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Table of 270edo intervals: Difference between revisions

VisualWikitext
Wikispaces>genewardsmith
**Imported revision 296891468 - Original comment: **
 
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:genewardsmith|genewardsmith]] and made on <tt>2012-01-31 02:02:46 UTC</tt>.<br>
: The original revision id was <tt>296891468</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 || 539/270 || 351/176 ||
|| 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]]
Retrieved from "https://en.xen.wiki/w/Table_of_270edo_intervals"