;; BEATS = from 0 to 200, contains two-part list: ;; first = all subdivs of this length that use 2,3,4,5-ples only ;; second = corresponding durations for those subdivisions (define beats '((nil nil) (( 1 2 3 4 5 ) ( 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 10 ) ( 2 1 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 9 12 15 ) ( 3 3/2 1 3/4 3/5 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 10 12 16 20 ) ( 4 2 4/3 1 4/5 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 10 15 20 25 ) ( 5 5/2 5/3 5/4 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 9 10 12 15 18 24 30 ) ( 6 3 2 3/2 6/5 1 3/4 2/3 3/5 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 7 14 21 28 35 ) ( 7 7/2 7/3 7/4 7/5 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 10 12 16 20 24 32 40 ) ( 8 4 8/3 2 8/5 4/3 1 4/5 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 9 12 15 18 27 36 45 ) ( 9 9/2 3 9/4 9/5 3/2 1 3/4 3/5 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 10 15 20 25 30 40 50 ) ( 10 5 10/3 5/2 2 5/3 5/4 1 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 11 22 33 44 55 ) ( 11 11/2 11/3 11/4 11/5 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 36 48 60 ) ( 12 6 4 3 12/5 2 3/2 4/3 6/5 1 4/5 3/4 2/3 3/5 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 13 26 39 52 65 ) ( 13 13/2 13/3 13/4 13/5 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 7 8 10 14 21 28 35 42 56 70 ) ( 14 7 14/3 7/2 14/5 7/3 2 7/4 7/5 1 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 9 10 12 15 20 25 30 45 60 75 ) ( 15 15/2 5 15/4 3 5/2 5/3 3/2 5/4 1 3/4 3/5 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 10 12 16 20 24 32 40 48 64 80 ) ( 16 8 16/3 4 16/5 8/3 2 8/5 4/3 1 4/5 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 17 34 51 68 85 ) ( 17 17/2 17/3 17/4 17/5 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 9 10 12 15 18 24 27 30 36 45 54 72 90 ) ( 18 9 6 9/2 18/5 3 9/4 2 9/5 3/2 6/5 1 3/4 2/3 3/5 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 19 38 57 76 95 ) ( 19 19/2 19/3 19/4 19/5 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 10 12 15 16 20 25 30 40 50 60 80 100 ) ( 20 10 20/3 5 4 10/3 5/2 2 5/3 4/3 5/4 1 4/5 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 7 9 12 14 15 21 28 35 42 63 84 105 ) ( 21 21/2 7 21/4 21/5 7/2 3 7/3 7/4 3/2 7/5 1 3/4 3/5 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 10 11 22 33 44 55 66 88 110 ) ( 22 11 22/3 11/2 22/5 11/3 11/4 11/5 2 1 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 23 46 69 92 115 ) ( 23 23/2 23/3 23/4 23/5 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 32 36 40 48 60 72 96 120 ) ( 24 12 8 6 24/5 4 3 8/3 12/5 2 8/5 3/2 4/3 6/5 1 4/5 3/4 2/3 3/5 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 10 15 20 25 50 75 100 125 ) ( 25 25/2 25/3 25/4 5 5/2 5/3 5/4 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 10 13 26 39 52 65 78 104 130 ) ( 26 13 26/3 13/2 26/5 13/3 13/4 13/5 2 1 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 9 12 15 18 27 36 45 54 81 108 135 ) ( 27 27/2 9 27/4 27/5 9/2 3 9/4 9/5 3/2 1 3/4 3/5 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 7 8 10 12 14 16 20 21 28 35 42 56 70 84 112 140 ) ( 28 14 28/3 7 28/5 14/3 4 7/2 14/5 7/3 2 7/4 7/5 4/3 1 4/5 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 29 58 87 116 145 ) ( 29 29/2 29/3 