|
|
Line 225: |
Line 225: |
| | 2<sup>-8</sup> • 5<sup>1</sup> • 7<sup>2</sup> | | | 2<sup>-8</sup> • 5<sup>1</sup> • 7<sup>2</sup> |
| | [[245/256]] | | | [[245/256]] |
| |}
| |
|
| |
| {| class="wikitable center-all left-2 right-3 right-5 left-6 mw-collapsible mw-collapsed"
| |
| |+style=white-space:nowrap| 7-limit ratios tempered out in 12-tet, maximal benedetti height = 3<sup>24</sup>
| |
| ! Ratio
| |
| ! Factorization
| |
| ! Cents
| |
| ! Limit
| |
| ! - Cents
| |
| ! 1 / Factorization
| |
| ! 1 / Ratio
| |
| |-
| |
| | [[531441/524288]]
| |
| | 2<sup>-19</sup> • 3<sup>12</sup>
| |
| | 23.460
| |
| | 3
| |
| | -23.460
| |
| | 2<sup>19</sup> • 3<sup>-12</sup>
| |
| | [[524288/531441]]
| |
| |-
| |
| | [[81/80]]
| |
| | 2<sup>-4</sup> • 3<sup>4</sup> • 5<sup>-1</sup>
| |
| | 21.506
| |
| | 5
| |
| | -21.506
| |
| | 2<sup>4</sup> • 3<sup>-4</sup> • 5<sup>1</sup>
| |
| | [[80/81]]
| |
| |-
| |
| | [[128/125]]
| |
| | 2<sup>7</sup> • 5<sup>-3</sup>
| |
| | 41.059
| |
| | 5
| |
| | -41.059
| |
| | 2<sup>-7</sup> • 5<sup>3</sup>
| |
| | [[125/128]]
| |
| |-
| |
| | [[648/625]]
| |
| | 2<sup>3</sup> • 3<sup>4</sup> • 5<sup>-4</sup>
| |
| | 62.565
| |
| | 5
| |
| | -62.565
| |
| | 2<sup>-3</sup> • 3<sup>-4</sup> • 5<sup>4</sup>
| |
| | [[625/648]]
| |
| |-
| |
| | [[2048/2025]]
| |
| | 2<sup>11</sup> • 3<sup>-4</sup> • 5<sup>-2</sup>
| |
| | 19.553
| |
| | 5
| |
| | -19.553
| |
| | 2<sup>-11</sup> • 3<sup>4</sup> • 5<sup>2</sup>
| |
| | [[2025/2048]]
| |
| |-
| |
| | [[6561/6250]]
| |
| | 2<sup>-1</sup> • 3<sup>8</sup> • 5<sup>-5</sup>
| |
| | 84.071
| |
| | 5
| |
| | -84.071
| |
| | 2<sup>1</sup> • 3<sup>-8</sup> • 5<sup>5</sup>
| |
| | [[6250/6561]]
| |
| |-
| |
| | [[6561/6400]]
| |
| | 2<sup>-8</sup> • 3<sup>8</sup> • 5<sup>-2</sup>
| |
| | 43.013
| |
| | 5
| |
| | -43.013
| |
| | 2<sup>8</sup> • 3<sup>-8</sup> • 5<sup>2</sup>
| |
| | [[6400/6561]]
| |
| |-
| |
| | [[16384/15625]]
| |
| | 2<sup>14</sup> • 5<sup>-6</sup>
| |
| | 82.118
| |
| | 5
| |
| | -82.118
| |
| | 2<sup>-14</sup> • 5<sup>6</sup>
| |
| | [[15625/16384]]
| |
| |-
| |
| | [[32805/32768]]
| |
| | 2<sup>-15</sup> • 3<sup>8</sup> • 5<sup>1</sup>
| |
| | 1.954
| |
| | 5
| |
| | -1.954
| |
| | 2<sup>15</sup> • 3<sup>-8</sup> • 5<sup>-1</sup>
| |
| | [[32768/32805]]
| |
| |-
| |
| | [[82944/78125]]
| |
| | 2<sup>10</sup> • 3<sup>4</sup> • 5<sup>-7</sup>
| |
| | 103.624
| |
| | 5
| |
| | -103.624
| |
| | 2<sup>-10</sup> • 3<sup>-4</sup> • 5<sup>7</sup>
| |
| | [[78125/82944]]
| |
| |-
| |
| | [[262144/253125]]
| |
| | 2<sup>18</sup> • 3<sup>-4</sup> • 5<sup>-5</sup>
| |
| | 60.611
| |
| | 5
| |
| | -60.611
| |
| | 2<sup>-18</sup> • 3<sup>4</sup> • 5<sup>5</sup>
| |
| | [[253125/262144]]
| |
| |-
| |
| | [[419904/390625]]
| |
| | 2<sup>6</sup> • 3<sup>8</sup> • 5<sup>-8</sup>
| |
| | 125.130
| |
| | 5
| |
| | -125.130
| |
| | 2<sup>-6</sup> • 3<sup>-8</sup> • 5<sup>8</sup>
| |
| | [[390625/419904]]
| |
| |-
| |
| | [[531441/500000]]
| |
