Table of 270edo intervals: Difference between revisions

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Prime 17 can be considered good enough
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This '''table of 270edo intervals''' assumes the [[31-limit]] [[patent val]] of [[270edo]] {{val| 270 428 647 758 934 999 1104 1147 1221 1312 1338 }}. [[Prime harmonic]]s are in '''bold'''; inconsistently mapped intervals are in ''italic''. As is analysed in the main article, besides being a strong 13-limit system, 270edo can be used in the full 23-limit with a handful of inconsistencies into the 27-odd-limit, or as a no-17/13 no-23 31-limit system, fully consistent to the 35-odd-limit. For this reason, intervals of 23 are given in parentheses.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:guest|guest]] and made on <tt>2012-04-25 21:19:17 UTC</tt>.<br>
: The original revision id was <tt>325313622</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<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 || Five limit || Seven limit || Eleven limit || Thirteen limit ||
|| 1 || 32805/32768 || 3136/3125 || 385/384 || 325/324 ||
|| 2 || 15625/15552 || 225/224 || 176/175 || 169/168 ||
|| 3 || 78732/78125 || 126/125 || 121/120 || 121/120 ||
|| 4 || 2048/2025 || 2048/2025 || 99/98 || 91/90 ||
|| 5 || 81/80 || 81/80 || 81/80 || 78/77 ||
|| 6 || 20000/19683 || 64/63 || 64/63 || 64/63 ||
|| 7 || 3125/3072 || 3125/3072 || 55/54 || 55/54 ||
|| 8 || 1594323/1562500 || 49/48 || 49/48 || 49/48 ||
|| 9 || 128/125 || 128/125 || 45/44 || 45/44 ||
|| 10 || 6561/6400 || 525/512 || 77/75 || 40/39 ||
|| 11 || 250/243 || 36/35 || 36/35 || 36/35 ||
|| 12 || 16875/16384 || 4096/3969 || 33/32 || 33/32 ||
|| 13 || 262144/253125 || 405/392 || 125/121 || 91/88 ||
|| 14 || 648/625 || 28/27 || 28/27 || 28/27 ||
|| 15 || 20480/19683 || 8192/7875 || 80/77 || 26/25 ||
|| 16 || 25/24 || 25/24 || 25/24 || 25/24 ||
|| 17 || 273375/262144 || 256/245 || 256/245 || 117/112 ||
|| 18 || 16384/15625 || 1875/1792 || 22/21 || 22/21 ||
|| 19 || 6561/6250 || 21/20 || 21/20 || 21/20 ||
|| 20 || 256/243 || 256/243 || 81/77 || 81/77 ||
|| 21 || 135/128 || 135/128 || 132/125 || 96/91 ||
|| 22 || 62500/59049 || 200/189 || 128/121 || 55/52 ||
|| 23 || 78125/73728 || 3584/3375 || 35/33 || 35/33 ||
|| 24 || 524288/492075 || 625/588 || 625/588 || 117/110 ||
|| 25 || 16/15 || 16/15 || 16/15 || 16/15 ||
|| 26 || 2187/2048 || 2187/2048 || 77/72 || 77/72 ||
|| 27 || 3125/2916 || 15/14 || 15/14 || 15/14 ||
|| 28 || 140625/131072 || 672/625 || 189/176 || 130/121 ||
|| 29 || 32768/30375 || 2205/2048 || 264/245 || 14/13 ||
|| 30 || 27/25 || 27/25 || 27/25 || 27/25 ||
|| 31 || 64000/59049 || 1024/945 || 250/231 || 13/12 ||
|| 32 || 625/576 || 243/224 || 88/81 || 88/81 ||
|| 33 || 2125764/1953125 || 49/45 || 49/45 || 49/45 ||
|| 34 || 2048/1875 || 2048/1875 || 12/11 || 12/11 ||
|| 35 || 2187/2000 || 35/32 || 35/32 || 35/32 ||
|| 36 || 800/729 || 192/175 || 192/175 || 169/154 ||
|| 37 || 1125/1024 || 1125/1024 || 11/10 || 11/10 ||
|| 38 || 390625/354294 || 54/49 || 54/49 || 54/49 ||
|| 39 || 3456/3125 || 448/405 || 243/220 || 243/220 ||
|| 40 || 65536/59049 || 567/512 || 256/231 || 72/65 ||
|| 41 || 10/9 || 10/9 || 10/9 || 10/9 ||
|| 42 || 18225/16384 || 4096/3675 || 49/44 || 39/35 ||
|| 43 || 78125/69984 || 125/112 || 125/112 || 125/112 ||
|| 44 || 17496/15625 || 28/25 || 28/25 || 28/25 ||
|| 45 || 4096/3645 || 4096/3645 || 55/49 || 55/49 ||
|| 46 || 9/8 || 9/8 || 9/8 || 9/8 ||
|| 47 || 200000/177147 || 640/567 || 640/567 || 44/39 ||
|| 48 || 15625/13824 || 2025/1792 || 112/99 || 112/99 ||
|| 49 || 177147/156250 || 245/216 || 245/216 || 143/126 ||
|| 50 || 256/225 || 256/225 || 25/22 || 25/22 ||
|| 51 || 729/640 || 729/640 || 154/135 || 154/135 ||
|| 52 || 2500/2187 || 8/7 || 8/7 || 8/7 ||
|| 53 || 9375/8192 || 3584/3125 || 55/48 || 55/48 ||
|| 54 || 524288/455625 || 147/128 || 147/128 || 147/128 ||
|| 55 || 144/125 || 144/125 || 121/105 || 121/105 ||
|| 56 || 59049/51200 || 4725/4096 || 231/200 || 15/13 ||
|| 57 || 125/108 || 81/70 || 81/70 || 81/70 ||
|| 58 || 151875/131072 || 512/441 || 297/256 || 65/56 ||
|| 59 || 32768/28125 || 3125/2688 || 64/55 || 64/55 ||
|| 60 || 729/625 || 7/6 || 7/6 || 7/6 ||
|| 61 || 2560/2187 || 1024/875 || 90/77 || 90/77 ||
|| 62 || 75/64 || 75/64 || 75/64 || 75/64 ||
|| 63 || 625000/531441 || 147/125 || 147/125 || 147/125 ||
|| 64 || 18432/15625 || 7168/6075 || 33/28 || 33/28 ||
|| 65 || 59049/50000 || 189/160 || 189/160 || 13/11 ||
|| 66 || 32/27 || 32/27 || 32/27 || 32/27 ||
|| 67 || 1215/1024 || 1215/1024 || 196/165 || 108/91 ||
|| 68 || 15625/13122 || 25/21 || 25/21 || 25/21 ||