29/4 29/5 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 9 10 12 15 18 20 24 25 30 40 45 50 60 75 90 120 150 ) ( 30 15 10 15/2 6 5 15/4 10/3 3 5/2 2 5/3 3/2 5/4 6/5 1 3/4 2/3 3/5 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 31 62 93 124 155 ) ( 31 31/2 31/3 31/4 31/5 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 10 12 16 20 24 32 40 48 64 80 96 128 160 ) ( 32 16 32/3 8 32/5 16/3 4 16/5 8/3 2 8/5 4/3 1 4/5 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 9 11 12 15 22 33 44 55 66 99 132 165 ) ( 33 33/2 11 33/4 33/5 11/2 11/3 3 11/4 11/5 3/2 1 3/4 3/5 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 10 17 34 51 68 85 102 136 170 ) ( 34 17 34/3 17/2 34/5 17/3 17/4 17/5 2 1 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 7 10 14 15 20 21 25 28 35 70 105 140 175 ) ( 35 35/2 35/3 35/4 7 5 7/2 5/2 7/3 7/4 5/3 7/5 5/4 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 27 30 36 45 48 54 60 72 90 108 144 180 ) ( 36 18 12 9 36/5 6 9/2 4 18/5 3 12/5 9/4 2 9/5 3/2 4/3 6/5 1 4/5 3/4 2/3 3/5 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 37 74 111 148 185 ) ( 37 37/2 37/3 37/4 37/5 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 10 19 38 57 76 95 114 152 190 ) ( 38 19 38/3 19/2 38/5 19/3 19/4 19/5 2 1 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 9 12 13 15 26 39 52 65 78 117 156 195 ) ( 39 39/2 13 39/4 39/5 13/2 13/3 13/4 3 13/5 3/2 1 3/4 3/5 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 10 12 15 16 20 24 25 30 32 40 50 60 80 100 120 160 200 ) ( 40 20 40/3 10 8 20/3 5 4 10/3 8/3 5/2 2 5/3 8/5 4/3 5/4 1 4/5 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 41 82 123 164 205 ) ( 41 41/2 41/3 41/4 41/5 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 7 8 9 10 12 14 15 18 21 24 28 30 35 42 56 63 70 84 105 126 168 210 ) ( 42 21 14 21/2 42/5 7 6 21/4 14/3 21/5 7/2 3 14/5 7/3 2 7/4 3/2 7/5 6/5 1 3/4 2/3 3/5 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 43 86 129 172 215 ) ( 43 43/2 43/3 43/4 43/5 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 10 11 12 16 20 22 33 44 55 66 88 110 132 176 220 ) ( 44 22 44/3 11 44/5 22/3 11/2 22/5 4 11/3 11/4 11/5 2 4/3 1 4/5 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 9 10 12 15 18 20 25 27 30 36 45 60 75 90 135 180 225 ) ( 45 45/2 15 45/4 9 15/2 5 9/2 15/4 3 5/2 9/4 9/5 5/3 3/2 5/4 1 3/4 3/5 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 10 23 46 69 92 115 138 184 230 ) ( 46 23 46/3 23/2 46/5 23/3 23/4 23/5 2 1 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 47 94 141 188 235 ) ( 47 47/2 47/3 47/4 47/5 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 32 36 40 48 60 64 72 80 96 120 144 192 240 ) ( 48 24 16 12 48/5 8 6 16/3 24/5 4 16/5 3 8/3 12/5 2 8/5 3/2 4/3 6/5 1 4/5 3/4 2/3 3/5 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 7 14 21 28 35 49 98 147 196 245 ) ( 49 49/2 49/3 49/4 49/5 7 7/2 7/3 7/4 7/5 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 10 15 20 25 30 40 50 75 100 125 150 200 250 ) ( 50 25 50/3 25/2 10 25/3 25/4 5 10/3 5/2 2 5/3 5/4 1 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 9 12 15 17 34 51 68 85 102 153 204 255 ) ( 51 51/2 17 51/4 51/5 17/2 17/3 17/4 17/5 3 3/2 1 3/4 3/5 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 10 12 13 16 20 26 39 52 65 78 104 130 156 208 260 ) ( 52 26 52/3 13 52/5 26/3 13/2 26/5 13/3 