Scala analysis: tapek-ribbon
Eq-diff ribbon extension of Superpyth, made of two Tapek sequences
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 1777/1656 122.089210 2: 209/184 220.556611 3: 173/138 391.324525 4: 4273/3312 441.055973 5: 1465/1104 489.792591 6: 131/92 611.833255 7: 104/69 710.298314 8: 3673/2208 881.062469 9: 315/184 930.775275 10: 81/46 979.545656 11: 1043/552 1101.598783 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 1104/1043 98.4012 1: 1777/1656 122.0892 2: 1881/1777 98.4674 3: 692/627 170.7679 4: 4273/4152 49.7314 5: 4395/4273 48.7366 6: 1572/1465 122.0407 7: 416/393 98.4651 8: 3673/3328 170.7642 9: 3780/3673 49.7128 10: 36/35 48.7704 septimal diesis, 1/4-tone 11: 1043/972 122.0531 12: 1104/1043 98.4012
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 4395/4273 48.737 cents 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 3780/3673 49.713 cents 1: 1 4273/4152 49.731 cents 1: 1 1104/1043 98.401 cents 1: 1 416/393 98.465 cents 1: 1 1881/1777 98.467 cents 1: 1 1572/1465 122.041 cents 1: 1 1043/972 122.053 cents 1: 1 1777/1656 122.089 cents 1: 1 3673/3328 170.764 cents 1: 1 692/627 170.768 cents 2: 1 1465/1384 98.468 cents 2: 1 3888/3673 98.483 cents 2: 1 4716/4273 170.777 cents 2: 1 149/135 170.824 cents 2: 1 92/81 220.454 cents 2: 1 945/832 220.477 cents 2: 1 3554/3129 220.490 cents 2: 1 4273/3762 220.499 cents 2: 1 1664/1465 220.506 cents 2: 1 209/184 220.557 cents 2: 1 3673/3144 269.229 cents 2: 1 2076/1777 269.235 cents 3: 1 393/346 220.509 cents 3: 1 4172/3673 220.536 cents 3: 1 368/315 269.225 cents 3: 1 1465/1254 269.236 cents 3: 1 4992/4273 269.242 cents 3: 1 243/208 269.247 cents 3: 1 315/262 318.942 cents 3: 1 1254/1043 318.958 cents 3: 1 4273/3554 318.967 cents 3: 1 1777/1458 342.544 cents 3: 1 3673/2930 391.270 cents 3: 1 173/138 391.325 cents 4: 1 4416/3673 318.938 cents 4: 1 208/173 318.974 cents 4: 1 4395/3554 367.703 cents 4: 1 162/131 367.712 cents 4: 1 262/209 391.277 cents 4: 1 1043/832 391.300 cents 4: 1 3554/2835 391.314 cents 4: 1 11019/8546 440.006 cents 4: 1 378/293 440.983 cents 4: 1 209/162 441.011 cents 4: 1 4273/3312 441.056 cents 4: 1 1384/1043 489.726 cents 5: 1 14216/11019 441.027 cents 5: 1 69/52 489.702 cents 5: 1 5670/4273 489.719 cents 5: 1 3673/2768 489.738 cents 5: 1 832/627 489.742 cents 5: 1 2358/1777 489.744 cents 5: 1 1944/1465 489.753 cents 5: 1 1043/786 489.766 cents 5: 1 418/315 489.781 cents 5: 1 1465/1104 489.793 cents 5: 1 4273/3129 539.457 cents 5: 1 346/243 611.779 cents 6: 1 5832/4273 538.490 cents 6: 1 945/692 539.451 cents 6: 1 5016/3673 539.494 cents 6: 1 184/131 588.167 cents 6: 1 1465/1043 588.194 cents 6: 1 2496/1777 588.209 cents 6: 1 1777/1248 611.791 cents 6: 1 2086/1465 611.806 cents 6: 1 131/92 611.833 cents 6: 1 3673/2508 660.506 cents 6: 1 1384/945 660.549 cents 6: 1 4273/2916 661.510 cents 7: 1 243/173 588.221 cents 7: 1 6258/4273 660.543 cents 7: 1 2208/1465 710.207 cents 7: 1 315/209 710.219 cents 7: 1 1572/1043 710.234 cents 7: 1 1465/972 710.247 cents 7: 1 1777/1179 