|| 69 || 78125/65536 || 448/375 || 105/88 || 105/88 ||
|| 70 || 65536/54675 || 1225/1024 || 176/147 || 140/117 ||
|| 71 || 6/5 || 6/5 || 6/5 || 6/5 ||
|| 72 || 19683/16384 || 2048/1701 || 77/64 || 65/54 ||
|| 73 || 3125/2592 || 135/112 || 135/112 || 135/112 ||
|| 74 || 472392/390625 || 98/81 || 98/81 || 98/81 ||
|| 75 || 4096/3375 || 4096/3375 || 40/33 || 40/33 ||
|| 76 || 243/200 || 175/144 || 147/121 || 147/121 ||
|| 77 || 8000/6561 || 128/105 || 128/105 || 39/32 ||
|| 78 || 625/512 || 625/512 || 11/9 || 11/9 ||
|| 79 || 1953125/1594323 || 49/40 || 49/40 || 49/40 ||
|| 80 || 768/625 || 768/625 || 27/22 || 27/22 ||
|| 81 || 19683/16000 || 315/256 || 154/125 || 16/13 ||
|| 82 || 100/81 || 100/81 || 100/81 || 100/81 ||
|| 83 || 10125/8192 || 8192/6615 || 99/80 || 26/21 ||
|| 84 || 390625/314928 || 243/196 || 150/121 || 150/121 ||
|| 85 || 3888/3125 || 56/45 || 56/45 || 56/45 ||
|| 86 || 8192/6561 || 5103/4096 || 96/77 || 81/65 ||
|| 87 || 5/4 || 5/4 || 5/4 || 5/4 ||
|| 88 || 164025/131072 || 784/625 || 441/352 || 351/280 ||
|| 89 || 78125/62208 || 1125/896 || 44/35 || 44/35 ||
|| 90 || 19683/15625 || 63/50 || 63/50 || 63/50 ||
|| 91 || 512/405 || 512/405 || 125/99 || 91/72 ||
|| 92 || 81/64 || 81/64 || 81/64 || 81/64 ||
|| 93 || 25000/19683 || 80/63 || 80/63 || 33/26 ||
|| 94 || 15625/12288 || 7168/5625 || 14/11 || 14/11 ||
|| 95 || 1048576/820125 || 125/98 || 125/98 || 125/98 ||
|| 96 || 32/25 || 32/25 || 32/25 || 32/25 ||
|| 97 || 6561/5120 || 2625/2048 || 77/60 || 50/39 ||
|| 98 || 625/486 || 9/7 || 9/7 || 9/7 ||
|| 99 || 84375/65536 || 1568/1215 || 165/128 || 156/121 ||
|| 100 || 65536/50625 || 1323/1024 || 128/99 || 84/65 ||
|| 101 || 162/125 || 35/27 || 35/27 || 35/27 ||
|| 102 || 25600/19683 || 2048/1575 || 100/77 || 13/10 ||
|| 103 || 125/96 || 125/96 || 125/96 || 125/96 ||
|| 104 || 1366875/1048576 || 64/49 || 64/49 || 64/49 ||
|| 105 || 4096/3125 || 4096/3125 || 55/42 || 55/42 ||
|| 106 || 6561/5000 || 21/16 || 21/16 || 21/16 ||
|| 107 || 320/243 || 320/243 || 320/243 || 154/117 ||
|| 108 || 675/512 || 675/512 || 33/25 || 33/25 ||
|| 109 || 78125/59049 || 250/189 || 160/121 || 143/108 ||
|| 110 || 20736/15625 || 896/675 || 175/132 || 65/49 ||
|| 111 || 131072/98415 || 1701/1280 || 512/385 || 117/88 ||
|| 112 || 4/3 || 4/3 || 4/3 || 4/3 ||
|| 113 || 10935/8192 || 8192/6125 || 147/110 || 147/110 ||
|| 114 || 15625/11664 || 75/56 || 75/56 || 75/56 ||
|| 115 || 104976/78125 || 168/125 || 121/90 || 121/90 ||
|| 116 || 8192/6075 || 8192/6075 || 66/49 || 35/26 ||
|| 117 || 27/20 || 27/20 || 27/20 || 27/20 ||
|| 118 || 80000/59049 || 256/189 || 256/189 || 65/48 ||
|| 119 || 3125/2304 || 1215/896 || 110/81 || 110/81 ||
|| 120 || 531441/390625 || 49/36 || 49/36 || 49/36 ||
|| 121 || 512/375 || 512/375 || 15/11 || 15/11 ||
|| 122 || 2187/1600 || 175/128 || 175/128 || 160/117 ||
|| 123 || 1000/729 || 48/35 || 48/35 || 48/35 ||
|| 124 || 5625/4096 || 5625/4096 || 11/8 || 11/8 ||
|| 125 || 1048576/759375 || 135/98 || 135/98 || 91/66 ||
|| 126 || 864/625 || 112/81 || 112/81 || 112/81 ||
|| 127 || 81920/59049 || 2835/2048 || 320/231 || 18/13 ||
|| 128 || 25/18 || 25/18 || 25/18 || 25/18 ||
|| 129 || 91125/65536 || 1024/735 || 245/176 || 39/28 ||
|| 130 || 65536/46875 || 625/448 || 88/63 || 88/63 ||
|| 131 || 4374/3125 || 7/5 || 7/5 || 7/5 ||
|| 132 || 1024/729 || 1024/729 || 108/77 || 108/77 ||
|| 133 || 45/32 || 45/32 || 45/32 || 45/32 ||
|| 134 || 250000/177147 || 343/243 || 343/243 || 55/39 ||
|| 135 || 78125/55296 || 10125/7168 || 99/70 || 99/70 ||
|| 136 || 177147/125000 || 486/343 || 343/242 || 78/55 ||
|| 137 || 64/45 || 64/45 || 64/45 || 64/45 ||
|| 138 || 729/512 || 729/512 || 77/54 || 77/54 ||
|| 139 || 3125/2187 || 10/7 || 10/7 || 10/7 ||
|| 140 || 46875/32768 || 896/625 || 63/44 || 63/44 ||
|| 141 || 131072/91125 || 735/512 || 352/245 || 56/39 ||
|| 142 || 36/25 || 36/25 || 36/25 || 36/25 ||
|| 143 || 59049/40960 || 4096/2835 || 231/160 || 13/9 ||
|| 144 || 625/432 || 81/56 || 81/56 || 81/56 ||
|| 145 || 759375/524288 || 196/135 || 196/135 || 132/91 ||
|| 146 || 8192/5625 || 8192/5625 || 16/11 || 16/11 ||
|| 147 || 729/500 || 35/24 || 35/24 || 35/24 ||
|| 148 || 3200/2187 || 256/175 || 225/154 || 117/80 ||
|| 149 || 375/256 || 375/256 || 22/15 || 22/15 ||
|| 150 || 781250/531441 || 72/49 || 72/49 || 72/49 ||
|| 151 || 4608/3125 || 1792/1215 || 81/55 || 81/55 ||
|| 152 || 59049/40000 || 189/128 || 189/128 || 65/44 ||
|| 153 || 40/27 || 40/27 || 40/27 || 40/27 ||
|| 154 || 6075/4096 || 6075/4096 || 49/33 || 49/33 ||
|| 155 || 78125/52488 || 125/84 || 125/84 || 125/84 ||
|| 156 || 23328/15625 || 112/75 || 112/75 || 112/75 ||