4 13/4 13/5 2 4/3 1 4/5 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 53 106 159 212 265 ) ( 53 53/2 53/3 53/4 53/5 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 9 10 12 15 18 24 27 30 36 45 54 72 81 90 108 135 162 216 270 ) ( 54 27 18 27/2 54/5 9 27/4 6 27/5 9/2 18/5 3 9/4 2 9/5 3/2 6/5 1 3/4 2/3 3/5 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 10 11 15 20 22 25 33 44 55 110 165 220 275 ) ( 55 55/2 55/3 55/4 11 11/2 5 11/3 11/4 5/2 11/5 5/3 5/4 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 7 8 10 12 14 16 20 21 24 28 32 35 40 42 56 70 84 112 140 168 224 280 ) ( 56 28 56/3 14 56/5 28/3 8 7 28/5 14/3 4 7/2 14/5 8/3 7/3 2 7/4 8/5 7/5 4/3 1 4/5 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 9 12 15 19 38 57 76 95 114 171 228 285 ) ( 57 57/2 19 57/4 57/5 19/2 19/3 19/4 19/5 3 3/2 1 3/4 3/5 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 10 29 58 87 116 145 174 232 290 ) ( 58 29 58/3 29/2 58/5 29/3 29/4 29/5 2 1 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 59 118 177 236 295 ) ( 59 59/2 59/3 59/4 59/5 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 30 36 40 45 48 50 60 75 80 90 100 120 150 180 240 300 ) ( 60 30 20 15 12 10 15/2 20/3 6 5 4 15/4 10/3 3 5/2 12/5 2 5/3 3/2 4/3 5/4 6/5 1 4/5 3/4 2/3 3/5 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 61 122 183 244 305 ) ( 61 61/2 61/3 61/4 61/5 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 10 31 62 93 124 155 186 248 310 ) ( 62 31 62/3 31/2 62/5 31/3 31/4 31/5 2 1 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 7 9 12 14 15 18 21 27 28 35 36 42 45 63 84 105 126 189 252 315 ) ( 63 63/2 21 63/4 63/5 21/2 9 7 21/4 9/2 21/5 7/2 3 7/3 9/4 9/5 7/4 3/2 7/5 1 3/4 3/5 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 10 12 16 20 24 32 40 48 64 80 96 128 160 192 256 320 ) ( 64 32 64/3 16 64/5 32/3 8 32/5 16/3 4 16/5 8/3 2 8/5 4/3 1 4/5 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 10 13 15 20 25 26 39 52 65 130 195 260 325 ) ( 65 65/2 65/3 65/4 13 13/2 5 13/3 13/4 13/5 5/2 5/3 5/4 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 9 10 11 12 15 18 22 24 30 33 44 55 66 88 99 110 132 165 198 264 330 ) ( 66 33 22 33/2 66/5 11 33/4 22/3 33/5 6 11/2 22/5 11/3 3 11/4 11/5 2 3/2 6/5 1 3/4 2/3 3/5 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 67 134 201 268 335 ) ( 67 67/2 67/3 67/4 67/5 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 10 12 16 17 20 34 51 68 85 102 136 170 204 272 340 ) ( 68 34 68/3 17 68/5 34/3 17/2 34/5 17/3 17/4 4 17/5 2 4/3 1 4/5 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 9 12 15 23 46 69 92 115 138 207 276 345 ) ( 69 69/2 23 69/4 69/5 23/2 23/3 23/4 23/5 3 3/2 1 3/4 3/5 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 7 8 10 14 15 20 21 25 28 30 35 40 42 50 56 70 105 140 175 210 280 350 ) ( 70 35 70/3 35/2 14 35/3 10 35/4 7 5 14/3 7/2 10/3 14/5 5/2 7/3 2 7/4 5/3 7/5 5/4 1 2/3 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 71 142 213 284 355 ) ( 71 71/2 71/3 71/4 71/5 1 1/2 1/3 1/4 1/5 )) (( 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 27 30 32 36 40 45 48 54 60 72 90 96 108 120 144 180 216 288 360 ) ( 72 36 24 18 72/5 12 9 8 36/5 6 24/5 9/2 4 18/5 3 8/3 12/5 9/4 2 9/5 8/5 3/2 4/3 6/5 1 4/5 3/4 2/3 3/5 1/2 2/5 1/3 1/4 1/5 )) (( 1 2 3 4 5 73 146 219 292 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