Scala analysis: xen18-erlich-porcupine-22
15L 7s MOS for Porcupine, L=60.67, s=40.98
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 60.670 cents 60.670000 2: 101.650 cents 101.650000 3: 162.320 cents 162.320000 4: 222.990 cents 222.990000 5: 263.970 cents 263.970000 6: 324.640 cents 324.640000 7: 385.310 cents 385.310000 8: 426.290 cents 426.290000 9: 486.960 cents 486.960000 10: 547.630 cents 547.630000 11: 588.610 cents 588.610000 12: 649.280 cents 649.280000 13: 709.950 cents 709.950000 14: 770.620 cents 770.620000 15: 811.600 cents 811.600000 16: 872.270 cents 872.270000 17: 932.940 cents 932.940000 18: 973.920 cents 973.920000 19: 1034.590 cents 1034.590000 20: 1095.260 cents 1095.260000 21: 1136.240 cents 1136.240000 22: 1196.910 cents 1196.910000
SHOW/INTERVAL
0: 60.6700 cents 60.6700 1: 60.6700 cents 60.6700 2: 40.9800 cents 40.9800 3: 60.6700 cents 60.6700 4: 60.6700 cents 60.6700 5: 40.9800 cents 40.9800 6: 60.6700 cents 60.6700 7: 60.6700 cents 60.6700 8: 40.9800 cents 40.9800 9: 60.6700 cents 60.6700 10: 60.6700 cents 60.6700 11: 40.9800 cents 40.9800 12: 60.6700 cents 60.6700 13: 60.6700 cents 60.6700 14: 60.6700 cents 60.6700 15: 40.9800 cents 40.9800 16: 60.6700 cents 60.6700 17: 60.6700 cents 60.6700 18: 40.9800 cents 40.9800 19: 60.6700 cents 60.6700 20: 60.6700 cents 60.6700 21: 40.9800 cents 40.9800 22: 60.6700 cents 60.6700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 40.98000 cents 1: 15 60.67000 cents 2: 14 101.65000 cents 2: 8 121.34000 cents 3: 21 162.32000 cents 3: 1 182.01000 cents 4: 6 203.30000 cents 4: 16 222.99000 cents 5: 13 263.97000 cents 5: 9 283.66000 cents 6: 20 324.64000 cents 6: 2 344.33000 cents 7: 5 365.62000 cents 7: 17 385.31000 cents 8: 12 426.29000 cents 8: 10 445.98000 cents 9: 19 486.96000 cents 9: 3 506.65000 cents 10: 4 527.94000 cents 10: 18 547.63000 cents 11: 11 588.61000 cents 11: 11 608.30000 cents 12: 18 649.28000 cents 12: 4 668.97000 cents 13: 3 690.26000 cents 13: 19 709.95000 cents 14: 10 750.93000 cents 14: 12 770.62000 cents 15: 17 811.60000 cents 15: 5 831.29000 cents 16: 2 852.58000 cents 16: 20 872.27000 cents 17: 9 913.25000 cents 17: 13 932.94000 cents 18: 16 973.92000 cents 18: 6 993.61000 cents 19: 1 1014.90000 cents 19: 21 1034.59000 cents 20: 8 1075.57000 cents 20: 14 1095.26000 cents 21: 15 1136.24000 cents 21: 7 1155.93000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0.0 : 60.7 101.7 162.3 223.0 264.0 324.6 385.3 426.3 487.0 547.6 588.6 649.3 710.0 770.6 811.6 872.3 932.9 973.9 1034.6 1095.3 1136.2 1196.9 60.7 : 41.0 101.6 162.3 203.3 264.0 324.6 365.6 426.3 487.0 527.9 588.6 649.3 709.9 750.9 811.6 872.3 913.2 973.9 1034.6 1075.6 1136.2 1196.9 