|| 157 || 16384/10935 || 6125/4096 || 220/147 || 175/117 ||
|| 158 || 3/2 || 3/2 || 3/2 || 3/2 ||
|| 159 || 98415/65536 || 2560/1701 || 385/256 || 176/117 ||
|| 160 || 15625/10368 || 675/448 || 264/175 || 98/65 ||
|| 161 || 118098/78125 || 189/125 || 121/80 || 121/80 ||
|| 162 || 1024/675 || 1024/675 || 50/33 || 50/33 ||
|| 163 || 243/160 || 243/160 || 243/160 || 117/77 ||
|| 164 || 10000/6561 || 32/21 || 32/21 || 32/21 ||
|| 165 || 3125/2048 || 3125/2048 || 55/36 || 55/36 ||
|| 166 || 2097152/1366875 || 49/32 || 49/32 || 49/32 ||
|| 167 || 192/125 || 192/125 || 135/88 || 135/88 ||
|| 168 || 19683/12800 || 1575/1024 || 77/50 || 20/13 ||
|| 169 || 125/81 || 54/35 || 54/35 || 54/35 ||
|| 170 || 50625/32768 || 2048/1323 || 99/64 || 65/42 ||
|| 171 || 131072/84375 || 1215/784 || 256/165 || 121/78 ||
|| 172 || 972/625 || 14/9 || 14/9 || 14/9 ||
|| 173 || 10240/6561 || 4096/2625 || 120/77 || 39/25 ||
|| 174 || 25/16 || 25/16 || 25/16 || 25/16 ||
|| 175 || 820125/524288 || 196/125 || 196/125 || 196/125 ||
|| 176 || 24576/15625 || 5625/3584 || 11/7 || 11/7 ||
|| 177 || 19683/12500 || 63/40 || 63/40 || 52/33 ||
|| 178 || 128/81 || 128/81 || 128/81 || 128/81 ||
|| 179 || 405/256 || 405/256 || 198/125 || 144/91 ||
|| 180 || 31250/19683 || 100/63 || 100/63 || 100/63 ||
|| 181 || 78125/49152 || 1792/1125 || 35/22 || 35/22 ||
|| 182 || 262144/164025 || 625/392 || 625/392 || 351/220 ||
|| 183 || 8/5 || 8/5 || 8/5 || 8/5 ||
|| 184 || 6561/4096 || 6561/4096 || 77/48 || 77/48 ||
|| 185 || 3125/1944 || 45/28 || 45/28 || 45/28 ||
|| 186 || 421875/262144 || 392/243 || 121/75 || 121/75 ||
|| 187 || 16384/10125 || 6615/4096 || 160/99 || 21/13 ||
|| 188 || 81/50 || 81/50 || 81/50 || 81/50 ||
|| 189 || 32000/19683 || 512/315 || 125/77 || 13/8 ||
|| 190 || 625/384 || 625/384 || 44/27 || 44/27 ||
|| 191 || 3188646/1953125 || 49/30 || 49/30 || 49/30 ||
|| 192 || 1024/625 || 1024/625 || 18/11 || 18/11 ||
|| 193 || 6561/4000 || 105/64 || 105/64 || 64/39 ||
|| 194 || 400/243 || 288/175 || 242/147 || 242/147 ||
|| 195 || 3375/2048 || 3375/2048 || 33/20 || 33/20 ||
|| 196 || 390625/236196 || 81/49 || 81/49 || 81/49 ||
|| 197 || 5184/3125 || 224/135 || 224/135 || 224/135 ||
|| 198 || 32768/19683 || 1701/1024 || 128/77 || 108/65 ||
|| 199 || 5/3 || 5/3 || 5/3 || 5/3 ||
|| 200 || 54675/32768 || 2048/1225 || 147/88 || 117/70 ||
|| 201 || 78125/46656 || 375/224 || 176/105 || 176/105 ||
|| 202 || 26244/15625 || 42/25 || 42/25 || 42/25 ||
|| 203 || 2048/1215 || 2048/1215 || 165/98 || 91/54 ||
|| 204 || 27/16 || 27/16 || 27/16 || 27/16 ||
|| 205 || 100000/59049 || 320/189 || 320/189 || 22/13 ||
|| 206 || 15625/9216 || 6075/3584 || 56/33 || 56/33 ||
|| 207 || 531441/312500 || 245/144 || 245/144 || 143/84 ||
|| 208 || 128/75 || 128/75 || 75/44 || 75/44 ||
|| 209 || 2187/1280 || 875/512 || 77/45 || 77/45 ||
|| 210 || 1250/729 || 12/7 || 12/7 || 12/7 ||
|| 211 || 28125/16384 || 5376/3125 || 55/32 || 55/32 ||
|| 212 || 262144/151875 || 441/256 || 441/256 || 112/65 ||
|| 213 || 216/125 || 140/81 || 121/70 || 121/70 ||
|| 214 || 102400/59049 || 8192/4725 || 343/198 || 26/15 ||
|| 215 || 125/72 || 125/72 || 125/72 || 125/72 ||
|| 216 || 455625/262144 || 256/147 || 256/147 || 195/112 ||
|| 217 || 16384/9375 || 3125/1792 || 96/55 || 96/55 ||
|| 218 || 2187/1250 || 7/4 || 7/4 || 7/4 ||
|| 219 || 1280/729 || 1280/729 || 135/77 || 135/77 ||
|| 220 || 225/128 || 225/128 || 44/25 || 44/25 ||
|| 221 || 312500/177147 || 432/245 || 432/245 || 143/81 ||
|| 222 || 27648/15625 || 3584/2025 || 99/56 || 99/56 ||
|| 223 || 177147/100000 || 567/320 || 567/320 || 39/22 ||
|| 224 || 16/9 || 16/9 || 16/9 || 16/9 ||
|| 225 || 3645/2048 || 3645/2048 || 98/55 || 98/55 ||
|| 226 || 15625/8748 || 25/14 || 25/14 || 25/14 ||
|| 227 || 139968/78125 || 224/125 || 224/125 || 224/125 ||
|| 228 || 32768/18225 || 3675/2048 || 88/49 || 70/39 ||
|| 229 || 9/5 || 9/5 || 9/5 || 9/5 ||
|| 230 || 59049/32768 || 1024/567 || 231/128 || 65/36 ||
|| 231 || 3125/1728 || 405/224 || 405/224 || 405/224 ||
|| 232 || 708588/390625 || 49/27 || 49/27 || 49/27 ||
|| 233 || 2048/1125 || 2048/1125 || 20/11 || 20/11 ||
|| 234 || 729/400 || 175/96 || 175/96 || 175/96 ||
|| 235 || 4000/2187 || 64/35 || 64/35 || 64/35 ||
|| 236 || 1875/1024 || 1875/1024 || 11/6 || 11/6 ||
|| 237 || 1953125/1062882 || 90/49 || 90/49 || 90/49 ||
|| 238 || 1152/625 || 448/243 || 81/44 || 81/44 ||
|| 239 || 59049/32000 || 945/512 || 231/125 || 24/13 ||
|| 240 || 50/27 || 50/27 || 50/27 || 50/27 ||
|| 241 || 30375/16384 || 4096/2205 || 245/132 || 13/7 ||
|| 242 || 262144/140625 || 625/336 || 225/121 || 121/65 ||
|| 243 || 5832/3125 || 28/15 || 28/15 || 28/15 ||
|| 244 || 4096/2187 || 4096/2187 || 144/77 || 144/77 ||
