099.678457 17/9, 66/35
286 1103.536977 70/37, 121/64
287 1107.395498 36/19, 74/39
288 1111.254019 19/10
289 1115.112540 40/21
290 1118.971061 21/11
291 1122.829582 44/23
292 1126.688103 23/13
293 1130.546624 48/25, 25/13, 123/64
294 1134.405145 52/27
295 1138.263666 27/14, 56/29
296 1142.122186 29/15, 60/31
297 1145.980707 31/16, 64/33
298 1149.839228 33/17, 68/35, 35/18
299 1153.697749 72/37, 37/19, 76/39
300 1157.556270 39/20, 80/41, 41/21, 125/64
301 1161.414791 88/45, 45/23
302 1165.273312 96/49, 49/25, 100/51, 51/26
303 1169.131833 108/55, 55/28, 112/57, 57/29
304 1172.990354 124/63, 63/32, 128/65, 65/33
305 1176.848875 148/75
306 1180.707395 89/45
307 1184.565916 335/169
308 1188.424437 149/75
309 1192.282958 223/112, 448/225
310 1196.141479 896/449

Mapping of the 41-prime-limited add-73 77-odd-limit

Ratio (ascending) Just value 311edo mapping Error (cents) MITTOOT? (Error < 1\1244 = 0.964630¢?)
Steps Cents
78/77 22.338814 6 23.151125 0.812312 TRUE
77/76 22.630833 6 23.151125 0.520293 TRUE
76/75 22.930588 6 23.151125 0.220538 TRUE
75/74 23.238390 6 23.151125 -0.087264 TRUE
74/73 23.554568 6 23.151125 -0.403443 TRUE
73/72 23.879469 6 23.151125 -0.728344 TRUE
70/69 24.910272 6 23.151125 -1.759147 FALSE
69/68 25.273939 7 27.009646 1.735708 FALSE
66/65 26.431568 7 27.009646 0.578079 TRUE
65/64 26.841376 7 27.009646 0.168271 TRUE
64/63 27.264092 7 27.009646 -0.254445 TRUE
63/62 27.700336 7 27.009646 -0.690689 TRUE
58/57 30.109177 8 30.868167 0.758990 TRUE
57/56 30.642111 8 30.868167 0.226057 TRUE
56/55 31.194250 8 30.868167 -0.326083 TRUE
55/54 31.766654 8 30.868167 -0.898486 TRUE
52/51 33.617251 9 34.726688 1.109437 FALSE
51/50 34.282983 9 34.726688 0.443705 TRUE
50/49 34.975615 9 34.726688 -0.248927 TRUE
49/48 35.696812 9 34.726688 -0.970124 FALSE
46/45 38.050632 10 38.585209 0.534577 TRUE
45/44 38.905773 10 38.585209 -0.320564 TRUE
42/41 41.718502 11 42.443730 0.725228 TRUE
41/40 42.748692 11 42.443730 -0.304962 TRUE
40/39 43.831051 11 42.443730 -1.387321 FALSE
39/38 44.969647 12 46.302251 1.332604 FALSE
77/75 45.561420 12 46.302251 0.740831 TRUE
38/37 46.168977 12 46.302251 0.133273 TRUE
75/73 46.792958 12 46.302251 -0.490707 TRUE
37/36 47.434037 12 46.302251 -1.131786 FALSE
36/35 48.770381 13 50.160772 1.390390 FALSE
35/34 50.184211 13 50.160772 -0.023439 TRUE
34/33 51.682466 13 50.160772 -1.521695 FALSE
33/32 53.272943 14 54.019293 0.746349 TRUE
65/63 54.105467 14 54.019293 -0.086175 TRUE
32/31 54.964428 14 54.019293 -0.945135 TRUE
31/30 56.766858 15 57.877814 1.110956 FALSE
30/29 58.691521 15 57.877814 -0.813707 TRUE
29/28 60.751288 16 61.736334 0.985047 FALSE
57/55 61.836361 16 61.736334 -0.100026 TRUE
28/27 62.960904 16 61.736334 -1.224569 FALSE
27/26 65.337341 17 65.594855 0.257514 TRUE
80/77 66.169865 17 65.594855 -0.575010 TRUE
26/25 67.900234 18 69.453376 1.553142 FALSE
77/74 68.799810 18 69.453376 0.653566 TRUE
51/49 69.258597 18 69.453376 0.194779 TRUE
76/73 69.723545 18 69.453376 -0.270169 TRUE
25/24 70.672427 18 69.453376 -1.219051 FALSE
73/70 72.649850 19 73.311897 0.662047 TRUE
24/23 73.680654 19 73.311897 -0.368756 TRUE
23/22 76.956405 20 77.170418 0.214013 TRUE
