User:Contribution/(31-Limit Factor Gradient) x (26 Tritaves Chain) x (Infinite Octaves or No-Twos) Comparison Table

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Purpose

See here.

Content

This table shows these sets:

  • ((5;7;0;3)-limit ∪ (5;13;0;2)-limit ∪ (5;31;0;1)-limit) × (3;3;0;26)-limit × (2;2;0;+∞)-limit
  • ((5;7;0;3)-limit ∪ (5;13;0;2)-limit ∪ (5;31;0;1)-limit) × (3;3;0;26)-limit


You'll find these columns:

  • Limit: the smaller maximal prime limit whose intervals belong
  • Factorization: exact factorization into primes of the second set, or factorization into primes ignoring octaves of the first set
  • Ratio: octave-reduced ratios of the first set
  • FJS name: octave-reduced FJS names of the first set
  • Cents value: octave-reduced cents values of the first set
  • Octaves: octave difference between the second set (no-twos just intonation) and the octave-reducing of the first set (infinite octaves just intonation). Intervals outside the human hearing range (10 octaves) are ignored.

Table

Limit Factorization Ratio FJS name Cents value Octaves
1 1/1 P1 0.000000000 0
13 3-20⋅131 3489660928/3486784401 ddd313 1.427644462
7 3-22⋅5-1⋅7-1 1099511627776/1098337086315 ddd35,7 1.850360628
5 38⋅51 32805/32768 -cA75 1.953720788
13 36⋅7-1⋅13-1 729/728 -cA77,13 2.376436954 3
11 3-9⋅71⋅111 19712/19683 d27,11 2.548841045 -8
13 325⋅5-1⋅131 11014751922759/10995116277760 -cAA6135 3.088969539
19 33⋅191 513/512 P119 3.378018728 9
13 3-12⋅51⋅131 532480/531441 d25,13 3.381365249
7 323⋅5-2⋅7-1 94143178827/93952409600 -cAA65,5,7 3.511685705
7 3-14⋅7-1 33554432/33480783 d27 3.804081415
5 316⋅52 1076168025/1073741824 -cAAA65,5 3.907441576
13 3-3⋅111⋅13-1 352/351 P11113 4.925277999 -5
7 3-6⋅51⋅7-1 5120/5103 P157 5.757802203 -10
5 324⋅53 35303692060125/35184372088832 -cAAAAA55,5,5 5.861162364
11 3-23⋅111 94489280512/94143178827 ddd311 6.352922461
13 313⋅132 269440587/268435456 -cM713,13 6.470334789
23 318⋅23-1 387420489/385875968 -cA723 6.915668309
11 35⋅11-2 243/242 A111,11 7.139119597 1
7 32⋅52⋅7-1 225/224 -cA75,57 7.711522991 5
11 322⋅5-1⋅111 345191655699/343597383680 -cAA6115 8.014247538
31 3-24⋅31-1 8796093022208/8755315630911 dddd431 8.044406766
11 3-15⋅51⋅111 14417920/14348907 d25,11 8.306643249
7 31⋅73 1029/1024 m27,7,7 8.432720273
17 37⋅17-1 2187/2176 -cA717 8.729596557 7
13 319⋅7-1⋅131 15109399071/15032385536 -cAA6137 8.846771743
7 317⋅5-1⋅7-2 129140163/128450560 -cAA65,7,7 9.269487909
7 3-20⋅51⋅7-2 171798691840/170852435649 d257,7 9.561883619
11 3-4⋅71⋅11-1 896/891 m2711 9.687960643 -7
29 3-10⋅291 59392/59049 d229 10.027185499
7 3-21⋅5-1⋅72 52613349376/52301766015 dddd47,75 10.283080900
7 325⋅7-2 847288609443/841813590016 -cAAAA57,7 11.223208696
13 310⋅111⋅131 8444007/8388608 -cM711,13 11.395612788
11 3-26⋅5-1⋅11-1 140737488355328/139802620558095 dddd45,11 11.538321270
31 3-17⋅311 130023424/129140163 d231 11.800557753
13 32⋅11-1⋅13-1 144/143 A111,13 12.064397597 -4
7 3-13⋅72 1605632/1594323 dd37,7 12.236801688
29 322⋅29-1 31381059609/31138512896 -cAAA629 13.432824885
11 3-18⋅11-1 4294967296/4261625379 dd311 13.492042058
11 316⋅7-1⋅111 473513931/469762048 -cAA6117 13.772049742
7 3-5⋅51⋅72 245/243 m25,7,7 14.190522476 0
13 3-7⋅71⋅13-1 28672/28431 m2713 14.613238642
17 35⋅171 4131/4096 P117 14.730413827
7 311⋅7-3 177147/175616 -cAA67,7,7 15.027290112 9
11 3-10⋅51⋅11-1 655360/649539 m2511 15.445762846
7 310⋅5-2⋅71 413343/409600 P175,5 15.748487393
11 37⋅112 264627/262144 -cM711,11 16.320890787
23 3-6⋅231 736/729 P123 16.544342076 -5
13 3-1⋅13-2 512/507 A113,13 16.989675596 -9
5 3-12⋅5-3 67108864/66430125 ddd35,5,5 17.598848021
7 318⋅5-1⋅71 2711943423/2684354560 -cA775 17.702208181
7 3-19⋅51⋅71 1174405120/1162261467 dd35,7 17.994603892
