Table of 494edo intervals: Difference between revisions

Line 1:

~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

{| class="wikitable"

~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~

|-

~~: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-07-24 10:24:45 UTC</tt>.<br>~~

| style="text-align:center;" | Step

~~: The original revision id was <tt>354572082</tt>.<br>~~

| | Seventeen limit ratio

~~: The revision comment was: <tt></tt><br>~~

| | Other ratio(s) over five limit

~~The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>~~

| | Five limit ratio

~~<h4>Original Wikitext content:</h4>~~

|-

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">||= Step || Seventeen limit ratio || Other ratio(s) over five limit || Five limit ratio ||

| style="text-align:center;" | 1

~~||= 1 || 442/441 || 540/539, 2401/2400 || 32805/32768 ||~~

| | 442/441

~~||= 2 || 289/288 || 325/324, 385/384, 5120/5103 || 1600000/1594323 ||~~

| | 540/539, 2401/2400

~~||= 3 || 221/220 || 225/224 || 15625/15552 ||~~

| | 32805/32768

~~||= 4 || 169/168 || 176/175, 1029/1024 || 2109375/2097152 ||~~

|-

~~||= 5 || 136/135 || 144/143, 1728/1715 || 393216/390625 ||~~

| style="text-align:center;" | 2

~~||= 6 || 120/119 || 121/120, 126/125 || 78732/78125 ||~~

| | 289/288

~~||= 7 || 99/98 || 33075/32768 || 67108864/66430125 ||~~

| | 325/324, 385/384, 5120/5103

~~||= 8 || 85/84 || 1617/1600 || 2048/2025 ||~~

| | 1600000/1594323

~~||= 9 || 78/77 || || 81/80 ||~~

|-

~~||= 10 || 224/221 || 507/500, 625/616, 51200/50421 || 531441/524288 ||~~

| style="text-align:center;" | 3

~~||= 11 || 64/63 || || 20000/19683 ||~~

| | 221/220

~~||= 12 || 119/117 || 648/637, 686\675 || 3125/3072 ||~~

| | 225/224

~~||= 13 || 55/54 || 83349/81920 || 34171875/33554432 ||~~

| | 15625/15552

~~||= 14 || 50/49 || || 1990656/1953125 ||~~

|-

~~||= 15 || 49/48 || || 1594323/1562500 ||~~

| style="text-align:center;" | 4

~~||= 16 || 45/44 || 12288/12005 || 4194304/4100625 ||~~

| | 169/168

~~||= 17 || 128/125 || || ||~~

| | 176/175, 1029/1024

~~||= 18 || 40/39 || 352/343, 525/512 || 6561/6400 ||~~

| | 2109375/2097152

~~||= 19 || 77/75 || 16807/16384 || 1638400/1594323 ||~~

|-

~~||= 20 || 36/35 || || 250/243 ||~~

| style="text-align:center;" | 5

~~||= 21 || 34/33 || 375/364, 1029/1000 || 16875/16384 ||~~

| | 136/135

~~||= 22 || 33/32 || 4096/3969 || 50331648/48828125 ||~~

| | 144/143, 1728/1715

~~||= 23 || 125/121 || 405/392 || 1953125/1889568 ||~~

| | 393216/390625

~~||= 24 || 91/88 || 512/495, 1323/1280 || 9765625/9437184 ||~~

|-

~~||= 25 || 88/85 || 175/169, 729/704, 3200/3087 || 262144/253125 ||~~

| style="text-align:center;" | 6

~~||= 26 || 28/27 || || 648/625 ||~~

| | 120/119

~~||= 27 || 27/26 || 80/77, 8505/8192 || 531441/512000 ||~~

| | 121/120, 126/125

~~||= 28 || 26/25 || 343/330, 2500/2401 || 20480/19683 ||~~

| | 78732/78125

~~||= 29 || 25/24 || || ||~~

|-

~~||= 30 || 169/162 || 704/675, 2401/2304 || 273375/262144 ||~~

| style="text-align:center;" | 7

~~||= 31 || 117/112 || 256/245 || 5000000/4782969 ||~~

| | 99/98

~~||= 32 || 68/65 || 392/375 || 390625/373248 ||~~

| | 33075/32768

~~||= 33 || 22/21 || 8575/8192 || 17578125/16777216 ||~~

| | 67108864/66430125

~~||= 34 || 85/81 || 150/143, 360/343 || 16384/15625 ||~~

|-

~~||= 35 || 21/20 || || 6561/6250 ||~~

| style="text-align:center;" | 8

~~||= 36 || 81/77 || 16807/16000 || 8388608/7971615 ||~~

| | 85/84

~~||= 37 || 255/242 || || 256/243 ||~~

| | 1617/1600

~~||= 38 || 96/91 || || ||~~

| | 2048/2025

~~||= 39 || 132/125 || 21609/20480 || 4428675/4194304 ||~~

|-

~~||= 40 || 55/52 || 128/121, 200/189 || 62500/59049 ||~~

| style="text-align:center;" | 9

~~||= 41 || 18/17 || 143/135, 343/324 || 78125/73728 ||~~

| | 78/77

~~||= 42 || 35/33 || 16384/15435 || 33554432/31640625 ||~~

| |

~~||= 43 || 17/16 || 625/588 || 82944/78125 ||~~

| | 81/80

~~||= 44 || 117/110 || 1029/968, 1225/1152 || 531441/500000 ||~~

|-

~~||= 45 || 180/169 || 375/352, 2560/2401 || 524288/492375 ||~~

| style="text-align:center;" | 10

~~||= 46 || 16/15 || || ||~~

| | 224/221

~~||= 47 || 125/117 || 576/539 || 2187/2048 ||~~

| | 507/500, 625/616, 51200/50421

~~||= 48 || 77/72 || 16384/15309 || 5120000/4782969 ||~~

| | 531441/524288

~~||= 49 || 15/14 || || 3125/2916 ||~~

|-

~~||= 50 || 338/315 || 338/315, 343/320 || 140625/131072 ||~~

| style="text-align:center;" | 11

~~||= 51 || 130/121 || 189/176, 9216/8575 || 2097152/1953125 ||~~

| | 64/63

~~||= 52 || 128/119 || 242/225, 672/625 || 419904/390625 ||~~

| |

~~||= 53 || 14/13 || 264/245, 2205/2048 || 43046721/4000000 ||~~