710.256 cents 7: 1 627/416 710.258 cents 7: 1 5536/3673 710.262 cents 7: 1 4273/2835 710.281 cents 7: 1 104/69 710.298 cents 7: 1 11019/7108 758.973 cents 8: 1 1043/692 710.274 cents 8: 1 6624/4273 758.944 cents 8: 1 324/209 758.989 cents 8: 1 293/189 759.017 cents 8: 1 17092/11019 759.994 cents 8: 1 2835/1777 808.686 cents 8: 1 1664/1043 808.700 cents 8: 1 209/131 808.723 cents 8: 1 131/81 832.288 cents 8: 1 7108/4395 832.297 cents 8: 1 173/104 881.026 cents 8: 1 3673/2208 881.062 cents 9: 1 276/173 808.675 cents 9: 1 5860/3673 808.730 cents 9: 1 2916/1777 857.456 cents 9: 1 7108/4273 881.033 cents 9: 1 1043/627 881.042 cents 9: 1 524/315 881.058 cents 9: 1 416/243 930.753 cents 9: 1 4273/2496 930.758 cents 9: 1 2508/1465 930.764 cents 9: 1 315/184 930.775 cents 9: 1 3673/2086 979.464 cents 9: 1 692/393 979.491 cents 10: 1 1777/1038 930.765 cents 10: 1 6288/3673 930.771 cents 10: 1 368/209 979.443 cents 10: 1 1465/832 979.494 cents 10: 1 7524/4273 979.501 cents 10: 1 3129/1777 979.510 cents 10: 1 1664/945 979.523 cents 10: 1 81/46 979.546 cents 10: 1 270/149 1029.176 cents 10: 1 4273/2358 1029.223 cents 10: 1 3673/1944 1101.517 cents 10: 1 2768/1465 1101.532 cents 11: 1 627/346 1029.232 cents 11: 1 6656/3673 1029.236 cents 11: 1 3312/1777 1077.911 cents 11: 1 1944/1043 1077.947 cents 11: 1 1465/786 1077.959 cents 11: 1 3554/1881 1101.533 cents 11: 1 393/208 1101.535 cents 11: 1 1043/552 1101.599 cents 11: 1 8304/4273 1150.269 cents 11: 1 3673/1890 1150.287 cents 11: 1 35/18 1151.230 cents septimal semi-diminished octave 11: 1 8546/4395 1151.263 cents Highest number of different intervals for one interval class: 12 Average number of different intervals per interval class: 12.00000 = 12
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 122.1 220.6 391.3 441.1 489.8 611.8 710.3 881.1 930.8 979.5 1101.6 1200.0 122.1 : 98.5 269.2 319.0 367.7 489.7 588.2 759.0 808.7 857.5 979.5 1077.9 1200.0 220.6 : 170.8 220.5 269.2 391.3 489.7 660.5 710.2 759.0 881.0 979.4 1101.5 1200.0 391.3 : 49.7 98.5 220.5 319.0 489.7 539.5 588.2 710.3 808.7 930.8 1029.2 1200.0 441.1 : 48.7 170.8 269.2 440.0 489.7 538.5 660.5 758.9 881.0 979.5 1150.3 1200.0 489.8 : 122.0 220.5 391.3 441.0 489.8 611.8 710.2 832.3 930.8 1101.5 1151.3 1200.0 611.8 : 98.5 269.2 318.9 367.7 489.8 588.2 710.3 808.7 979.5 1029.2 1078.0 1200.0 710.3 : 170.8 220.5 269.2 391.3 489.7 611.8 710.3 881.0 930.8 979.5 1101.5 1200.0 881.1 : 49.7 98.5 220.5 318.9 441.0 539.5 710.3 760.0 808.7 930.8 1029.2 1200.0 930.8 : 48.8 170.8 269.2 391.3 489.8 660.5 710.3 759.0 881.1 979.5 1150.3 1200.0 979.5 : 122.1 220.5 342.5 441.0 611.8 661.5 710.2 832.3 930.8 1101.5 1151.2 1200.0 1101.6: 98.4 220.5 319.0 489.7 539.5 588.2 710.2 808.7 979.5 1029.2 1077.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7366 .. 170.7679 cents 2956916/2755665, 122.0313 cents 4395/4273, 48.7366 cents 2: 98.4681 .. 269.2353 cents 2873184/2603305, 170.7672 cents 918555/957728,-72.2998 cents 3: 220.5087 .. 391.3245 cents 29929/27117, 170.8158 cents 232787/239432,-48.7266 cents 4: 318.9375 .. 