13 3-21⋅13-1 137438953472/135984591639 dd313 18.417320058
13 315⋅11-1⋅131 186535791/184549376 -cA71311 18.534732385
5 3-4⋅5-2 2048/2025 d25,5 19.552568809
7 326⋅71 17793060798303/17592186044416 -cAAA67 19.655928969
7 3-11⋅52⋅71 179200/177147 m25,5,7 19.948324680 -10
13 324⋅5-1⋅13-1 282429536481/279172874240 -cAAA65,13 20.078645135
19 39⋅19-1 19683/19456 -cA719 20.081991656
13 3-13⋅51⋅13-1 20971520/20726199 m2513 20.371040845
11 321⋅7-1⋅11-1 10460353203/10334765056 -cAAA67,11 20.911169339
13 36⋅71⋅131 66339/65536 P17,13 21.083573431
5 34⋅5-1 81/80 P15 21.506289597 4
13 3-16⋅5-1⋅131 218103808/215233605 ddd3135 22.933934058
7 3-18⋅5-2⋅7-1 68719476736/67798585575 ddd35,5,7 23.356650224
3 312 531441/524288 -cA7 23.460010385
5 3-25⋅52 858993459200/847288609443 dd35,5 23.752406095
13 3-8⋅131 6656/6561 d213 24.887654846 -9
7 3-10⋅5-1⋅7-1 2097152/2066715 d25,7 25.310371012
5 320⋅51 17433922005/17179869184 -cAAA65 25.413731173
5 3-17⋅53 131072000/129140163 m25,5,5 25.706126883
13 318⋅7-1⋅13-1 387420489/381681664 -cAAA67,13 25.836447339
11 33⋅71⋅111 2079/2048 P17,11 26.008851430
23 3-23⋅23-1 2199023255552/2165293113021 dddd423 26.760632828
19 315⋅191 272629233/268435456 -cA719 26.838029113
13 51⋅131 65/64 P15,13 26.841375634 6
7 3-2⋅7-1 64/63 P17 27.264091800 -6
11 3-19⋅5-1⋅111 5905580032/5811307335 ddd3115 27.859212058
13 39⋅111⋅13-1 216513/212992 -cA71113 28.385288384
13 3-22⋅7-1⋅131 223338299392/219667417263 ddd3137 28.691736262
7 3-24⋅5-1⋅7-2 70368744177664/69195236437845 ddd35,7,7 29.114452428
7 36⋅51⋅7-1 3645/3584 -cA757 29.217812588 9
11 3-11⋅111 180224/177147 d211 29.812932845
13 325⋅132 143191774995867/140737488355328 -cAA613,13 29.930345173
11 317⋅11-2 129140163/126877696 -cAA711,11 30.599129982
7 3-16⋅7-2 2147483648/2109289329 d27,7 31.068173216
7 314⋅52⋅7-1 119574225/117440512 -cAAA65,57 31.171533376
31 3-12⋅31-1 16777216/16474671 dd331 31.504417151
11 3-3⋅51⋅111 55/54 P15,11 31.766653633 1
7 313⋅73 546852789/536870912 A17,7,7 31.892730657
17 319⋅17-1 1162261467/1140850688 -cAAA617 32.189606942
7 3-8⋅51⋅7-2 327680/321489 P157,7 33.021894003
11 38⋅71⋅11-1 45927/45056 A1711 33.147971027
29 3-19⋅29-1 34359738368/33705582543 dd329 33.277789405
29 32⋅291 261/256 P129 33.487195884 8
11 3-25⋅7-1⋅111 6047313952768/5931020266101 ddd3117 33.617014261
7 3-9⋅5-1⋅72 100352/98415 dd37,75 33.743091285
13 322⋅111⋅131 4487491524087/4398046511104 -cAA611,13 34.855623173
11 3-14⋅5-1⋅11-1 268435456/263063295 dd35,11 34.998331655
31 3-5⋅311 248/243 P131 35.260568137 -3
13 314⋅11-1⋅13-1 4782969/4685824 -cAA711,13 35.524407981
7 3-1⋅72 49/48 m27,7 35.696812073 4
11 3-6⋅11-1 8192/8019 m211 36.952052443
7 3-23⋅5-1⋅71 481036337152/470715894135 dddd475 37.547172700
7 37⋅51⋅72 535815/524288 A15,7,7 37.650532861
13 35⋅71⋅13-1 1701/1664 A1713 38.073249027 7
17 317⋅171 2195382771/2147483648 -cA717 38.190424212
13 3-26⋅11-1⋅131 28587302322176/27960524111619 dddd41311 38.379696904
7 323⋅7-3 94143178827/92073361408 -cAAAA57,7,7 38.487300497
11 32⋅51⋅11-1 45/44 A1511 38.905773231 2
7 322⋅5-2⋅71 219667417263/214748364800 -cA775,5 39.208497778
7 3-15⋅71 14680064/14348907 dd37 39.500893488
11 319⋅112 140633637507/137438953472 -cAA611,11 39.780901172
13 3-17⋅5-1⋅13-1 8589934592/8394110595 dd35,13 39.923609654
23 36⋅231 16767/16384 -cA723 40.004352461
13 311⋅13-2 177147/173056 -cAA713,13 40.449685981
11 3-20⋅7-1⋅11-1 274877906944/268482398877 dd37,11 40.756133858
5 5-3 128/125 d25,5,5 41.058858405 -7
7 3-7⋅51⋅71 2240/2187 m25,7 41.454614276 -6
13 3-9⋅13-1 262144/255879 m213 41.877330442
5 38⋅5-2 6561/6400 P15,5 43.012579193 8
7 31⋅52⋅71 525/512 A15,5,7 43.408335064 9
19 321⋅19-1 10460353203/10200547328 -cAAA619 43.542002041
13 3-1⋅51⋅13-1 40/39 A1513 43.831051230 -3