| | 2<sup>-5</sup> • 3<sup>12</sup> • 5<sup>-6</sup>
| |
| | 105.578
| |
| | 5
| |
| | -105.578
| |
| | 2<sup>5</sup> • 3<sup>-12</sup> • 5<sup>6</sup>
| |
| | [[500000/531441]]
| |
| |-
| |
| | [[531441/512000]]
| |
| | 2<sup>-12</sup> • 3<sup>12</sup> • 5<sup>-3</sup>
| |
| | 64.519
| |
| | 5
| |
| | -64.519
| |
| | 2<sup>12</sup> • 3<sup>-12</sup> • 5<sup>3</sup>
| |
| | [[512000/531441]]
| |
| |-
| |
| | [[36/35]]
| |
| | 2<sup>2</sup> • 3<sup>2</sup> • 5<sup>-1</sup> • 7<sup>-1</sup>
| |
| | 48.770
| |
| | 7
| |
| | -48.770
| |
| | 2<sup>-2</sup> • 3<sup>-2</sup> • 5<sup>1</sup> • 7<sup>1</sup>
| |
| | [[35/36]]
| |
| |-
| |
| | [[50/49]]
| |
| | 2<sup>1</sup> • 5<sup>2</sup> • 7<sup>-2</sup>
| |
| | 34.976
| |
| | 7
| |
| | -34.976
| |
| | 2<sup>-1</sup> • 5<sup>-2</sup> • 7<sup>2</sup>
| |
| | [[49/50]]
| |
| |-
| |
| | [[64/63]]
| |
| | 2<sup>6</sup> • 3<sup>-2</sup> • 7<sup>-1</sup>
| |
| | 27.264
| |
| | 7
| |
| | -27.264
| |
| | 2<sup>-6</sup> • 3<sup>2</sup> • 7<sup>1</sup>
| |
| | [[63/64]]
| |
| |-
| |
| | [[126/125]]
| |
| | 2<sup>1</sup> • 3<sup>2</sup> • 5<sup>-3</sup> • 7<sup>1</sup>
| |
| | 13.795
| |
| | 7
| |
| | -13.795
| |
| | 2<sup>-1</sup> • 3<sup>-2</sup> • 5<sup>3</sup> • 7<sup>-1</sup>
| |
| | [[125/126]]
| |
| |-
| |
| | [[225/224]]
| |
| | 2<sup>-5</sup> • 3<sup>2</sup> • 5<sup>2</sup> • 7<sup>-1</sup>
| |
| | 7.712
| |
| | 7
| |
| | -7.712
| |
| | 2<sup>5</sup> • 3<sup>-2</sup> • 5<sup>-2</sup> • 7<sup>1</sup>
| |
| | [[224/225]]
| |
| |-
| |
| | [[256/245]]
| |
| | 2<sup>8</sup> • 5<sup>-1</sup> • 7<sup>-2</sup>
| |
| | 76.034
| |
| | 7
| |
| | -76.034
| |
| | 2<sup>-8</sup> • 5<sup>1</sup> • 7<sup>2</sup>
| |
| | [[245/256]]
| |
| |-
| |
| | [[360/343]]
| |
| | 2<sup>3</sup> • 3<sup>2</sup> • 5<sup>1</sup> • 7<sup>-3</sup>
| |
| | 83.746
| |
| | 7
| |
| | -83.746
| |
| | 2<sup>-3</sup> • 3<sup>-2</sup> • 5<sup>-1</sup> • 7<sup>3</sup>
| |
| | [[343/360]]
| |
| |-
| |
| | [[405/392]]
| |
| | 2<sup>-3</sup> • 3<sup>4</sup> • 5<sup>1</sup> • 7<sup>-2</sup>
| |
| | 56.482
| |
| | 7
| |
| | -56.482
| |
| | 2<sup>3</sup> • 3<sup>-4</sup> • 5<sup>-1</sup> • 7<sup>2</sup>
| |
| | [[392/405]]
| |
| |-
| |
| | [[729/686]]
| |
| | 2<sup>-1</sup> • 3<sup>6</sup> • 7<sup>-3</sup>
| |
| | 105.252
| |
| | 7
| |
| | -105.252
| |
| | 2<sup>1</sup> • 3<sup>-6</sup> • 7<sup>3</sup>
| |
| | [[686/729]]
| |
| |-
| |
| | [[729/700]]
| |
| | 2<sup>-2</sup> • 3<sup>6</sup> • 5<sup>-2</sup> • 7<sup>-1</sup>
| |
| | 70.277
| |
| | 7
| |
| | -70.277
| |
| | 2<sup>2</sup> • 3<sup>-6</sup> • 5<sup>2</sup> • 7<sup>1</sup>
| |
| | [[700/729]]
| |
| |-
| |
| | [[1296/1225]]
| |
| | 2<sup>4</sup> • 3<sup>4</sup> • 5<sup>-2</sup> • 7<sup>-2</sup>
| |
| | 97.541
| |
| | 7
| |
| | -97.541
| |
| | 2<sup>-4</sup> • 3<sup>-4</sup> • 5<sup>2</sup> • 7<sup>2</sup>
| |
| | [[1225/1296]]
| |
| |-
| |
| | [[2500/2401]]
| |
| | 2<sup>2</sup> • 5<sup>4</sup> • 7<sup>-4</sup>
| |
| | 69.951
| |
| | 7
| |
| | -69.951
| |