101.7 : 60.7 121.3 162.3 223.0 283.7 324.6 385.3 446.0 487.0 547.6 608.3 669.0 709.9 770.6 831.3 872.3 932.9 993.6 1034.6 1095.3 1155.9 1196.9 162.3 : 60.7 101.7 162.3 223.0 264.0 324.6 385.3 426.3 487.0 547.6 608.3 649.3 709.9 770.6 811.6 872.3 932.9 973.9 1034.6 1095.3 1136.2 1196.9 223.0 : 41.0 101.6 162.3 203.3 264.0 324.6 365.6 426.3 487.0 547.6 588.6 649.3 709.9 750.9 811.6 872.3 913.2 973.9 1034.6 1075.6 1136.2 1196.9 264.0 : 60.7 121.3 162.3 223.0 283.7 324.6 385.3 446.0 506.7 547.6 608.3 669.0 709.9 770.6 831.3 872.3 932.9 993.6 1034.6 1095.3 1155.9 1196.9 324.6 : 60.7 101.7 162.3 223.0 264.0 324.6 385.3 446.0 487.0 547.6 608.3 649.3 709.9 770.6 811.6 872.3 932.9 973.9 1034.6 1095.3 1136.2 1196.9 385.3 : 41.0 101.7 162.3 203.3 264.0 324.6 385.3 426.3 487.0 547.6 588.6 649.3 710.0 750.9 811.6 872.3 913.3 973.9 1034.6 1075.6 1136.2 1196.9 426.3 : 60.7 121.3 162.3 223.0 283.7 344.3 385.3 446.0 506.7 547.6 608.3 669.0 709.9 770.6 831.3 872.3 932.9 993.6 1034.6 1095.3 1155.9 1196.9 487.0 : 60.7 101.6 162.3 223.0 283.7 324.6 385.3 446.0 487.0 547.6 608.3 649.3 709.9 770.6 811.6 872.3 932.9 973.9 1034.6 1095.3 1136.2 1196.9 547.6 : 41.0 101.7 162.3 223.0 264.0 324.6 385.3 426.3 487.0 547.6 588.6 649.3 710.0 750.9 811.6 872.3 913.3 973.9 1034.6 1075.6 1136.2 1196.9 588.6 : 60.7 121.3 182.0 223.0 283.7 344.3 385.3 446.0 506.7 547.6 608.3 669.0 710.0 770.6 831.3 872.3 932.9 993.6 1034.6 1095.3 1155.9 1196.9 649.3 : 60.7 121.3 162.3 223.0 283.7 324.6 385.3 446.0 487.0 547.6 608.3 649.3 709.9 770.6 811.6 872.3 932.9 973.9 1034.6 1095.3 1136.2 1196.9 710.0 : 60.7 101.6 162.3 223.0 264.0 324.6 385.3 426.3 487.0 547.6 588.6 649.3 709.9 750.9 811.6 872.3 913.2 973.9 1034.6 1075.6 1136.2 1196.9 770.6 : 41.0 101.6 162.3 203.3 264.0 324.6 365.6 426.3 487.0 527.9 588.6 649.3 690.3 750.9 811.6 852.6 913.2 973.9 1014.9 1075.6 1136.2 1196.9 811.6 : 60.7 121.3 162.3 223.0 283.7 324.6 385.3 446.0 487.0 547.6 608.3 649.3 709.9 770.6 811.6 872.3 932.9 973.9 1034.6 1095.3 1155.9 1196.9 872.3 : 60.7 101.7 162.3 223.0 264.0 324.6 385.3 426.3 487.0 547.6 588.6 649.3 709.9 750.9 811.6 872.3 913.3 973.9 1034.6 1095.3 1136.2 1196.9 932.9 : 41.0 101.6 162.3 203.3 264.0 324.6 365.6 426.3 487.0 527.9 588.6 649.3 690.3 750.9 811.6 852.6 913.2 973.9 1034.6 1075.6 1136.2 1196.9 973.9 : 60.7 121.3 162.3 223.0 283.7 324.6 385.3 446.0 487.0 547.6 608.3 649.3 710.0 770.6 811.6 872.3 932.9 993.6 1034.6 1095.3 1155.9 1196.9 1034.6: 60.7 101.6 162.3 223.0 264.0 324.6 385.3 426.3 487.0 547.6 588.6 649.3 709.9 750.9 811.6 872.3 932.9 973.9 1034.6 1095.3 1136.2 1196.9 1095.3: 41.0 101.7 162.3 203.3 264.0 324.6 365.6 426.3 487.0 527.9 588.6 649.3 690.3 750.9 811.6 872.3 913.2 973.9 1034.6 1075.6 1136.2 1196.9 1136.2: 60.7 121.3 162.3 223.0 283.7 324.6 385.3 446.0 487.0 547.6 608.3 649.3 710.0 770.6 831.3 872.3 932.9 993.6 1034.6 1095.3 1155.9 1196.9 1196.9