68/65 78.114034 20 77.170418 -0.943616 TRUE
22/21 80.537035 21 81.028939 0.491904 TRUE
65/62 81.805803 21 81.028939 -0.776864 TRUE
21/20 84.467193 22 84.887460 0.420266 TRUE
41/39 86.579743 22 84.887460 -1.692283 FALSE
20/19 88.800698 23 88.745981 -0.054717 TRUE
39/37 91.138624 24 92.604502 1.465878 FALSE
58/55 91.945538 24 92.604502 0.658964 TRUE
77/73 92.354378 24 92.604502 0.250123 TRUE
19/18 93.603014 24 92.604502 -0.998513 FALSE
37/35 96.204418 25 96.463023 0.258604 TRUE
55/52 97.103994 25 96.463023 -0.640972 TRUE
73/69 97.560123 25 96.463023 -1.097100 FALSE
18/17 98.954592 26 100.321543 1.366951 FALSE
35/33 101.866677 26 100.321543 -1.545134 FALSE
52/49 102.875849 27 104.180064 1.304215 FALSE
69/65 103.387972 27 104.180064 0.792092 TRUE
17/16 104.955410 27 104.180064 -0.775345 TRUE
33/31 108.237371 28 108.038585 -0.198786 TRUE
82/77 108.918557 28 108.038585 -0.879971 TRUE
49/46 109.377466 28 108.038585 -1.338880 FALSE
16/15 111.731285 29 111.897106 0.165821 TRUE
78/73 114.693192 30 115.755627 1.062435 FALSE
31/29 115.458378 30 115.755627 0.297249 TRUE
77/72 116.233847 30 115.755627 -0.478220 TRUE
15/14 119.442808 31 119.614148 0.171340 TRUE
74/69 121.114691 31 119.614148 -1.500543 FALSE
44/41 122.255537 32 123.472669 1.217132 FALSE
73/68 122.834061 32 123.472669 0.638608 TRUE
29/27 123.712192 32 123.472669 -0.239523 TRUE
14/13 128.298245 33 127.331190 -0.967055 FALSE
69/64 130.229348 34 131.189711 0.960362 TRUE
55/51 130.721246 34 131.189711 0.468465 TRUE
41/38 131.549389 34 131.189711 -0.359679 TRUE
68/63 132.219501 34 131.189711 -1.029791 FALSE
27/25 133.237575 35 135.048232 1.810657 FALSE
40/37 134.969675 35 135.048232 0.078556 TRUE
13/12 138.572661 36 138.906752 0.334092 TRUE
38/35 142.373396 37 142.765273 0.391878 TRUE
63/58 143.158714 37 142.765273 -0.393441 TRUE
25/23 144.353080 37 142.765273 -1.587807 FALSE
62/57 145.567555 38 146.623794 1.056239 FALSE
37/34 146.388629 38 146.623794 0.235165 TRUE
49/45 147.428097 38 146.623794 -0.804303 TRUE
12/11 150.637059 39 150.482315 -0.154743 TRUE
82/75 154.479977 40 154.340836 -0.139141 TRUE
35/32 155.139620 40 154.340836 -0.798784 TRUE
23/21 157.493440 41 158.199357 0.705917 TRUE
80/73 158.524243 41 158.199357 -0.324886 TRUE
57/52 158.940355 41 158.199357 -0.740998 TRUE
34/31 159.919837 41 158.199357 -1.720480 FALSE
45/41 161.161310 42 162.057878 0.896568 TRUE
56/51 161.915496 42 162.057878 0.142382 TRUE
11/10 165.004228 43 165.916399 0.912170 TRUE
76/69 167.283668 43 165.916399 -1.367269 FALSE
54/49 168.213190 44 169.774920 1.561730 FALSE
75/68 169.627019 44 169.774920 0.147901 TRUE
32/29 170.422806 44 169.774920 -0.647886 TRUE
21/19 173.267891 45 173.633441 0.365549 TRUE
73/66 174.516527 45 173.633441 -0.883087 TRUE
31/28 176.209666 46 177.491961 1.282295 FALSE
72/65 177.068626 46 177.491961 0.423335 TRUE
41/37 177.718367 46 177.491961 -0.226405 TRUE
51/46 178.636063 46 177.491961 -1.144102 FALSE
10/9 182.403712 47 181.350482 -1.053230 FALSE
69/62 185.193776 48 185.209003 0.015228 TRUE
49/44 186.333871 48 185.209003 -1.124867 FALSE
39/35 187.343042 49 189.067524 1.724482 FALSE
29/26 189.049532 49 189.067524 0.017992 TRUE
