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Line 669: Line 669:
| [-8 1 0 1 0 1⟩
| [-8 1 0 1 0 1⟩
| 111.309
| 111.309
|-
| [[16/15]]
| [4 -1 -1⟩
| 111.731
|}
== Commas with numerator <= 1048576, size <= 16/15, and primes <= 13 ==
{| class="wikitable mw-collapsible mw-collapsed"
! [[Ratio]]
! [[Monzo]]
! [[Cent]]s
|-
| [[123201/123200]]
| [-6 6 -2 -1 -1 2⟩
| 0.014
|-
| [[151263/151250]]
| [-1 2 -4 5 -2⟩
| 0.149
|-
| [[196625/196608]]
| [-16 -1 3 0 2 1⟩
| 0.150
|-
| [[10648/10647]]
| [3 -2 0 -1 3 -2⟩
| 0.163
|-
| [[9801/9800]]
| [-3 4 -2 -2 2⟩
| 0.177
|-
| [[492128/492075]]
| [5 -9 -2 1 0 3⟩
| 0.186
|-
| [[371293/371250]]
| [-1 -3 -4 0 -1 5⟩
| 0.201
|-
| [[140625/140608]]
| [-6 2 6 0 0 -3⟩
| 0.209
|-
| [[6656/6655]]
| [9 0 -1 0 -3 1⟩
| 0.260
|-
| [[823680/823543]]
| [7 2 1 -7 1 1⟩
| 0.288
|-
| [[655473/655360]]
| [-17 1 -1 5 0 1⟩
| 0.298
|-
| [[105644/105625]]
| [2 0 -4 4 1 -2⟩
| 0.311
|-
| [[250047/250000]]
| [-4 6 -6 3⟩
| 0.325
|-
| [[4375/4374]]
| [-1 -7 4 1⟩
| 0.396
|-
| [[4225/4224]]
| [-7 -1 2 0 -1 2⟩
| 0.410
|-
| [[4096/4095]]
| [12 -2 -1 -1 0 -1⟩
| 0.423
|-
| [[67392/67375]]
| [6 4 -3 -2 -1 1⟩
| 0.437
|-
| [[225000/224939]]
| [3 2 5 0 -3 -2⟩
| 0.469
|-
| [[820125/819896]]
| [-3 8 3 -1 -4⟩
| 0.483
|-
| [[117649/117612]]
| [-2 -5 0 6 -2⟩
| 0.545
|-
| [[3025/3024]]
| [-4 -3 2 -1 2⟩
| 0.572
|-
| [[50193/50176]]
| [-10 3 0 -2 1 2⟩
| 0.586
|-
| [[557568/557375]]
| [9 2 -3 -3 2 -1⟩
| 0.599
|-
| [[200000/199927]]
| [6 0 5 -1 0 -4⟩
| 0.632
|-
| [[91125/91091]]
| [0 6 3 -2 -1 -2⟩
| 0.646
|-
| [[43940/43923]]
| [2 -1 1 0 -4 3⟩
| 0.670
|-
| [[823875/823543]]
| [0 1 3 -7 0 3⟩
| 0.698
|-
| [[369754/369603]]
| [1 -7 0 5 1 -2⟩
| 0.707
|-
| [[2401/2400]]
| [-5 -1 -2 4⟩
| 0.721
|-
| [[1016064/1015625]]
| [8 4 -7 2 0 -1⟩
| 0.748
|-
| [[43923/43904]]
| [-7 1 0 -3 4⟩
| 0.749
|-
| [[531674/531441]]
| [1 -12 0 0 2 3⟩
| 0.759
|-
| [[256000/255879]]
| [11 -9 3 0 0 -1⟩
| 0.818
|-
| [[2080/2079]]
| [5 -3 1 -1 -1 1⟩
| 0.833
|-
| [[59319/59290]]
| [-1 3 -1 -2 -2 3⟩
| 0.847
|-
| [[234375/234256]]
| [-4 1 7 0 -4⟩
| 0.879
|-
| [[456533/456300]]
| [-2 -3 -2 3 3 -2⟩
| 0.884
|-
| [[160083/160000]]
| [-8 3 -4 2 2⟩
| 0.898
|-
| [[142884/142805]]
| [2 6 -1 2 0 -4⟩
| 0.957
|-
| [[499408/499125]]
| [4 -1 -3 4 -3 1⟩
| 0.981
|-
| [[154880/154791]]
| [8 -5 1 -2 2 -1⟩
| 0.995
|-
| [[1716/1715]]