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 40.9800 .. 60.6700 cents 19.69000 cents 40.98000 cents 2: 101.6500 .. 121.3400 cents 19.69000 cents 40.98000 cents 3: 162.3200 .. 182.0100 cents 19.69000 cents 40.98000 cents 4: 203.3000 .. 222.9900 cents 19.69000 cents 21.29000 cents 5: 263.9700 .. 283.6600 cents 19.69000 cents 40.98000 cents 6: 324.6400 .. 344.3300 cents 19.69000 cents 40.98000 cents 7: 365.6200 .. 385.3100 cents 19.69000 cents 21.29000 cents 8: 426.2900 .. 445.9800 cents 19.69000 cents 40.98000 cents 9: 486.9600 .. 506.6500 cents 19.69000 cents 40.98000 cents 10: 527.9400 .. 547.6300 cents 19.69000 cents 21.29000 cents 11: 588.6100 .. 608.3000 cents 19.69000 cents 40.98000 cents 12: 649.2800 .. 668.9700 cents 19.69000 cents 40.98000 cents 13: 690.2600 .. 709.9500 cents 19.69000 cents 21.29000 cents 14: 750.9300 .. 770.6200 cents 19.69000 cents 40.98000 cents 15: 811.6000 .. 831.2900 cents 19.69000 cents 40.98000 cents 16: 852.5800 .. 872.2700 cents 19.69000 cents 21.29000 cents 17: 913.2500 .. 932.9400 cents 19.69000 cents 40.98000 cents 18: 973.9200 .. 993.6100 cents 19.69000 cents 40.98000 cents 19: 1014.9000 .. 1034.5900 cents 19.69000 cents 21.29000 cents 20: 1075.5700 .. 1095.2600 cents 19.69000 cents 40.98000 cents 21: 1136.2400 .. 1155.9300 cents 19.69000 cents 40.98000 cents
SHOW DATA
Number of notes : 22 -- Interval properties -- Smallest interval : 40.98000 cents, class 1 Average step (divided formal octave): 54.4050 cents Largest one step interval : 60.67000 cents Average / Smallest step : 1.327599 Largest / Average step : 1.115155 Largest / Smallest step : 1.480478 Median interval of one step : 60.67000 cents, amount: 15 Most common interval of one step : 60.67000 cents, amount: 15 Least squares average step : 54.39722 cents, oct.: 1196.73878 cents Scale is strictly proper Scale has Myhill's property chromas: 19.69000 cents and 21.29000 cents, ratio: 1.081260 generators: 3 of 162.32000 cents and 19 of 1034.59000 cents ET pair of linear temperament : 15&22 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1519-tone equal temperament with octave 1196.910 cents degrees: 77 129 206 283 335 412 489 541 618 695 747 824 901 978 1030 1107 1184 1236 1313 1390 1442 1519 generators: 206 and 1313 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAABAABAAABAABAABA Step pattern size order : LSLLSLLSLLSLLLSLLSLLSL Scale is a Constant Structure, by a margin of 21.29000 cents Scale diversity : 1.178639 