| | 20000/19683

~~||= 54 || 55/51 || 539/500, 2592/2401 || 32768/30375 ||~~

|-

~~||= 55 || 27/25 || || ||~~

| style="text-align:center;" | 12

~~||= 56 || 119/110 || 225/208, 250/231, 16807/15552 || 177147/163840 ||~~

| | 119/117

~~||= 57 || 13/12 || 693/640, 1024/945 || 64000/59049 ||~~

| | 648/637, 686\675

~~||= 58 || 243/224 || || 625/576 ||~~

| | 3125/3072

~~||= 59 || 88/81 || 27783/25600 || 2278125/2097152 ||~~

|-

~~||= 60 || 99/91 || 160/147 || 10616832/9765625 ||~~

| style="text-align:center;" | 13

~~||= 61 || 49/45 || || 2125764/1953125 ||~~

| | 55/54

~~||= 62 || 12/11 || 35721/32768 || 67108864/61509375 ||~~

| | 83349/81920

~~||= 63 || 130/119 || 273/250, 375/343 || 2048/1875 ||~~

| | 34171875/33554432

~~||= 64 || 35/32 || || 2187/2000 ||~~

|-

~~||= 65 || 242/221 || 675/616, 16807/15360 || 5242880/4782969 ||~~

| style="text-align:center;" | 14

~~||= 66 || 169/154 || 192/175 || 800/729 ||~~

| | 50/49

~~||= 67 || 56/51 || 100/91, 686/625 || 1125/1024 ||~~

| |

~~||= 68 || 11/10 || 36015/32768 || 3695625/33554432 ||~~

| | 1990656/1953125

~~||= 69 || 54/49 || || 390625/354294 ||~~

|-

~~||= 70 || 75/68 || 182/165, 441/400 || 1953125/1769472 ||~~

| style="text-align:center;" | 15

~~||= 71 || 169/153 || 243/220, 10240/9261 || 4194304/3796875 ||~~

| | 49/48

~~||= 72 || 187/169 || 448/405 || 3456/3125 ||~~

| |

~~||= 73 || 72/65 || 256/231, 567/512 || 177147/160000 ||~~

| | 1594323/1562500

~~||= 74 || 132/119 || 375/338, 539/486, 8000/7203 || 65536/59049 ||~~

|-

~~||= 75 || 10/9 || || ||~~

| style="text-align:center;" | 16

~~||= 76 || 187/168 || 405/364, 600/539, 2401/2160 || 18225/16384 ||~~

| | 45/44

~~||= 77 || 39/35 || 49/44, 4096/3675 || 16000000/14348907 ||~~

| | 12288/12005

~~||= 78 || 125/112 || || 78125/69984 ||~~

| | 4194304/4100625

~~||= 79 || 143/128 || 352/315, 1715/1536 || 1771875/1048576 ||~~

|-

~~||= 80 || 160/143 || 384/343 || 262144/234375 ||~~

| style="text-align:center;" | 17

~~||= 81 || 28/25 || || 17496/15625 ||~~

| | 128/125

~~||= 82 || 55/49 || 16807/15000 || 14348907/12800000 ||~~

| |

~~||= 83 || 91/81 || 539/480, 2700/2401 || 4096/3645 ||~~

| |

~~||= 84 || 9/8 || || ||~~

|-

~~||= 85 || 169/150 || 704/625, 7203/6400 || 295245/262144 ||~~

| style="text-align:center;" | 18

~~||= 86 || 44/39 || 640/567 || 200000/177147 ||~~

| | 40/39

~~||= 87 || 96/85 || 720/637, 847/750, 1372/1215 || 15625/13824 ||~~

| | 352/343, 525/512

~~||= 88 || 112/99 || 9261/8192 || 18984375/1677216 ||~~

| | 6561/6400

~~||= 89 || 17/15 || 162/143, 500/441 || 442368/390625 ||~~

|-

~~||= 90 || 135/119 || 143/126, 245/216 || 177147/156250 ||~~

| style="text-align:center;" | 19

~~||= 91 || 25/22 || 8192/7203 || 8388608/7381125 ||~~

| | 77/75

~~||= 92 || 91/80 || || 256/225 ||~~

| | 16807/16384

~~||= 93 || 351/308 || || 729/640 ||~~

| | 1638400/1594323

~~||= 94 || 154/135 || 19200/16807 || 4782969/4194304 ||~~

|-

~~||= 95 || 8/7 || || 2500/2187 ||~~

| style="text-align:center;" | 20

~~||= 96 || 119/104 || 143/125, 343/300 || 9375/8192 ||~~

| | 36/35

~~||= 97 || 55/48 || 40960/35721 || 33554432/29296875 ||~~

| |

~~||= 98 || 39/34 || 225/196 || 2239488/1953125 ||~~

| | 250/243

~~||= 99 || 147/128 || || 14348907/12500000 ||~~

|-

~~||= 100 || 176/153 || 405/352, 13824/12005 || 524288/455625 ||~~

| style="text-align:center;" | 21

~~||= 101 || 121/105 || || 144/125 ||~~

| | 34/33

~~||= 102 || 15/13 || 396/343, 4725/4096 || 59049/51200 ||~~

| | 375/364, 1029/1000

~~||= 103 || 52/45 || 231/200, 16384/14175 || 204800/177147 ||~~

| | 16875/16384

~~||= 104 || 81/70 || || 125/108 ||~~

|-

~~||= 105 || 51/44 || 625/539, 9261/8000 || 151875/131072 ||~~

| style="text-align:center;" | 22

~~||= 106 || 65/56 || 297/256, 512/441 || 50000000/430446721 ||~~

| | 33/32

~~||= 107 || 136/117 || 726/625, 784/675 || 1953125/1679616 ||~~

| | 4096/3969

~~||= 108 || 64/55 || 11907/10240 || 9765625/8388608 ||~~

| | 50331648/48828125

~~||= 109 || 99/85 || 400/343 || 32768/28125 ||~~

|-

~~||= 110 || 7/6 || || 729/625 ||~~

| style="text-align:center;" | 23

~~||= 111 || 90/77 || 16807/14400 || 4782969/4096000 ||~~

| | 125/121

~~||= 112 || 117/100 || 1024/875 || 2560/2187 ||~~

| | 405/392

~~||= 113 || 75/64 || || ||~~

| | 1953125/1889568

~~||= 114 || 88/75 || 2401/2048 || 2460375/2097152 ||~~

|-

~~||= 115 || 168/143 || 168/143, 288/245 || 625000/531441 ||~~

| style="text-align:center;" | 24

~~||= 116 || 20/17 || 147/125 || 390625/331776 ||~~

| | 91/88

~~||= 117 || 33/28 || 32768/27783 || 67108864/56953125 ||~~