| | 2<sup>-2</sup> • 5<sup>-4</sup> • 7<sup>4</sup>
| |
| | [[2401/2500]]
| |
| |-
| |
| | [[2560/2401]]
| |
| | 2<sup>9</sup> • 5<sup>1</sup> • 7<sup>-4</sup>
| |
| | 111.010
| |
| | 7
| |
| | -111.010
| |
| | 2<sup>-9</sup> • 5<sup>-1</sup> • 7<sup>4</sup>
| |
| | [[2401/2560]]
| |
| |-
| |
| | [[2592/2401]]
| |
| | 2<sup>5</sup> • 3<sup>4</sup> • 7<sup>-4</sup>
| |
| | 132.516
| |
| | 7
| |
| | -132.516
| |
| | 2<sup>-5</sup> • 3<sup>-4</sup> • 7<sup>4</sup>
| |
| | [[2401/2592]]
| |
| |-
| |
| | [[3125/3087]]
| |
| | 3<sup>-2</sup> • 5<sup>5</sup> • 7<sup>-3</sup>
| |
| | 21.181
| |
| | 7
| |
| | -21.181
| |
| | 3<sup>2</sup> • 5<sup>-5</sup> • 7<sup>3</sup>
| |
| | [[3087/3125]]
| |
| |-
| |
| | [[3136/3125]]
| |
| | 2<sup>6</sup> • 5<sup>-5</sup> • 7<sup>2</sup>
| |
| | 6.083
| |
| | 7
| |
| | -6.083
| |
| | 2<sup>-6</sup> • 5<sup>5</sup> • 7<sup>-2</sup>
| |
| | [[3125/3136]]
| |
| |-
| |
| | [[3200/3087]]
| |
| | 2<sup>7</sup> • 3<sup>-2</sup> • 5<sup>2</sup> • 7<sup>-3</sup>
| |
| | 62.240
| |
| | 7
| |
| | -62.240
| |
| | 2<sup>-7</sup> • 3<sup>2</sup> • 5<sup>-2</sup> • 7<sup>3</sup>
| |
| | [[3087/3200]]
| |
| |-
| |
| | [[3645/3584]]
| |
| | 2<sup>-9</sup> • 3<sup>6</sup> • 5<sup>1</sup> • 7<sup>-1</sup>
| |
| | 29.218
| |
| | 7
| |
| | -29.218
| |
| | 2<sup>9</sup> • 3<sup>-6</sup> • 5<sup>-1</sup> • 7<sup>1</sup>
| |
| | [[3584/3645]]
| |
| |-
| |
| | [[4000/3969]]
| |
| | 2<sup>5</sup> • 3<sup>-4</sup> • 5<sup>3</sup> • 7<sup>-2</sup>
| |
| | 13.469
| |
| | 7
| |
| | -13.469
| |
| | 2<sup>-5</sup> • 3<sup>4</sup> • 5<sup>-3</sup> • 7<sup>2</sup>
| |
| | [[3969/4000]]
| |
| |-
| |
| | [[4096/3969]]
| |
| | 2<sup>12</sup> • 3<sup>-4</sup> • 7<sup>-2</sup>
| |
| | 54.528
| |
| | 7
| |
| | -54.528
| |
| | 2<sup>-12</sup> • 3<sup>4</sup> • 7<sup>2</sup>
| |
| | [[3969/4096]]
| |
| |-
| |
| | [[4608/4375]]
| |
| | 2<sup>9</sup> • 3<sup>2</sup> • 5<sup>-4</sup> • 7<sup>-1</sup>
| |
| | 89.829
| |
| | 7
| |
| | -89.829
| |
| | 2<sup>-9</sup> • 3<sup>-2</sup> • 5<sup>4</sup> • 7<sup>1</sup>
| |
| | [[4375/4608]]
| |
| |-
| |
| | [[5103/5000]]
| |
| | 2<sup>-3</sup> • 3<sup>6</sup> • 5<sup>-4</sup> • 7<sup>1</sup>
| |
| | 35.301
| |
| | 7
| |
| | -35.301
| |
| | 2<sup>3</sup> • 3<sup>-6</sup> • 5<sup>4</sup> • 7<sup>-1</sup>
| |
| | [[5000/5103]]
| |
| |-
| |
| | [[5120/5103]]
| |
| | 2<sup>10</sup> • 3<sup>-6</sup> • 5<sup>1</sup> • 7<sup>-1</sup>
| |
| | 5.758
| |
| | 7
| |
| | -5.758
| |
| | 2<sup>-10</sup> • 3<sup>6</sup> • 5<sup>-1</sup> • 7<sup>1</sup>
| |
| | [[5103/5120]]
| |
| |-
| |
| | [[5625/5488]]
| |
| | 2<sup>-4</sup> • 3<sup>2</sup> • 5<sup>4</sup> • 7<sup>-3</sup>
| |
| | 42.687
| |
| | 7
| |
| | -42.687
| |
| | 2<sup>4</sup> • 3<sup>-2</sup> • 5<sup>-4</sup> • 7<sup>3</sup>
| |
| | [[5488/5625]]
| |
| |-
| |
| | [[6561/6125]]
| |
| | 3<sup>8</sup> • 5<sup>-3</sup> • 7<sup>-2</sup>
| |
| | 119.047
| |
| | 7
| |
| | -119.047
| |
| | 3<sup>-8</sup> • 5<sup>3</sup> • 7<sup>2</sup>
| |
| | [[6125/6561]]
