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Line 281: Line 281:
== Commas of the 2.3.5.7 subgroup tempered out in 171edo patent val ==
== Commas of the 2.3.5.7 subgroup tempered out in 171edo patent val ==


Commas with numerator <= 2^40:
Commas with numerator <= 2^48:


{| class="wikitable mw-collapsible mw-collapsed sortable"
{| class="wikitable mw-collapsible mw-collapsed sortable"
Line 288: Line 288:
! [[Cent]]s
! [[Cent]]s
|-
|-
| [[1076168025/1073741824]]
| [[2401/2400]]
| [-30 16 2⟩
| [-5 -1 -2 4⟩
| 3.91
| 0.72
|-
| [[4375/4374]]
| [-1 -7 4 1⟩
| 0.40
|-
|-
| [[10763703445887/10737418240000]]
| [[32805/32768]]
| [-34 22 -4 3⟩
| [-15 8 1⟩
| 4.23
| 1.95
|-
|-
| [[1220703125/1219784832]]
| [[65625/65536]]
| [-7 -4 13 -6⟩
| [-16 1 5 1⟩
| 1.30
| 2.35
|-
|-
| [[128184160768461/128000000000000]]
| [[250047/250000]]
| [-19 3 -12 15⟩
| [-4 6 -6 3⟩
| 2.49
| 0.33
|-
|-
| [[129746337890625/129586085429248]]
| [[420175/419904]]
| [-16 12 12 -11⟩
| [-6 -8 2 5⟩
| 2.14
| 1.12
|-
|-
| [[1312993546389/1310720000000]]
| [[703125/702464]]
| [-24 13 -7 7⟩
| [-11 2 7 -3⟩
| 3.00
| 1.63
|-
|-
| [[137869921875/137438953472]]
| [[2100875/2097152]]
| [-37 1 8 6⟩
| [-21 0 3 5⟩
| 5.42
| 3.07
|-
|-
| [[13841287201/13824000000]]
| [[2460375/2458624]]
| [-15 -3 -6 12⟩
| [-10 9 3 -4⟩
| 2.16
| 1.23
|-
|-
| [[13841287201/13839609375]]
| [[5250987/5242880]]
| [0 -11 -7 12⟩
| [-20 7 -1 4⟩
| 0.21
| 2.67
|-
|-
| [[141279345703125/140737488355328]]
| [[5764801/5760000]]
| [-47 10 11 2⟩
| [-10 -2 -4 8⟩
| 6.65
| 1.44
|-
|-
| [[14348907/14336000]]
| [[14348907/14336000]]
Line 332: Line 336:
| 1.56
| 1.56
|-
|-
| [[152587890625/152202903552]]
| [[19140625/19131876]]
| [-28 -4 16 -1⟩
| [-2 -14 8 2⟩
| 4.37
| 0.79
|-
|-
| [[160137547184727/160000000000000]]
| [[40353607/40310784]]
| [-17 28 -13 1⟩
| [-11 -9 0 9⟩
| 1.49
| 1.84
|-
|-
| [[160163466183/160000000000]]
| [[43046721/43025920]]
| [-14 4 -10 11⟩
| [-9 16 -1 -5⟩
| 1.77
| 0.84
|-
|-
| [[1640558367/1638400000]]
| [[48828125/48771072]]
| [-19 14 -5 3⟩
| [-12 -5 11 -2⟩
| 2.28
| 2.02
|-
|-
| [[16955576821225/16926659444736]]
| [[52734375/52706752]]
| [-17 -17 2 14⟩
| [-6 3 9 -7⟩
| 2.96
| 0.91
|-
|-
| [[1729951171875/1727094849536]]
| [[78125000/78121827]]
| [-21 11 10 -7⟩
| [3 -13 10 -2⟩
| 2.86
| 0.07
|-
|-
| [[176547030625/176319369216]]
| [[95703125/95551488]]
| [-12 -16 4 10⟩