| | 512/495, 1323/1280

~~||= 118 || 85/72 || 405/343 || 18432/15625 ||~~

| | 9765625/9437184

~~||= 119 || 13/11 || 189/160 || 59049/50000 ||~~

|-

~~||= 120 || 200/169 || 625/528, 25600/21609 || 1048576/885735 ||~~

| style="text-align:center;" | 25

~~||= 121 || 32/27 || || ||~~

| | 88/85

~~||= 122 || 108/91 || 640/539 || 1215/1024 ||~~

| | 175/169, 729/704, 3200/3087

~~||= 123 || 170/143 || 196/165, 20000/16807 || 39858075/33554432 ||~~

| | 262144/253125

~~||= 124 || 25/21 || || 15625/13122 ||~~

|-

~~||= 125 || 81/68 || 143/120, 343/288 || 78125/65536 ||~~

| style="text-align:center;" | 26

~~||= 126 || 105/88 || 2048/1715 || 4194304/3515625 ||~~

| | 28/27

~~||= 127 || 153/128 || 448/375 || 93312/78125 ||~~

| |

~~||= 128 || 140/117 || 176/147, 1225/1024 || 4782969/4000000 ||~~

| | 648/625

~~||= 129 || 187/156 || 405/338, 539/450, 2880/2401 || 65536/54675 ||~~

|-

~~||= 130 || 6/5 || || ||~~

| style="text-align:center;" | 27

~~||= 131 || 119/99 || 125/104, 648/539, 2401/2000 || 19683/16384 ||~~

| | 27/26

~~||= 132 || 65/54 || 77/64, 2048/1701 || 640000/531441 ||~~

| | 80/77, 8505/8192

~~||= 133 || 135/112 || || 3125/2592 ||~~

| | 531441/512000

~~||= 134 || 169/140 || 880/729, 3087/2560 || 1265625/1048576 ||~~

|-

~~||= 135 || 110/91 || 1024/847, 1600/1323 || 2359296/1953125 ||~~

| style="text-align:center;" | 28

~~||= 136 || 98/81 || || 472392/390625 ||~~

| | 26/25

~~||= 137 || 40/33 || 19845/16384 || 134217728/110716875 ||~~

| | 343/330, 2500/2401

~~||= 138 || 17/14 || 91/75, 1250/1029 || 4096/3375 ||~~

| | 20480/19683

~~||= 139 || 147/121 || 175/144 || 243/200 ||~~

|-

~~||= 140 || 375/308 || 16807/13824 || 1594323/1310720 ||~~

| style="text-align:center;" | 29

~~||= 141 || 39/32 || 128/105 || 8000/6561 ||~~

| | 25/24

~~||= 142 || 238/195 || || 625/512 ||~~

| |

~~||= 143 || 11/9 || 60025/49152 || 20503125/16777216 ||~~

| |

~~||= 144 || 60/49 || || 1953125/1594323 ||~~

|-

~~||= 145 || 49/40 || || 4782969/3906250 ||~~

| style="text-align:center;" | 30

~~||= 146 || 27/22 || 73728/60025 || 8388608/6834375 ||~~

| | 169/162

~~||= 147 || 338/275 || || 768/625 ||~~

| | 704/675, 2401/2304

~~||= 148 || 16/13 || 315/256 || 19683/16000 ||~~

| | 273375/262144

~~||= 149 || 154/125 || 154/125, 20736/16807 || 655360/531441 ||~~

|-

~~||= 150 || 100/81 || || ||~~

| style="text-align:center;" | 31

~~||= 151 || 21/17 || 225/182, 2000/1617, 2401/1944 || 10125/8192 ||~~

| | 117/112

~~||= 152 || 26/21 || 99/80, 8192/6615 || 160000000/129140163 ||~~

| | 256/245

~~||= 153 || 119/96 || 150/121, 243/196 || 390625/314928 ||~~

| | 5000000/4782969

~~||= 154 || 242/195 || 704/567, 3969/3200 || 1953125/1572864 ||~~

|-

~~||= 155 || 169/136 || 210/169, 875/704, 1280/1029 || 524288/421875 ||~~

| style="text-align:center;" | 32

~~||= 156 || 56/45 || || 3888/3125 ||~~

| | 68/65

~~||= 157 || 81/65 || 96/77, 5103/4096 || 1594323/1280000 ||~~

| | 392/375

~~||= 158 || 156/125 || 343/275, 3000/2401 || 8192/6561 ||~~

| | 390625/373248

~~||= 159 || 5/4 || || ||~~

|-

~~||= 160 || 169/135 || 675/539, 2401/1920 || 164025/131072 ||~~

| style="text-align:center;" | 33

~~||= 161 || 351/280 || 441/352, 1536/1225 || 2000000/1594323 ||~~

| | 22/21

~~||= 162 || 64/51 || 784/625 || 78125/62208 ||~~

| | 8575/8192

~~||= 163 || 44/35 || 5145/4096 || 10546875/8388608 ||~~

| | 17578125/16777216

~~||= 164 || 34/27 || 180/143, 432/343 || 98304/78125 ||~~

|-

~~||= 165 || 63/50 || || 19683/15625 ||~~

| style="text-align:center;" | 34

~~||= 166 || 125/99 || 50421/40000 || 16777216/13286025 ||~~

| | 85/81

~~||= 167 || 91/72 || || 512/405 ||~~

| | 150/143, 360/343

~~||= 168 || 81/64 || || ||~~

| | 16384/15625

~~||= 169 || 280/221 || 308/243, 64000/50421 || 2657205/2097152 ||~~

|-

~~||= 170 || 33/26 || 80/63 || 25000/19683 ||~~

| style="text-align:center;" | 35

~~||= 171 || 108/85 || 286/225, 343/270 || 15625/12288 ||~~

| | 21/20

~~||= 172 || 14/11 || 32768/25725 || 67108864/52734375 ||~~

| |

~~||= 173 || 51/40 || 125/98 || 497664/390625 ||~~

| | 6561/6250

~~||= 174 || 143/112 || 245/192 || 1594323/1250000 ||~~

|-

~~||= 175 || 216/169 || 225/176, 3072/2401 || 1048576/820125 ||~~

| style="text-align:center;" | 36

~~||= 176 || 32/25 || || ||~~

| | 81/77

~~||= 177 || 50/39 || 440/343, 2401/1875 || 6561/5120 ||~~

| | 16807/16000

~~||= 178 || 77/60 || 21600/16807 || 2048000/1594323 ||~~

| | 8388608/7971615

~~||= 179 || 9/7 || || 625/486 ||~~

|-

~~||= 180 || 85/66 || 637/495, 1029/800 || 84375/65536 ||~~

| style="text-align:center;" | 37

~~||= 181 || 156/121 || 165/128, 5120/3969 || 12582912/9765625 ||~~