13 318⋅71⋅131 35255264499/34359738368 -cA77,13 44.543583815
5 316⋅5-1 43046721/41943040 -cA75 44.966299981
5 3-21⋅51 10737418240/10460353203 dd35 45.258695692
13 3-23⋅7-1⋅13-1 8796093022208/8567029273257 dd37,13 45.681411858
13 3-4⋅5-1⋅131 416/405 d2135 46.393944443 -5
19 3-26⋅191 2611340115968/2541865828329 dddd419 46.682993632
7 3-6⋅5-2⋅7-1 131072/127575 d25,5,7 46.816660609
3 324 282429536481/274877906944 -cAAA6 46.920020769
5 3-13⋅52 1638400/1594323 m25,5 47.212416480
13 34⋅131 1053/1024 P113 48.347665231
7 32⋅5-1⋅7-1 36/35 P15,7 48.770381397 -2
5 3-5⋅53 250/243 A15,5,5 49.166137268 -1
11 315⋅71⋅111 1104865839/1073741824 -cA77,11 49.468861815
13 3-16⋅132 44302336/43046721 ddd313,13 49.775309692
23 3-11⋅23-1 4194304/4074381 dd323 50.220643212
13 312⋅51⋅131 34543665/33554432 -cA75,13 50.301386019
11 3-24⋅11-2 35184372088832/34173973914201 ddd411,11 50.444094501
7 310⋅7-1 59049/57344 -cA77 50.724102185
11 3-7⋅5-1⋅111 11264/10935 d2115 51.319222442 -10
13 321⋅111⋅13-1 115063885233/111669149696 -cAAA61113 51.845298769
17 3-22⋅17-1 549755813888/533478013353 dd317 52.034571461
13 3-10⋅7-1⋅131 425984/413343 d2137 52.151746646
7 3-12⋅5-1⋅7-2 134217728/130203045 d25,7,7 52.574462812
7 318⋅51⋅7-1 1937102445/1879048192 -cAAA657 52.677822973
11 31⋅111 33/32 P111 53.272943230 5
7 3-4⋅7-2 4096/3969 P17,7 54.528183600
7 326⋅52⋅7-1 63546645708225/61572651155456 -cAAAAA55,57 54.631543761
13 3-19⋅111⋅131 1199570944/1162261467 ddd311,13 54.700587692
31 31-1 32/31 m231 54.964427536 -5
11 39⋅51⋅111 1082565/1048576 -cA75,11 55.226664018
7 325⋅73 290619993038949/281474976710656 -cAA77,7,7 55.352741042
7 34⋅51⋅7-2 405/392 -cA757,7 56.481904388 3
11 320⋅71⋅11-1 24407490807/23622320128 -cAA7711 56.607981412
29 3-7⋅29-1 65536/63423 m229 56.737799789
29 314⋅291 138706101/134217728 -cA729 56.947206269
11 3-13⋅7-1⋅111 11534336/11160261 d2117 57.077024646
7 33⋅5-1⋅72 1323/1280 m27,75 57.203101670 8
17 3-24⋅171 292057776128/282429536481 dddd417 58.035388731
7 3-18⋅7-3 137438953472/132885227727 d27,7,7 58.332265016
11 3-2⋅5-1⋅11-1 512/495 m25,11 58.458342040 -9
31 37⋅311 67797/65536 -cA731 58.720578522
13 326⋅11-1⋅13-1 2541865828329/2456721293312 -cAAAA611,13 58.984418366
7 3-19⋅5-2⋅71 30064771072/29056536675 dddd475,5 59.053462297
7 311⋅72 8680203/8388608 A17,7 59.156822458
11 3-22⋅112 32480690176/31381059609 ddd311,11 59.625865691
11 36⋅11-1 729/704 A111 60.412062828 6
7 3-11⋅5-1⋅71 917504/885735 dd375 61.007183085
7 319⋅51⋅72 284754059415/274877906944 -cAA75,7,7 61.110543245
13 317⋅71⋅13-1 903981141/872415232 -cAA7713 61.533259411
13 3-14⋅11-1⋅131 54525952/52612659 dd31311 61.839707289
11 314⋅51⋅11-1 23914845/23068672 -cAA7511 62.365783616
7 3-3⋅71 28/27 m27 62.960903873 -2
13 3-5⋅5-1⋅13-1 16384/15795 m25,13 63.383620039
19 3-20⋅19-1 68719476736/66248903619 dd319 63.386966560
23 318⋅231 8910671247/8589934592 -cAAA623 63.464362845
13 323⋅13-2 94143178827/90731184128 -cAAAA613,13 63.909696365
11 3-8⋅7-1⋅11-1 524288/505197 m27,11 64.216144243
13 3-23⋅71⋅131 97710505984/94143178827 dddd47,13 64.388548335
5 312⋅5-3 531441/512000 P15,5,5 64.518868790
5 3-25⋅5-1 4398046511104/4236443047215 dddd45 64.811264500
7 35⋅51⋅71 8505/8192 A15,7 64.914624661
13 33⋅13-1 27/26 A113 65.337340827 1
5 320⋅5-2 3486784401/3355443200 -cA75,5 66.472589578
3 3-17 134217728/129140163 dd3 66.764985288
7 313⋅52⋅71 279006525/268435456 -cAA75,5,7 66.868345449
13 311⋅51⋅13-1 885735/851968 -cAA7513 67.291061615
5 3-9⋅51 20480/19683 m25 68.718706076
13 3-11⋅7-1⋅13-1 16777216/16120377 m27,13 69.141422242
11 3-26⋅71⋅111 2645699854336/2541865828329 dddd47,11 69.313826334
13 38⋅5-1⋅131 85293/81920 P1135 69.853954828
19 3-14⋅191 4980736/4782969 dd319 70.143004017
7 36⋅5-2⋅7-1 729/700 P15,5,7 70.276670994 2