| [-17 -6 9 2⟩
| 2.23
| 2.75
|-
| [[1838265625/1836660096]]
| [-7 -15 6 6⟩
| 1.51
|-
|-
| [[184528125/184473632]]
| [[184528125/184473632]]
| [-5 10 5 -8⟩
| [-5 10 5 -8⟩
| 0.51
| 0.51
|-
| [[19073486328125/19042491875328]]
| [-14 -19 19⟩
| 2.82
|-
| [[19073486328125/19062721117944]]
| [-3 -10 19 -9⟩
| 0.98
|-
| [[19140625/19131876]]
| [-2 -14 8 2⟩
| 0.79
|-
| [[19534128475869/19531250000000]]
| [-7 19 -16 5⟩
| 0.26
|-
|-
| [[200120949/200000000]]
| [[200120949/200000000]]
| [-9 5 -8 7⟩
| [-9 5 -8 7⟩
| 1.05
| 1.05
|-
| [[201060302734375/200385994162176]]
| [-38 -6 12 7⟩
| 5.82
|-
|-
| [[201768035/201326592]]
| [[201768035/201326592]]
Line 396: Line 376:
| 3.79
| 3.79
|-
|-
| [[205891132094649/205520896000000]]
| [[645700815/645657712]]
| [-28 30 -6 -2⟩
| [-4 17 1 -9⟩
| 3.12
| 0.12
|-
|-
| [[205891132094649/205885750000000]]
| [[1076168025/1073741824]]
| [-7 30 -9 -7⟩
| [-30 16 2⟩
| 0.05
| 3.91
|-
|-
| [[2093505859375/2087354105856]]
| [[1220703125/1219784832]]
| [-33 -5 14 3⟩
| [-7 -4 13 -6⟩
| 5.09
| 1.30
|-
|-
| [[2100875/2097152]]
| [[1640558367/1638400000]]
| [-21 0 3 5⟩
| [-19 14 -5 3⟩
| 3.07
| 2.28
|-
|-
| [[21182215236075/21156911906816]]
| [[1838265625/1836660096]]
| [-19 25 2 -9⟩
| [-7 -15 6 6⟩
| 2.07
| 1.51
|-
|-
| [[2152828125/2147483648]]
| [[2152828125/2147483648]]
Line 420: Line 400:
| 4.30
| 4.30
|-
|-
| [[216243896484375/215504279044096]]
| [[3955078125/3954653486]]
| [-42 11 13 -2⟩
| [-1 4 11 -11⟩
| 5.93
| 0.19
|-
| [[4202539929/4194304000]]
| [-25 6 -3 8⟩
| 3.40
|-
|-
| [[2206333462725/2199023255552]]
| [[4306640625/4294967296]]
| [-41 7 2 9⟩
| [-32 2 10 2⟩
| 5.75
| 4.70
|-
|-
| [[23066015625/23018340352]]
| [[6591796875/6576668672]]
| [-26 10 8 -3⟩
| [-27 3 12 -2⟩
| 3.58
| 3.98
|-
|-
| [[232630513987207/231928233984000]]
| [[9191328125/9172942848]]
| [-36 -3 -3 17⟩
| [-22 -7 7 6⟩
| 5.23
| 3.47
|-
|-
| [[232630513987207/232190115840000]]
| [[13841287201/13824000000]]
| [-21 -11 -4 17⟩
| [-15 -3 -6 12⟩
| 3.28
| 2.16
|-
|-
| [[232630513987207/232452293400000]]
| [[13841287201/13839609375]]
| [-6 -19 -5 17⟩
| [0 -11 -7 12⟩
| 1.33
| 0.21
|-
|-
| [[2401/2400]]
| [[23066015625/23018340352]]
| [-5 -1 -2 4⟩
| [-26 10 8 -3⟩
| 0.72
| 3.58
|-
|-
| [[24414062500/24407490807]]
| [[24414062500/24407490807]]
| [2 -20 14 -1⟩
| [2 -20 14 -1⟩
| 0.47
| 0.47
|-
| [[2460375/2458624]]
| [-10 9 3 -4⟩
| 1.23
|-