| | 255/242

~~||= 182 || 351/272 || 484/375, 1568/1215 || 2519424/1953125 ||~~

| |

~~||= 183 || 84/65 || 128/99, 1323/1024 || 48828125/37748736 ||~~

| | 256/243

~~||= 184 || 22/17 || 825/637, 1617/1250, 4000/3087 || 65536/50625 ||~~

|-

~~||= 185 || 35/27 || || 162/125 ||~~

| style="text-align:center;" | 38

~~||= 186 || 100/77 || 16807/12960 || 531441/409600 ||~~

| | 96/91

~~||= 187 || 13/10 || 343/264, 2048/1575 || 25600/19683 ||~~

| |

~~||= 188 || 125/96 || || ||~~

| |

~~||= 189 || 176/135 || 12005/9216 || 1366875/1048576 ||~~

|-

~~||= 190 || 64/49 || || 6250000/4782969 ||~~

| style="text-align:center;" | 39

~~||= 191 || 17/13 || || 1953125/1492992 ||~~

| | 132/125

~~||= 192 || 55/42 || 42875/32768 || 87890625/67108864 ||~~

| | 21609/20480

~~||= 193 || 156/119 || 375/286 || 4096/3125 ||~~

| | 4428675/4194304

~~||= 194 || 21/16 || || 6561/5000 ||~~

|-

~~||= 195 || 221/168 || 405/308, 16807/12800 || 2097152/1594323 ||~~

| style="text-align:center;" | 40

~~||= 196 || 154/117 || || 320/243 ||~~

| | 55/52

~~||= 197 || 112/85 || 120/91 || 675/512 ||~~

| | 128/121, 200/189

~~||= 198 || 33/25 || 21609/16384 || 22143375/16777216 ||~~

| | 62500/59049

~~||= 199 || 119/90 || 160/121, 250/189 || 78125/59049 ||~~

|-

~~||= 200 || 45/34 || 143/108, 847/640, 1323/1000 || 390625/294912 ||~~

| style="text-align:center;" | 41

~~||= 201 || 65/49 || 175/132, 4096/3087 || 8388608/6328125 ||~~

| | 18/17

~~||= 202 || 85/64 || 637/480, 896/675 || 20736/15625 ||~~

| | 143/135, 343/324

~~||= 203 || 117/88 || 512/385, 1701/1280 || 531441/400000 ||~~

| | 78125/73728

~~||= 204 || 225/169 || 539/405, 3200/2401 || 131072/98415 ||~~

|-

~~||= 205 || 4/3 || || ||~~

| style="text-align:center;" | 42

~~||= 206 || 187/140 || 243/182, 720/539, 2401/1800 || 10935/8192 ||~~

| | 35/33

~~||= 207 || 147/110 || 8192/6125 || 6400000/4782969 ||~~

| | 16384/15435

~~||= 208 || 75/56 || || 15625/11664 ||~~

| | 33554432/31640625

~~||= 209 || 169/126 || 343/256 || 703125/524288 ||~~

|-

~~||= 210 || 192/143 || 945/704, 2304/1715 || 524288/390625 ||~~

| style="text-align:center;" | 43

~~||= 211 || 121/90 || 168/125 || 104976/78125 ||~~

| | 17/16

~~||= 212 || 35/26 || 66/49, 11025/8192 || 43046721/32000000 ||~~

| | 625/588

~~||= 213 || 85/63 || 182/135, 539/400, 3240/2401 || 8192/6075 ||~~

| | 82944/78125

~~||= 214 || 27/20 || || ||~~

|-

~~||= 215 || 119/88 || 169/125, 625/462, 21609/16000 || 177147/131072 ||~~

| style="text-align:center;" | 44

~~||= 216 || 65/48 || 256/189 || 80000/59049 ||~~

| | 117/110

~~||= 217 || 476/351 || 847/625, 1215/896 || 3125/2304 ||~~

| | 1029/968, 1225/1152

~~||= 218 || 110/81 || 27783/20480 || 11390625/8388608 ||~~

| | 531441/500000

~~||= 219 || 34/25 || 200/147 || 2654208/1953125 ||~~

|-

~~||= 220 || 49/36 || || 531441/390625 ||~~

| style="text-align:center;" | 45

~~||= 221 || 15/11 || 16384/12005 || 16777216/12301875 ||~~

| | 180/169

~~||= 222 || 153/112 || 273/200 || 512/375 ||~~

| | 375/352, 2560/2401

~~||= 223 || 160/117 || 175/128 || 2187/1600 ||~~

| | 524288/492375

~~||= 224~~

|-

| style="text-align:center;" | 46

| | 16/15

| |

|-

| style="text-align:center;" | 47

| | 125/117

| | 576/539

| | 2187/2048

|-

| style="text-align:center;" | 48

| | 77/72

| | 16384/15309

| | 5120000/4782969

|-

| style="text-align:center;" | 49

| | 15/14

| |

| | 3125/2916

|-

| style="text-align:center;" | 50

| | 338/315

| | 338/315, 343/320

| | 140625/131072

|-

| style="text-align:center;" | 51

| | 130/121

| | 189/176, 9216/8575

| | 2097152/1953125

|-

| style="text-align:center;" | 52

| | 128/119

| | 242/225, 672/625

| | 419904/390625

|-

| style="text-align:center;" | 53

| | 14/13

| | 264/245, 2205/2048

| | 43046721/4000000

|-

| style="text-align:center;" | 54

| | 55/51

| | 539/500, 2592/2401

| | 32768/30375

|-

| style="text-align:center;" | 55

| | 27/25

| |

|-

| style="text-align:center;" | 56

| | 119/110

| | 225/208, 250/231, 16807/15552

| | 177147/163840

|-

| style="text-align:center;" | 57

| | 13/12

| | 693/640, 1024/945

| | 64000/59049

|-

| style="text-align:center;" | 58

| | 243/224

| |

| | 625/576

|-

| style="text-align:center;" | 59

| | 88/81

| | 27783/25600

| | 2278125/2097152

|-

| style="text-align:center;" | 60

| | 99/91

| | 160/147

| | 10616832/9765625

|-

| style="text-align:center;" | 61

| | 49/45

| |

| | 2125764/1953125

|-

| style="text-align:center;" | 62

| | 12/11

| | 35721/32768

| | 67108864/61509375

|-

| style="text-align:center;" | 63

| | 130/119