|| 245 || 15/8 || 15/8 || 15/8 || 15/8 ||
|| 246 || 492075/262144 || 1176/625 || 847/450 || 220/117 ||
|| 247 || 78125/41472 || 3375/1792 || 66/35 || 49/26 ||
|| 248 || 59049/31250 || 189/100 || 121/64 || 104/55 ||
|| 249 || 256/135 || 256/135 || 125/66 || 91/48 ||
|| 250 || 243/128 || 243/128 || 154/81 || 154/81 ||
|| 251 || 12500/6561 || 40/21 || 40/21 || 40/21 ||
|| 252 || 15625/8192 || 3584/1875 || 21/11 || 21/11 ||
|| 253 || 524288/273375 || 245/128 || 245/128 || 224/117 ||
|| 254 || 48/25 || 48/25 || 48/25 || 48/25 ||
|| 255 || 19683/10240 || 7875/4096 || 77/40 || 25/13 ||
|| 256 || 625/324 || 27/14 || 27/14 || 27/14 ||
|| 257 || 253125/131072 || 784/405 || 242/125 || 176/91 ||
|| 258 || 32768/16875 || 3969/2048 || 64/33 || 64/33 ||
|| 259 || 243/125 || 35/18 || 35/18 || 35/18 ||
|| 260 || 12800/6561 || 1024/525 || 150/77 || 39/20 ||
|| 261 || 125/64 || 125/64 || 88/45 || 88/45 ||
|| 262 || 3125000/1594323 || 49/25 || 49/25 || 49/25 ||
|| 263 || 6144/3125 || 6144/3125 || 55/28 || 55/28 ||
|| 264 || 19683/10000 || 63/32 || 63/32 || 63/32 ||
|| 265 || 160/81 || 160/81 || 160/81 || 77/39 ||
|| 266 || 2025/1024 || 2025/1024 || 99/50 || 99/50 ||
|| 267 || 78125/39366 || 125/63 || 125/63 || 125/63 ||
|| 268 || 31104/15625 || 448/225 || 175/88 || 175/88 ||
|| 269 || 65536/32805 || 3125/1568 || 768/385 || 648/325 ||
|| 270 || 2 || 2 || 2 || 2 ||</pre></div>
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Table of 270edo intervals&lt;/title&gt;&lt;/head&gt;&lt;body&gt;


&lt;table class="wiki_table"&gt;
{| class="wikitable center-all right-1 right-2"
    &lt;tr&gt;
|-
        &lt;td&gt;Step&lt;br /&gt;
! #
&lt;/td&gt;
! Cents
        &lt;td&gt;Five limit&lt;br /&gt;
! Marks
&lt;/td&gt;
! 5-limit
        &lt;td&gt;Seven limit&lt;br /&gt;
! 7-limit
&lt;/td&gt;
! 11-limit
        &lt;td&gt;Eleven limit&lt;br /&gt;
! 13-limit
&lt;/td&gt;
! 23-limit
        &lt;td&gt;Thirteen limit&lt;br /&gt;
! 31-limit
&lt;/td&gt;
|-
    &lt;/tr&gt;
| 0
    &lt;tr&gt;
| 0.0
        &lt;td&gt;1&lt;br /&gt;
| P1
&lt;/td&gt;
| '''[[1/1]]'''
        &lt;td&gt;32805/32768&lt;br /&gt;
| "
&lt;/td&gt;
| "
        &lt;td&gt;3136/3125&lt;br /&gt;
| "
&lt;/td&gt;
| "
        &lt;td&gt;385/384&lt;br /&gt;
| "
&lt;/td&gt;
|-
        &lt;td&gt;325/324&lt;br /&gt;
| 1
&lt;/td&gt;
| 4.{{overline|4}}
    &lt;/tr&gt;
|
    &lt;tr&gt;
| ''[[32805/32768]]''
        &lt;td&gt;2&lt;br /&gt;
| [[3136/3125]]
&lt;/td&gt;
| [[385/384]]
        &lt;td&gt;15625/15552&lt;br /&gt;
| "
&lt;/td&gt;
| "
        &lt;td&gt;225/224&lt;br /&gt;
| "
&lt;/td&gt;
|-
        &lt;td&gt;176/175&lt;br /&gt;
| 2
&lt;/td&gt;
| 8.{{overline|8}}
        &lt;td&gt;169/168&lt;br /&gt;
|
&lt;/td&gt;
| [[15625/15552]]
    &lt;/tr&gt;
| [[225/224]]
    &lt;tr&gt;
| [[176/175]]
        &lt;td&gt;3&lt;br /&gt;
| [[196/195]]
&lt;/td&gt;
| "
        &lt;td&gt;78732/78125&lt;br /&gt;
| "
&lt;/td&gt;
|-
        &lt;td&gt;126/125&lt;br /&gt;
| 3
&lt;/td&gt;
| 13.{{overline|3}}
        &lt;td&gt;121/120&lt;br /&gt;
|
&lt;/td&gt;
| [[78732/78125]]
        &lt;td&gt;121/120&lt;br /&gt;
| [[126/125]]
&lt;/td&gt;
| "
    &lt;/tr&gt;
| "
    &lt;tr&gt;
| "
        &lt;td&gt;4&lt;br /&gt;
| "
&lt;/td&gt;
|-
        &lt;td&gt;2048/2025&lt;br /&gt;
| 4
&lt;/td&gt;
| 17.{{overline|7}}
        &lt;td&gt;2048/2025&lt;br /&gt;
|
&lt;/td&gt;
| [[2048/2025]]
        &lt;td&gt;99/98&lt;br /&gt;
| "
&lt;/td&gt;
| [[99/98]]
        &lt;td&gt;91/90&lt;br /&gt;
| "
&lt;/td&gt;
| "
    &lt;/tr&gt;
| "
    &lt;tr&gt;
|-
        &lt;td&gt;5&lt;br /&gt;
| 5
&lt;/td&gt;
| 22.{{overline|2}}
        &lt;td&gt;81/80&lt;br /&gt;
|
&lt;/td&gt;
| [[81/80]]
        &lt;td&gt;81/80&lt;br /&gt;
| "
&lt;/td&gt;
| "
        &lt;td&gt;81/80&lt;br /&gt;
| [[78/77]]
&lt;/td&gt;
| "
        &lt;td&gt;78/77&lt;br /&gt;
| "
&lt;/td&gt;
|-
    &lt;/tr&gt;
| 6
    &lt;tr&gt;
| 26.{{overline|6}}
        &lt;td&gt;6&lt;br /&gt;
|
&lt;/td&gt;
| [[20000/19683]]
        &lt;td&gt;20000/19683&lt;br /&gt;
| [[64/63]]
&lt;/td&gt;
| "
        &lt;td&gt;64/63&lt;br /&gt;
| [[65/64]]
&lt;/td&gt;
| "
        &lt;td&gt;64/63&lt;br /&gt;
| "
&lt;/td&gt;
|-
        &lt;td&gt;64/63&lt;br /&gt;
| 7
&lt;/td&gt;
| 31.{{overline|1}}
    &lt;/tr&gt;
|
    &lt;tr&gt;
| [[3125/3072]]
        &lt;td&gt;7&lt;br /&gt;
| "
&lt;/td&gt;
| [[56/55]]
        &lt;td&gt;3125/3072&lt;br /&gt;
| "
&lt;/td&gt;
| "
        &lt;td&gt;3125/3072&lt;br /&gt;
| "
&lt;/td&gt;
|-
        &lt;td&gt;55/54&lt;br /&gt;
| 8
&lt;/td&gt;
| 35.{{overline|5}}
        &lt;td&gt;55/54&lt;br /&gt;
|
&lt;/td&gt;
| [[1594323/1562500]]
    &lt;/tr&gt;
| [[49/48]]
    &lt;tr&gt;
| "
        &lt;td&gt;8&lt;br /&gt;
| "