77/69 189.914501 49 189.067524 -0.846977 TRUE
19/17 192.557607 50 192.926045 0.368438 TRUE
28/25 196.198479 51 196.784566 0.586087 TRUE
65/58 197.264181 51 196.784566 -0.479616 TRUE
37/33 198.071096 51 196.784566 -1.286530 FALSE
46/41 199.211942 52 200.643087 1.431145 FALSE
55/49 199.979843 52 200.643087 0.663244 TRUE
64/57 200.531983 52 200.643087 0.111104 TRUE
73/65 200.948095 52 200.643087 -0.305008 TRUE
82/73 201.272935 52 200.643087 -0.629848 TRUE
9/8 203.910002 53 204.501608 0.591606 TRUE
62/55 207.403916 54 208.360129 0.956212 TRUE
44/39 208.835280 54 208.360129 -0.475151 TRUE
35/31 210.104048 54 208.360129 -1.743919 FALSE
26/23 212.253315 55 212.218650 -0.034665 TRUE
77/68 215.188439 56 216.077170 0.888731 TRUE
17/15 216.686695 56 216.077170 -0.609524 TRUE
42/37 219.436869 57 219.935691 0.498823 TRUE
25/22 221.309485 57 219.935691 -1.373794 FALSE
58/51 222.666784 58 223.794212 1.127428 FALSE
33/29 223.695749 58 223.794212 0.098463 TRUE
74/65 224.502663 58 223.794212 -0.708451 TRUE
41/36 225.152404 58 223.794212 -1.358192 FALSE
57/50 226.840589 59 227.652733 0.812144 TRUE
65/57 227.373359 59 227.652733 0.279374 TRUE
73/64 227.789471 59 227.652733 -0.136738 TRUE
8/7 231.174094 60 231.511254 0.337160 TRUE
63/55 235.104252 61 235.369775 0.265523 TRUE
55/48 235.676655 61 235.369775 -0.306880 TRUE
39/34 237.527253 62 239.228296 1.701043 FALSE
31/27 239.170570 62 239.228296 0.057726 TRUE
23/20 241.960633 63 243.086817 1.126183 FALSE
84/73 242.991437 63 243.086817 0.095380 TRUE
38/33 244.240073 63 243.086817 -1.153256 FALSE
15/13 247.741053 64 246.945338 -0.795715 TRUE
52/45 250.303946 65 250.803859 0.499912 TRUE
37/32 251.344039 65 250.803859 -0.540180 TRUE
22/19 253.804926 66 254.662379 0.857453 TRUE
73/63 255.053562 66 254.662379 -0.391183 TRUE
51/44 255.592468 66 254.662379 -0.930089 TRUE
80/69 256.084366 66 254.662379 -1.421986 FALSE
29/25 256.949766 67 258.520900 1.571134 FALSE
65/56 258.015469 67 258.520900 0.505431 TRUE
36/31 258.874429 67 258.520900 -0.353529 TRUE
57/49 261.816204 68 262.379421 0.563217 TRUE
64/55 262.368344 68 262.379421 0.011077 TRUE
7/6 266.870906 69 266.237942 -0.632963 TRUE
90/77 270.079867 70 270.096463 0.016596 TRUE
76/65 270.671640 70 270.096463 -0.575177 TRUE
48/41 272.892595 71 273.954984 1.062389 FALSE
41/35 273.922785 71 273.954984 0.032199 TRUE
75/64 274.582429 71 273.954984 -0.627445 TRUE
34/29 275.378215 71 273.954984 -1.423231 FALSE
88/75 276.735514 72 277.813505 1.077991 FALSE
27/23 277.590655 72 277.813505 0.222849 TRUE
74/63 278.608131 72 277.813505 -0.794626 TRUE
20/17 281.358304 73 281.672026 0.313721 TRUE
73/62 282.753898 73 281.672026 -1.081872 FALSE
33/28 284.447037 74 285.530547 1.083510 FALSE
46/39 285.791685 74 285.530547 -0.261138 TRUE
13/11 289.209719 75 289.389068 0.179348 TRUE
58/49 291.925381 76 293.247588 1.322207 FALSE
45/38 292.710699 76 293.247588 0.536889 TRUE
77/65 293.302473 76 293.247588 -0.054885 TRUE
32/27 294.134997 76 293.247588 -0.887409 TRUE
19/16 297.513016 77 297.106109 -0.406907 TRUE
82/69 298.833057 77 297.106109 -1.726948 FALSE
44/37 299.973904 78 300.964630 0.990727 FALSE
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