| | 273/250, 375/343

| | 2048/1875

|-

| style="text-align:center;" | 64

| | 35/32

| |

| | 2187/2000

|-

| style="text-align:center;" | 65

| | 242/221

| | 675/616, 16807/15360

| | 5242880/4782969

|-

| style="text-align:center;" | 66

| | 169/154

| | 192/175

| | 800/729

|-

| style="text-align:center;" | 67

| | 56/51

| | 100/91, 686/625

| | 1125/1024

|-

| style="text-align:center;" | 68

| | 11/10

| |

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{| class="wikitable"
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+|-
-: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-07-24 10:24:45 UTC</tt>.<br>
+| style="text-align:center;" | Step
-: The original revision id was <tt>354572082</tt>.<br>
+| | Seventeen limit ratio
-: The revision comment was: <tt></tt><br>
+| | Other ratio(s) over five limit
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
+| | Five limit ratio
-<h4>Original Wikitext content:</h4>
+|-
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">||= Step || Seventeen limit ratio || Other ratio(s) over five limit || Five limit ratio ||
+| style="text-align:center;" | 1
-||= 1 || 442/441 || 540/539, 2401/2400 || 32805/32768 ||
+| | 442/441
-||= 2 || 289/288 || 325/324, 385/384, 5120/5103 || 1600000/1594323 ||
+| | 540/539, 2401/2400
-||= 3 || 221/220 || 225/224 || 15625/15552 ||
+| | 32805/32768
-||= 4 || 169/168 || 176/175, 1029/1024 || 2109375/2097152 ||
+|-
-||= 5 || 136/135 || 144/143, 1728/1715 || 393216/390625 ||
+| style="text-align:center;" | 2
-||= 6 || 120/119 || 121/120, 126/125 || 78732/78125 ||
+| | 289/288
-||= 7 || 99/98 || 33075/32768 || 67108864/66430125 ||
+| | 325/324, 385/384, 5120/5103
-||= 8 || 85/84 || 1617/1600 || 2048/2025 ||
+| | 1600000/1594323
-||= 9 || 78/77 ||   || 81/80 ||
+|-
-||= 10 || 224/221 || 507/500, 625/616, 51200/50421 || 531441/524288 ||
+| style="text-align:center;" | 3
-||= 11 || 64/63 ||   || 20000/19683 ||
+| | 221/220
-||= 12 || 119/117 || 648/637, 686\675 || 3125/3072 ||
+| | 225/224
-||= 13 || 55/54 || 83349/81920 || 34171875/33554432 ||
+| | 15625/15552
-||= 14 || 50/49 ||   || 1990656/1953125 ||
+|-
-||= 15 || 49/48 ||   || 1594323/1562500 ||
+| style="text-align:center;" | 4
-||= 16 || 45/44 || 12288/12005 || 4194304/4100625 ||
+| | 169/168
-||= 17 || 128/125 ||   ||   ||
+| | 176/175, 1029/1024
-||= 18 || 40/39 || 352/343, 525/512 || 6561/6400 ||
+| | 2109375/2097152
-||= 19 || 77/75 || 16807/16384 || 1638400/1594323 ||
+|-
-||= 20 || 36/35 ||   || 250/243 ||
+| style="text-align:center;" | 5
-||= 21 || 34/33 || 375/364, 1029/1000 || 16875/16384 ||
+| | 136/135
-||= 22 || 33/32 || 4096/3969 || 50331648/48828125 ||
+| | 144/143, 1728/1715
-||= 23 || 125/121 || 405/392 || 1953125/1889568 ||
+| | 393216/390625
-||= 24 || 91/88 || 512/495, 1323/1280 || 9765625/9437184 ||
+|-
-||= 25 || 88/85 || 175/169, 729/704, 3200/3087 || 262144/253125 ||
+| style="text-align:center;" | 6
-||= 26 || 28/27 ||   || 648/625 ||
+| | 120/119
-||= 27 || 27/26 || 80/77, 8505/8192 || 531441/512000 ||
+| | 121/120, 126/125
-||= 28 || 26/25 || 343/330, 2500/2401 || 20480/19683 ||
+| | 78732/78125
-||= 29 || 25/24 ||   ||   ||
+|-
-||= 30 || 169/162 || 704/675, 2401/2304 || 273375/262144 ||
+| style="text-align:center;" | 7
-||= 31 || 117/112 || 256/245 || 5000000/4782969 ||
+| | 99/98
-||= 32 || 68/65 || 392/375 || 390625/373248 ||
+| | 33075/32768
-||= 33 || 22/21 || 8575/8192 || 17578125/16777216 ||
+| | 67108864/66430125
-||= 34 || 85/81 || 150/143, 360/343 || 16384/15625 ||
+|-
-||= 35 || 21/20 ||   || 6561/6250 ||
+| style="text-align:center;" | 8
-||= 36 || 81/77 || 16807/16000 || 8388608/7971615 ||
+| | 85/84
-||= 37 || 255/242 ||   || 256/243 ||
+| | 1617/1600
-||= 38 || 96/91 ||   ||   ||
+| | 2048/2025
-||= 39 || 132/125 || 21609/20480 || 4428675/4194304 ||
+|-
-||= 40 || 55/52 || 128/121, 200/189 || 62500/59049 ||
+| style="text-align:center;" | 9
-||= 41 || 18/17 || 143/135, 343/324 || 78125/73728 ||
+| | 78/77
-||= 42 || 35/33 || 16384/15435 || 33554432/31640625 ||
+| |
-||= 43 || 17/16 || 625/588 || 82944/78125 ||
+| | 81/80
-||= 44 || 117/110 || 1029/968, 1225/1152 || 531441/500000 ||
+|-
-||= 45 || 180/169 || 375/352, 2560/2401 || 524288/492375 ||
+| style="text-align:center;" | 10
-||= 46 || 16/15 ||   ||   ||
+| | 224/221
-||= 47 || 125/117 || 576/539 || 2187/2048 ||
+| | 507/500, 625/616, 51200/50421
-||= 48 || 77/72 || 16384/15309 || 5120000/4782969 ||
+| | 531441/524288
-||= 49 || 15/14 ||   || 3125/2916 ||
+|-
-||= 50 || 338/315 || 338/315, 343/320 || 140625/131072 ||
+| style="text-align:center;" | 11