&lt;/td&gt;
| "
        &lt;td&gt;1594323/1562500&lt;br /&gt;
| "
&lt;/td&gt;
|-
        &lt;td&gt;49/48&lt;br /&gt;
| 9
&lt;/td&gt;
| 40.0
        &lt;td&gt;49/48&lt;br /&gt;
|
&lt;/td&gt;
| [[128/125]]
        &lt;td&gt;49/48&lt;br /&gt;
| "
&lt;/td&gt;
| [[45/44]]
    &lt;/tr&gt;
| "
    &lt;tr&gt;
| "
        &lt;td&gt;9&lt;br /&gt;
| "
&lt;/td&gt;
|-
        &lt;td&gt;128/125&lt;br /&gt;
| 10
&lt;/td&gt;
| 44.{{overline|4}}
        &lt;td&gt;128/125&lt;br /&gt;
|
&lt;/td&gt;
| [[6561/6400]]
        &lt;td&gt;45/44&lt;br /&gt;
| [[525/512]]
&lt;/td&gt;
| [[77/75]]
        &lt;td&gt;45/44&lt;br /&gt;
| [[40/39]]
&lt;/td&gt;
| [[39/38]]
    &lt;/tr&gt;
| "
    &lt;tr&gt;
|-
        &lt;td&gt;10&lt;br /&gt;
| 11
&lt;/td&gt;
| 48.{{overline|8}}
        &lt;td&gt;6561/6400&lt;br /&gt;
|
&lt;/td&gt;
| [[250/243]]
        &lt;td&gt;525/512&lt;br /&gt;
| [[36/35]]
&lt;/td&gt;
| "
        &lt;td&gt;77/75&lt;br /&gt;
| "
&lt;/td&gt;
| "
        &lt;td&gt;40/39&lt;br /&gt;
| "
&lt;/td&gt;
|-
    &lt;/tr&gt;
| 12
    &lt;tr&gt;
| 53.{{overline|3}}
        &lt;td&gt;11&lt;br /&gt;
|
&lt;/td&gt;
| [[16875/16384]]
        &lt;td&gt;250/243&lt;br /&gt;
| [[4096/3969]]
&lt;/td&gt;
| [[33/32]]
        &lt;td&gt;36/35&lt;br /&gt;
| "
&lt;/td&gt;
| "
        &lt;td&gt;36/35&lt;br /&gt;
| '''[[32/31]]'''
&lt;/td&gt;
|-
        &lt;td&gt;36/35&lt;br /&gt;
| 13
&lt;/td&gt;
| 57.{{overline|7}}
    &lt;/tr&gt;
| sA1
    &lt;tr&gt;
| ''[[262144/253125]]''
        &lt;td&gt;12&lt;br /&gt;
| [[405/392]]
&lt;/td&gt;
| [[125/121]]
        &lt;td&gt;16875/16384&lt;br /&gt;
| [[91/88]]
&lt;/td&gt;
| "
        &lt;td&gt;4096/3969&lt;br /&gt;
| [[30/29]]
&lt;/td&gt;
|-
        &lt;td&gt;33/32&lt;br /&gt;
| 14
&lt;/td&gt;
| 62.{{overline|2}}
        &lt;td&gt;33/32&lt;br /&gt;
|
&lt;/td&gt;
| [[648/625]]
    &lt;/tr&gt;
| [[28/27]]
    &lt;tr&gt;
| "
        &lt;td&gt;13&lt;br /&gt;
| "
&lt;/td&gt;
| "
        &lt;td&gt;262144/253125&lt;br /&gt;
| "
&lt;/td&gt;
|-
        &lt;td&gt;405/392&lt;br /&gt;
| 15
&lt;/td&gt;
| 66.{{overline|6}}
        &lt;td&gt;125/121&lt;br /&gt;
|
&lt;/td&gt;
| [[20480/19683]]
        &lt;td&gt;91/88&lt;br /&gt;
| [[8192/7875]]
&lt;/td&gt;
| [[80/77]]
    &lt;/tr&gt;
| [[26/25]]
    &lt;tr&gt;
| "
        &lt;td&gt;14&lt;br /&gt;
| "
&lt;/td&gt;
|-
        &lt;td&gt;648/625&lt;br /&gt;
| 16
&lt;/td&gt;
| 71.{{overline|1}}
        &lt;td&gt;28/27&lt;br /&gt;
|
&lt;/td&gt;
| [[25/24]]
        &lt;td&gt;28/27&lt;br /&gt;
| "
&lt;/td&gt;
| "
        &lt;td&gt;28/27&lt;br /&gt;
| "
&lt;/td&gt;
| "
    &lt;/tr&gt;
| "
    &lt;tr&gt;
|-
        &lt;td&gt;15&lt;br /&gt;
| 17
&lt;/td&gt;
| 75.{{overline|5}}
        &lt;td&gt;20480/19683&lt;br /&gt;
|
&lt;/td&gt;
| ''[[273375/262144]]''
        &lt;td&gt;8192/7875&lt;br /&gt;
| [[256/245]]
&lt;/td&gt;
| "
        &lt;td&gt;80/77&lt;br /&gt;
| [[117/112]]
&lt;/td&gt;
| ([[23/22]])
        &lt;td&gt;26/25&lt;br /&gt;
| "
&lt;/td&gt;
|-
    &lt;/tr&gt;
| 18
    &lt;tr&gt;
| 80.0
        &lt;td&gt;16&lt;br /&gt;
|
&lt;/td&gt;
| [[16384/15625]]
        &lt;td&gt;25/24&lt;br /&gt;
| [[1875/1792]]
&lt;/td&gt;
| [[22/21]]
        &lt;td&gt;25/24&lt;br /&gt;
| "
&lt;/td&gt;
| "
        &lt;td&gt;25/24&lt;br /&gt;
| "
&lt;/td&gt;
|-
        &lt;td&gt;25/24&lt;br /&gt;
| 19
&lt;/td&gt;
| 84.{{overline|4}}
    &lt;/tr&gt;
|
    &lt;tr&gt;
| [[6561/6250]]
        &lt;td&gt;17&lt;br /&gt;
| [[21/20]]
&lt;/td&gt;
| "
        &lt;td&gt;273375/262144&lt;br /&gt;
| "
&lt;/td&gt;
| "
        &lt;td&gt;256/245&lt;br /&gt;
| "
&lt;/td&gt;
|-
        &lt;td&gt;256/245&lt;br /&gt;
| 20
&lt;/td&gt;
| 88.{{overline|8}}
        &lt;td&gt;117/112&lt;br /&gt;
| m2
&lt;/td&gt;
| [[256/243]]
    &lt;/tr&gt;
| "
    &lt;tr&gt;
| [[81/77]]
        &lt;td&gt;18&lt;br /&gt;
| "
&lt;/td&gt;
| [[20/19]]
        &lt;td&gt;16384/15625&lt;br /&gt;
| "
&lt;/td&gt;
|-
        &lt;td&gt;1875/1792&lt;br /&gt;
| 21
&lt;/td&gt;
| 93.{{overline|3}}
        &lt;td&gt;22/21&lt;br /&gt;
|
&lt;/td&gt;
| [[135/128]]
        &lt;td&gt;22/21&lt;br /&gt;
| "
&lt;/td&gt;
| [[132/125]]
    &lt;/tr&gt;
| [[96/91]]
    &lt;tr&gt;
| [[19/18]]
        &lt;td&gt;19&lt;br /&gt;
| "
&lt;/td&gt;
|-
        &lt;td&gt;6561/6250&lt;br /&gt;
| 22
&lt;/td&gt;
| 97.{{overline|7}}
        &lt;td&gt;21/20&lt;br /&gt;
|
&lt;/td&gt;
| [[62500/59049]]
        &lt;td&gt;21/20&lt;br /&gt;
| [[200/189]]
&lt;/td&gt;
| [[128/121]]
        &lt;td&gt;21/20&lt;br /&gt;
| [[55/52]]
&lt;/td&gt;
| [[18/17]]
    &lt;/tr&gt;
| "
    &lt;tr
|-
| 23
| 102.{{overline|2}}
|
| [[78125/73728]]
| [[3584/3375]]
| [[35/33]]
| "
| "
| "
|-
| 24
| 106.{{overline|6}}
|
| ''[[524288/492075]]''
| [[625/588]]
| "
| [[117/110]]