| [2 1 -1 -3 1 1⟩
| 1.009
|-
| [[78125/78078]]
| [-1 -1 7 -1 -1 -2⟩
| 1.042
|-
| [[759375/758912]]
| [-7 5 5 -2 -2⟩
| 1.056
|-
| [[420175/419904]]
| [-6 -8 2 5⟩
| 1.117
|-
| [[405769/405504]]
| [-12 -2 0 4 -1 2⟩
| 1.131
|-
| [[43904/43875]]
| [7 -3 -3 3 0 -1⟩
| 1.144
|-
| [[34398/34375]]
| [1 3 -5 2 -1 1⟩
| 1.158
|-
| [[468512/468195]]
| [5 -1 -1 -4 4 -1⟩
| 1.172
|-
| [[900375/899756]]
| [-2 1 3 4 -3 -2⟩
| 1.191
|-
| [[928125/927472]]
| [-4 3 5 -3 1 -2⟩
| 1.218
|-
| [[650000/649539]]
| [4 -10 5 0 -1 1⟩
| 1.228
|-
| [[274625/274428]]
| [-2 -4 3 -1 -2 3⟩
| 1.242
|-
| [[131072/130977]]
| [17 -5 0 -2 -1⟩
| 1.255
|-
| [[1038336/1037575]]
| [11 1 -2 -3 -2 2⟩
| 1.269
|-
| [[41503/41472]]
| [-9 -4 0 3 2⟩
| 1.294
|-
| [[819819/819200]]
| [-15 2 -2 2 1 2⟩
| 1.308
|-
| [[40656/40625]]
| [4 1 -5 1 2 -1⟩
| 1.321
|-
| [[312741/312500]]
| [-2 7 -7 0 1 1⟩
| 1.335
|-
| [[85750/85683]]
| [1 -1 3 3 0 -4⟩
| 1.353
|-
| [[59535/59488]]
| [-5 5 1 2 -1 -2⟩
| 1.367
|-
| [[35750/35721]]
| [1 -6 3 -2 1 1⟩
| 1.405
|-
| [[10985/10976]]
| [-5 0 1 -3 0 3⟩
| 1.419
|-
| [[180224/180075]]
| [14 -1 -2 -4 1⟩
| 1.432
|-
| [[102487/102400]]
| [-12 0 -2 1 4⟩
| 1.470
|-
| [[540000/539539]]
| [5 3 4 -3 -2 -1⟩
| 1.479
|-
| [[114345/114244]]
| [-2 3 1 1 2 -4⟩
| 1.530
|-
| [[768320/767637]]
| [6 -10 1 4 0 -1⟩
| 1.540
|-
| [[216513/216320]]
| [-8 9 -1 0 1 -2⟩
| 1.544
|-
| [[4459/4455]]
| [0 -4 -1 3 -1 1⟩
| 1.554
|-
| [[968877/968000]]
| [-6 2 -3 2 -2 3⟩
| 1.568
|-
| [[172032/171875]]
| [13 1 -6 1 -1⟩
| 1.581
|-
| [[86515/86436]]
| [-2 -2 1 -4 3 1⟩
| 1.582
|-
| [[190512/190333]]
| [4 5 0 2 -4 -1⟩
| 1.627
|-
| [[703125/702464]]
| [-11 2 7 -3⟩
| 1.628
|-
| [[218700/218491]]
| [2 7 2 -5 0 -1⟩
| 1.655
|-
| [[456976/456533]]
| [4 0 0 -3 -3 4⟩
| 1.679
|-
| [[47432/47385]]
| [3 -6 -1 2 2 -1⟩
| 1.716
|-
| [[1001/1000]]
| [-3 0 -3 1 1 1⟩
| 1.730
|-
| [[496125/495616]]
| [-12 4 3 2 -2⟩
| 1.777
|-
| [[24192/24167]]
| [7 3 0 1 -1 -3⟩
| 1.790
|-
| [[39366/39325]]
| [1 9 -2 0 -2 -1⟩
| 1.804
|-
| [[21632/21609]]
| [7 -2 0 -4 0 2⟩
| 1.842
|-
| [[14641/14625]]
| [0 -2 -3 0 4 -1⟩
| 1.893
|-
| [[86625/86528]]
| [-9 2 3 1 1 -2⟩
| 1.940
|-
| [[371712/371293]]
| [10 1 0 0 2 -5⟩
| 1.953
|-
| [[32805/32768]]
| [-15 8 1⟩
| 1.954
|-
| [[384912/384475]]
| [4 7 -2 -1 1 -3⟩
| 1.967
|-
| [[200704/200475]]
| [12 -6 -2 2 -1⟩
| 1.976
|-
| [[75712/75625]]