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.654535 Rothenberg efficiency : 0.696970 redundancy: 0.303030 Efficiency x scale size : 15.333333 Number of different interval sizes : 42 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 19.69000 cents Most common intervals : 162.32000 cents & inv., amount: 21 Scale is a chain of 11 triads 0.0 426.290 1034.590 cents Most common triad is 0.0 162.320 1034.590 cents, amount: 20 Number of recognisable fifths : 22, average 707.2650 cents Number of recognisable fourths : 22, average 489.6450 cents Scale contains two identical disjunct "tetrachords" of 10 notes Best fifths form a closed circle Best major thirds form a closed circle Formal octave complements present : 21 = 95.4545% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 12-13 -- Rational properties --
FIT/MODE
22: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 5.6957 c. M:-9.8450 c. 37: 2 1 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2 1 2 P M ME SD: 3.6619 c. M: 6.3295 c. 59: 3 2 3 3 2 3 3 2 3 3 2 3 3 3 2 3 3 2 3 3 2 3 SP M ME SD: 0.1726 c. M: 0.2983 c. 376: 19 13 19 19 13 19 19 13 19 19 13 19 19 19 13 19 19 13 19 19 13 19 SP M DE SD: 0.1708 c. M:-0.2952 c. 435: 22 15 22 22 15 22 22 15 22 22 15 22 22 22 15 22 22 15 22 22 15 22 SP M DE SD: 0.1242 c. M:-0.2147 c. 494: 25 17 25 25 17 25 25 17 25 25 17 25 25 25 17 25 25 17 25 25 17 25 SP M DE SD: 0.0888 c. M:-0.1534 c. 553: 28 19 28 28 19 28 28 19 28 28 19 28 28 28 19 28 28 19 28 28 19 28 SP M DE SD: 0.0609 c. M:-0.1052 c. 612: 31 21 31 31 21 31 31 21 31 31 21 31 31 31 21 31 31 21 31 31 21 31 SP M DE SD: 0.0384 c. M:-0.0663 c. 671: 34 23 34 34 23 34 34 23 34 34 23 34 34 34 23 34 34 23 34 34 23 34 SP M DE SD: 0.0198 c. M:-0.0343 c. 730: 37 25 37 37 25 37 37 25 37 37 25 37 37 37 25 37 37 25 37 37 25 37 SP M DE SD: 0.0043 c. M:-0.0074 c. 1519: 77 52 77 77 52 77 77 52 77 77 52 77 77 77 52 77 77 52 77 77 52 77 SP M DE SD: 0.0026 c. M: 0.0045 c. 2249: 114 77 114 114 77 114 114 77 114 114 77 114 114 114 77 114 114 77 114 114 77 114 SP M DE SD: 0.0004 c. M: 0.0006 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 3.0900 cents 2 .. 4 match: 2 H SD: 4.2857 cents 3 .. 6 match: 3 H SD: 5.5634 cents 4 .. 8 match: 4 H SD: 2.5053 cents 5 .. 10 match: 5 H SD: 4.1029 cents 6 .. 12 match: 6 H SD: 3.9761 cents 7 .. 14 match: 7 H SD: 5.8620 cents 8 .. 16 match: 8 H SD: 4.6161 cents 9 .. 18 match: 9 H SD: 4.8663 cents 10 .. 20 match: 10 H SD: 4.1596 cents 11 .. 22 match: 11 H SD: 4.1735 cents 12 .. 24 match: 12 H SD: 3.4590 cents 13 .. 26 match: 13 H SD: 5.3569 cents 14 .. 28 match: 14 H SD: 4.2935 cents 15 .. 30 match: 15 H SD: 3.5464 cents 16 .. 32 match: 16 H SD: 3.7776 cents 17 .. 