| '''[[17/16]]'''
| "
|-
| 25
| 111.{{overline|1}}
|
| [[16/15]]
| "
| "
| "
| "
| "
|-
| 26
| 115.{{overline|5}}
| A1
| [[2187/2048]]
| "
| [[77/72]]
| "
| "
| [[31/29]]
|-
| 27
| 120.0
|
| [[3125/2916]]
| [[15/14]]
| "
| "
| "
| "
|-
| 28
| 124.{{overline|4}}
|
| ''[[140625/131072]]''
| [[672/625]]
| [[189/176]]
| [[130/121]]
| [[102/95]]
| [[29/27]]
|-
| 29
| 128.{{overline|8}}
|
| ''[[32768/30375]]''
| [[2205/2048]]
| [[264/245]]
| [[14/13]]
| "
| "
|-
| 30
| 133.{{overline|3}}
|
| [[27/25]]
| "
| "
| "
| "
| "
|-
| 31
| 137.{{overline|7}}
|
| [[64000/59049]]
| [[1024/945]]
| [[250/231]]
| [[13/12]]
| "
| "
|-
| 32
| 142.{{overline|2}}
|
| [[625/576]]
| [[243/224]]
| [[88/81]]
| "
| [[38/35]]
| "
|-
| 33
| 146.{{overline|6}}
| n2
| [[2125764/1953125]]
| [[49/45]]
| "
| "
| (''[[25/23]]'')
| "
|-
| 34
| 151.{{overline|1}}
|
| [[2048/1875]]
| "
| [[12/11]]
| "
| "
| "
|-
| 35
| 155.{{overline|5}}
|
| [[2187/2000]]
| [[35/32]]
| "
| "
| ([[23/21]])
| "
|-
| 36
| 160.0
|
| [[800/729]]
| [[192/175]]
| "
| [[169/154]]
| [[56/51]]
| [[34/31]]
|-
| 37
| 164.{{overline|4}}
|
| [[1125/1024]]
| "
| [[11/10]]
| "
| "
| "
|-
| 38
| 168.{{overline|8}}
|
| [[390625/354294]]
| [[54/49]]
| "
| "
| "
| '''[[32/29]]'''
|-
| 39
| 173.{{overline|3}}
|
| [[3456/3125]]
| [[448/405]]
| [[243/220]]
| "
| [[21/19]]
| "
|-
| 40
| 177.{{overline|7}}
|
| ''[[65536/59049]]''
| [[567/512]]
| [[256/231]]
| [[72/65]]
| "
| [[31/28]]
|-
| 41
| 182.{{overline|2}}
|
| [[10/9]]
| "
| "
| "
| "
| "
|-
| 42
| 186.{{overline|6}}
|
| ''[[18225/16384]]''
| [[4096/3675]]
| [[49/44]]
| [[39/35]]
| "
| "
|-
| 43
| 191.{{overline|1}}
|
| [[78125/69984]]
| [[125/112]]
| "
| "
| [[19/17]]
| "
|-
| 44
| 195.{{overline|5}}
|
| [[17496/15625]]
| [[28/25]]
| "
| "
| "
| "
|-
| 45
| 200.0
|
| [[4096/3645]]
| "
| [[55/49]]
| "
| "
| "
|-
| 46
| 204.{{overline|4}}
| M2
| [[9/8]]
| "
| "
| "
| "
| "
|-
| 47
| 208.{{overline|8}}
|
| [[200000/177147]]
| [[640/567]]
| "
| [[44/39]]
| "
| [


&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Category:Tables of edo intervals]]
[[Category:270edo]]

Latest revision as of 07:46, 30 January 2026

This table of 270edo intervals assumes the 31-limit patent val of 270edo ⟨270 428 647 758 934 999 1104 1147 1221 1312 1338]. Prime harmonics are in bold; inconsistently mapped intervals are in italic. As is analysed in the main article, besides being a strong 13-limit system, 270edo can be used in the full 23-limit with a handful of inconsistencies into the 27-odd-limit, or as a no-17/13 no-23 31-limit system, fully consistent to the 35-odd-limit. For this reason, intervals of 23 are given in parentheses.

# Cents Marks 5-limit 7-limit 11-limit 13-limit 23-limit 31-limit
0 0.0 P1 1/1 " " " " "
1 4.4 32805/32768 3136/3125 385/384 " " "
2 8.8 15625/15552 225/224 176/175 196/195 " "
3 13.3 78732/78125 126/125 " " " "
4 17.7 2048/2025 " 99/98 " " "
5 22.2 81/80 " " 78/77 " "
6 26.6 20000/19683 64/63 " 65/64 " "
7 31.1 3125/3072 " 56/55 " " "
8 35.5 1594323/1562500 49/48 " " " "
9 40.0 128/125 " 45/44 " " "
10 44.4 6561/6400 525/512 77/75 40/39 39/38 "
11 48.8 250/243 36/35 " " " "
12 53.3 16875/16384 4096/3969 33/32 " " 32/31
13 57.7 sA1 262144/253125 405/392 125/121 91/88 " 30/29
14 62.2 648/625 28/27 " " " "
15 66.6 20480/19683 8192/7875 80/77 26/25 " "
16 71.1 25/24 " " " " "
17 75.5 273375/262144 256/245 " 117/112 (23/22) "
18 80.0 16384/15625 1875/1792 22/21 " " "
19 84.4 6561/6250 21/20 " " " "
20 88.8 m2 256/243 " 81/77 " 20/19 "
21 93.3 135/128 " 132/125 96/91 19/18 "
22 97.7 62500/59049 200/189 128/121 55/52 18/17 "
23 102.2 78125/73728 3584/3375 35/33 " " "
24 106.6 524288/492075 625/588 " 117/110 17/16 "
25 111.1 16/15 " " " " "
26 115.5 A1 2187/2048 " 77/72 " " 31/29
27 120.0 3125/2916 15/14 " " " "
28 124.4 140625/131072 672/625 189/176 130/121 102/95 29/27
29 128.8 32768/30375 2205/2048 264/245 14/13 " "
30 133.3 27/25 " " " " "
31 137.7 64000/59049 1024/945 250/231 13/12 " "
32 142.2 625/576 243/224 88/81 " 38/35 "
33 146.6 n2 2125764/1953125 49/45 " " (25/23) "
34 151.1 2048/1875 " 12/11 " " "
35 155.5 2187/2000 35/32 " " (23/21) "
36 160.0 800/729 192/175 " 169/154 56/51 34/31
37 164.4 1125/1024 " 11/10 " " "
38 168.8 390625/354294 54/49 " " " 32/29
39 173.3 3456/3125 448/405 243/220 " 21/19 "
40 177.7 65536/59049 567/512 256/231 72/65 " 31/28
41 182.2 10/9 " " " " "
42 186.6 18225/16384 4096/3675 49/44 39/35 " "
43 191.1 78125/69984 125/112 " " 19/17 "
44 195.5 17496/15625 28/25 " " " "
45 200.0 4096/3645 " 55/49 " " "
46 204.4 M2 9/8 " " " " "
47 208.8 200000/177147 640/567 " 44/39 " 35/31
48 213.3 15625/13824 2025/1792 112/99 " (26/23) "