| |
| |-
| |
| | [[6561/6272]]
| |
| | 2<sup>-7</sup> • 3<sup>8</sup> • 7<sup>-2</sup>
| |
| | 77.988
| |
| | 7
| |
| | -77.988
| |
| | 2<sup>7</sup> • 3<sup>-8</sup> • 7<sup>2</sup>
| |
| | [[6272/6561]]
| |
| |-
| |
| | [[8192/7875]]
| |
| | 2<sup>13</sup> • 3<sup>-2</sup> • 5<sup>-3</sup> • 7<sup>-1</sup>
| |
| | 68.323
| |
| | 7
| |
| | -68.323
| |
| | 2<sup>-13</sup> • 3<sup>2</sup> • 5<sup>3</sup> • 7<sup>1</sup>
| |
| | [[7875/8192]]
| |
| |-
| |
| | [[9216/8575]]
| |
| | 2<sup>10</sup> • 3<sup>2</sup> • 5<sup>-2</sup> • 7<sup>-3</sup>
| |
| | 124.805
| |
| | 7
| |
| | -124.805
| |
| | 2<sup>-10</sup> • 3<sup>-2</sup> • 5<sup>2</sup> • 7<sup>3</sup>
| |
| | [[8575/9216]]
| |
| |-
| |
| | [[10125/9604]]
| |
| | 2<sup>-2</sup> • 3<sup>4</sup> • 5<sup>3</sup> • 7<sup>-4</sup>
| |
| | 91.458
| |
| | 7
| |
| | -91.458
| |
| | 2<sup>2</sup> • 3<sup>-4</sup> • 5<sup>-3</sup> • 7<sup>4</sup>
| |
| | [[9604/10125]]
| |
| |-
| |
| | [[13122/12005]]
| |
| | 2<sup>1</sup> • 3<sup>8</sup> • 5<sup>-1</sup> • 7<sup>-4</sup>
| |
| | 154.023
| |
| | 7
| |
| | -154.023
| |
| | 2<sup>-1</sup> • 3<sup>-8</sup> • 5<sup>1</sup> • 7<sup>4</sup>
| |
| | [[12005/13122]]
| |
| |-
| |
| | [[15876/15625]]
| |
| | 2<sup>2</sup> • 3<sup>4</sup> • 5<sup>-6</sup> • 7<sup>2</sup>
| |
| | 27.590
| |
| | 7
| |
| | -27.590
| |
| | 2<sup>-2</sup> • 3<sup>-4</sup> • 5<sup>6</sup> • 7<sup>-2</sup>
| |
| | [[15625/15876]]
| |
| |-
| |
| | [[16128/15625]]
| |
| | 2<sup>8</sup> • 3<sup>2</sup> • 5<sup>-6</sup> • 7<sup>1</sup>
| |
| | 54.854
| |
| | 7
| |
| | -54.854
| |
| | 2<sup>-8</sup> • 3<sup>-2</sup> • 5<sup>6</sup> • 7<sup>-1</sup>
| |
| | [[15625/16128]]
| |
| |-
| |
| | [[16384/15435]]
| |
| | 2<sup>14</sup> • 3<sup>-2</sup> • 5<sup>-1</sup> • 7<sup>-3</sup>
| |
| | 103.299
| |
| | 7
| |
| | -103.299
| |
| | 2<sup>-14</sup> • 3<sup>2</sup> • 5<sup>1</sup> • 7<sup>3</sup>
| |
| | [[15435/16384]]
| |
| |-
| |
| | [[18000/16807]]
| |
| | 2<sup>4</sup> • 3<sup>2</sup> • 5<sup>3</sup> • 7<sup>-5</sup>
| |
| | 118.722
| |
| | 7
| |
| | -118.722
| |
| | 2<sup>-4</sup> • 3<sup>-2</sup> • 5<sup>-3</sup> • 7<sup>5</sup>
| |
| | [[16807/18000]]
| |
| |-
| |
| | [[18225/16807]]
| |
| | 3<sup>6</sup> • 5<sup>2</sup> • 7<sup>-5</sup>
| |
| | 140.228
| |
| | 7
| |
| | -140.228
| |
| | 3<sup>-6</sup> • 5<sup>-2</sup> • 7<sup>5</sup>
| |
| | [[16807/18225]]
| |
| |-
| |
| | [[18432/16807]]
| |
| | 2<sup>11</sup> • 3<sup>2</sup> • 7<sup>-5</sup>
| |
| | 159.780
| |
| | 7
| |
| | -159.780
| |
| | 2<sup>-11</sup> • 3<sup>-2</sup> • 7<sup>5</sup>
| |
| | [[16807/18432]]
| |
| |-
| |
| | [[23328/21875]]
| |
| | 2<sup>5</sup> • 3<sup>6</sup> • 5<sup>-5</sup> • 7<sup>-1</sup>
| |
| | 111.336
| |
| | 7
| |
| | -111.336
| |
| | 2<sup>-5</sup> • 3<sup>-6</sup> • 5<sup>5</sup> • 7<sup>1</sup>
| |
| | [[21875/23328]]
| |
| |-
| |
| | [[28672/28125]]
| |
| | 2<sup>12</sup> • 3<sup>-2</sup> • 5<sup>-5</sup> • 7<sup>1</sup>
| |
| | 33.347
| |
| | 7
| |