| [[250047/250000]]
| [-4 6 -6 3⟩
| 0.33
|-
| [[27572864474169/27487790694400]]
| [-40 14 -2 8⟩
| 5.35
|-
| [[282429536481/281974669312]]
| [-24 24 0 -5⟩
| 2.79
|-
| [[282475249000/282429536481]]
| [3 -24 3 10⟩
| 0.28
|-
|-
| [[30517578125/30474952704]]
| [[30517578125/30474952704]]
Line 484: Line 448:
| 1.16
| 1.16
|-
|-
| [[32805/32768]]
| [[34451725707/34359738368]]
| [-15 8 1⟩
| [-35 15 0 4⟩
| 1.95
| 4.63
|-
| [[62523502209/62500000000]]
| [-8 12 -12 6⟩
| 0.65
|-
| [[68919204375/68719476736]]
| [-36 8 4 5⟩
| 5.02
|-
| [[80712601875/80564191232]]
| [-25 17 4 -4⟩
| 3.19
|-
| [[83740234375/83682825624]]
| [-3 -21 12 3⟩
| 1.19
|-
|-
| [[33232930569601/33177600000000]]
| [[94143178827/93952409600]]
| [-20 -4 -8 16⟩
| [-29 23 -2 -1⟩
| 2.88
| 3.51
|-
|-
| [[33232930569601/33215062500000]]
| [[94143178827/94119200000]]
| [-5 -12 -9 16⟩
| [-8 23 -5 -6⟩
| 0.93
| 0.44
|-
|-
| [[3363432789843/3355443200000]]
| [[96889010407/96636764160]]
| [-30 5 -5 12⟩
| [-31 -2 -1 13⟩
| 4.12
| 4.51
|-
|-
| [[3391115364245/3389154437772]]
| [[96889010407/96745881600]]
| [-2 -25 1 14⟩
| [-16 -10 -2 13⟩
| 1.00
| 2.56
|-
|-
| [[34451725707/34359738368]]
| [[96889010407/96855122250]]
| [-35 15 0 4⟩
| [-1 -18 -3 13⟩
| 4.63
| 0.61
|-
|-
| [[35303692060125/35184372088832]]
| [[137869921875/137438953472]]
| [-45 24 3⟩
| [-37 1 8 6⟩
| 5.86
| 5.42
|-
|-
| [[37078857421875/37024595836928]]
| [[152587890625/152202903552]]
| [-17 5 16 -10⟩
| [-28 -4 16 -1⟩
| 2.54
| 4.37
|-
|-
| [[3814697265625/3806658035712]]
| [[160163466183/160000000000]]
| [-23 -3 18 -5⟩
| [-14 4 -10 11⟩
| 3.65
| 1.77
|-
|-
| [[3955078125/3954653486]]
| [[176547030625/176319369216]]
| [-1 4 11 -11⟩
| [-12 -16 4 10⟩
| 0.19
| 2.23
|-
|-
| [[40212060546875/40122452017152]]
| [[282429536481/281974669312]]
| [-23 -14 11 7⟩
| [-24 24 0 -5⟩
| 3.86
| 2.79
|-
|-
| [[40353607/40310784]]
| [[282475249000/282429536481]]
| [-11 -9 0 9⟩
| [3 -24 3 10⟩
| 1.84
| 0.28
|-
|-
| [[418701171875/417942208512]]
| [[418701171875/417942208512]]
Line 536: Line 516:
| 3.14
| 3.14
|-
|-
| [[420175/419904]]
| [[494384765625/493455671296]]
| [-6 -8 2 5⟩
| [-22 4 14 -6⟩
| 1.12
| 3.26
|-
| [[512557306947/512000000000]]
| [-18 21 -9 2⟩
| 1.88
|-
| [[762939453125/762191265024]]
| [-8 -11 17 -5⟩
| 1.70
|-
| [[882735153125/880602513408]]
| [-27 -8 5 10⟩
| 4.19
|-
| [[1312993546389/1310720000000]]
| [-24 13 -7 7⟩
| 3.00