49 217.7 177147/156250 245/216 " 143/126 17/15 "
50 222.2 256/225 " 25/22 " " "
51 226.6 729/640 " 154/135 " 57/50 "
52 231.1 2500/2187 8/7 " " " "
53 235.5 sA2 9375/8192 3584/3125 55/48 " 39/34 "
54 240.0 524288/455625 147/128 " " (23/20) 31/27
55 244.4 144/125 " 121/105 " 38/33 "
56 248.8 59049/51200 4725/4096 231/200 15/13 " "
57 253.3 125/108 81/70 " " 22/19 "
58 257.7 151875/131072 512/441 297/256 65/56 " 29/25
59 262.2 32768/28125 3125/2688 64/55 " 57/49 "
60 266.6 729/625 7/6 " " " "
61 271.1 2560/2187 1024/875 90/77 " 76/65 "
62 275.5 75/64 " " " " 34/29
63 280.0 625000/531441 147/125 " " 20/17 "
64 284.4 18432/15625 7168/6075 33/28 " " "
65 288.8 59049/50000 189/160 " 13/11 " "
66 293.3 m3 32/27 " " " " "
67 297.7 1215/1024 " 196/165 108/91 19/16 "
68 302.2 15625/13122 25/21 " " " "
69 306.6 78125/65536 448/375 105/88 " 68/57 31/26
70 311.1 65536/54675 1225/1024 176/147 140/117 91/76 "
71 315.5 6/5 " " " " "
72 320.0 19683/16384 2048/1701 77/64 65/54 " "
73 324.4 3125/2592 135/112 " " 76/63 35/29
74 328.8 472392/390625 98/81 " " (23/19) 29/24
75 333.3 4096/3375 " 40/33 " " "
76 337.7 243/200 175/144 147/121 " 17/14 "
77 342.2 8000/6561 128/105 " 39/32 (28/23) "
78 346.6 625/512 " 11/9 " " "
79 351.1 n3 1953125/1594323 49/40 " " " 38/31
80 355.5 768/625 " 27/22 " " "
81 360.0 19683/16000 315/256 154/125 16/13 " "
82 364.4 100/81 " " " 21/17 "
83 368.8 10125/8192 8192/6615 99/80 26/21 " "
84 373.3 390625/314928 243/196 150/121 " (57/46) 31/25
85 377.7 3888/3125 56/45 " " " "
86 382.2 8192/6561 5103/4096 96/77 81/65 " "
87 386.6 5/4 " " " " "
88 391.1 164025/131072 784/625 441/352 351/280 64/51 "
89 395.5 78125/62208 1125/896 44/35 " " "
90 400.0 19683/15625 63/50 " " 34/27 "
91 404.4 512/405 " 125/99 91/72 24/19 "
92 408.8 M3 81/64 " " " 19/15 "
93 413.3 25000/19683 80/63 " 33/26 " "
94 417.7 15625/12288 7168/5625 14/11 " " "
95 422.2 1048576/820125 125/98 " " (23/18) "
96 426.6 32/25 " " " " "
97 431.1 6561/5120 2625/2048 77/60 50/39 " "
98 435.5 625/486 9/7 " " " "
99 440.0 sd4 84375/65536 1568/1215 165/128 156/121 49/38 40/31
100 444.4 65536/50625 1323/1024 128/99 84/65 22/17 "
101 448.8 162/125 35/27 " " " "
102 453.3 25600/19683 2048/1575 100/77 13/10 " "
103 457.7 125/96 " " " 99/76 "
104 462.2 1366875/1048576 64/49 " " (30/23) "
105 466.6 4096/3125 " 55/42 " 17/13 38/29
106 471.1 6561/5000 21/16 " " " "
107 475.5 320/243 " " 154/117 25/19 "
108 480.0 675/512 " 33/25 " " 29/22
109 484.4 78125/59049 250/189 160/121 143/108 45/34 "
110 488.8 20736/15625 896/675 175/132 65/49 " "
111 493.3 131072/98415 1701/1280 512/385 117/88 85/64 "
112 497.7 P4 4/3 " " " " "
113 502.2 10935/8192 8192/6125 147/110 " 91/68 "
114 506.6 15625/11664 75/56 " " " "
115 511.1 104976/78125 168/125 121/90 " 51/38 39/29
116 515.5 8192/6075 " 66/49 35/26 " "
117 520.0 27/20 " " " (23/17) "
118 524.4 80000/59049 256/189 " 65/48 " 42/31
119 528.8 3125/2304 1215/896 110/81 " 19/14 "
120 533.3 531441/390625 49/36 " " 34/25 "
121 537.7 512/375 " 15/11 " " "
122 542.2 2187/1600 175/128 " 160/117 26/19 "
123 546.6 1000/729 48/35 " " " "
124 551.1 5625/4096 " 11/8 " " "
125 555.5 sA4 1048576/759375 135/98 " 91/66 (69/50) 40/29
126 560.0 864/625 112/81 " " 105/76 29/21
127 564.4 81920/59049 2835/2048 320/231 18/13 " "
128 568.8 25/18 " " " " "
129 573.3 91125/65536 1024/735 245/176 39/28 (32/23) "
130 577.7 65536/46875 625/448 88/63 " " "
131 582.2 4374/3125 7/5 " " " "
132 586.6 d5 1024/729 " 108/77 " 80/57 "
133 591.1 45/32 " " " 38/27 "
134 595.5 250000/177147 343/243 " 55/39 24/17 "
135 600.0 78125/55296 10125/7168 99/70 " " "
136 604.4 177147/125000 486/343 343/242 78/55 17/12 "
137 608.8 64/45 " " " 27/19 "
138 613.3 A4 729/512 " 77/54 " 57/40 "
139 617.7 3125/2187 10/7 " " " "
140 622.2 46875/32768 896/625 63/44 " " "
141 626.6 131072/91125 735/512 352/245 56/39 (23/16) "
142 631.1 36/25 " " " " "
143 635.5 59049/40960 4096/2835 231/160 13/9 " "
144 640.0 625/432 81/56 " " " 42/29
145 644.4 sd5 759375/524288 196/135 " 132/91 (100/69) 29/20
146 648.8 8192/5625 " 16/11 " " "
147 653.3 729/500 35/24 " " " "
148 657.7 3200/2187 256/175 225/154 117/80 19/13 "
149 662.2 375/256 " 22/15 " " "
150 666.6 781250/531441 72/49 " " 25/17 "
151 671.1 4608/3125 1792/1215 81/55 " 28/19 "
152 675.5 59049/40000 189/128 " 65/44 " 31/21
153 680.0 40/27 " " " (34/23) "
154 684.4 6075/4096 " 49/33 " " "
155 688.8 78125/52488 125/84 " " 76/51 58/39
156 693.3 23328/15625 112/75 " " 85/57 "
157 697.7 16384/10935 6125/4096 220/147 175/117 136/91 "
158 702.2 P5 3/2 " " " " "
159 706.6 98415/65536 2560/1701 385/256 176/117 128/85 "
160 711.1 15625/10368 675/448 264/175 98/65 95/63 "
161 715.5 118098/78125 189/125 121/80 " 68/45 "