| | -33.347
| |
| | 2<sup>-12</sup> • 3<sup>2</sup> • 5<sup>5</sup> • 7<sup>-1</sup>
| |
| | [[28125/28672]]
| |
| |-
| |
| | [[32768/30625]]
| |
| | 2<sup>15</sup> • 5<sup>-4</sup> • 7<sup>-2</sup>
| |
| | 117.093
| |
| | 7
| |
| | -117.093
| |
| | 2<sup>-15</sup> • 5<sup>4</sup> • 7<sup>2</sup>
| |
| | [[30625/32768]]
| |
| |-
| |
| | [[46656/42875]]
| |
| | 2<sup>6</sup> • 3<sup>6</sup> • 5<sup>-3</sup> • 7<sup>-3</sup>
| |
| | 146.311
| |
| | 7
| |
| | -146.311
| |
| | 2<sup>-6</sup> • 3<sup>-6</sup> • 5<sup>3</sup> • 7<sup>3</sup>
| |
| | [[42875/46656]]
| |
| |-
| |
| | [[50625/50176]]
| |
| | 2<sup>-10</sup> • 3<sup>4</sup> • 5<sup>4</sup> • 7<sup>-2</sup>
| |
| | 15.423
| |
| | 7
| |
| | -15.423
| |
| | 2<sup>10</sup> • 3<sup>-4</sup> • 5<sup>-4</sup> • 7<sup>2</sup>
| |
| | [[50176/50625]]
| |
| |-
| |
| | [[59049/54880]]
| |
| | 2<sup>-5</sup> • 3<sup>10</sup> • 5<sup>-1</sup> • 7<sup>-3</sup>
| |
| | 126.759
| |
| | 7
| |
| | -126.759
| |
| | 2<sup>5</sup> • 3<sup>-10</sup> • 5<sup>1</sup> • 7<sup>3</sup>
| |
| | [[54880/59049]]
| |
| |-
| |
| | [[59049/56000]]
| |
| | 2<sup>-6</sup> • 3<sup>10</sup> • 5<sup>-3</sup> • 7<sup>-1</sup>
| |
| | 91.783
| |
| | 7
| |
| | -91.783
| |
| | 2<sup>6</sup> • 3<sup>-10</sup> • 5<sup>3</sup> • 7<sup>1</sup>
| |
| | [[56000/59049]]
| |
| |-
| |
| | [[59049/57344]]
| |
| | 2<sup>-13</sup> • 3<sup>10</sup> • 7<sup>-1</sup>
| |
| | 50.724
| |
| | 7
| |
| | -50.724
| |
| | 2<sup>13</sup> • 3<sup>-10</sup> • 7<sup>1</sup>
| |
| | [[57344/59049]]
| |
| |-
| |
| | [[65536/60025]]
| |
| | 2<sup>16</sup> • 5<sup>-2</sup> • 7<sup>-4</sup>
| |
| | 152.069
| |
| | 7
| |
| | -152.069
| |
| | 2<sup>-16</sup> • 5<sup>2</sup> • 7<sup>4</sup>
| |
| | [[60025/65536]]
| |
| |-
| |
| | [[78125/76832]]
| |
| | 2<sup>-5</sup> • 5<sup>7</sup> • 7<sup>-4</sup>
| |
| | 28.892
| |
| | 7
| |
| | -28.892
| |
| | 2<sup>5</sup> • 5<sup>-7</sup> • 7<sup>4</sup>
| |
| | [[76832/78125]]
| |
| |-
| |
| | [[81648/78125]]
| |
| | 2<sup>4</sup> • 3<sup>6</sup> • 5<sup>-7</sup> • 7<sup>1</sup>
| |
| | 76.360
| |
| | 7
| |
| | -76.360
| |
| | 2<sup>-4</sup> • 3<sup>-6</sup> • 5<sup>7</sup> • 7<sup>-1</sup>
| |
| | [[78125/81648]]
| |
| |-
| |
| | [[93312/84035]]
| |
| | 2<sup>7</sup> • 3<sup>6</sup> • 5<sup>-1</sup> • 7<sup>-5</sup>
| |
| | 181.287
| |
| | 7
| |
| | -181.287
| |
| | 2<sup>-7</sup> • 3<sup>-6</sup> • 5<sup>1</sup> • 7<sup>5</sup>
| |
| | [[84035/93312]]
| |
| |-
| |
| | [[91125/87808]]
| |
| | 2<sup>-8</sup> • 3<sup>6</sup> • 5<sup>3</sup> • 7<sup>-3</sup>
| |
| | 64.193
| |
| | 7
| |
| | -64.193
| |
| | 2<sup>8</sup> • 3<sup>-6</sup> • 5<sup>-3</sup> • 7<sup>3</sup>
| |
| | [[87808/91125]]
| |
| |-
| |
| | [[118098/109375]]
| |
| | 2<sup>1</sup> • 3<sup>10</sup> • 5<sup>-6</sup> • 7<sup>-1</sup>
| |
| | 132.842
| |
| | 7
| |
| | -132.842
| |
| | 2<sup>-1</sup> • 3<sup>-10</sup> • 5<sup>6</sup> • 7<sup>1</sup>
| |
| | [[109375/118098]]
| |
| |-
| |
| | [[125000/117649]]
| |