| [6 0 -4 1 -2 2⟩
| 1.990
|-
| [[31250/31213]]
| [1 0 6 -4 0 -1⟩
| 2.051
|-
| [[35035/34992]]
| [-4 -7 1 2 1 1⟩
| 2.126
|-
| [[15379/15360]]
| [-10 -1 -1 1 0 3⟩
| 2.140
|-
| [[5632/5625]]
| [9 -2 -4 0 1⟩
| 2.153
|-
| [[109512/109375]]
| [3 4 -6 -1 0 2⟩
| 2.167
|-
| [[1575/1573]]
| [0 2 2 1 -2 -1⟩
| 2.200
|-
| [[85293/85184]]
| [-6 8 0 0 -3 1⟩
| 2.214
|-
| [[714025/713097]]
| [0 -3 2 -4 -1 4⟩
| 2.252
|-
| [[512435/511758]]
| [-1 -9 1 1 4 -1⟩
| 2.289
|-
| [[17303/17280]]
| [-7 -3 -1 0 3 1⟩
| 2.303
|-
| [[766656/765625]]
| [6 2 -6 -2 3⟩
| 2.330
|-
| [[65625/65536]]
| [-16 1 5 1⟩
| 2.349
|-
| [[2200/2197]]
| [3 0 2 0 1 -3⟩
| 2.362
|-
| [[729/728]]
| [-3 6 0 -1 0 -1⟩
| 2.376
|-
| [[264992/264627]]
| [5 -7 0 2 -2 2⟩
| 2.386
|-
| [[199927/199650]]
| [-1 -1 -2 1 -3 4⟩
| 2.400
|-
| [[942513/941192]]
| [-3 1 0 -6 1 4⟩
| 2.428
|-
| [[161280/161051]]
| [9 2 1 1 -5⟩
| 2.460
|-
| [[605052/604175]]
| [2 2 -2 5 -1 -3⟩
| 2.511
|-
| [[107811/107653]]
| [0 4 0 -2 3 -3⟩
| 2.539
|-
| [[19712/19683]]
| [8 -9 0 1 1⟩
| 2.549
|-
| [[676/675]]
| [2 -3 -2 0 0 2⟩
| 2.563
|-
| [[771147/770000]]
| [-4 3 -4 -1 -1 4⟩
| 2.577
|-
| [[765625/764478]]
| [-1 -5 6 2 -2 -1⟩
| 2.596
|-
| [[170625/170368]]
| [-7 1 4 1 -3 1⟩
| 2.610
|-
| [[20480/20449]]
| [12 0 1 0 -2 -2⟩
| 2.623
|-
| [[46656/46585]]
| [6 6 -1 -1 -3⟩
| 2.637
|-
| [[42592/42525]]
| [5 -5 -2 -1 3⟩
| 2.725
|-
| [[61347/61250]]
| [-1 1 -4 -2 2 2⟩
| 2.740
|-
| [[625/624]]
| [-4 -1 4 0 0 -1⟩
| 2.772
|-
| [[78975/78848]]
| [-10 5 2 -1 -1 1⟩
| 2.786
|-
| [[41472/41405]]
| [9 4 -1 -2 0 -2⟩
| 2.799
|-
| [[472392/471625]]
| [3 10 -3 -3 -1⟩
| 2.813
|-
| [[422576/421875]]
| [4 -3 -6 4 1⟩
| 2.874
|-
| [[644204/643125]]
| [2 -1 -4 -3 5⟩
| 2.902
|-
| [[50421/50336]]
| [-5 1 0 5 -2 -1⟩
| 2.921
|-
| [[831875/830466]]
| [-1 -3 4 -1 3 -3⟩
| 2.935
|-
| [[81675/81536]]
| [-7 3 2 -2 2 -1⟩
| 2.949
|-
| [[59150/59049]]
| [1 -10 2 1 0 2⟩
| 2.959
|-
| [[28561/28512]]
| [-5 -4 0 0 -1 4⟩
| 2.973
|-
| [[212992/212625]]
| [14 -5 -3 -1 0 1⟩
| 2.986
|-
| [[4000/3993]]
| [5 -1 3 0 -3⟩
| 3.032
|-
| [[205335/204974]]
| [-1 5 1 -1 -4 2⟩
| 3.046
|-
| [[391314/390625]]
| [1 1 -8 2 3⟩
| 3.051
|-
| [[825000/823543]]
| [3 1 5 -7 1⟩
| 3.060
|-
| [[26411/26364]]
| [-2 -1 0 4 1 -3⟩
| 3.084
|-
| [[83349/83200]]
| [-8 5 -2 3 0 -1⟩
| 3.098
|-
| [[532400/531441]]
| [4 -12 2 0 3⟩
| 3.121
|-