162 720.0 1024/675 " 50/33 " " 44/29
163 724.4 243/160 " " 117/77 38/25 "
164 728.8 10000/6561 32/21 " " " "
165 733.3 3125/2048 " 55/36 " 26/17 29/19
166 737.7 2097152/1366875 49/32 " " (23/15) "
167 742.2 192/125 " 135/88 " " "
168 746.6 19683/12800 1575/1024 77/50 20/13 " "
169 751.1 125/81 54/35 " " " "
170 755.5 50625/32768 2048/1323 99/64 65/42 17/11 "
171 760.0 sA5 131072/84375 1215/784 256/165 121/78 76/49 31/20
172 764.4 972/625 14/9 " " " "
173 768.8 10240/6561 4096/2625 120/77 39/25 " "
174 773.3 25/16 " " " " "
175 777.7 820125/524288 196/125 " " (36/23) "
176 782.2 24576/15625 5625/3584 11/7 " " "
177 786.6 19683/12500 63/40 " 52/33 " "
178 791.1 m6 128/81 " " " 30/19 "
179 795.5 405/256 " 198/125 144/91 19/12 "
180 800.0 31250/19683 100/63 " " 27/17 "
181 804.4 78125/49152 1792/1125 35/22 " " "
182 808.8 262144/164025 625/392 " 351/220 51/32 "
183 813.3 8/5 " " " " "
184 817.7 6561/4096 " 77/48 " " "
185 822.2 3125/1944 45/28 " " " "
186 826.6 421875/262144 392/243 121/75 " (92/57) 29/18
187 831.1 16384/10125 6615/4096 160/99 21/13 " "
188 835.5 81/50 " " " 34/21 "
189 840.0 32000/19683 512/315 125/77 13/8 " "
190 844.4 625/384 " 44/27 " " "
191 848.8 n6 3188646/1953125 49/30 " " " 31/19
192 853.3 1024/625 " 18/11 " " "
193 857.7 6561/4000 105/64 " 64/39 (23/14) "
194 862.2 400/243 288/175 242/147 " 28/17 "
195 866.6 3375/2048 " 33/20 " " "
196 871.1 390625/236196 81/49 " " (38/23) 48/29
197 875.5 5184/3125 224/135 " " 63/38 58/35
198 880.0 32768/19683 1701/1024 128/77 108/65 " "
199 884.4 5/3 " " " " "
200 888.8 54675/32768 2048/1225 147/88 117/70 " "
201 893.3 78125/46656 375/224 176/105 " 57/34 52/31
202 897.7 26244/15625 42/25 " " " "
203 902.2 2048/1215 " 165/98 91/54 32/19 "
204 906.6 M6 27/16 " " " " "
205 911.1 100000/59049 320/189 " 22/13 " "
206 915.5 15625/9216 6075/3584 56/33 " (39/23) "
207 920.0 531441/312500 245/144 " 143/84 17/10 "
208 924.4 128/75 " 75/44 " " 29/17
209 928.8 2187/1280 875/512 77/45 " 65/38 "
210 933.3 1250/729 12/7 " " " "
211 937.7 sd7 28125/16384 5376/3125 55/32 " " "
212 942.2 262144/151875 441/256 " 112/65 (69/40) 31/18
213 946.6 216/125 140/81 121/70 " 19/11 "
214 951.1 102400/59049 8192/4725 343/198 26/15 " "
215 955.5 125/72 " " " 33/19 "
216 960.0 455625/262144 256/147 " 195/112 (40/23) 54/31
217 964.4 16384/9375 3125/1792 96/55 " 68/39 "
218 968.8 2187/1250 7/4 " " " "
219 973.3 1280/729 " 135/77 " 100/57 "
220 977.7 225/128 " 44/25 " " "
221 982.2 312500/177147 432/245 " 143/81 30/17 "
222 986.6 27648/15625 3584/2025 99/56 " (23/13) "
223 991.1 177147/100000 567/320 " 39/22 " "
224 995.5 m7 16/9 " " " " "
225 1000.0 3645/2048 " 98/55 " 57/32 "
226 1004.4 15625/8748 25/14 " " " "
227 1008.8 139968/78125 224/125 " " 34/19 "
228 1013.3 32768/18225 3675/2048 88/49 70/39 " "
229 1017.7 9/5 " " " " "
230 1022.2 59049/32768 1024/567 231/128 65/36 " 56/31
231 1026.6 3125/1728 405/224 " " 38/21 "
232 1031.1 708588/390625 49/27 " " " 29/16
233 1035.5 2048/1125 " 20/11 " " "
234 1040.0 729/400 175/96 " " 51/28 31/17
235 1044.4 4000/2187 64/35 " " (42/23) "
236 1048.8 1875/1024 " 11/6 " " "
237 1053.3 n7 1953125/1062882 90/49 " " (46/25) "
238 1057.7 1152/625 448/243 81/44 " 35/19 "
239 1062.2 59049/32000 945/512 231/125 24/13 " "
240 1066.6 50/27 " " " " "
241 1071.1 30375/16384 4096/2205 245/132 13/7 " "
242 1075.5 262144/140625 625/336 225/121 121/65 95/51 54/29
243 1080.0 5832/3125 28/15 " " " "
244 1084.4 4096/2187 " 144/77 " " 58/31
245 1088.8 15/8 " " " " "
246 1093.3 492075/262144 1176/625 847/450 220/117 32/17 62/33
247 1097.7 78125/41472 3375/1792 66/35 49/26 " "
248 1102.2 59049/31250 189/100 121/64 104/55 17/9 "
249 1106.6 256/135 " 125/66 91/48 36/19 "
250 1111.1 M7 243/128 " 154/81 " 19/10 "
251 1115.5 12500/6561 40/21 " " " "
252 1120.0 15625/8192 3584/1875 21/11 " " "
253 1124.4 524288/273375 245/128 " 224/117 (23/12) "
254 1128.8 48/25 " " " " "
255 1133.3 19683/10240 7875/4096 77/40 25/13 " "
256 1137.7 625/324 27/14 " " " "
257 1142.2 sd8 253125/131072 784/405 242/125 176/91 85/44 29/15
258 1146.6 32768/16875 3969/2048 64/33 " 33/17 31/16
259 1151.1 243/125 35/18 " " " "
260 1155.5 12800/6561 1024/525 150/77 39/20 " "
261 1160.0 125/64 " 88/45 " " "
262 1164.4 3125000/1594323 49/25 " " (45/23) "
263 1168.8 6144/3125 " 55/28 " 51/26 "
264 1173.3 19683/10000 63/32 " " " "
265 1177.7 160/81 " " 77/39 75/38 "
266 1182.2 2025/1024 " 99/50 " (91/46) 87/44
267 1186.6 78125/39366 125/63 " " " "
268 1191.1 31104/15625 448/225 175/88 " " "
269 1195.5 65536/32805 3125/1568 539/270 351/176 255/128 "
270 1200.0 P8 2/1 " " " " "
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