|-
| [[1729951171875/1727094849536]]
| [-21 11 10 -7⟩
| 2.86
|-
| [[2093505859375/2087354105856]]
| [-33 -5 14 3⟩
| 5.09
|-
|-
| [[4202539929/4194304000]]
| [[2206333462725/2199023255552]]
| [-25 6 -3 8⟩
| [-41 7 2 9⟩
| 3.40
| 5.75
|-
|-
| [[43046721/43025920]]
| [[3363432789843/3355443200000]]
| [-9 16 -1 -5⟩
| [-30 5 -5 12⟩
| 0.84
| 4.12
|-
|-
| [[4306640625/4294967296]]
| [[3391115364245/3389154437772]]
| [-32 2 10 2⟩
| [-2 -25 1 14⟩
| 4.70
| 1.00
|-
|-
| [[4375/4374]]
| [[3814697265625/3806658035712]]
| [-1 -7 4 1⟩
| [-23 -3 18 -5⟩
| 0.40
| 3.65
|-
|-
| [[4413675765625/4398046511104]]
| [[4413675765625/4398046511104]]
Line 564: Line 568:
| 0.54
| 0.54
|-
|-
| [[48828125/48771072]]
| [[6053445140625/6044831973376]]
| [-12 -5 11 -2⟩
| [-20 18 6 -8⟩
| 2.02
| 2.47
|-
| [[6104007655641/6103515625000]]
| [-3 2 -17 14⟩
| 0.14
|-
| [[7629394531250/7625597484987]]
| [1 -27 18⟩
| 0.86
|-
| [[8042412109375/8033551259904]]
| [-8 -22 10 7⟩
| 1.91
|-
| [[10763703445887/10737418240000]]
| [-34 22 -4 3⟩
| 4.23
|-
|-
| [[494384765625/493455671296]]
| [[16955576821225/16926659444736]]
| [-22 4 14 -6⟩
| [-17 -17 2 14⟩
| 3.26
| 2.96
|-
|-
| [[50039642934603/50000000000000]]
| [[19073486328125/19042491875328]]
| [-13 11 -14 10⟩
| [-14 -19 19⟩
| 1.37
| 2.82
|-
|-
| [[512557306947/512000000000]]
| [[19073486328125/19062721117944]]
| [-18 21 -9 2⟩
| [-3 -10 19 -9⟩
| 1.88
| 0.98
|-
|-
| [[5250987/5242880]]
| [[19534128475869/19531250000000]]
| [-20 7 -1 4⟩
| [-7 19 -16 5⟩
| 2.67
| 0.26
|-
|-
| [[52734375/52706752]]
| [[21182215236075/21156911906816]]
| [-6 3 9 -7⟩
| [-19 25 2 -9⟩
| 0.91
| 2.07
|-
|-
| [[5764801/5760000]]
| [[27572864474169/27487790694400]]
| [-10 -2 -4 8⟩
| [-40 14 -2 8⟩
| 1.44
| 5.35
|-
|-
| [[6053445140625/6044831973376]]
| [[33232930569601/33177600000000]]
| [-20 18 6 -8⟩
| [-20 -4 -8 16⟩
| 2.47
| 2.88
|-
|-
| [[6104007655641/6103515625000]]
| [[33232930569601/33215062500000]]
| [-3 2 -17 14⟩
| [-5 -12 -9 16⟩
| 0.14
| 0.93
|-
|-
| [[61798095703125/61572651155456]]
| [[35303692060125/35184372088832]]
| [-43 4 17 -1⟩
| [-45 24 3⟩
| 6.33
| 5.86
|-
|-
| [[62523502209/62500000000]]
| [[37078857421875/37024595836928]]
| [-8 12 -12 6⟩
| [-17 5 16 -10⟩
| 0.65
| 2.54
|-
|-
| [[645700815/645657712]]
| [[40212060546875/40122452017152]]
| [-4 17 1 -9⟩
| [-23 -14 11 7⟩
| 0.12
| 3.86
|-
|-
| [[65625/65536]]
