Table of 494edo intervals: Difference between revisions

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<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
| |

Revision as of 00:00, 17 July 2018

Step Seventeen limit ratio Other ratio(s) over five limit Five limit ratio
1 442/441 540/539, 2401/2400 32805/32768
2 289/288 325/324, 385/384, 5120/5103 1600000/1594323
3 221/220 225/224 15625/15552
4 169/168 176/175, 1029/1024 2109375/2097152
5 136/135 144/143, 1728/1715 393216/390625
6 120/119 121/120, 126/125 78732/78125
7 99/98 33075/32768 67108864/66430125
8 85/84 1617/1600 2048/2025
9 78/77 81/80
10 224/221 507/500, 625/616, 51200/50421 531441/524288
11 64/63 20000/19683
12 119/117 648/637, 686\675 3125/3072
13 55/54 83349/81920 34171875/33554432
14 50/49 1990656/1953125
15 49/48 1594323/1562500
16 45/44 12288/12005 4194304/4100625
17 128/125
18 40/39 352/343, 525/512 6561/6400
19 77/75 16807/16384 1638400/1594323
20 36/35 250/243
21 34/33 375/364, 1029/1000 16875/16384
22 33/32 4096/3969 50331648/48828125
23 125/121 405/392 1953125/1889568
24 91/88 512/495, 1323/1280 9765625/9437184
25 88/85 175/169, 729/704, 3200/3087 262144/253125
26 28/27 648/625
27 27/26 80/77, 8505/8192 531441/512000
28 26/25 343/330, 2500/2401 20480/19683
29 25/24
30 169/162 704/675, 2401/2304 273375/262144
31 117/112 256/245 5000000/4782969
32 68/65 392/375 390625/373248
33 22/21 8575/8192 17578125/16777216
34 85/81 150/143, 360/343 16384/15625
35 21/20 6561/6250
36 81/77 16807/16000 8388608/7971615
37 255/242 256/243
38 96/91
39 132/125 21609/20480 4428675/4194304
40 55/52 128/121, 200/189 62500/59049
41 18/17 143/135, 343/324 78125/73728
42 35/33 16384/15435 33554432/31640625
43 17/16 625/588 82944/78125
44 117/110 1029/968, 1225/1152 531441/500000
45 180/169 375/352, 2560/2401 524288/492375
46 16/15
47 125/117 576/539 2187/2048
48 77/72 16384/15309 5120000/4782969
49 15/14 3125/2916
50 338/315 338/315, 343/320 140625/131072
51 130/121 189/176, 9216/8575 2097152/1953125
52 128/119 242/225, 672/625 419904/390625
53 14/13 264/245, 2205/2048 43046721/4000000
54 55/51 539/500, 2592/2401 32768/30375
55 27/25
56 119/110 225/208, 250/231, 16807/15552 177147/163840
57 13/12 693/640, 1024/945 64000/59049
58 243/224 625/576
59 88/81 27783/25600 2278125/2097152
60 99/91 160/147 10616832/9765625
61 49/45 2125764/1953125
62 12/11 35721/32768 67108864/61509375
63 130/119 273/250, 375/343 2048/1875
64 35/32 2187/2000
65 242/221 675/616, 16807/15360 5242880/4782969
66 169/154 192/175 800/729
67 56/51 100/91, 686/625 1125/1024
68 11/10 36015/32768 3695625/33554432
69 54/49 390625/354294
70 75/68 182/165, 441/400 1953125/1769472
71 169/153 243/220, 10240/9261 4194304/3796875
72 187/169 448/405 3456/3125
73 72/65 256/231, 567/512 177147/160000
74 132/119 375/338, 539/486, 8000/7203 65536/59049
75 10/9
76 187/168 405/364, 600/539, 2401/2160 18225/16384
77 39/35 49/44, 4096/3675 16000000/14348907
78 125/112 78125/69984
79 143/128 352/315, 1715/1536 1771875/1048576
80 160/143 384/343 262144/234375
81 28/25 17496/15625
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
86 44/39 640/567 200000/177147
87 96/85 720/637, 847/750, 1372/1215 15625/13824
88 112/99 9261/8192 18984375/1677216
89 17/15 162/143, 500/441 442368/390625
90 135/119 143/126, 245/216 177147/156250
91 25/22 8192/7203 8388608/7381125
92 91/80 256/225
93 351/308 729/640
94 154/135 19200/16807 4782969/4194304
95 8/7 2500/2187
96 119/104 143/125, 343/300 9375/8192