-||= 51 || 130/121 || 189/176, 9216/8575 || 2097152/1953125 ||
+| | 64/63
-||= 52 || 128/119 || 242/225, 672/625 || 419904/390625 ||
+| |
-||= 53 || 14/13 || 264/245, 2205/2048 || 43046721/4000000 ||
+| | 20000/19683
-||= 54 || 55/51 || 539/500, 2592/2401 || 32768/30375 ||
+|-
-||= 55 || 27/25 ||   ||   ||
+| style="text-align:center;" | 12
-||= 56 || 119/110 || 225/208, 250/231, 16807/15552 || 177147/163840 ||
+| | 119/117
-||= 57 || 13/12 || 693/640, 1024/945 || 64000/59049 ||
+| | 648/637, 686\675
-||= 58 || 243/224 ||   || 625/576 ||
+| | 3125/3072
-||= 59 || 88/81 || 27783/25600 || 2278125/2097152 ||
+|-
-||= 60 || 99/91 || 160/147 || 10616832/9765625 ||
+| style="text-align:center;" | 13
-||= 61 || 49/45 ||   || 2125764/1953125 ||
+| | 55/54
-||= 62 || 12/11 || 35721/32768 || 67108864/61509375 ||
+| | 83349/81920
-||= 63 || 130/119 || 273/250, 375/343 || 2048/1875 ||
+| | 34171875/33554432
-||= 64 || 35/32 ||   || 2187/2000 ||
+|-
-||= 65 || 242/221 || 675/616, 16807/15360 || 5242880/4782969 ||
+| style="text-align:center;" | 14
-||= 66 || 169/154 || 192/175 || 800/729 ||
+| | 50/49
-||= 67 || 56/51 || 100/91, 686/625 || 1125/1024 ||
+| |
-||= 68 || 11/10 || 36015/32768 || 3695625/33554432 ||
+| | 1990656/1953125
-||= 69 || 54/49 ||   || 390625/354294 ||
+|-
-||= 70 || 75/68 || 182/165, 441/400 || 1953125/1769472 ||
+| style="text-align:center;" | 15
-||= 71 || 169/153 || 243/220, 10240/9261 || 4194304/3796875 ||
+| | 49/48
-||= 72 || 187/169 || 448/405 || 3456/3125 ||
+| |
-||= 73 || 72/65 || 256/231, 567/512 || 177147/160000 ||
+| | 1594323/1562500
-||= 74 || 132/119 || 375/338, 539/486, 8000/7203 || 65536/59049 ||
+|-
-||= 75 || 10/9 ||   ||   ||
+| style="text-align:center;" | 16
-||= 76 || 187/168 || 405/364, 600/539, 2401/2160 || 18225/16384 ||
+| | 45/44
-||= 77 || 39/35 || 49/44, 4096/3675 || 16000000/14348907 ||
+| | 12288/12005
-||= 78 || 125/112 ||   || 78125/69984 ||
+| | 4194304/4100625
-||= 79 || 143/128 || 352/315, 1715/1536 || 1771875/1048576 ||
+|-
-||= 80 || 160/143 || 384/343 || 262144/234375 ||
+| style="text-align:center;" | 17
-||= 81 || 28/25 ||   || 17496/15625 ||
+| | 128/125
-||= 82 || 55/49 || 16807/15000 || 14348907/12800000 ||
+| |
-||= 83 || 91/81 || 539/480, 2700/2401 || 4096/3645 ||
+| |
-||= 84 || 9/8 ||   ||   ||
+|-
-||= 85 || 169/150 || 704/625, 7203/6400 || 295245/262144 ||
+| style="text-align:center;" | 18
-||= 86 || 44/39 || 640/567 || 200000/177147 ||
+| | 40/39
-||= 87 || 96/85 || 720/637, 847/750, 1372/1215 || 15625/13824 ||
+| | 352/343, 525/512
-||= 88 || 112/99 || 9261/8192 || 18984375/1677216 ||
+| | 6561/6400
-||= 89 || 17/15 || 162/143, 500/441 || 442368/390625 ||
+|-
-||= 90 || 135/119 || 143/126, 245/216 || 177147/156250 ||
+| style="text-align:center;" | 19
-||= 91 || 25/22 || 8192/7203 || 8388608/7381125 ||
+| | 77/75
-||= 92 || 91/80 ||   || 256/225 ||
+| | 16807/16384
-||= 93 || 351/308 ||   || 729/640 ||
+| | 1638400/1594323
-||= 94 || 154/135 || 19200/16807 || 4782969/4194304 ||
+|-
-||= 95 || 8/7 ||   || 2500/2187 ||
+| style="text-align:center;" | 20
-||= 96 || 119/104 || 143/125, 343/300 || 9375/8192 ||
+| | 36/35
-||= 97 || 55/48 || 40960/35721 || 33554432/29296875 ||
+| |
-||= 98 || 39/34 || 225/196 || 2239488/1953125 ||
+| | 250/243
-||= 99 || 147/128 ||   || 14348907/12500000 ||
+|-
-||= 100 || 176/153 || 405/352, 13824/12005 || 524288/455625 ||
+| style="text-align:center;" | 21
-||= 101 || 121/105 ||   || 144/125 ||
+| | 34/33
-||= 102 || 15/13 || 396/343, 4725/4096 || 59049/51200 ||
+| | 375/364, 1029/1000
-||= 103 || 52/45 || 231/200, 16384/14175 || 204800/177147 ||
+| | 16875/16384
-||= 104 || 81/70 ||   || 125/108 ||
+|-
-||= 105 || 51/44 || 625/539, 9261/8000 || 151875/131072 ||
+| style="text-align:center;" | 22
-||= 106 || 65/56 || 297/256, 512/441 || 50000000/430446721 ||
+| | 33/32
-||= 107 || 136/117 || 726/625, 784/675 || 1953125/1679616 ||
+| | 4096/3969
-||= 108 || 64/55 || 11907/10240 || 9765625/8388608 ||
+| | 50331648/48828125
-||= 109 || 99/85 || 400/343 || 32768/28125 ||
+|-
-||= 110 || 7/6 ||   || 729/625 ||
+| style="text-align:center;" | 23
-||= 111 || 90/77 || 16807/14400 || 4782969/4096000 ||
+| | 125/121
-||= 112 || 117/100 || 1024/875 || 2560/2187 ||
+| | 405/392
-||= 113 || 75/64 ||   ||   ||
+| | 1953125/1889568
-||= 114 || 88/75 || 2401/2048 || 2460375/2097152 ||
+|-
-||= 115 || 168/143 || 168/143, 288/245 || 625000/531441 ||
+| style="text-align:center;" | 24
-||= 116 || 20/17 || 147/125 || 390625/331776 ||
+| | 91/88
-||= 117 || 33/28 || 32768/27783 || 67108864/56953125 ||
+| | 512/495, 1323/1280
-||= 118 || 85/72 || 405/343 || 18432/15625 ||