| [[20449/20412]]
| [-2 -6 0 -1 2 2⟩
| 3.135
|-
| [[314171/313600]]
| [-8 0 -2 -2 1 4⟩
| 3.149
|-
| [[806736/805255]]
| [4 1 -1 5 -5⟩
| 3.181
|-
| [[203125/202752]]
| [-11 -2 6 0 -1 1⟩
| 3.182
|-
| [[32000/31941]]
| [8 -3 3 -1 0 -2⟩
| 3.195
|-
| [[540/539]]
| [2 3 1 -2 -1⟩
| 3.209
|-
| [[405769/405000]]
| [-3 -4 -4 4 0 2⟩
| 3.284
|-
| [[322102/321489]]
| [1 -8 0 -2 5⟩
| 3.298
|-
| [[307328/306735]]
| [7 -1 -1 4 -2 -2⟩
| 3.344
|-
| [[166698/166375]]
| [1 5 -3 3 -3⟩
| 3.358
|-
| [[804375/802816]]
| [-14 2 4 -2 1 1⟩
| 3.359
|-
| [[58080/57967]]
| [5 1 1 -3 2 -2⟩
| 3.372
|-
| [[532480/531441]]
| [13 -12 1 0 0 1⟩
| 3.381
|-
| [[24057/24010]]
| [-1 7 -1 -4 1⟩
| 3.386
|-
| [[281216/280665]]
| [7 -6 -1 -1 -1 3⟩
| 3.395
|-
| [[742586/741125]]
| [1 0 -3 -2 -2 5⟩
| 3.409
|-
| [[528125/527076]]
| [-2 -2 5 0 -4 2⟩
| 3.442
|-
| [[456533/455625]]
| [0 -6 -4 3 3⟩
| 3.447
|-
| [[1002001/1000000]]
| [-6 0 -6 2 2 2⟩
| 3.461
|-
| [[718848/717409]]
| [11 3 0 -2 -4 1⟩
| 3.469
|-
| [[60025/59904]]
| [-9 -2 2 4 0 -1⟩
| 3.493
|-
| [[361179/360448]]
| [-15 4 0 3 -1 1⟩
| 3.507
|-
| [[21168/21125]]
| [4 3 -3 2 0 -2⟩
| 3.520
|-
| [[137781/137500]]
| [-2 9 -5 1 -1⟩
| 3.534
|-
| [[386672/385875]]
| [4 -2 -3 -3 1 3⟩
| 3.572
|-
| [[6250/6237]]
| [1 -4 5 -1 -1⟩
| 3.605
|-
| [[190125/189728]]
| [-5 2 3 -2 -2 2⟩
| 3.619
|-
| [[49152/49049]]
| [14 1 0 -3 -1 -1⟩
| 3.632
|-
| [[53361/53248]]
| [-12 2 0 2 2 -1⟩
| 3.670
|-
| [[529254/528125]]
| [1 7 -5 0 2 -2⟩
| 3.697
|-
| [[861224/859375]]
| [3 0 -7 2 -1 3⟩
| 3.721
|-
| [[12005/11979]]
| [0 -2 1 4 -3⟩
| 3.754
|-
| [[1375/1372]]
| [-2 0 3 -3 1⟩
| 3.781
|-
| [[616005/614656]]
| [-8 6 1 -4 0 2⟩
| 3.795
|-
| [[704704/703125]]
| [6 -2 -7 1 2 1⟩
| 3.883
|-
| [[13720/13689]]
| [3 -4 1 3 0 -2⟩
| 3.916
|-
| [[441/440]]
| [-3 2 -1 2 -1⟩
| 3.930
|-
| [[539055/537824]]
| [-5 4 1 -5 3⟩
| 3.958
|-
| [[966680/964467]]
| [3 -9 1 -2 1 3⟩
| 3.968
|-
| [[371293/370440]]
| [-3 -3 -1 -3 0 5⟩
| 3.982
|-
| [[41600/41503]]
| [7 0 2 -3 -2 1⟩
| 4.041
|-
| [[525525/524288]]
| [-19 1 2 2 1 1⟩
| 4.080
|-
| [[847/845]]
| [0 0 -1 1 2 -2⟩
| 4.093
|-
| [[8019/8000]]
| [-6 6 -3 0 1⟩
| 4.107
|-
| [[314928/314171]]
| [4 9 0 0 -1 -4⟩
| 4.166
|-
| [[859375/857304]]
| [-3 -7 7 -2 1⟩
| 4.177
|-
| [[366912/366025]]
| [6 2 -2 2 -4 1⟩
| 4.190
|-
| [[528125/526848]]
| [-9 -1 5 -3 0 2⟩
| 4.191
|-
| [[281600/280917]]