5 3-1⋅52 25/24 A15,5 70.672426864 3
13 3-20⋅111⋅13-1 47244640256/45328197213 dd31113 71.690263288
13 316⋅131 559607373/536870912 -cA713 71.807675616
7 314⋅5-1⋅7-1 4782969/4587520 -cA75,7 72.230391781
7 3-23⋅51⋅7-1 687194767360/659002251789 dd357 72.522787492
5 37⋅53 273375/262144 -cAA75,5,5 72.626147652
13 3-4⋅132 169/162 d213,13 73.235320077 1
23 31⋅23-1 24/23 m223 73.680653597 -3
13 324⋅51⋅131 18357919871265/17592186044416 -cAAA65,13 73.761396403
11 3-12⋅11-2 67108864/64304361 d311,11 73.904104886
7 322⋅7-1 31381059609/30064771072 -cAAA67 74.184112569
7 3-15⋅52⋅7-1 104857600/100442349 m25,57 74.476508280
11 35⋅5-1⋅111 2673/2560 P1115 74.779232827 9
7 3-16⋅73 44957696/43046721 ddd47,7,7 75.197705561
17 3-10⋅17-1 1048576/1003833 m217 75.494581846
13 32⋅7-1⋅131 117/112 P1137 75.611757031 4
7 5-1⋅7-2 256/245 P15,7,7 76.034473197 -8
11 3-21⋅71⋅11-1 120259084288/115063885233 ddd4711 76.452945931
11 313⋅111 17537553/16777216 -cA711 76.732953615
7 38⋅7-2 6561/6272 -cA77,7 77.988193985 7
13 3-7⋅111⋅131 2288/2187 d211,13 78.160598076 -4
31 312⋅31-1 531441/507904 A131 78.424437920
11 321⋅51⋅111 575319426165/549755813888 -cAAA65,11 78.686674403
13 3-15⋅11-1⋅13-1 2147483648/2051893701 d311,13 78.829382885
7 316⋅51⋅7-2 215233605/205520896 -cAAA657,7 79.941914773
29 35⋅29-1 243/232 A129 80.197810174 3
29 326⋅291 73714109021541/70368744177664 -cAAA629 80.407216653
11 3-1⋅7-1⋅111 22/21 P1117 80.537035030 -1
7 315⋅5-1⋅72 703096443/671088640 A17,75 80.663112054
7 3-22⋅51⋅72 32883343360/31381059609 ddd45,7,7 80.955507765
13 3-24⋅71⋅13-1 3848290697216/3671583974253 ddd4713 81.378223931
17 3-12⋅171 557056/531441 dd317 81.495399116
7 3-6⋅7-3 262144/250047 P17,7,7 81.792275400
11 310⋅5-1⋅11-1 59049/56320 A15,11 81.918352424
31 319⋅311 36030105477/34359738368 -cAAA631 82.180588907
7 3-7⋅5-2⋅71 57344/54675 dd375,5 82.513472682
7 323⋅72 4613015762523/4398046511104 -cAA77,7 82.616832842
11 3-10⋅112 61952/59049 d211,11 83.085876076 -9
23 3-23⋅231 98784247808/94143178827 dd323 83.309327365
13 3-18⋅13-2 68719476736/65474062641 d313,13 83.754660884
11 318⋅11-1 387420489/369098752 -cAA711 83.872073212
7 31⋅5-1⋅71 21/20 m275 84.467193470 2
13 3-2⋅11-1⋅131 104/99 m21311 85.299717674 -3
11 326⋅51⋅11-1 12709329141645/12094627905536 -cAAAA6511 85.825794000
5 3-21⋅5-2 274877906944/261508830075 dddd45,5 86.317554097
7 39⋅71 137781/131072 A17 86.420914258
13 37⋅5-1⋅13-1 2187/2080 A15,13 86.843630424 5
19 3-8⋅19-1 131072/124659 m219 86.846976945
11 34⋅7-1⋅11-1 81/77 A17,11 87.676154628 0
13 3-11⋅71⋅131 186368/177147 dd37,13 87.848558719
5 324⋅5-3 282429536481/268435456000 -cA75,5,5 87.978879175
5 3-13⋅5-1 8388608/7971615 dd35 88.271274885
7 317⋅51⋅71 4519905705/4294967296 -cAA75,7 88.374635046
13 315⋅13-1 14348907/13631488 -cAA713 88.797351212
3 3-5 256/243 m2 90.224995673 -8
7 325⋅52⋅71 148275506652525/140737488355328 -cAAAA65,5,7 90.328355833
13 323⋅51⋅13-1 470715894135/446676598784 -cAAAA6513 90.751071999
13 3-25⋅131 893353197568/847288609443 dddd413 91.652640135
5 33⋅51 135/128 A15 92.178716461 7
13 31⋅7-1⋅13-1 96/91 A17,13 92.601432627 -5
11 3-14⋅71⋅111 5046272/4782969 dd37,11 92.773836718
13 320⋅5-1⋅131 45328197213/42949672960 -cA7135 93.313965212
19 3-2⋅191 19/18 m219 93.603014402 1
13 3-17⋅51⋅131 136314880/129140163 dd35,13 93.606360923
7 318⋅5-2⋅7-1 387420489/367001600 -cA75,5,7 93.736681378
7 3-19⋅7-1 8589934592/8135830269 dd37 94.029077089
5 311⋅52 4428675/4194304 -cAA75,5 94.132437249
13 3-8⋅111⋅13-1 90112/85293 m21113 95.150273672
7 326⋅5-1⋅7-1 2541865828329/2405181685760 -cAAA65,7 95.690402166
7 3-11⋅51⋅7-1 1310720/1240029 m257 95.982797876
5 319⋅53 145282683375/137438953472 -cAAAA65,5,5 96.086158037
13 38⋅132 1108809/1048576 P113,13 96.695330462