97 55/48 40960/35721 33554432/29296875
98 39/34 225/196 2239488/1953125
99 147/128 14348907/12500000
100 176/153 405/352, 13824/12005 524288/455625
101 121/105 144/125
102 15/13 396/343, 4725/4096 59049/51200
103 52/45 231/200, 16384/14175 204800/177147
104 81/70 125/108
105 51/44 625/539, 9261/8000 151875/131072
106 65/56 297/256, 512/441 50000000/430446721
107 136/117 726/625, 784/675 1953125/1679616
108 64/55 11907/10240 9765625/8388608
109 99/85 400/343 32768/28125
110 7/6 729/625
111 90/77 16807/14400 4782969/4096000
112 117/100 1024/875 2560/2187
113 75/64
114 88/75 2401/2048 2460375/2097152
115 168/143 168/143, 288/245 625000/531441
116 20/17 147/125 390625/331776
117 33/28 32768/27783 67108864/56953125
118 85/72 405/343 18432/15625
119 13/11 189/160 59049/50000
120 200/169 625/528, 25600/21609 1048576/885735
121 32/27
122 108/91 640/539 1215/1024
123 170/143 196/165, 20000/16807 39858075/33554432
124 25/21 15625/13122
125 81/68 143/120, 343/288 78125/65536
126 105/88 2048/1715 4194304/3515625
127 153/128 448/375 93312/78125
128 140/117 176/147, 1225/1024 4782969/4000000
129 187/156 405/338, 539/450, 2880/2401 65536/54675
130 6/5
131 119/99 125/104, 648/539, 2401/2000 19683/16384
132 65/54 77/64, 2048/1701 640000/531441
133 135/112 3125/2592
134 169/140 880/729, 3087/2560 1265625/1048576
135 110/91 1024/847, 1600/1323 2359296/1953125
136 98/81 472392/390625
137 40/33 19845/16384 134217728/110716875
138 17/14 91/75, 1250/1029 4096/3375
139 147/121 175/144 243/200
140 375/308 16807/13824 1594323/1310720
141 39/32 128/105 8000/6561
142 238/195 625/512
143 11/9 60025/49152 20503125/16777216
144 60/49 1953125/1594323
145 49/40 4782969/3906250
146 27/22 73728/60025 8388608/6834375
147 338/275 768/625
148 16/13 315/256 19683/16000
149 154/125 154/125, 20736/16807 655360/531441
150 100/81
151 21/17 225/182, 2000/1617, 2401/1944 10125/8192
152 26/21 99/80, 8192/6615 160000000/129140163
153 119/96 150/121, 243/196 390625/314928
154 242/195 704/567, 3969/3200 1953125/1572864
155 169/136 210/169, 875/704, 1280/1029 524288/421875
156 56/45 3888/3125
157 81/65 96/77, 5103/4096 1594323/1280000
158 156/125 343/275, 3000/2401 8192/6561
159 5/4
160 169/135 675/539, 2401/1920 164025/131072
161 351/280 441/352, 1536/1225 2000000/1594323
162 64/51 784/625 78125/62208
163 44/35 5145/4096 10546875/8388608
164 34/27 180/143, 432/343 98304/78125
165 63/50 19683/15625
166 125/99 50421/40000 16777216/13286025
167 91/72 512/405
168 81/64
169 280/221 308/243, 64000/50421 2657205/2097152
170 33/26 80/63 25000/19683
171 108/85 286/225, 343/270 15625/12288
172 14/11 32768/25725 67108864/52734375
173 51/40 125/98 497664/390625
174 143/112 245/192 1594323/1250000
175 216/169 225/176, 3072/2401 1048576/820125
176 32/25
177 50/39 440/343, 2401/1875 6561/5120
178 77/60 21600/16807 2048000/1594323
179 9/7 625/486
180 85/66 637/495, 1029/800 84375/65536
181 156/121 165/128, 5120/3969 12582912/9765625
182 351/272 484/375, 1568/1215 2519424/1953125
183 84/65 128/99, 1323/1024 48828125/37748736
184 22/17 825/637, 1617/1250, 4000/3087 65536/50625
185 35/27 162/125
186 100/77 16807/12960 531441/409600
187 13/10 343/264, 2048/1575 25600/19683
188 125/96
189 176/135 12005/9216 1366875/1048576
190 64/49 6250000/4782969
191 17/13 1953125/1492992
192 55/42 42875/32768 87890625/67108864
193 156/119 375/286 4096/3125
194 21/16 6561/5000
195 221/168 405/308, 16807/12800 2097152/1594323
196 154/117 320/243
197 112/85 120/91 675/512
