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- 0.120757092 | |||
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| | -P1<sup>13</sup><sub>37</sub> | ||
| | - 0.913628207 | ||
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-P1<sup>29,53</sup> | |||
- 1.126738764 | |||
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- 1.187810715 | |||
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-d2<sup>19</sup><sub>5</sub> | |||
- 1.424297941 | |||
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-m2<sub>11,31</sub> | |||
- 1.691484306 | |||
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-d2<sub>53,61</sub> | |||
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-m2<sup>59</sup><sub>31</sub> | |||
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- 5.878567719 | |||
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-m2<sup>47</sup><sub>37</sub> | |||
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-P1<sup>43</sup><sub>61</sub> | |||
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-m2<sub>13,31</sub> | |||
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-m2<sub>31,37</sub> | |||
- 7.530390512 | |||
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--cA7<sup>31,59</sup> | |||
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-d2<sup>13</sup><sub>23</sub> | |||
- 8.343312770 | |||
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-61 | |||
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--cA7<sup>5,61</sup> | |||
- 9.063521536 | |||
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-P1<sup>7</sup><sub>47</sub> | |||
- 9.184287052 | |||
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-37 | |||
-262144/260739 | |||
-m2<sub>29,37</sub> | |||
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-P1<sup>23</sup><sub>61</sub> | |||
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-m2<sup>7</sup><sub>11</sub> | |||
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-A1<sup>59</sup><sub>11</sub> | |||
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-P1<sup>43</sup><sub>19</sub> | |||
- 10.094687779 | |||
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--cA7<sup>31</sup><sub>13</sub> | |||
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-53 | |||
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-m2<sup>53</sup><sub>37</sub> | |||
- 10.430501529 | |||
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-37 | |||
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--cM7<sup>11,37</sup> | |||
- 10.481984581 | |||
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-P1<sup>19,61</sup> | |||
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- 10.854167524 | |||
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--cA7<sup>41</sup><sub>29</sub> | |||
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-A1<sub>11,13</sub> | |||
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-d2<sup>19</sup><sub>53</sub> | |||
- 12.278465464 | |||
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--cA7<sup>41,53</sup> | |||
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-A1<sup>59,59</sup> | |||
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-d2<sup>17</sup><sub>5</sub> | |||
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-P1<sup>37</sup><sub>29</sub> | |||
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- 14.018166057 | |||
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-P1<sup>47</sup><sub>59</sub> | |||
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-P1<sup>5</sup><sub>47</sub> | |||
- 14.942089256 | |||
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-31 | |||
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-dd3<sub>23,31</sub> | |||
- 14.960075075 | |||
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- 15.073579904 | |||
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- 15.205976772 | |||
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-m2<sup>7</sup><sub>37</sub> | |||
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- 15.647623941 | |||
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--cA7<sup>61</sup><sub>17</sub> | |||
- 15.839397306 | |||
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- 17.097104625 | |||
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-P8<sup>37</sup><sub>13</sub> | |||
-1199.086371793 | |||
|- | |||
-59 | |||
-28672/14337 | |||
-cd2<sup>7</sup><sub>59</sub> | |||
-1199.879242908 | |||
|} | |} | ||
Revision as of 19:12, 11 May 2020
In 61-limit Just Intonation, all ratios in the system will contain no primes higher than 61.