23 313⋅23-1 1594323/1507328 A123 97.140663982
11 11-2 128/121 M211,11 97.364115270 -7
7 3-3⋅52⋅7-1 200/189 A15,57 97.936518664 -3
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7 34⋅7-3 648/343 A67,7,7 1101.342284054 -3
11 320⋅5-1⋅11-1 3486784401/1845493760 AA65,11 1101.468361078
11 3-17⋅51⋅11-1 2684354560/1420541793 cd2511 1101.760756788
7 33⋅5-2⋅71 189/100 d875,5 1102.063481336 2
11 112 121/64 m711,11 1102.635884730 6
23 3-13⋅231 3014656/1594323 d823 1102.859336018
13 3-8⋅13-2 2097152/1108809 P813,13 1103.304669538
5 3-19⋅5-3 274877906944/145282683375 cdddd35,5,5 1103.913841963
7 311⋅5-1⋅71 1240029/655360 M775 1104.017202124
7 3-26⋅51⋅71 4810363371520/2541865828329 cddd35,7 1104.309597834
13 38⋅11-1⋅131 85293/45056 M71311 1104.849726328
5 3-11⋅5-2 8388608/4428675 cdd25,5 1105.867562751
7 319⋅71 8135830269/4294967296 AA67 1105.970922911
7 3-18⋅52⋅71 734003200/387420489 cd25,5,7 1106.263318622
13 317⋅5-1⋅13-1 129140163/68157440 AA65,13 1106.393639077
19 32⋅19-1 36/19 M719 1106.396985598 -2
13 3-20⋅51⋅13-1 85899345920/45328197213 cd2513 1106.686034788
11 314⋅7-1⋅11-1 4782969/2523136 AA67,11 1107.226163282
13 3-1⋅71⋅131 91/48 d87,13 1107.398567373 4
5 3-3⋅5-1 256/135 d85 1107.821283539 -8
13 325⋅13-1 847288609443/446676598784 AAAA513 1108.347359865
13 3-23⋅5-1⋅131 893353197568/470715894135 cdddd3135 1109.248928001
7 3-25⋅5-2⋅7-1 281474976710656/148275506652525 cdddd35,5,7 1109.671644167
3 35 243/128 M7 1109.775004327 7
13 3-15⋅131 27262976/14348907 cdd213 1111.202648788
7 3-17⋅5-1⋅7-1 8589934592/4519905705 cdd25,7 1111.625364954
5 313⋅51 7971615/4194304 AA65 1111.728725115
5 3-24⋅53 536870912000/282429536481 cd25,5,5 1112.021120825
13 311⋅7-1⋅13-1 177147/93184 AA67,13 1112.151441281
11 3-4⋅71⋅111 154/81 d87,11 1112.323845372 -1
19 38⋅191 124659/65536 M719 1113.153023055
13 3-7⋅51⋅131 4160/2187 d85,13 1113.156369576 -6
7 3-9⋅7-1 262144/137781 d87 1113.579085742
5 321⋅52 261508830075/137438953472 AAAA55,5 1113.682445903
11 3-26⋅5-1⋅111 24189255811072/12709329141645 cdddd3115 1114.174206000
13 32⋅111⋅13-1 99/52 M71113 1114.700282326 2
7 3-1⋅51⋅7-1 40/21 M757 1115.532806530 -3
11 3-18⋅111 738197504/387420489 cdd211 1116.127926788
13 318⋅132 65474062641/34359738368 A613,13 1116.245339116
23 323⋅23-1 94143178827/49392123904 AA623 1116.690672635
11 310⋅11-2 59049/30976 A711,11 1116.914123924 8
7 3-23⋅7-2 8796093022208/4613015762523 cdd27,7 1117.383167158
7 37⋅52⋅7-1 54675/28672 AA65,57 1117.486527318
31 3-19⋅31-1 68719476736/36030105477 cddd331 1117.819411093
11 3-10⋅51⋅111 112640/59049 d85,11 1118.081647576
7 36⋅73 250047/131072 P87,7,7 1118.207724600
17 312⋅17-1 531441/278528 AA617 1118.504600884
13 324⋅7-1⋅131 3671583974253/1924145348608 AAA5137 1118.621776069
7 322⋅5-1⋅7-2 31381059609/16441671680 AAA55,7,7 1119.044492235
7 3-15⋅51⋅7-2 1342177280/703096443 d857,7 1119.336887946
11 31⋅71⋅11-1 21/11 P8711 1119.462964970 0
29 3-26⋅29-1 140737488355328/73714109021541 cddd329 1119.592783347
29 3-5⋅291 464/243 d829 1119.802189826 -4
7 3-16⋅5-1⋅72 411041792/215233605 cddd37,75 1120.058085227
13 315⋅111⋅131 2051893701/1073741824 A611,13 1121.170617115
11 3-21⋅5-1⋅11-1 1099511627776/575319426165 cddd35,11 1121.313325597
31 3-12⋅311 1015808/531441 d831 1121.575562080
13 37⋅11-1⋅13-1 2187/1144 A711,13 1121.839401924 3
7 3-8⋅72 12544/6561 cd27,7 1122.011806015 -8
11 3-13⋅11-1 33554432/17537553 cd211 1123.267046385
11 321⋅7-1⋅111 115063885233/60129542144 AAA5117 1123.547054069
7 51⋅72 245/128 P85,7,7 1123.965526803 7
13 3-2⋅71⋅13-1 224/117 P8713 1124.388242969 -5
17 310⋅171 1003833/524288 M717 1124.505418154
7 316⋅7-3 43046721/22478848 AAA57,7,7 1124.802294439
11 3-5⋅51⋅11-1 5120/2673 P8511 1125.220767173 -10
7 315⋅5-2⋅71 100442349/52428800 M775,5 1125.523491720