198 33/25 21609/16384 22143375/16777216
199 119/90 160/121, 250/189 78125/59049
200 45/34 143/108, 847/640, 1323/1000 390625/294912
201 65/49 175/132, 4096/3087 8388608/6328125
202 85/64 637/480, 896/675 20736/15625
203 117/88 512/385, 1701/1280 531441/400000
204 225/169 539/405, 3200/2401 131072/98415
205 4/3
206 187/140 243/182, 720/539, 2401/1800 10935/8192
207 147/110 8192/6125 6400000/4782969
208 75/56 15625/11664
209 169/126 343/256 703125/524288
210 192/143 945/704, 2304/1715 524288/390625
211 121/90 168/125 104976/78125
212 35/26 66/49, 11025/8192 43046721/32000000
213 85/63 182/135, 539/400, 3240/2401 8192/6075
214 27/20
215 119/88 169/125, 625/462, 21609/16000 177147/131072
216 65/48 256/189 80000/59049
217 476/351 847/625, 1215/896 3125/2304
218 110/81 27783/20480 11390625/8388608
219 34/25 200/147 2654208/1953125
220 49/36 531441/390625
221 15/11 16384/12005 16777216/12301875
222 153/112 273/200 512/375
223 160/117 175/128 2187/1600
224 256/187 6553600/4782969
225 48/35 308/225. 16807/12288 1000/729
226 70/51 343/250 5625/4096
227 11/8 16384/11907 67108864/48828125
228 117/85 1953125/1417176
229 91/66 441/320 9765625/7077888
230 221/160 243/176, 12800/9261 1048576/759375
231 112/81 864/625
232 18/13 320/231, 2835/2048 177147/128000
233 68/49 104/75, 686/495, 10000/7203 81920/59049
234 25/18
235 153/110 338/243, 750/539, 2401/1728 91125/65536
236 39/28 245/176, 1024/735 20000000/14348907
237 272/195 625/448 390625/279936
238 88/63 8575/6144 5859375/4194304
239 200/143 480/343 65536/46875
240 7/5 4374/3125
241 108/77 16807/12000 14348907/10240000
242 170/121 351/250, 539/384 1024/729
243 45/32 45/32
244 169/120 176/125, 7203/5120 1476225/1048576
245 55/39 484/343, 800/567 250000/177147
246 24/17 343/243 78125/55296
247 99/70 94921875/67108864
248 17/12 405/286, 486/343 110592/78125
249 78/55 343/242, 567/400 177147/125000
250 125/88 10240/7203 2097152/1476225
251 64/45
252 121/85 500/351 729/512
253 77/54 24000/16807 20480000/14348907
254 10/7 3125/2187
255 143/100 343/240 46875/32768
256 63/44 12288/8575 8388608/5859375
257 195/136 896/625 559872/390625
258 56/39 352/245, 735/512 14348907/10000000
259 187/130 243/169, 539/375, 3456/2401 131072/91125
260 36/25
261 49/34 75/52, 495/343, 7203/5000 59049/40960
262 13/9 231/160, 4096/2835 256000/177147
263 81/56 625/432
264 255/176 352/243, 9261/6400 759375/524288
265 132/91 640/441 14155776/9765625
266 170/117 196/135 2834352/1953125
267 16/11 11907/8192 48828125/33554432
268 51/35 182/125, 500/343 8192/5625
269 35/24 729/500
270 187/128 225/154, 16807/11520 4782969/3276800
271 117/80 256/175 3200/2187
272 224/153 375/256
273 22/15 12005/8192 12301875/8388608
274 72/49 781250/531441
275 25/17 147/100 1953125/1327104
276 81/55 40960/27783 16777216/11390625
277 351/238 637/432, 1250/847, 1792/1215 4608/3125
278 65/44 189/128 59049/40000
279 176/119 250/169, 924/625, 32000/21609 262144/177147
280 40/27
281 126/85 135/91, 800/539, 2401/1620 6075/4096
282 49/33 16384/11025 64000000/43046721
283 119/80 78125/52488
284 143/96 1408/945, 1715/1152 390625/262144
285 252/169 512/343 1048576/703125
286 112/75 23328/15625
287 175/117 220/147, 6125/4096 4782969/3200000
288 280/187 364/243, 539/360, 3600/2401 16384/10935
289 3/2
290 221/147 338/225, 810/539, 2401/1600 98415/65536
291 176/117 385/256, 2560/1701 800000/531441
292 128/85 675/448 15625/10368
293 98/65 264/175, 3087/2048 6328125/4194304
294 68/45 216/143, 1280/847, 2000/1323 589824/390625