Intervals
-0 -1/1 -P1 - 0.000000000 -59 -14337/14336 --cA7597 - 0.120757092 -37 -9477/9472 -P11337 - 0.913628207 -53 -1537/1536 -P129,53 - 1.126738764 -47 -1458/1457 -P131,47 - 1.187810715 -43 -1377/1376 -P11743 - 1.257707319 -19 -1216/1215 -d2195 - 1.424297941 -31 -1024/1023 -m211,31 - 1.691484306 -61 -262144/261873 -d253,61 - 1.790645987 -59 -768/767 -P113,59 - 2.255679862 -13 -729/728 --cA77,13 - 2.376436954 -59 -649/648 -P111,59 - 2.669598137 -61 -14848/14823 -d22961 - 2.917384751 -47 -4096/4089 -P129,47 - 2.961182968 -19 -513/512 -P119 - 3.378018728 -47 -262683/262144 --cA723,47 - 3.555973609 -41 -3328/3321 -d21341 - 3.645252766 -53 -424/423 -P15347 - 4.087921732 -59 -7552/7533 -m25931 - 4.361082443 -37 -4107/4096 --cM737,37 - 4.643078375 -41 -369/368 -P14123 - 4.698060004 -43 -731/729 -d217,43 - 4.743109951 -13 -352/351 -P11113 - 4.925277999 -53 -1701/1696 -P1753 - 5.096365320 -19 -324/323 --cA717,19 - 5.351577829 -31 -22599/22528 --cA73111 - 5.447635292 -7 -5120/5103 -P157 - 5.757802203 -37 -297/296 -P11137 - 5.838906206 -61 -2097152/2090043 -d247,61 - 5.878567719 -59 -65536/65313 -d241,59 - 5.900932628 -17 -289/288 -d217,17 - 6.000817270 -41 -288/287 -P17,41 - 6.021689720 -29 -16443/16384 -P17,29 - 6.223104084 -47 -3008/2997 -m24737 - 6.342579797 -61 -31347/31232 -P14361 - 6.362905759 -29 -1863/1856 --cA72329 - 6.517156577 -31 -32768/32643 -m213,31 - 6.616762305 -19 -263169/262144 -P119,19 - 6.756037457 -17 -256/255 -P15,17 - 6.775875769 -61 -244/243 -P161 - 7.109800749 -11 -243/242 -A111,11 - 7.139119597 -37 -1152/1147 -m231,37 - 7.530390512 -53 -32913/32768 --cA723,53 - 7.643895340 -43 -10496/10449 -P14143 - 7.769695572 -31 -217/216 -P17,31 - 7.996476337 -43 -216/215 -P15,43 - 8.033583089 -59 -16461/16384 --cA731,59 - 8.117233429 -23 -208/207 -d21323 - 8.343312770 -61 -8235/8192 --cA75,61 - 9.063521536 -47 -189/188 -P1747 - 9.184287052 -37 -262144/260739 -m229,37 - 9.303762765 -61 -184/183 -P12361 - 9.434541328 -11 -896/891 -m2711 - 9.687960643 -59 -177/176 -A15911 - 9.808717735 -43 -172/171 -P14319 - 10.094687779 -31 -837/832 --cA73113 - 10.372913291 -53 -27136/26973 -m25337 - 10.430501529 -37 -32967/32768 --cM711,37 - 10.481984581 -61 -1159/1152 -P119,61 - 10.487819477 -59 -4096/4071 -d223,59 - 10.598992632 -23 -162/161 -P17,23 - 10.719749724 -53 -160/159 -P1553 - 10.854167524 -47 -1739/1728 -P137,47 - 10.985658172 -41 -29889/29696 --cA74129 - 11.215216581 -19 -153/152 -P11719 - 11.352395099 -47 -16497/16384 -P113,47 - 11.899286379 -29 -145/144 -P15,29 - 11.980906287 -13 -144/143 -A111,13 - 12.064397597 -37 -999/992 -P13731 - 12.173468887 -41 -21141/20992 -P12941 - 12.244793804 -53 -38912/38637 -d21953 - 12.278465464 -53 -528039/524288 --cA741,53 - 12.341955344 -59 -3481/3456 -A159,59 - 12.478315872 -17 -136/135 -d2175 - 12.776693039 -23 -5632/5589 -d21123 - 13.268590769 -43 -129/128 -P143 - 