| | 2<sup>3</sup> • 5<sup>6</sup> • 7<sup>-6</sup>
| |
| | 104.927
| |
| | 7
| |
| | -104.927
| |
| | 2<sup>-3</sup> • 5<sup>-6</sup> • 7<sup>6</sup>
| |
| | [[117649/125000]]
| |
| |-
| |
| | [[128000/117649]]
| |
| | 2<sup>10</sup> • 5<sup>3</sup> • 7<sup>-6</sup>
| |
| | 145.986
| |
| | 7
| |
| | -145.986
| |
| | 2<sup>-10</sup> • 5<sup>-3</sup> • 7<sup>6</sup>
| |
| | [[117649/128000]]
| |
| |-
| |
| | [[129600/117649]]
| |
| | 2<sup>6</sup> • 3<sup>4</sup> • 5<sup>2</sup> • 7<sup>-6</sup>
| |
| | 167.492
| |
| | 7
| |
| | -167.492
| |
| | 2<sup>-6</sup> • 3<sup>-4</sup> • 5<sup>-2</sup> • 7<sup>6</sup>
| |
| | [[117649/129600]]
| |
| |-
| |
| | [[131072/117649]]
| |
| | 2<sup>17</sup> • 7<sup>-6</sup>
| |
| | 187.045
| |
| | 7
| |
| | -187.045
| |
| | 2<sup>-17</sup> • 7<sup>6</sup>
| |
| | [[117649/131072]]
| |
| |-
| |
| | [[131220/117649]]
| |
| | 2<sup>2</sup> • 3<sup>8</sup> • 5<sup>1</sup> • 7<sup>-6</sup>
| |
| | 188.998
| |
| | 7
| |
| | -188.998
| |
| | 2<sup>-2</sup> • 3<sup>-8</sup> • 5<sup>-1</sup> • 7<sup>6</sup>
| |
| | [[117649/131220]]
| |
| |-
| |
| | [[131072/127575]]
| |
| | 2<sup>17</sup> • 3<sup>-6</sup> • 5<sup>-2</sup> • 7<sup>-1</sup>
| |
| | 46.817
| |
| | 7
| |
| | -46.817
| |
| | 2<sup>-17</sup> • 3<sup>6</sup> • 5<sup>2</sup> • 7<sup>1</sup>
| |
| | [[127575/131072]]
| |
| |-
| |
| | [[140625/134456]]
| |
| | 2<sup>-3</sup> • 3<sup>2</sup> • 5<sup>6</sup> • 7<sup>-5</sup>
| |
| | 77.663
| |
| | 7
| |
| | -77.663
| |
| | 2<sup>3</sup> • 3<sup>-2</sup> • 5<sup>-6</sup> • 7<sup>5</sup>
| |
| | [[134456/140625]]
| |
| |-
| |
| | [[156250/151263]]
| |
| | 2<sup>1</sup> • 3<sup>-2</sup> • 5<sup>7</sup> • 7<sup>-5</sup>
| |
| | 56.156
| |
| | 7
| |
| | -56.156
| |
| | 2<sup>-1</sup> • 3<sup>2</sup> • 5<sup>-7</sup> • 7<sup>5</sup>
| |
| | [[151263/156250]]
| |
| |-
| |
| | [[160000/151263]]
| |
| | 2<sup>8</sup> • 3<sup>-2</sup> • 5<sup>4</sup> • 7<sup>-5</sup>
| |
| | 97.215
| |
| | 7
| |
| | -97.215
| |
| | 2<sup>-8</sup> • 3<sup>2</sup> • 5<sup>-4</sup> • 7<sup>5</sup>
| |
| | [[151263/160000]]
| |
| |-
| |
| | [[163840/151263]]
| |
| | 2<sup>15</sup> • 3<sup>-2</sup> • 5<sup>1</sup> • 7<sup>-5</sup>
| |
| | 138.274
| |
| | 7
| |
| | -138.274
| |
| | 2<sup>-15</sup> • 3<sup>2</sup> • 5<sup>-1</sup> • 7<sup>5</sup>
| |
| | [[151263/163840]]
| |
| |-
| |
| | [[164025/153664]]
| |
| | 2<sup>-6</sup> • 3<sup>8</sup> • 5<sup>2</sup> • 7<sup>-4</sup>
| |
| | 112.964
| |
| | 7
| |
| | -112.964
| |
| | 2<sup>6</sup> • 3<sup>-8</sup> • 5<sup>-2</sup> • 7<sup>4</sup>
| |
| | [[153664/164025]]
| |
| |-
| |
| | [[165888/153125]]
| |
| | 2<sup>11</sup> • 3<sup>4</sup> • 5<sup>-5</sup> • 7<sup>-2</sup>
| |
| | 138.600
| |
| | 7
| |
| | -138.600
| |
| | 2<sup>-11</sup> • 3<sup>-4</sup> • 5<sup>5</sup> • 7<sup>2</sup>
| |
| | [[153125/165888]]
| |
| |-
| |
| | [[200000/194481]]
| |
| | 2<sup>6</sup> • 3<sup>-4</sup> • 5<sup>5</sup> • 7<sup>-4</sup>
| |
| | 48.445
| |
| | 7
| |
| | -48.445
| |