295 121/80 189/125 118098/78125
296 50/33 32768/21609 33554432/22143375
297 85/56 91/60 1024/675
298 117/77 243/160
299 336/221 616/405, 25600/16807 1594323/1048576
300 32/21 10000/6561
301 119/78 343/225 3125/2048
302 55/36 65536/42875 102515625/67108864
303 26/17 2985984/1953125
304 49/32 4782969/3125000
305 135/88 18432/12005 2097152/1366875
306 169/110 192/125
307 20/13 528/343, 1575/1024 19683/12800
308 77/50 25920/16807 819200/531441
309 54/35 125/81
310 17/11 1001/648, 2500/1617, 3087/2000 50625/32768
311 65/42 99/64, 2048/1323 75497472/48828125
312 375/242 375/242, 1215/784 1953125/1259712
313 121/78 256/165, 3969/2560 9765625/6291456
314 132/85 525/338, 1600/1029 131072/84375
315 14/9 972/625
316 81/52 120/77, 16807/10800 1594323/1024000
317 39/25 343/220, 3750/2401 10240/6561
318 25/16
319 169/108 352/225, 2401/1536 820125/524288
320 224/143 384/245 2500000/1594323
321 80/51 196/125 390625/248832
322 11/7 25725/16384 52734375/33554432
323 85/54 225/143, 540/343 24576/15625
324 52/33 63/40 19683/12500
325 221/140 243/154, 50421/32000 4194304/2657205
326 128/81
327 144/91 405/256
328 198/125 64827/40960 13286025/8388608
329 100/63 31250/19683
330 27/17 143/90, 343/216 78125/49152
331 35/22 8192/5145 16777216/10546875
332 51/32 625/392 124416/78125
333 351/220 704/441, 1225/768 1594323/1000000
334 187/117 270/169, 1078/675, 3840/2401 262144/164025
335 8/5
336 125/78 550/343, 2401/1500 6561/4096
337 77/48 8192/5103 2560000/1594323
338 45/28 3125/1944
339 169/105 1029/640 421875/262144
340 195/121 567/352, 6400/3969 3145728/1953125
341 121/75 392/243 629856/390625
342 21/13 160/99, 6615/4096 129140163/80000000
343 34/21 364/225, 1617/1000, 3888/2401 16384/10125
344 81/50
345 125/77 16807/10368 531441/327680
346 13/8 512/315 32000/19683
347 275/169 625/384
348 44/27 60025/36864 6834375/4194304
349 80/49 7812500/4782969
350 49/30 3188646/1953125
351 18/11 98304/60025 33554432/20503125
352 195/119 819/500 1024/625
353 64/39 105/64 6561/4000
354 363/221 616/375, 16807/10240 2621440/1594323
355 242/147 288/175 400/243
356 28/17 150/91, 1029/625 3375/2048
357 33/20 32768/19845 110716875/67108864
358 81/49 390625/236196
359 91/55 847/512, 1323/800 1953125/1179648
360 169/102 280/169, 729/440, 5120/3087 2097152/1265625
361 224/135 5184/3125
362 108/65 128/77, 1701/1024 531441/320000
363 198/119 208/125, 539/324, 4000/2401 32768/19683
364 5/3
365 187/112 676/405, 900/539, 2401/1440 54675/32768
366 117/70 147/88, 2048/1225 8000000/4782969
367 221/132 375/224 78125/46656
368 176/105 1715/1024 3515625/2097152
369 136/81 240/143, 576/343 131072/78125
370 42/25 26244/15625
371 143/85 165/98, 16807/10000 43046721/25600000
372 91/54 539/320 2048/1215
373 27/16
374 169/100 1056/625, 21609/12800 885735/524288
375 22/13 320/189 100000/59049
376 144/85 686/405 15625/9216
377 56/33 27783/16384 56953125/33554432
378 17/10 243/143, 250/147 663552/390625
379 143/84 245/144 531441/312500
380 75/44 4096/2401 4194304/2460375
381 128/75
382 200/117 875/512 2187/1280
383 77/45 28800/16807 8192000/4782969
384 12/7 1250/729
385 170/99 343/200 28125/16384
386 55/32 20480/11907 16777216/9765625
387 117/68 625/363, 675/392 3359232/1953125
388 112/65 441/256 43046721/25000000
389 88/51 875/507, 1078/625, 16000/9261 262144/151875
390 121/70 140/81 216/125
391 45/26 400/231, 14175/8192 177147/102400
392 26/15 343/198, 8192/4725 102400/59049
393 125/72
394 153/88 704/405, 12005/6912 455625/262144