489.7257 cents 635429/575736, 170.7882 cents 609408/635429,-72.3870 cents 5: 441.0267 .. 611.7789 cents 635429/575748, 170.7521 cents 1853411/1906287,-48.6990 cents 6: 538.4897 .. 661.5103 cents 18258529/17006112, 123.0206 cents 708588/739229,-73.2892 cents 7: 588.2211 .. 758.9733 cents 635429/575748, 170.7521 cents 708588/739229,-73.2892 cents 8: 710.2743 .. 881.0625 cents 635429/575736, 170.7882 cents 1853411/1906287,-48.6990 cents 9: 808.6755 .. 979.4913 cents 29929/27117, 170.8158 cents 609408/635429,-72.3870 cents 10: 930.7647 .. 1101.5319 cents 2873184/2603305, 170.7672 cents 232787/239432,-48.7266 cents 11: 1029.2321 .. 1151.2634 cents 2956916/2755665, 122.0313 cents 918555/957728,-72.2998 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 4395/4273, 48.7366 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 692/627, 170.7679 cents Average / Smallest step : 2.051845 Largest / Average step : 1.707679 Largest / Smallest step : 3.503893 Median interval of one step : 98.46623 cents, amount: 0 Least squares average step : 102.04919 cents, oct.: 1224.59023 cents Scale is not proper Step pattern alph. order: ABCDEFGHIJKL Step pattern size order : JGLDAHFKCBIE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.00067 cents Scale diversity : 1.329326 Lumma stability : 0.081228 Lumma impropriety factor : 0.506038 Rothenberg efficiency : 0.166667 redundancy: 0.833333 Efficiency x scale size : 2.000000 Number of different interval sizes : 132 = 12.00000 / class Number of one step interval sizes : 12 Highest interval variety : 12 Mean interval variety : 12.00000 = 12 Median interval variety : 12 Lowest interval variety : 12 Smallest interval difference : 2603305/2603304, 0.0007 cents Number of recognisable fifths : 10, average 710.2537 cents Formal octave complements present : 1 = 8.3333% -- Rational properties -- Prime limit : 4273 Odd number limit : 11019 (O: 11019 U: 11019) Highest odd numerator or denominator: 4273 Harmonicity values : limit above prime count Fundamental : 1/6624, -12.6935 octaves, 0.0395 Hz. Guide tone : too high to compute Sum of Mann's harmonic distance : 11396.0, average 949.66667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 29.55067, average 2.46256 Sum of Tenney's harmonic distance : 58.03285, average 4.83607 Vogel's harmonic complexity : 888.08333 Wille's k value : 5509 Lattice compactness : 290.48329, average 3.72414 Lattice compactness (without 2's) : 170.91740, average 2.19125 Number of different primes : 15 Prime exponents' range, average, count, tones@limit: 2: -5 .. 3 -2.08333 33 1 3: -2 .. 4 -0.25000 15 5: 0 .. 1 0.16667 2 7: 0 .. 1 0.16667 2 11: 0 .. 1 0.08333 1 13: 0 .. 1 0.08333 1 19: 0 .. 1 0.08333 1 23: -1 .. 0 -0.91667 11 4 131: 0 .. 1 0.08333 1 1 149: 0 .. 1 0.08333 1 1 173: 0 .. 1 0.08333 1 1 293: 0 .. 1 0.08333 1 1 1777: 0 .. 1 0.08333 1 1 3673: 0 .. 1 0.08333 1 1 4273: 0 .. 1 0.08333 1 1 Average exponent except 2's : 0 / 12 = 0.00000 Average absolute exponent except 2's: 40 / 12 = 3.33333
FIT/MODE