+| | 9765625/9437184
-||= 119 || 13/11 || 189/160 || 59049/50000 ||
+|-
-||= 120 || 200/169 || 625/528, 25600/21609 || 1048576/885735 ||
+| style="text-align:center;" | 25
-||= 121 || 32/27 ||   ||   ||
+| | 88/85
-||= 122 || 108/91 || 640/539 || 1215/1024 ||
+| | 175/169, 729/704, 3200/3087
-||= 123 || 170/143 || 196/165, 20000/16807 || 39858075/33554432 ||
+| | 262144/253125
-||= 124 || 25/21 ||   || 15625/13122 ||
+|-
-||= 125 || 81/68 || 143/120, 343/288 || 78125/65536 ||
+| style="text-align:center;" | 26
-||= 126 || 105/88 || 2048/1715 || 4194304/3515625 ||
+| | 28/27
-||= 127 || 153/128 || 448/375 || 93312/78125 ||
+| |
-||= 128 || 140/117 || 176/147, 1225/1024 || 4782969/4000000 ||
+| | 648/625
-||= 129 || 187/156 || 405/338, 539/450, 2880/2401 || 65536/54675 ||
+|-
-||= 130 || 6/5 ||   ||   ||
+| style="text-align:center;" | 27
-||= 131 || 119/99 || 125/104, 648/539, 2401/2000 || 19683/16384 ||
+| | 27/26
-||= 132 || 65/54 || 77/64, 2048/1701 || 640000/531441 ||
+| | 80/77, 8505/8192
-||= 133 || 135/112 ||   || 3125/2592 ||
+| | 531441/512000
-||= 134 || 169/140 || 880/729, 3087/2560 || 1265625/1048576 ||
+|-
-||= 135 || 110/91 || 1024/847, 1600/1323 || 2359296/1953125 ||
+| style="text-align:center;" | 28
-||= 136 || 98/81 ||   || 472392/390625 ||
+| | 26/25
-||= 137 || 40/33 || 19845/16384 || 134217728/110716875 ||
+| | 343/330, 2500/2401
-||= 138 || 17/14 || 91/75, 1250/1029 || 4096/3375 ||
+| | 20480/19683
-||= 139 || 147/121 || 175/144 || 243/200 ||
+|-
-||= 140 || 375/308 || 16807/13824 || 1594323/1310720 ||
+| style="text-align:center;" | 29
-||= 141 || 39/32 || 128/105 || 8000/6561 ||
+| | 25/24
-||= 142 || 238/195 ||   || 625/512 ||
+| |
-||= 143 || 11/9 || 60025/49152 || 20503125/16777216 ||
+| |
-||= 144 || 60/49 ||   || 1953125/1594323 ||
+|-
-||= 145 || 49/40 ||   || 4782969/3906250 ||
+| style="text-align:center;" | 30
-||= 146 || 27/22 || 73728/60025 || 8388608/6834375 ||
+| | 169/162
-||= 147 || 338/275 ||   || 768/625 ||
+| | 704/675, 2401/2304
-||= 148 || 16/13 || 315/256 || 19683/16000 ||
+| | 273375/262144
-||= 149 || 154/125 || 154/125, 20736/16807 || 655360/531441 ||
+|-
-||= 150 || 100/81 ||   ||   ||
+| style="text-align:center;" | 31
-||= 151 || 21/17 || 225/182, 2000/1617, 2401/1944 || 10125/8192 ||
+| | 117/112
-||= 152 || 26/21 || 99/80, 8192/6615 || 160000000/129140163 ||
+| | 256/245
-||= 153 || 119/96 || 150/121, 243/196 || 390625/314928 ||
+| | 5000000/4782969
-||= 154 || 242/195 || 704/567, 3969/3200 || 1953125/1572864 ||
+|-
-||= 155 || 169/136 || 210/169, 875/704, 1280/1029 || 524288/421875 ||
+| style="text-align:center;" | 32
-||= 156 || 56/45 ||   || 3888/3125 ||
+| | 68/65
-||= 157 || 81/65 || 96/77, 5103/4096 || 1594323/1280000 ||
+| | 392/375
-||= 158 || 156/125 || 343/275, 3000/2401 || 8192/6561 ||
+| | 390625/373248
-||= 159 || 5/4 ||   ||   ||
+|-
-||= 160 || 169/135 || 675/539, 2401/1920 || 164025/131072 ||
+| style="text-align:center;" | 33
-||= 161 || 351/280 || 441/352, 1536/1225 || 2000000/1594323 ||
+| | 22/21
-||= 162 || 64/51 || 784/625 || 78125/62208 ||
+| | 8575/8192
-||= 163 || 44/35 || 5145/4096 || 10546875/8388608 ||
+| | 17578125/16777216
-||= 164 || 34/27 || 180/143, 432/343 || 98304/78125 ||
+|-
-||= 165 || 63/50 ||   || 19683/15625 ||
+| style="text-align:center;" | 34
-||= 166 || 125/99 || 50421/40000 || 16777216/13286025 ||
+| | 85/81
-||= 167 || 91/72 ||   || 512/405 ||
+| | 150/143, 360/343
-||= 168 || 81/64 ||   ||   ||
+| | 16384/15625
-||= 169 || 280/221 || 308/243, 64000/50421 || 2657205/2097152 ||
+|-
-||= 170 || 33/26 || 80/63 || 25000/19683 ||
+| style="text-align:center;" | 35
-||= 171 || 108/85 || 286/225, 343/270 || 15625/12288 ||
+| | 21/20
-||= 172 || 14/11 || 32768/25725 || 67108864/52734375 ||
+| |
-||= 173 || 51/40 || 125/98 || 497664/390625 ||
+| | 6561/6250
-||= 174 || 143/112 || 245/192 || 1594323/1250000 ||
+|-
-||= 175 || 216/169 || 225/176, 3072/2401 || 1048576/820125 ||
+| style="text-align:center;" | 36
-||= 176 || 32/25 ||   ||   ||
+| | 81/77
-||= 177 || 50/39 || 440/343, 2401/1875 || 6561/5120 ||
+| | 16807/16000
-||= 178 || 77/60 || 21600/16807 || 2048000/1594323 ||
+| | 8388608/7971615
-||= 179 || 9/7 ||   || 625/486 ||
+|-
-||= 180 || 85/66 || 637/495, 1029/800 || 84375/65536 ||
+| style="text-align:center;" | 37
-||= 181 || 156/121 || 165/128, 5120/3969 || 12582912/9765625 ||
+| | 255/242
-||= 182 || 351/272 || 484/375, 1568/1215 || 2519424/1953125 ||
+| |
-||= 183 || 84/65 || 128/99, 1323/1024 || 48828125/37748736 ||
+| | 256/243
-||= 184 || 22/17 || 825/637, 1617/1250, 4000/3087 || 65536/50625 ||
+|-
-||= 185 || 35/27 ||   || 162/125 ||