| | 2<sup>-6</sup> • 3<sup>4</sup> • 5<sup>-5</sup> • 7<sup>4</sup>
| |
| | [[194481/200000]]
| |
| |-
| |
| | [[204800/194481]]
| |
| | 2<sup>13</sup> • 3<sup>-4</sup> • 5<sup>2</sup> • 7<sup>-4</sup>
| |
| | 89.504
| |
| | 7
| |
| | -89.504
| |
| | 2<sup>-13</sup> • 3<sup>4</sup> • 5<sup>-2</sup> • 7<sup>4</sup>
| |
| | [[194481/204800]]
| |
| |-
| |
| | [[236196/214375]]
| |
| | 2<sup>2</sup> • 3<sup>10</sup> • 5<sup>-4</sup> • 7<sup>-3</sup>
| |
| | 167.817
| |
| | 7
| |
| | -167.817
| |
| | 2<sup>-2</sup> • 3<sup>-10</sup> • 5<sup>4</sup> • 7<sup>3</sup>
| |
| | [[214375/236196]]
| |
| |-
| |
| | [[253125/235298]]
| |
| | 2<sup>-1</sup> • 3<sup>4</sup> • 5<sup>5</sup> • 7<sup>-6</sup>
| |
| | 126.433
| |
| | 7
| |
| | -126.433
| |
| | 2<sup>1</sup> • 3<sup>-4</sup> • 5<sup>-5</sup> • 7<sup>6</sup>
| |
| | [[235298/253125]]
| |
| |-
| |
| | [[250047/250000]]
| |
| | 2<sup>-4</sup> • 3<sup>6</sup> • 5<sup>-6</sup> • 7<sup>3</sup>
| |
| | 0.325
| |
| | 7
| |
| | -0.325
| |
| | 2<sup>4</sup> • 3<sup>-6</sup> • 5<sup>6</sup> • 7<sup>-3</sup>
| |
| | [[250000/250047]]
| |
| |-
| |
| | [[256000/250047]]
| |
| | 2<sup>11</sup> • 3<sup>-6</sup> • 5<sup>3</sup> • 7<sup>-3</sup>
| |
| | 40.733
| |
| | 7
| |
| | -40.733
| |
| | 2<sup>-11</sup> • 3<sup>6</sup> • 5<sup>-3</sup> • 7<sup>3</sup>
| |
| | [[250047/256000]]
| |
| |-
| |
| | [[262144/250047]]
| |
| | 2<sup>18</sup> • 3<sup>-6</sup> • 7<sup>-3</sup>
| |
| | 81.792
| |
| | 7
| |
| | -81.792
| |
| | 2<sup>-18</sup> • 3<sup>6</sup> • 7<sup>3</sup>
| |
| | [[250047/262144]]
| |
| |-
| |
| | [[295245/268912]]
| |
| | 2<sup>-4</sup> • 3<sup>10</sup> • 5<sup>1</sup> • 7<sup>-5</sup>
| |
| | 161.734
| |
| | 7
| |
| | -161.734
| |
| | 2<sup>4</sup> • 3<sup>-10</sup> • 5<sup>-1</sup> • 7<sup>5</sup>
| |
| | [[268912/295245]]
| |
| |-
| |
| | [[331776/300125]]
| |
| | 2<sup>12</sup> • 3<sup>4</sup> • 5<sup>-3</sup> • 7<sup>-4</sup>
| |
| | 173.575
| |
| | 7
| |
| | -173.575
| |
| | 2<sup>-12</sup> • 3<sup>-4</sup> • 5<sup>3</sup> • 7<sup>4</sup>
| |
| | [[300125/331776]]
| |
| |-
| |
| | [[321489/312500]]
| |
| | 2<sup>-2</sup> • 3<sup>8</sup> • 5<sup>-7</sup> • 7<sup>2</sup>
| |
| | 49.096
| |
| | 7
| |
| | -49.096
| |
| | 2<sup>2</sup> • 3<sup>-8</sup> • 5<sup>7</sup> • 7<sup>-2</sup>
| |
| | [[312500/321489]]
| |
| |-
| |
| | [[321489/320000]]
| |
| | 2<sup>-9</sup> • 3<sup>8</sup> • 5<sup>-4</sup> • 7<sup>2</sup>
| |
| | 8.037
| |
| | 7
| |
| | -8.037
| |
| | 2<sup>9</sup> • 3<sup>-8</sup> • 5<sup>4</sup> • 7<sup>-2</sup>
| |
| | [[320000/321489]]
| |
| |-
| |
| | [[327680/321489]]
| |
| | 2<sup>16</sup> • 3<sup>-8</sup> • 5<sup>1</sup> • 7<sup>-2</sup>
| |
| | 33.022
| |
| | 7
| |
| | -33.022
| |
| | 2<sup>-16</sup> • 3<sup>8</sup> • 5<sup>-1</sup> • 7<sup>2</sup>
| |
| | [[321489/327680]]
| |
| |-
| |
| | [[390625/388962]]
| |
| | 2<sup>-1</sup> • 3<sup>-4</sup> • 5<sup>8</sup> • 7<sup>-4</sup>
| |
| | 7.386
| |
| | 7
| |
| | -7.386
| |
| | 2<sup>1</sup> • 3<sup>4</sup> • 5<sup>-8</sup> • 7<sup>4</sup>