12: 1 1 2 0 1 1 1 2 0 1 1 1 N T3 SD: 19.8920 c. M: 41.0560 c. 15: 2 1 2 1 0 2 1 2 1 0 2 1 N SD: 22.2980 c. M:-38.9440 c. 16: 2 1 2 1 1 1 1 3 0 1 2 1 N SD: 21.6888 c. M: 35.2983 c. 17: 2 1 3 0 1 2 1 3 0 1 2 1 N SD: 19.8629 c. M:-36.5846 c. 18: 2 1 3 1 0 2 2 2 1 1 2 1 N SD: 18.5402 c. M:-31.7346 c. 19: 2 1 3 1 1 2 1 3 1 1 1 2 N SD: 18.3348 c. M: 31.0829 c. 21: 2 2 3 1 1 2 1 3 1 1 2 2 N SD: 16.0880 c. M: 24.5840 c. 22: 2 2 3 1 1 2 2 3 1 1 2 2 N SD: 7.2508 c. M: 12.9983 c. 27: 3 2 4 1 1 3 2 4 1 1 3 2 N SD: 6.3690 c. M:-11.2441 c. 37: 4 3 5 2 1 4 3 5 2 1 4 3 N SD: 6.3445 c. M:-12.9981 c. 49: 5 4 7 2 2 5 4 7 2 2 5 4 N SD: 0.3161 c. M:-0.5702 c. 316: 32 26 45 13 13 32 26 45 13 13 32 26 N SD: 0.3284 c. M: 0.5702 c. 365: 37 30 52 15 15 37 30 52 15 15 37 30 N SD: 0.2740 c. M: 0.5080 c. 414: 42 34 59 17 17 42 34 59 17 17 42 34 N SD: 0.2381 c. M: 0.4763 c. 463: 47 38 66 19 19 47 38 66 19 19 47 38 N SD: 0.2150 c. M: 0.4512 c. 512: 52 42 73 21 21 52 42 73 21 21 52 42 N SD: 0.2009 c. M: 0.4310 c. 561: 57 46 80 23 23 57 46 80 23 23 57 46 N SD: 0.1931 c. M: 0.4143 c. 610: 62 50 87 25 25 62 50 87 25 25 62 50 N SD: 0.1895 c. M: 0.4002 c. 647: 66 53 92 27 26 66 53 92 27 26 66 53 N SD: 0.2047 c. M:-0.3660 c. 659: 67 54 94 27 27 67 54 94 27 27 67 54 N SD: 0.1888 c. M: 0.3883 c. 669: 68 55 95 28 27 68 55 95 28 27 68 55 N SD: 0.1887 c. M: 0.3450 c. 696: 71 57 99 29 28 71 57 99 29 28 71 57 N SD: 0.1928 c. M:-0.3246 c. 708: 72 58 101 29 29 72 58 101 29 29 72 58 N SD: 0.1899 c. M: 0.3780 c. 718: 73 59 102 30 29 73 59 102 30 29 73 59 N SD: 0.1559 c. M: 0.2825 c. 767: 78 63 109 32 31 78 63 109 32 31 78 63 N SD: 0.1277 c. M: 0.2280 c. 816: 83 67 116 34 33 83 67 116 34 33 83 67 N SD: 0.1036 c. M: 0.1801 c. 865: 88 71 123 36 35 88 71 123 36 35 88 71 N SD: 0.0832 c. M: 0.1376 c. 914: 93 75 130 38 37 93 75 130 38 37 93 75 N SD: 0.0665 c. M: 0.1146 c. 963: 98 79 137 40 39 98 79 137 40 39 98 79 N SD: 0.0538 c. M: 0.1064 c. 1012: 103 83 144 42 41 103 83 144 42 41 103 83 N SD: 0.0459 c. M: 0.0990 c. 1061: 108 87 151 44 43 108 87 151 44 43 108 87 N SD: 0.0432 c. M: 0.0923 c. 1110: 113 91 158 46 45 113 91 158 46 45 113 91 N SD: 0.0453 c. M: 0.0862 c. 1159: 118 95 165 48 47 118 95 165 48 47 118 95 N SD: 0.0506 c. M:-0.0851 c. 1377: 140 113 196 57 56 140 113 196 57 56 140 113 N SD: 0.0598 c. M: 0.0974 c. 1426: 145 117 203 59 58 145 117 203 59 58 145 117 N SD: 0.0552 c. M: 0.1023 c. 1475: 150 121 210 61 60 150 121 210 61 60 150 121 N SD: 0.0530 c. M: 0.1068 c. 1524: 155 125 217 63 62 155 125 217 63 62 155 125 N SD: 0.0528 c. M: 0.1111 c. 1975: 201 162 281 82 80 201 162 281 82 80 201 162 N SD: 0.0492 c. M: 0.1026 c. 2073: 211 170 295 86 84 211 170 295 86 84 211 170 N SD: 0.0439 c. M: 0.0956 c. 2171: 221 178 309 90 88 221 178 309 90 88 221 178 N SD: 0.0438 c. M: 0.0892 c. 2242: 228 184 319 93 91 228 184 319 93 91 228 184 N SD: 0.0515 c. M: 0.0823 c. 2269: 231 186 323 94 92 231 186 323 94 92 231 186 N SD: 0.0477 c. M: 0.0833 c. 2291: 233 188 326 95 93 233 188 326 95 93 233 188 N SD: 0.0458 c. M: 0.0711 c. 2340: 238 192 333 