395 195/112 256/147 25000000/14348907
396 68/39 392/225 1953125/1119744
397 96/55 35721/20480 29296875/16777216
398 208/119 250/143, 600/343 16384/9375
399 7/4 2187/1250
400 135/77 16807/9600 8388608/4782969
401 351/200 1280/729
402 160/91 225/128
403 44/25 7203/4096 7381125/4194304
404 238/135 252/143, 432/245 312500/177147
405 30/17 143/81, 441/250 390625/221184
406 99/56 16384/9261 33554432/18984375
407 85/48 637/360, 1215/686 27648/15625
408 39/22 567/320 177147/100000
409 300/169 625/352, 12800/7203 524288/295245
410 16/9
411 121/68 162/91, 960/539, 2401/1350 3645/2048
412 98/55 30000/16807 25600000/14348907
413 25/14 15625/8748
414 143/80 343/192 234375/131072
415 256/143 315/176, 3072/1715 2097152/1171875
416 224/125 139968/78125
417 70/39 88/49, 3675/2048 14348907/8000000
418 187/104 539/300, 4320/2401 32768/18225
419 9/5
420 119/66 375/208, 972/539, 7203/4000 59049/32768
421 65/36 231/128, 1024/567 320000/177147
422 338/187 405/224 3125/1728
423 306/169 440/243, 9261/5120 3796875/2097152
424 136/75 165/91, 800/441 3538944/1953125
425 49/27 708588/390625
426 20/11 59535/32768 67108864/36905625
427 51/28 91/50, 625/343 2048/1125
428 175/96 729/400
429 221/121 1125/616, 16807/9216 4782969/2621440
430 64/35 4000/2187
431 119/65 500/273, 686/375 1875/1024
432 11/6 60025/32768 61509375/33554432
433 90/49 1953125/1062882
434 125/68 147/80 9765625/5308416
435 81/44 51200/27783 4194304/2278125
436 448/243 1152/625
437 24/13 945/512 59049/32000
438 220/119 231/125, 31104/16807 327680/177147
439 50/27
440 63/34 675/364, 1000/539, 2401/1296 30375/16384
441 13/7 245/132, 4096/2205 80000000/43046721
442 119/64 225/121, 625/336 390625/209952
443 121/65 352/189, 8575/4608 1953125/1048576
444 315/169 640/343 262144/140625
445 28/15 5832/3125
446 144/77 15309/8192 4782969/2560000
447 234/125 539/288 4096/2187
448 15/8
449 169/90 704/375, 2401/1280 492075/262144
450 220/117 1323/704, 2304/1225 1000000/531441
451 32/17 847/450, 1176/625 78125/41472
452 49/26 66/35, 15435/8192 31640625/16777216
453 17/9 270/143, 648/343 147456/78125
454 104/55 121/64, 189/100 59049/31250
455 125/66 40960/21609 8388608/4428675
456 91/48 256/135
457 243/128
458 154/81 32000/16807 7971615/4194304
459 40/21 12500/6561
460 143/75 343/180 15625/8192
461 21/11 16384/8575 33554432/17578125
462 65/34 375/196 746496/390625
463 224/117 245/128 4782969/2500000
464 324/169 675/352, 4608/2401 524288/273375
465 48/25
466 25/13 660/343, 2401/1250 19683/10240
467 52/27 77/40, 16384/8505 1024000/531441
468 27/14 625/324
469 85/44 338/175, 1408/729, 3087/1600 253125/131072
470 176/91 495/256, 2560/1323 18874368/9765625
471 242/125 784/405 3779136/1953125
472 64/33 3969/2048 48828125/25165824
473 33/17 728/375, 2000/1029 32768/16875
474 35/18 243/125
475 150/77 16807/8640 1594323/819200
476 39/20 343/176, 1024/525 12800/6561
477 125/64
478 88/45 12005/6144 4100625/2097152
479 96/49 3125000/1594323
480 49/25 1953125/995328
481 55/28 117649/60000 67108864/34171875
482 234/119 637/324, 675/343 6144/3125
483 63/32 19683/10000
484 221/112 1000/507, 1215/616, 50421/25600 1048576/531441
485 77/39 160/81
486 168/85 180/91 2025/1024
487 99/50 64827/32768 66430125/33554432
488 119/60 125/63 78125/39366
489 135/68 143/72, 1715/864 390625/196608
490 169/85 175/88, 2048/1029 4194304/2109375
491 255/128 448/225 31104/15625
492 351/176 351/176 1594323/800000
493 441/221 539/270, 4800/2401 65536/32805
494 2
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