| [[50039642934603/50000000000000]]
| [-16 1 5 1⟩
| [-13 11 -14 10⟩
| 2.35
| 1.37
|-
|-
| [[6591796875/6576668672]]
| [[61798095703125/61572651155456]]
| [-27 3 12 -2⟩
| [-43 4 17 -1⟩
| 3.98
| 6.33
|-
|-
| [[68630377364883/68600000000000]]
| [[68630377364883/68600000000000]]
| [-12 29 -11 -3⟩
| [-12 29 -11 -3⟩
| 0.77
| 0.77
|-
| [[68919204375/68719476736]]
| [-36 8 4 5⟩
| 5.02
|-
| [[703125/702464]]
| [-11 2 7 -3⟩
| 1.63
|-
|-
| [[70623526640625/70368744177664]]
| [[70623526640625/70368744177664]]
Line 639: Line 651:
| [-46 6 0 13⟩
| [-46 6 0 13⟩
| 6.47
| 6.47
|-
| [[762939453125/762191265024]]
| [-8 -11 17 -5⟩
| 1.70
|-
| [[7629394531250/7625597484987]]
| [1 -27 18⟩
| 0.86
|-
| [[78125000/78121827]]
| [3 -13 10 -2⟩
| 0.07
|-
| [[8042412109375/8033551259904]]
| [-8 -22 10 7⟩
| 1.91
|-
| [[80712601875/80564191232]]
| [-25 17 4 -4⟩
| 3.19
|-
| [[83740234375/83682825624]]
| [-3 -21 12 3⟩
| 1.19
|-
|-
| [[84777884106125/84537841287168]]
| [[84777884106125/84537841287168]]
| [-32 -9 3 14⟩
| [-32 -9 3 14⟩
| 4.91
| 4.91
|-
| [[882735153125/880602513408]]
| [-27 -8 5 10⟩
| 4.19
|-
| [[9191328125/9172942848]]
| [-22 -7 7 6⟩
| 3.47
|-
| [[94143178827/93952409600]]
| [-29 23 -2 -1⟩
| 3.51
|-
| [[94143178827/94119200000]]
| [-8 23 -5 -6⟩
| 0.44
|-
|-
| [[95367431640625/95105071448064]]
| [[95367431640625/95105071448064]]
Line 692: Line 664:
| 2.93
| 2.93
|-
|-
| [[95703125/95551488]]
| [[128184160768461/128000000000000]]
| [-17 -6 9 2⟩
| [-19 3 -12 15⟩
| 2.75
| 2.49
|-
| [[129746337890625/129586085429248]]
| [-16 12 12 -11⟩
| 2.14
|-
| [[141279345703125/140737488355328]]
| [-47 10 11 2⟩
| 6.65
|-
| [[160137547184727/160000000000000]]
| [-17 28 -13 1⟩
| 1.49
|-
| [[201060302734375/200385994162176]]
| [-38 -6 12 7⟩
| 5.82
|-
| [[205891132094649/205520896000000]]
| [-28 30 -6 -2⟩
| 3.12
|-
| [[205891132094649/205885750000000]]
| [-7 30 -9 -7⟩
| 0.05
|-
| [[216243896484375/215504279044096]]
| [-42 11 13 -2⟩
| 5.93
|-
|-
| [[96889010407/96636764160]]
| [[232630513987207/231928233984000]]
| [-31 -2 -1 13⟩
| [-36 -3 -3 17⟩
| 4.51
| 5.23
|-
|-
| [[96889010407/96745881600]]
| [[232630513987207/232190115840000]]
| [-16 -10 -2 13⟩
| [-21 -11 -4 17⟩
| 2.56
| 3.28
|-
|-
| [[96889010407/96855122250]]
| [[232630513987207/232452293400000]]
| [-1 -18 -3 13⟩
| [-6 -19 -5 17⟩
| 0.61
| 1.33
|}
|}


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