7 3-22⋅71 60129542144/31381059609 cddd37 1125.815887431
11 312⋅112 64304361/33554432 A611,11 1126.095895114
13 3-24⋅5-1⋅13-1 35184372088832/18357919871265 cddd35,13 1126.238603597
23 3-1⋅231 23/12 M723 1126.319346403 2
13 34⋅13-2 324/169 A713,13 1126.764679923 -2
5 3-7⋅5-3 524288/273375 cdd25,5,5 1127.373852348
7 323⋅5-1⋅71 659002251789/343597383680 AA675 1127.477212508
7 3-14⋅51⋅71 9175040/4782969 cd25,7 1127.769608219
13 3-16⋅13-1 1073741824/559607373 cd213 1128.192324384
13 320⋅11-1⋅131 45328197213/23622320128 AA61311 1128.309736712
5 31⋅5-2 48/25 d85,5 1129.327573136 -4
7 3-6⋅52⋅71 1400/729 P85,5,7 1129.723329006 -3
19 314⋅19-1 4782969/2490368 AA619 1129.856995983
13 3-8⋅51⋅13-1 163840/85293 P8513 1130.146045172
11 326⋅7-1⋅11-1 2541865828329/1322849927168 AAAA57,11 1130.686173666
13 311⋅71⋅131 16120377/8388608 M77,13 1130.858577758
5 39⋅5-1 19683/10240 M75 1131.281293924
13 3-11⋅5-1⋅131 1703936/885735 cdd2135 1132.708938385
7 3-13⋅5-2⋅7-1 536870912/279006525 cdd25,5,7 1133.131654551
3 317 129140163/67108864 AA6 1133.235014712
5 3-20⋅52 6710886400/3486784401 cd25,5 1133.527410422
13 3-3⋅131 52/27 d813 1134.662659173 -2
7 3-5⋅5-1⋅7-1 16384/8505 d85,7 1135.085375339
5 325⋅51 4236443047215/2199023255552 AAAA55 1135.188735500
5 3-12⋅53 1024000/531441 P85,5,5 1135.481131210
13 323⋅7-1⋅13-1 94143178827/48855252992 AAAA57,13 1135.611451665
11 38⋅71⋅111 505197/262144 M77,11 1135.783855757
13 3-23⋅132 181462368256/94143178827 cdddd313,13 1136.090303635
23 3-18⋅23-1 17179869184/8910671247 cddd323 1136.535637155
19 320⋅191 66248903619/34359738368 AA619 1136.613033440
13 35⋅51⋅131 15795/8192 M75,13 1136.616379961
7 33⋅7-1 27/14 M77 1137.039096127 1
11 3-14⋅5-1⋅111 46137344/23914845 cdd2115 1137.634216384
13 314⋅111⋅13-1 52612659/27262976 AA61113 1138.160292711
13 3-17⋅7-1⋅131 1744830464/903981141 cdd2137 1138.466740589
7 3-19⋅5-1⋅7-2 549755813888/284754059415 cdd25,7,7 1138.889456755
7 311⋅51⋅7-1 885735/458752 AA657 1138.992816915
11 3-6⋅111 1408/729 d811 1139.587937172 -7
11 322⋅11-2 31381059609/16240345088 AAA611,11 1140.374134309
7 3-11⋅7-2 16777216/8680203 d87,7 1140.843177542
7 319⋅52⋅7-1 29056536675/15032385536 AAAA55,57 1140.946537703
13 3-26⋅111⋅131 4913442586624/2541865828329 cdddd311,13 1141.015581634
31 3-7⋅31-1 131072/67797 cd231 1141.279421478
11 32⋅51⋅111 495/256 M75,11 1141.541657960 8
7 318⋅73 132885227727/68719476736 A77,7,7 1141.667734984
17 324⋅17-1 282429536481/146028888064 AAAA517 1141.964611269
7 3-3⋅51⋅7-2 2560/1323 M757,7 1142.796898330 -9
11 313⋅71⋅11-1 11160261/5767168 A7711 1142.922975354
29 3-14⋅29-1 268435456/138706101 cd229 1143.052793731
29 37⋅291 63423/32768 M729 1143.262200211
11 3-20⋅7-1⋅111 47244640256/24407490807 cdd2117 1143.392018588
7 3-4⋅5-1⋅72 784/405 cd27,75 1143.518095612 -4
7 3-25⋅7-3 562949953421312/290619993038949 cdd27,7,7 1144.647258958
11 3-9⋅5-1⋅11-1 2097152/1082565 cd25,11 1144.773335982
31 311 31/16 M731 1145.035572464 4
13 319⋅11-1⋅13-1 1162261467/599785472 AAA611,13 1145.299412308
7 3-26⋅5-2⋅71 123145302310912/63546645708225 cddddd475,5 1145.368456239
7 34⋅72 3969/2048 P87,7 1145.471816400
11 3-1⋅11-1 64/33 P811 1146.727056770 -6
7 3-18⋅5-1⋅71 3758096384/1937102445 cddd375 1147.322177027
7 312⋅51⋅72 130203045/67108864 A75,7,7 1147.425537188
13 310⋅71⋅13-1 413343/212992 A7713 1147.848253354
17 322⋅171 533478013353/274877906944 AA617 1147.965428539
13 3-21⋅11-1⋅131 223338299392/115063885233 cddd31311 1148.154701231
11 37⋅51⋅11-1 10935/5632 A7511 1148.680777558 9
7 3-10⋅71 114688/59049 cd27 1149.275897815
11 324⋅112 34173973914201/17592186044416 AAA511,11 1149.555905499
13 3-12⋅5-1⋅13-1 67108864/34543665 cd25,13 1149.698613981
23 311⋅231 4074381/2097152 AA623 1149.779356788