| [10 -2 2 -4 1 -1⟩
| 4.204
|-
| [[16848/16807]]
| [4 4 0 -5 0 1⟩
| 4.218
|-
| [[169169/168750]]
| [-1 -3 -5 1 1 3⟩
| 4.293
|-
| [[42875/42768]]
| [-4 -5 3 3 -1⟩
| 4.326
|-
| [[124215/123904]]
| [-10 1 1 2 -2 2⟩
| 4.340
|-
| [[3584/3575]]
| [9 0 -2 1 -1 -1⟩
| 4.353
|-
| [[75816/75625]]
| [3 6 -4 0 -2 1⟩
| 4.367
|-
| [[761332/759375]]
| [2 -5 -5 0 4 1⟩
| 4.456
|-
| [[741125/739206]]
| [-1 -7 3 2 2 -2⟩
| 4.489
|-
| [[385/384]]
| [-7 -1 1 1 1⟩
| 4.503
|-
| [[495616/494325]]
| [12 -2 -2 0 2 -3⟩
| 4.515
|-
| [[41067/40960]]
| [-13 5 -1 0 0 2⟩
| 4.517
|-
| [[57024/56875]]
| [6 4 -4 -1 1 -1⟩
| 4.530
|-
| [[767637/765625]]
| [0 10 -6 -2 0 1⟩
| 4.544
|-
| [[315000/314171]]
| [3 2 4 1 -1 -4⟩
| 4.562
|-
| [[164025/163592]]
| [-3 8 2 0 -2 -2⟩
| 4.576
|-
| [[322959/322102]]
| [-1 1 0 2 -5 3⟩
| 4.600
|-
| [[65000/64827]]
| [3 -3 4 -4 0 1⟩
| 4.614
|-
| [[823543/821340]]
| [-2 -5 -1 7 0 -2⟩
| 4.637
|-
| [[589824/588245]]
| [16 2 -1 -6⟩
| 4.641
|-
| [[352947/352000]]
| [-8 1 -3 6 -1⟩
| 4.651
|-
| [[73205/73008]]
| [-4 -3 1 0 4 -2⟩
| 4.665
|-
| [[35937/35840]]
| [-10 3 -1 -1 3⟩
| 4.679
|-
| [[200475/199927]]
| [0 6 2 -1 1 -4⟩
| 4.739
|-
| [[313600/312741]]
| [8 -7 2 2 -1 -1⟩
| 4.749
|-
| [[531441/529984]]
| [-6 12 0 -2 0 -2⟩
| 4.753
|-
| [[364/363]]
| [2 -1 0 1 -2 1⟩
| 4.763
|-
| [[533871/532400]]
| [-4 5 -2 0 -3 3⟩
| 4.777
|-
| [[117975/117649]]
| [0 1 2 -6 2 1⟩
| 4.791
|-
| [[147875/147456]]
| [-14 -2 3 1 0 2⟩
| 4.912
|-
| [[352/351]]
| [5 -3 0 0 1 -1⟩
| 4.925
|-
| [[351/350]]
| [-1 3 -2 -1 0 1⟩
| 4.939
|-
| [[328125/327184]]
| [-4 1 6 1 -2 -2⟩
| 4.972
|-
| [[268912/268125]]
| [4 -1 -4 5 -1 -1⟩
| 5.074
|-
| [[166375/165888]]
| [-11 -4 3 0 3⟩
| 5.075
|-
| [[920205/917504]]
| [-17 2 1 -1 2 2⟩
| 5.089
|-
| [[15972/15925]]
| [2 1 -2 -2 3 -1⟩
| 5.102
|-
| [[456976/455625]]
| [4 -6 -4 0 0 4⟩
| 5.126
|-
| [[171875/171366]]
| [-1 -1 6 0 1 -4⟩
| 5.135
|-
| [[151875/151424]]
| [-7 5 4 -1 0 -2⟩
| 5.149
|-
| [[796250/793881]]
| [1 -8 4 2 -2 1⟩
| 5.158
|-
| [[384475/383328]]
| [-5 -2 2 1 -3 3⟩
| 5.172
|-
| [[16384/16335]]
| [14 -3 -1 0 -2⟩
| 5.185
|-
| [[184877/184320]]
| [-12 -2 -1 5 1⟩
| 5.224
|-
| [[203742/203125]]
| [1 3 -6 3 1 -1⟩
| 5.251
|-
| [[805255/802816]]
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|-
|-
| [[16/15]]
| [[16/15]]
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