97 95 238 192 333 97 95 238 192 N SD: 0.0410 c. M: 0.0603 c. 2389: 243 196 340 99 97 243 196 340 99 97 243 196 N SD: 0.0371 c. M: 0.0563 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 4.1717 cents 3 x x x x 4 x x 5 x x x 6 S SD: 2.9621 cents 4 x x 5 x x x 6 x x 7 x 8 S SD: 3.6197 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 22.4277 cents 6 x 7 x x 8 x 9:10 x x 11:12 S SD: 11.8112 cents 7 x 8 x 9 x 10:11 x 12 x 13:14 S SD: 11.3314 cents 8 x 9:10 x x 11:12:13 x 14:15:16 S SD: 9.6579 cents 9 x 10:11 x 12:13:14:15 x 16:17:18 S SD: 9.5158 cents 10:11 x x 13 x 14:15 x 17:18:19:20 SD: 8.5068 cents 11:12:13 x 14:15:16:17:18:19 x 21:22 SD: 11.3623 cents 12:13:14:15 x 16:17:18:20 x 21:23:24 SD: 5.8262 cents 13:14:15:16:17 x 19:20 x 22:23:25:26 SD: 8.3865 cents 14:15:16 x 18:19:20:21:23:24:25:26:28 SD: 5.5482 cents 15:16:17:19 x 20:21:23:25:26 x 28:30 SD: 5.6293 cents 16:17:18:20 x 21:23:24:27 x 28:30:32 SD: 4.6957 cents 18:19:20 x 23:24:26:27:30:31:32:34:36 SD: 5.5221 cents 19:20:22:24 x 25:27:29:32 x 33:36:38 SD: 6.4302 cents 20:21:23:25:26:27:28:30:33:34:35:38:40 SD: 5.5527 cents 21:23:24:26:27:28:30:32:35:36:37:40:42 SD: 4.1975 cents 22:24:25 x 28:29:31:33:37:38:39:42:44 SD: 4.9396 cents 23:25:26:29:30:31:33:35:38:39:41:43:46 SD: 4.8594 cents 24:26:27:30:31:32:34:36:40:41:42:45:48 S SD: 2.7772 cents 28:30:32:35:36:37:40:42:47:48:49:53:56 SD: 2.2187 cents 38:41:43:48:49:50:54:57:63:65:67:72:76 SD: 2.1518 cents 42:45:48:53:54:56:60:63:70:72:74:79:84 SD: 1.9257 cents 45:48:51:56:58:60:64:68:75:77:79:85:90 SD: 1.7043 cents 51:55:58:64:66:68:73:77:85:87:90:96:102 SD: 1.6130 cents 52:56:59:65:67:69:74:78:87:89:92:98:104 SD: 1.5126 cents 59:63:67:74:76:78:84:89:98:101:104:111:118 SD: 1.1510 cents 79:85:90:99:102:105:112:119:131:135:139:149:158 SD: 1.0779 cents 80:86:91:100:103:106:114:121:133:137:141:151:160 SD: 0.8572 cents 83:89:94:104:107:110:118:125:138:142:146:157:166 SD: 0.6076 cents 110:118:125:138:142:146:157:166:183:188:194:208:220 SD: 0.5418 cents 125:134:142:157:161:166:178:188:208:214:220:236:250 SD: 0.5317 cents 134:144:152:168:173:178:191:202:223:229:236:253:268 SD: 0.4657 cents 162:174:184:203:209:215:231:244:269:277:285:306:324 SD: 0.4392 cents 177:190:201:222:228:235:252:267:294:303:312:334:354 SD: 0.4301 cents 189:203:215:237:244:251:269:285:314:324:333:357:378 SD: 0.4223 cents 193:207:219:242:249:256:275:291:321:330:340:365:386 SD: 0.3107 cents 264:283:300:331:341:350:376:398:439:452:465:499:528 SD: 0.2863 cents 272:292:309:341:351:361:387:410:452:466:479:514:544 SD: 0.2312 cents 288:309:327:361:372:382:410:434:479:493:507:544:576 SD: 0.2072 cents 300:322:341:376:387:398:427:452:499:514:528:567:600 SD: 0.2024 cents 368:395:418:461:475:488:524:555:612:630:648:695:736 SD: 0.2016 cents 382:410:434:479:493:507:544:576:635:654:673:722:764 SD: 0.1670 cents 410:440:466:514:529:544:584:618:682:702:722:775:820 SD: 0.1228 cents 434:466:493:544:560:576:618:654:722:743:764:820:868 SD: 0.1100 cents 493:529:560:618:636:654:702:743:820:844:868:932:986 SD: 0.0934 cents