13 316⋅13-2 43046721/22151168 AAA613,13 1150.224690308
11 3-15⋅7-1⋅11-1 2147483648/1104865839 cd27,11 1150.531138185
5 35⋅5-3 243/125 d85,5,5 1150.833862732 0
7 3-2⋅51⋅71 35/18 P85,7 1151.229618603 1
13 3-4⋅13-1 2048/1053 P813 1151.652334769
5 313⋅5-2 1594323/819200 M75,5 1152.787583520
3 3-24 549755813888/282429536481 cddd3 1153.079979231
7 36⋅52⋅71 127575/65536 A75,5,7 1153.183339391
19 326⋅19-1 2541865828329/1305670057984 AAAA519 1153.317006368
13 34⋅51⋅13-1 405/208 A7513 1153.606055557 4
13 323⋅71⋅131 8567029273257/4398046511104 AA67,13 1154.318588142
5 321⋅5-1 10460353203/5368709120 AA65 1154.741304308
5 3-16⋅51 83886080/43046721 cd25 1155.033700019
13 3-18⋅7-1⋅13-1 68719476736/35255264499 cd27,13 1155.456416185
13 31⋅5-1⋅131 39/20 d8135 1156.168948770 2
19 3-21⋅191 20401094656/10460353203 cddd319 1156.457997959
7 3-1⋅5-2⋅7-1 1024/525 d85,5,7 1156.591664936 -10
5 3-8⋅52 12800/6561 P85,5 1156.987420807 -9
13 39⋅131 255879/131072 M713 1158.122669558
7 37⋅5-1⋅7-1 2187/1120 M75,7 1158.545385724 5
5 53 125/64 A75,5,5 1158.941141595 6
11 320⋅71⋅111 268482398877/137438953472 AA67,11 1159.243866142
13 3-11⋅132 346112/177147 cdd213,13 1159.550314019
23 3-6⋅23-1 32768/16767 cd223 1159.995647539
13 317⋅51⋅131 8394110595/4294967296 AA65,13 1160.076390346
11 3-19⋅11-2 274877906944/140633637507 cdd311,11 1160.219098828
7 315⋅7-1 14348907/7340032 AA67 1160.499106512
7 3-22⋅52⋅7-1 429496729600/219667417263 cd25,57 1160.791502222
11 3-2⋅5-1⋅111 88/45 d8115 1161.094226769 -3
7 3-23⋅73 184146722816/94143178827 cdddd47,7,7 1161.512699503
13 326⋅111⋅13-1 27960524111619/14293651161088 AAAA51113 1161.620303096
17 3-17⋅17-1 4294967296/2195382771 cd217 1161.809575788
13 3-5⋅7-1⋅131 3328/1701 d8137 1161.926750973 -8
7 3-7⋅5-1⋅7-2 1048576/535815 d85,7,7 1162.349467139
7 323⋅51⋅7-1 470715894135/240518168576 AAAA557 1162.452827300
11 36⋅111 8019/4096 M711 1163.047947557
7 31⋅7-2 96/49 M77,7 1164.303187927 -5
13 3-14⋅111⋅131 9371648/4782969 cdd211,13 1164.475592019
31 35⋅31-1 243/124 P831 1164.739431863 2
11 314⋅51⋅111 263063295/134217728 AA65,11 1165.001668345
13 3-22⋅11-1⋅13-1 8796093022208/4487491524087 cdd311,13 1165.144376827
7 39⋅51⋅7-2 98415/50176 AA657,7 1166.256908715
11 325⋅71⋅11-1 5931020266101/3023656976384 AAA6711 1166.382985739
29 3-2⋅29-1 512/261 P829 1166.512804116 -9
29 319⋅291 33705582543/17179869184 AA629 1166.722210595
11 3-8⋅7-1⋅111 90112/45927 d8117 1166.852028973
7 38⋅5-1⋅72 321489/163840 P87,75 1166.978105997
17 3-19⋅171 2281701376/1162261467 cddd317 1167.810393058
7 3-13⋅7-3 1073741824/546852789 d87,7,7 1168.107269343
11 33⋅5-1⋅11-1 108/55 P85,11 1168.233346367 -2
31 312⋅311 16474671/8388608 AA631 1168.495582849
7 3-14⋅5-2⋅71 234881024/119574225 cddd375,5 1168.828466624
7 316⋅72 2109289329/1073741824 A77,7 1168.931826784
11 3-17⋅112 253755392/129140163 cdd211,11 1169.400870018
13 3-25⋅13-2 281474976710656/143191774995867 cdd313,13 1170.069654827
11 311⋅11-1 177147/90112 A711 1170.187067155
7 3-6⋅5-1⋅71 7168/3645 cd275 1170.782187412 -10
7 324⋅51⋅72 69195236437845/35184372088832 AAA65,7,7 1170.885547572
13 322⋅71⋅13-1 219667417263/111669149696 AAA6713 1171.308263738
13 3-9⋅11-1⋅131 425984/216513 cd21311 1171.614711616
11 319⋅51⋅11-1 5811307335/2952790016 AAA6511 1172.140787942
7 32⋅71 63/32 P87 1172.735908200 5
13 5-1⋅13-1 128/65 P85,13 1173.158624366 -7
19 3-15⋅19-1 536870912/272629233 cd219 1173.161970887
23 323⋅231 2165293113021/1099511627776 AAAA523 1173.239367172
11 3-3⋅7-1⋅11-1 4096/2079 P87,11 1173.991148570
13 3-18⋅71⋅131 763363328/387420489 cddd37,13 1174.163552661
5 317⋅5-3 129140163/65536000 M75,5,5 1174.293873117
5 3-20⋅5-1 34359738368/17433922005 cddd35 1174.586268827
7 310⋅51⋅71 2066715/1048576 A75,7 1174.689628988
13 38⋅13-1 6561/3328 A713 1175.112345154 8