13.472706508 -43 -8192/8127 -P17,43 - 13.791385292 -37 -2368/2349 -P13729 - 13.946841140 -41 -124/123 -P13141 - 14.018166057 -61 -123/122 -P14161 - 14.132601332 -59 -3807/3776 -P14759 - 14.154966241 -17 -4131/4096 -P117 - 14.730413827 -59 -118/117 -A15913 - 14.733995734 -29 -117/116 -P11329 - 14.860469347 -47 -1280/1269 -P1547 - 14.942089256 -31 -524288/519777 -dd323,31 - 14.960075075 -53 -1961/1944 -P137,53 - 15.073579904 -47 -1944/1927 -P141,47 - 15.205976772 -37 -112/111 -m2737 - 15.526866849 -59 -4779/4736 -A15937 - 15.647623941 -41 -4096/4059 -m211,41 - 15.709650363 -61 -549/544 --cA76117 - 15.839397306 -53 -2067/2048 -P113,53 - 15.987208111 -23 -736/729 -P123 - 16.544342076 -19 -729/722 --cA719,19 - 16.703972928 -47 -517/512 -P111,47 - 16.824564378 -43 -66177/65536 -P119,43 - 16.850725236 -13 -512/507 -A113,13 - 16.989675596 -61 -44469/44032 --cA76143 - 17.097104625 -59 -1728/1711 -P129,59 - 17.116149209 -53 -8192/8109 -P117,53 - 17.630043293 -61 -1664/1647 -d21361 - 17.777854098 -37 -486/481 -A113,37 - 17.903303803 -31 -8019/7936 -P11131 - 18.012375093 -19 -96/95 -P15,19 - 18.128270868 -59 -477/472 -P15359 - 18.242887972 -59 -30208/29889 -m25941 - 18.379248500 -23 -1035/1024 --cA75,23 - 18.498062864 -47 -94/93 -m24731 - 18.516048684 -31 -93/92 -P13123 - 18.716226061 -29 -464/459 -P12917 - 18.756782057 -53 -2304/2279 -P143,53 - 18.887750612 -5 -2048/2025 -d25,5 - 19.552568809 -31 -972/961 -m231,31 - 19.703859398 -29 -88/87 -P11129 - 19.785747346 -23 -437/432 -P119,23 - 19.922360805 -43 -87/86 -P12943 - 20.014489376 -61 -32768/32391 -d259,61 - 20.033533960 -61 -432/427 -P17,61 - 20.154291052 -37 -259/256 -P17,37 - 20.169945224 -59 -530469/524288 --cA737,59 - 20.290702316 -23 -256/253 -m211,23 - 20.407710367 -61 -2623/2592 -P143,61 - 20.582507256 -41 -131072/129519 -m213,41 - 20.634928362 -53 -583/576 -P111,53 - 20.912486110 -13 -66339/65536 -P17,13 - 21.083573431 -41 -82/81 -P141 - 21.242402080 -31 -8192/8091 -m229,31 - 21.477231652 -5 -81/80 -P15 - 21.506289597 -41 -1536/1517 -m237,41 - 21.548556569 -47 -65536/64719 -P117,47 - 21.717965025 -43 -31744/31347 -P13143 - 21.787861629 -61 -1037/1024 -P117,61 - 21.840214576 -47 -1062153/1048576 --cA731,47 - 22.272199670 -37 -26973/26624 --cA73713 - 22.546382178 -53 -848/837 -m25331 - 22.603970415 -61 -45056/44469 -d21161 - 22.703132097 -47 -2048/2021 -P143,47 - 22.975672344 -59 -1888/1863 -m25923 - 23.077308504 -41 -16605/16384 --cA75,41 - 23.196122868 -53 -4352/4293 -d21753 - 23.630860563 -19 -32768/32319 -P17,19 - 23.886073072 -47 -11421/11264 -A14711 - 23.963683975 -41 -779/768 -P119,41 - 24.620420809 -29 -493/486 -d217,29 - 24.757599327 -31 -7533/7424 --cA73129 - 25.233382638 -23 -69/68 --cA72317 - 25.273938633 -23 -8192/8073 -m213,23 - 25.332988366 -37 -740/729 -P15,37 - 25.927747427 -11 -2079/2048 -P17,11 - 26.008851430 -41 -333/328 -P13741 - 26.191634944 -37 -864/851 -m223,37 - 26.246616573 -53 -133083/131072 --cA731,53 - 26.360121402 -47 -329/324 -m27,47 - 26.512525021 -43 -5589/5504 --cA72343 - 26.531645953 -59 -8319/8192 -A147,59 - 26.633282113 -13 -65/64 -P15,13 - 26.841375634 -29 -324/319 -A111,29 - 26.924866944 -43 -16641/16384 -P143,43 - 26.945413016 -61 -4941/4864 --cA76119 - 27.191792405 -7 -64/63 -P17 - 27.264091800 -31 -63/62 -m2731 - 27.700335736 -47 -34816/34263 -d21747 - 27.718782295 -53 -1431/1408 -A15311 - 28.051605707 -61 -62/61 -P13161 - 28.150767389 -43 -532899/524288 -P117,43 - 28.203120335 -19 -247/243 -d213,19 - 28.265673575 -61 -61/60 -P1615 - 28.616090345 -47 -423/416 -A14713 - 28.888961975 -53 -1024/1007 -P119,53 - 28.982438392 -59 -60/59 -P1559 - 29.097055496 -7 -3645/3584 --cA757 - 29.217812588 -43 -131072/128871 -m237,43 - 29.318252141 -61 -2916/2867 -P147,61 - 29.338578104 -29 -7168/7047 -m2729 - 29.473707989 -59 -59/58 -A15929 - 29.594465081 -61 -2048/2013 -m211,61 - 29.842251694 -41 -1107/1088 --cA74117 - 29.971998637 -43 -989/972 -P123,43 - 30.017048584 -29 -58/57 -P12919 - 30.109177155 -53 -65536/64395 -d25,53 - 30.406736332 -59 -4864/4779 -d21959 - 30.521353437 -53 -742/729 -m27,53 - 30.600446753 -19 -57/56 -P1197 - 30.642110529 -59 -3127/3072 -A153,59 - 30.721203845 -37 -2997/2944 -P13723 - 30.889694948 -23 -391/384 -P117,23 - 31.274755903 -29 -3712/3645 -d2295 - 31.533475096 -11 -55/54 -P15,11 - 31.766653633 -29 -384/377 -A113,29 - 31.850144943 -41 -2673/2624 -P11141 - 32.030541150 -53 -54/53 -P153 - 32.360457120 -61 -15104/14823 -m25961 - 32.511849832 -47 -376/369 -m24741 - 32.534214741 -53 -53/52 -A15313 - 32.976883707 -47 -8192/8037 -P119,47 - 33.070360124 -31 -2560/2511 -m2531 - 33.458137939 -29 -261/256 -P129 - 33.487195884 -17 -52/51 -P11317 - 33.617251404 -23 -131072/128547 -dd323,23 - 33.676301136 -41 -1296/1271 -m231,41 - 33.722025456 -53 -38637/37888 -A15337 - 33.890511913 -43 -1184/1161 -P13743 - 33.961330516 -43 -1763/1728 -P141,43 - 34.715108588 -61 -65536/64233 -m213,61 - 34.767529694 -43 -351/344 -P11343 - 34.874958723 -43 -10449/10240 -P1435 - 34.978996105 -31 -248/243 -P131 - 35.260568137 -41 -32768/32103 -m229,41 - 35.495397709 -61 -2304/2257 -m237,61 - 35.681157901 -7 -49/48 -m27,7 - 35.696812073 -53 -13851/13568 -P11953 - 35.738475849 -59 -33453/32768 -A17,59 - 35.817569165 -59 -1024/1003 -P117,59 - 35.872931265 -41 -2091/2048 -P117,41 - 35.972815907 -17 -243/238 --cA77,17 - 35.993688357 -47 -48/47 -P147 - 36.448378852 -53 -3392/3321 -m25341 - 36.622136473 -23 -621/608 --cA72319 - 36.626333732 -29 -133893/131072 -P119,29 - 36.865214612 -11 -8192/8019 -m211 - 36.952052443 -59 -2592/2537 -P143,59 - 37.130638585 -31 -4185/4096 --cA75,31 - 37.214288925 -47 -47/46 -m24723 - 37.232274745 -61 -33489/32768 --cA761,61 - 37.679611882 -23 -46/45 -P1235 - 38.050631673 -13 -1701/1664 -A1713 - 38.073249027 -31 -729/713 -m223,31 - 38.420085460 -17 -1408/1377 -P11117 - 38.542529403 -31 -589/576 -P119,31 - 38.638586866 -11 -45/44 -A1511 - 38.905773231 -37 -524288/512487 -m219,37 - 39.412939921 -61 -488/477 -P16153 - 39.470257869 -17 -221/216 -d213,17 - 39.618068674 -43 -44/43 -P11143 - 39.800236722 -47 -1539/1504 -P11947 - 39.826397581 -23 -16767/16384 --cA723 - 40.004352461 -29 -2048/2001 -m223,29 - 40.193457713 -31 -131072/128061 -m217,31 - 40.234013708 -61 -999/976 -P13761 - 40.324236275 -19 -304/297 -m21911 - 40.330071171 -61 -1769/1728 -P129,61 - 40.596996632 -59 -44032/43011 -d24359 - 40.616041216 -43 -43/42 -P1437 - 40.736798308 -47 -536787/524288 -A147,47 - 40.788248353 -53 -2097152/2047761 -d253,53 - 41.260903856 -53 -212/207 -m25323 - 41.320196477 -41 -9963/9728 --cA74119 - 41.324393736 -43 -4096/3999 -m231,43 - 41.491721028 -59 -295/288 -A15,59 - 41.575371368 -41 -42/41 -m2741 - 41.718501793 -59 -43011/41984 -A15941 - 41.839258885 -59 -544/531 -d21759 - 41.873748535 -17 -459/448 -P1177 - 41.994505627 -41 -41/40 -P1415 - 42.748691677 -37 -1024/999 -m237 - 42.790958649 -61 -1048576/1022787 -dd323,61 - 43.110842464 -61 -3904/3807 -P16147 - 43.558179601 -47 -3807/3712 -A14729 - 43.749431322 -13 -40/39 -A1513 - 43.831051230 -31 -279/272 --cA73117 - 43.990164695 -37 -4736/4617 -P13719 - 44.056018296 -17 -748/729 -d211,17 - 44.543346673 -37 -1215/1184 -A1537 - 44.744679437 -53 -67257/65536 -A147,53 - 44.876170085 -19 -39/38 -P11319 - 44.969646502 -43 -22599/22016 --cA73143 - 45.247872014 -19 -9728/9477 -m21913 - 45.255349171 -17 -192/187 -A111,17 - 45.681649000 -53 -3483/3392 -P14353 - 45.833163628 -61 -8019/7808 -P11161 - 46.163142482 -37 -38/37 -m21937 - 46.168977378 -13 -416/405 -d2135 - 46.393944443 -23 -189/184 -m2723 - 46.416561797 -61 -188/183 -m24761 - 46.666816072 -29 -864/841 -A129,29 - 46.710614290 -43 -486/473 -A111,43 - 46.939356320 -43 -33669/32768 -P129,43 - 46.959902392 -61 -4209/4096 --cA723,61 - 47.114153209 -59 -1152/1121 -P119,59 - 47.225326364 -37 -37/36 -P137 - 47.434037024 -41 -10240/9963 -m2541 - 47.476303996 -41 -1728/1681 -m241,41 - 47.740191513 -53 -477/464 -A15329 - 47.837353054 -61 -1944/1891 -m231,61 - 47.854626787 -13 -1053/1024 -P113 - 48.347665231 -59 -472/459 -A15917 - 48.351247138 -41 -5248/5103 -P1417 - 48.506493880 -59 -8192/7965 -d25,59 - 48.649624305 -43 -1333/1296 -P131,43 - 48.733274645 -7 -36/35 -P15,7 - 48.770381397 -53 -1472/1431 -P12353 - 48.904799196 -53 -8427/8192 -A153,53 - 48.964091817 -37 -134865/131072 --cA75,37 - 49.387757812 -43 -3584/3483 -m2743 - 49.488197365 -59 -177/172 -A15943 - 49.608954457 -61 -16384/15921 -m229,61 - 49.627999041 -19 -176/171 -P11119 - 49.894924502 -47 -387/376 -P14347 - 49.921085360 -31 -527/512 -P117,31 - 49.990981965 -29 -667/648 -P123,29 - 50.031537960 -43 -2752/2673 -m24311 - 50.424758951 -59 -243/236 -P159 - 50.603345093 -17 -2048/1989 -A113,17 - 50.606927000 -61 -1696/1647 -m25361 - 50.754737804 -37 -2109/2048 -P119,37 - 50.812055752 -47 -12393/12032 -P11747 - 51.178792680 -37 -648/629 -A117,37 - 51.520555206 -31 -16384/15903 -m219,31 - 51.586408807 -17 -34/33 -m21711 - 51.682466270 -61 -67527/65536 --cA741,61 - 51.812213213 -43 -576/559 -A113,43 - 51.864634319 -23 -640/621 -m2523 - 52.174364000 -41 -972/943 -m223,41 - 52.438251517 -47 -11776/11421 -P12347 - 52.992720928 -11 -33/32 -P111 - 53.272943230 -53 -164/159 -P14153 - 53.602859200 -47 -752/729 -m247 - 53.776616821 -53 -270459/262144 -A17,53 - 54.060457137 -41 -524288/508113 -m217,41 - 54.252179766 -59 -1003/972 -m217,59 - 54.352064408 -7 -4096/3969 -P17,7 - 54.528183600 -41 -1189/1152 -P129,41 - 54.729597964 -31 -32/31 -m231 - 54.964427536 -29 -21141/20480 -P1295 - 54.993485481 -31 -2511/2432 --cA73119 - 55.342559793 -61 -793/768 -P113,61 - 55.457465979 -43 -16384/15867 -m241,43 - 55.509887085 -47 -2115/2048 -A15,47 - 55.730337609 -61 -63/61 -m2761 - 55.851103124 -37 -8991/8704 --cA73717 - 56.163633581 -43 -344/333 -m24337 - 56.263665157 -23 -529/512 --cA723,23 - 56.548694537 -17 -1088/1053 -m21713 - 56.607744270 -19 -16929/16384 -P111,19 - 56.650961959 -31 -31/30 -P1315 - 56.766857734 -19 -216/209 -A111,19 - 57.034044099 -47 -893/864 -m219,47 - 57.154635549 -53 -13312/12879 -d21353 - 57.248111967 -37 -153/148 -m21737 - 57.521372476 -47 -1312/1269 -P14147 - 57.690780932 -61 -61/59 -P16159 - 57.713145841 -61 -14823/14336 --cA7617 - 57.833902933 -47 -243/235 -P15,47 - 57.954668449 -31 -513/496 -m21931 - 58.342446264 -29 -754/729 -d213,29 - 58.374850730 -11 -512/495 -m25,11 - 58.458342040 -29 -30/29 -A1529 - 58.691520577 -23 -32768/31671 -m217,23 - 58.950239770 -59 -262144/253287 -d253,59 - 59.503791828 -19 -14336/13851 -m2719 - 59.582885144 -53 -384/371 -P17,53 - 59.624548920 -59 -59/57 -A15919 - 59.703642237 -53 -265/256 -A15,53 - 59.818259341 -29 -2432/2349 -m21929 - 60.115818518 -43 -1024/989 -m223,43 - 60.207947089 -61 -671/648 -P111,61 - 60.382743979 -11 -729/704 -A111 - 60.412062828 -59 -14848/14337 -d22959 - 60.630530592 -29 -29/28 -P1297 - 60.751287684 -43 -1591/1536 -P137,43 - 60.906743532 -59 -3776/3645 -m2595 - 61.127940177 -53 -1007/972 -m219,53 - 61.242557281 -41 -8487/8192 --cA723,41 - 61.246754541 -61 -5120/4941 -m2561 - 61.608905328 -43 -135837/131072 -P113,43 - 61.820371739 -61 -2592/2501 -m241,61 - 61.872792844 -19 -256/247 -A113,19 - 61.959322098 -61 -7808/7533 -m26131 - 62.074228284 -37 -16983/16384 -P117,37 - 62.164450851 -47 -141/136 -A14717 - 62.506213378 -37 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-47 -1457/729 -P831,47 -1198.812189285 -53 -3072/1537 -P829,53 -1198.873261236 -37 -18944/9477 -P83713 -1199.086371793 -59 -28672/14337 -cd2759 -1199.879242908| Limit | Ratio | FJS name | Cents Value |
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