34 match: 17 H SD: 3.8079 cents 18 .. 36 match: 18 H SD: 3.1242 cents 19 .. 38 match: 17 SD: 4.0065 cents 20 .. 40 match: 19 S SD: 3.2461 cents 21 .. 42 match: 19 S SD: 3.6173 cents 22 .. 44 match: 20 S SD: 3.2017 cents 23 .. 46 match: 19 SD: 3.4711 cents 24 .. 48 match: 21 S SD: 2.6257 cents 25 .. 50 match: 21 SD: 2.7919 cents 26 .. 52 match: 21 SD: 3.5646 cents 27 .. 54 match: 21 SD: 2.7964 cents 28 .. 56 match: 22 SD: 2.2866 cents 29 .. 58 match: 22 SD: 2.0069 cents 32 .. 64 match: 22 SD: 1.9335 cents 33 .. 66 match: 21 SD: 2.2165 cents 35 .. 70 match: 22 SD: 1.9734 cents 37 .. 74 match: 22 SD: 1.8152 cents 43 .. 86 match: 22 SD: 1.6542 cents 44 .. 88 match: 22 SD: 1.6378 cents 48 .. 96 match: 22 SD: 1.5805 cents 49 .. 98 match: 22 SD: 1.2006 cents 53 .. 106 match: 22 SD: 1.1705 cents 59 .. 118 match: 22 SD: 1.1358 cents 61 .. 122 match: 22 SD: 1.1302 cents 64 .. 128 match: 22 SD: 1.0872 cents 67 .. 134 match: 22 SD: 1.0464 cents 72 .. 144 match: 22 SD: 1.0110 cents 73 .. 146 match: 22 SD: 0.9712 cents 79 .. 158 match: 22 SD: 0.8321 cents 81 .. 162 match: 22 SD: 0.7956 cents 92 .. 184 match: 22 SD: 0.7859 cents 93 .. 186 match: 22 SD: 0.7607 cents 101 .. 202 match: 22 SD: 0.6721 cents 110 .. 220 match: 22 SD: 0.6169 cents 111 .. 222 match: 22 SD: 0.5793 cents 116 .. 232 match: 22 SD: 0.5351 cents 132 .. 264 match: 22 SD: 0.4783 cents 136 .. 272 match: 22 SD: 0.4761 cents 150 .. 299 match: 22 SD: 0.4732 cents 151 .. 301 match: 22 SD: 0.4501 cents 160 .. 319 match: 22 SD: 0.4391 cents 164 .. 327 match: 22 SD: 0.3754 cents 169 .. 337 match: 22 SD: 0.3745 cents 193 .. 385 match: 22 SD: 0.3460 cents 194 .. 387 match: 22 SD: 0.3443 cents 196 .. 391 match: 22 SD: 0.3286 cents 204 .. 407 match: 22 SD: 0.3261 cents 212 .. 423 match: 22 SD: 0.3203 cents 218 .. 435 match: 22 SD: 0.3193 cents 224 .. 447 match: 22 SD: 0.3111 cents 225 .. 449 match: 22 SD: 0.2877 cents 232 .. 463 match: 22 SD: 0.2692 cents 247 .. 493 match: 22 SD: 0.2672 cents 248 .. 495 match: 22 SD: 0.2637 cents 253 .. 505 match: 22 SD: 0.2509 cents 261 .. 521 match: 22 SD: 0.2385 cents 262 .. 523 match: 22 SD: 0.2303 cents 284 .. 567 match: 22 SD: 0.2204 cents 286 .. 571 match: 22 SD: 0.2135 cents 304 .. 607 match: 22 SD: 0.2097 cents 314 .. 627 match: 22 SD: 0.1686 cents 365 .. 729 match: 22 SD: 0.1644 cents 398 .. 795 match: 22 SD: 0.1606 cents 430 .. 858 match: 22 SD: 0.1477 cents 444 .. 886 match: 22 SD: 0.1375 cents 479 .. 956 match: 22 SD: 0.1334 cents 481 .. 960 match: 22 SD: 0.1290 cents 499 .. 996 match: 22 SD: 0.1286 cents 510 .. 1018 match: 22 SD: 0.1151 cents 530 .. 1058 match: 22 SD: 0.1112 cents 591 .. 1180 match: 22 SD: 0.1095 cents 597 .. 1192 match: 22 SD: 0.1030 cents