+| style="text-align:center;" | 38
-||= 186 || 100/77 || 16807/12960 || 531441/409600 ||
+| | 96/91
-||= 187 || 13/10 || 343/264, 2048/1575 || 25600/19683 ||
+| |
-||= 188 || 125/96 ||   ||   ||
+| |
-||= 189 || 176/135 || 12005/9216 || 1366875/1048576 ||
+|-
-||= 190 || 64/49 ||   || 6250000/4782969 ||
+| style="text-align:center;" | 39
-||= 191 || 17/13 ||   || 1953125/1492992 ||
+| | 132/125
-||= 192 || 55/42 || 42875/32768 || 87890625/67108864 ||
+| | 21609/20480
-||= 193 || 156/119 || 375/286 || 4096/3125 ||
+| | 4428675/4194304
-||= 194 || 21/16 ||   || 6561/5000 ||
+|-
-||= 195 || 221/168 || 405/308, 16807/12800 || 2097152/1594323 ||
+| style="text-align:center;" | 40
-||= 196 || 154/117 ||   || 320/243 ||
+| | 55/52
-||= 197 || 112/85 || 120/91 || 675/512 ||
+| | 128/121, 200/189
-||= 198 || 33/25 || 21609/16384 || 22143375/16777216 ||
+| | 62500/59049
-||= 199 || 119/90 || 160/121, 250/189 || 78125/59049 ||
+|-
-||= 200 || 45/34 || 143/108, 847/640, 1323/1000 || 390625/294912 ||
+| style="text-align:center;" | 41
-||= 201 || 65/49 || 175/132, 4096/3087 || 8388608/6328125 ||
+| | 18/17
-||= 202 || 85/64 || 637/480, 896/675 || 20736/15625 ||
+| | 143/135, 343/324
-||= 203 || 117/88 || 512/385, 1701/1280 || 531441/400000 ||
+| | 78125/73728
-||= 204 || 225/169 || 539/405, 3200/2401 || 131072/98415 ||
+|-
-||= 205 || 4/3 ||   ||   ||
+| style="text-align:center;" | 42
-||= 206 || 187/140 || 243/182, 720/539, 2401/1800 || 10935/8192 ||
+| | 35/33
-||= 207 || 147/110 || 8192/6125 || 6400000/4782969 ||
+| | 16384/15435
-||= 208 || 75/56 ||   || 15625/11664 ||
+| | 33554432/31640625
-||= 209 || 169/126 || 343/256 || 703125/524288 ||
+|-
-||= 210 || 192/143 || 945/704, 2304/1715 || 524288/390625 ||
+| style="text-align:center;" | 43
-||= 211 || 121/90 || 168/125 || 104976/78125 ||
+| | 17/16
-||= 212 || 35/26 || 66/49, 11025/8192 || 43046721/32000000 ||
+| | 625/588
-||= 213 || 85/63 || 182/135, 539/400, 3240/2401 || 8192/6075 ||
+| | 82944/78125
-||= 214 || 27/20 ||   ||   ||
+|-
-||= 215 || 119/88 || 169/125, 625/462, 21609/16000 || 177147/131072 ||
+| style="text-align:center;" | 44
-||= 216 || 65/48 || 256/189 || 80000/59049 ||
+| | 117/110
-||= 217 || 476/351 || 847/625, 1215/896 || 3125/2304 ||
+| | 1029/968, 1225/1152
-||= 218 || 110/81 || 27783/20480 || 11390625/8388608 ||
+| | 531441/500000
-||= 219 || 34/25 || 200/147 || 2654208/1953125 ||
+|-
-||= 220 || 49/36 ||   || 531441/390625 ||
+| style="text-align:center;" | 45
-||= 221 || 15/11 || 16384/12005 || 16777216/12301875 ||
+| | 180/169
-||= 222 || 153/112 || 273/200 || 512/375 ||
+| | 375/352, 2560/2401
-||= 223 || 160/117 || 175/128 || 2187/1600 ||
+| | 524288/492375
-||= 224
+|-
+| style="text-align:center;" | 46
+| | 16/15
+| |
+| |
+|-
+| style="text-align:center;" | 47
+| | 125/117
+| | 576/539
+| | 2187/2048
+|-
+| style="text-align:center;" | 48
+| | 77/72
+| | 16384/15309
+| | 5120000/4782969
+|-
+| style="text-align:center;" | 49
+| | 15/14
+| |
+| | 3125/2916
+|-
+| style="text-align:center;" | 50
+| | 338/315
+| | 338/315, 343/320
+| | 140625/131072
+|-
+| style="text-align:center;" | 51
+| | 130/121
+| | 189/176, 9216/8575
+| | 2097152/1953125
+|-
+| style="text-align:center;" | 52
+| | 128/119
+| | 242/225, 672/625
+| | 419904/390625
+|-
+| style="text-align:center;" | 53
+| | 14/13
+| | 264/245, 2205/2048
+| | 43046721/4000000
+|-
+| style="text-align:center;" | 54
+| | 55/51
+| | 539/500, 2592/2401
+| | 32768/30375
+|-
+| style="text-align:center;" | 55
+| | 27/25
+| |
+| |
+|-
+| style="text-align:center;" | 56
+| | 119/110
+| | 225/208, 250/231, 16807/15552
+| | 177147/163840
+|-
+| style="text-align:center;" | 57
+| | 13/12
+| | 693/640, 1024/945
+| | 64000/59049
+|-
+| style="text-align:center;" | 58
+| | 243/224
+| |
+| | 625/576
+|-
+| style="text-align:center;" | 59
+| | 88/81
+| | 27783/25600
+| | 2278125/2097152
+|-
+| style="text-align:center;" | 60
+| | 99/91
+| | 160/147
+| | 10616832/9765625
+|-
+| style="text-align:center;" | 61
+| | 49/45
+| |
+| | 2125764/1953125
+|-
+| style="text-align:center;" | 62
+| | 12/11
+| | 35721/32768
+| | 67108864/61509375
+|-
+| style="text-align:center;" | 63
+| | 130/119
+| | 273/250, 375/343
+| | 2048/1875
+|-
+| style="text-align:center;" | 64
+| | 35/32
+| |
+| | 2187/2000
+|-
+| style="text-align:center;" | 65
+| | 242/221
+| | 675/616, 16807/15360
+| | 5242880/4782969
+|-
+| style="text-align:center;" | 66
+| | 169/154
+| | 192/175
+| | 800/729
+|-
+| style="text-align:center;" | 67
+| | 56/51
+| | 100/91, 686/625
+| | 1125/1024
+|-
+| style="text-align:center;" | 68
+| | 11/10
+| |