| |
| | [[388962/390625]]
| |
| |-
| |
| | [[395136/390625]]
| |
| | 2<sup>7</sup> • 3<sup>2</sup> • 5<sup>-8</sup> • 7<sup>3</sup>
| |
| | 19.878
| |
| | 7
| |
| | -19.878
| |
| | 2<sup>-7</sup> • 3<sup>-2</sup> • 5<sup>8</sup> • 7<sup>-3</sup>
| |
| | [[390625/395136]]
| |
| |-
| |
| | [[401408/390625]]
| |
| | 2<sup>13</sup> • 5<sup>-8</sup> • 7<sup>2</sup>
| |
| | 47.142
| |
| | 7
| |
| | -47.142
| |
| | 2<sup>-13</sup> • 5<sup>8</sup> • 7<sup>-2</sup>
| |
| | [[390625/401408]]
| |
| |-
| |
| | [[413343/390625]]
| |
| | 3<sup>10</sup> • 5<sup>-8</sup> • 7<sup>1</sup>
| |
| | 97.866
| |
| | 7
| |
| | -97.866
| |
| | 3<sup>-10</sup> • 5<sup>8</sup> • 7<sup>-1</sup>
| |
| | [[390625/413343]]
| |
| |-
| |
| | [[413343/400000]]
| |
| | 2<sup>-7</sup> • 3<sup>10</sup> • 5<sup>-5</sup> • 7<sup>1</sup>
| |
| | 56.807
| |
| | 7
| |
| | -56.807
| |
| | 2<sup>7</sup> • 3<sup>-10</sup> • 5<sup>5</sup> • 7<sup>-1</sup>
| |
| | [[400000/413343]]
| |
| |-
| |
| | [[413343/409600]]
| |
| | 2<sup>-14</sup> • 3<sup>10</sup> • 5<sup>-2</sup> • 7<sup>1</sup>
| |
| | 15.748
| |
| | 7
| |
| | -15.748
| |
| | 2<sup>14</sup> • 3<sup>-10</sup> • 5<sup>2</sup> • 7<sup>-1</sup>
| |
| | [[409600/413343]]
| |
| |-
| |
| | [[472392/420175]]
| |
| | 2<sup>3</sup> • 3<sup>10</sup> • 5<sup>-2</sup> • 7<sup>-5</sup>
| |
| | 202.793
| |
| | 7
| |
| | -202.793
| |
| | 2<sup>-3</sup> • 3<sup>-10</sup> • 5<sup>2</sup> • 7<sup>5</sup>
| |
| | [[420175/472392]]
| |
| |-
| |
| | [[458752/455625]]
| |
| | 2<sup>16</sup> • 3<sup>-6</sup> • 5<sup>-4</sup> • 7<sup>1</sup>
| |
| | 11.841
| |
| | 7
| |
| | -11.841
| |
| | 2<sup>-16</sup> • 3<sup>6</sup> • 5<sup>4</sup> • 7<sup>-1</sup>
| |
| | [[455625/458752]]
| |
| |-
| |
| | [[531441/470596]]
| |
| | 2<sup>-2</sup> • 3<sup>12</sup> • 7<sup>-6</sup>
| |
| | 210.505
| |
| | 7
| |
| | -210.505
| |
| | 2<sup>2</sup> • 3<sup>-12</sup> • 7<sup>6</sup>
| |
| | [[470596/531441]]
| |
| |-
| |
| | [[531441/480200]]
| |
| | 2<sup>-3</sup> • 3<sup>12</sup> • 5<sup>-2</sup> • 7<sup>-4</sup>
| |
| | 175.529
| |
| | 7
| |
| | -175.529
| |
| | 2<sup>3</sup> • 3<sup>-12</sup> • 5<sup>2</sup> • 7<sup>4</sup>
| |
| | [[480200/531441]]
| |
| |-
| |
| | [[524288/496125]]
| |
| | 2<sup>19</sup> • 3<sup>-4</sup> • 5<sup>-3</sup> • 7<sup>-2</sup>
| |
| | 95.587
| |
| | 7
| |
| | -95.587
| |
| | 2<sup>-19</sup> • 3<sup>4</sup> • 5<sup>3</sup> • 7<sup>2</sup>
| |
| | [[496125/524288]]
| |
| |-
| |
| | [[531441/490000]]
| |
| | 2<sup>-4</sup> • 3<sup>12</sup> • 5<sup>-4</sup> • 7<sup>-2</sup>
| |
| | 140.553
| |
| | 7
| |
| | -140.553
| |
| | 2<sup>4</sup> • 3<sup>-12</sup> • 5<sup>4</sup> • 7<sup>2</sup>
| |
| | [[490000/531441]]
| |
| |-
| |
| | [[531441/501760]]
| |
| | 2<sup>-11</sup> • 3<sup>12</sup> • 5<sup>-1</sup> • 7<sup>-2</sup>
| |
| | 99.494
| |
| | 7
| |
| | -99.494
| |
| | 2<sup>11</sup> • 3<sup>-12</sup> • 5<sup>1</sup> • 7<sup>2</sup>
| |
| | [[501760/531441]]
| |
| |} | | |} |