5 325⋅5-2 847288609443/429496729600 AA65,5 1176.247593905
3 3-12 1048576/531441 cd2 1176.539989615
7 318⋅52⋅71 67798585575/34359738368 AAA65,5,7 1176.643349776
13 316⋅51⋅13-1 215233605/109051904 AAA6513 1177.066065942
5 3-4⋅51 160/81 P85 1178.493710403 -5
13 3-6⋅7-1⋅13-1 131072/66339 P87,13 1178.916426569
11 3-21⋅71⋅111 20669530112/10460353203 cddd37,11 1179.088830661
13 313⋅5-1⋅131 20726199/10485760 M7135 1179.628959155
19 3-9⋅191 38912/19683 cd219 1179.918008344
13 3-24⋅51⋅131 558345748480/282429536481 cddd35,13 1179.921354865
7 311⋅5-2⋅7-1 177147/89600 M75,5,7 1180.051675320 9
7 3-26⋅7-1 35184372088832/17793060798303 cddd37 1180.344071031
5 34⋅52 2025/1024 A75,5 1180.447431191
13 3-15⋅111⋅13-1 369098752/186535791 cd21113 1181.465267615
13 321⋅131 135984591639/68719476736 AA613 1181.582679942
7 319⋅5-1⋅7-1 1162261467/587202560 AA65,7 1182.005396108
7 3-18⋅51⋅7-1 5368709120/2711943423 cd257 1182.297791819
5 312⋅53 66430125/33554432 AAA65,5,5 1182.401151979
13 31⋅132 507/256 d813,13 1183.010324404 8
23 36⋅23-1 729/368 P823 1183.455657924 4
11 3-7⋅11-2 524288/264627 cm211,11 1183.679109213
7 3-10⋅52⋅7-1 819200/413343 P85,57 1184.251512607
11 310⋅5-1⋅111 649539/327680 M7115 1184.554237154
7 3-11⋅73 351232/177147 cdd37,7,7 1184.972709888 -10
17 3-5⋅17-1 8192/4131 P817 1185.269586173
13 37⋅7-1⋅131 28431/14336 M7137 1185.386761358
7 35⋅5-1⋅7-2 486/245 M75,7,7 1185.809477524 -1
11 3-16⋅71⋅11-1 939524096/473513931 cdd3711 1186.227950258
11 318⋅111 4261625379/2147483648 AA611 1186.507957942
29 3-22⋅291 62277025792/31381059609 cddd329 1186.567175115
7 313⋅7-2 1594323/802816 AA67,7 1187.763198312
13 3-2⋅111⋅131 143/72 d811,13 1187.935602403 3
31 317⋅31-1 129140163/65011712 A731 1188.199442247
11 326⋅51⋅111 139802620558095/70368744177664 AAAA55,11 1188.461678730
13 3-10⋅11-1⋅13-1 16777216/8444007 cm211,13 1188.604387212
7 3-25⋅72 1683627180032/847288609443 cdddd47,7 1188.776791304
7 321⋅51⋅7-2 52301766015/26306674688 AAAA557,7 1189.716919100
29 310⋅29-1 59049/29696 A729 1189.972814501
11 34⋅7-1⋅111 891/448 M7117 1190.312039357 6
7 320⋅5-1⋅72 170852435649/85899345920 A77,75 1190.438116381
7 3-17⋅51⋅72 256901120/129140163 cdd35,7,7 1190.730512091
13 3-19⋅71⋅13-1 30064771072/15109399071 cdd3713 1191.153228257
17 3-7⋅171 4352/2187 cd217 1191.270403443 -8
7 3-1⋅7-3 2048/1029 M77,7,7 1191.567279727
11 315⋅5-1⋅11-1 14348907/7208960 A75,11 1191.693356751
31 324⋅311 8755315630911/4398046511104 AAAA531 1191.955593234
11 3-22⋅51⋅11-1 687194767360/345191655699 cdd3511 1191.985752462
7 3-2⋅5-2⋅71 448/225 cd275,5 1192.288477009 -6
11 3-5⋅112 484/243 d811,11 1192.860880403 -2
23 3-18⋅231 771751936/387420489 cd223 1193.084331691
13 3-13⋅13-2 536870912/269440587 cm213,13 1193.529665211
11 323⋅11-1 94143178827/47244640256 AAA611 1193.647077539
5 3-24⋅5-3 70368744177664/35303692060125 cddddd45,5,5 1194.138837636
7 36⋅5-1⋅71 5103/2560 P875 1194.242197797 9
13 33⋅11-1⋅131 351/176 P81311 1195.074722001 4
5 3-16⋅5-2 2147483648/1076168025 cddd35,5 1196.092558424
7 314⋅71 33480783/16777216 A77 1196.195918585
7 3-23⋅52⋅71 187904819200/94143178827 cdd35,5,7 1196.488314295
13 312⋅5-1⋅13-1 531441/266240 A75,13 1196.618634751
19 3-3⋅19-1 1024/513 P819 1196.621981272 -10
13 3-25⋅51⋅13-1 21990232555520/11014751922759 cdd3513 1196.911030461
11 39⋅7-1⋅11-1 19683/9856 A77,11 1197.451158955 7
13 3-6⋅71⋅131 1456/729 cd27,13 1197.623563046 -4
5 3-8⋅5-1 65536/32805 cd25 1198.046279212
7 322⋅51⋅71 1098337086315/549755813888 AAA65,7 1198.149639372
13 320⋅13-1 3486784401/1744830464 AAA613 1198.572355538

Compact version

(31-Limit Factor Gradient) x (3 Tritaves Chain) x (Infinite Octaves or No-Twos) Comparison Table.

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