Scala analysis: xen18-erlich-hedgehog-22
8L 14s MOS for Hedgehog, L=60.66, s=50.83
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 50.830 cents 50.830000 2: 111.490 cents 111.490000 3: 162.320 cents 162.320000 4: 213.150 cents 213.150000 5: 273.810 cents 273.810000 6: 324.640 cents 324.640000 7: 385.300 cents 385.300000 8: 436.130 cents 436.130000 9: 486.960 cents 486.960000 10: 547.620 cents 547.620000 11: 598.450 cents 598.450000 12: 649.280 cents 649.280000 13: 709.940 cents 709.940000 14: 760.770 cents 760.770000 15: 811.600 cents 811.600000 16: 872.260 cents 872.260000 17: 923.090 cents 923.090000 18: 983.750 cents 983.750000 19: 1034.580 cents 1034.580000 20: 1085.410 cents 1085.410000 21: 1146.070 cents 1146.070000 22: 1196.900 cents 1196.900000
SHOW/INTERVAL
0: 50.8300 cents 50.8300 1: 50.8300 cents 50.8300 2: 60.6600 cents 60.6600 3: 50.8300 cents 50.8300 4: 50.8300 cents 50.8300 5: 60.6600 cents 60.6600 6: 50.8300 cents 50.8300 7: 60.6600 cents 60.6600 8: 50.8300 cents 50.8300 9: 50.8300 cents 50.8300 10: 60.6600 cents 60.6600 11: 50.8300 cents 50.8300 12: 50.8300 cents 50.8300 13: 60.6600 cents 60.6600 14: 50.8300 cents 50.8300 15: 50.8300 cents 50.8300 16: 60.6600 cents 60.6600 17: 50.8300 cents 50.8300 18: 60.6600 cents 60.6600 19: 50.8300 cents 50.8300 20: 50.8300 cents 50.8300 21: 60.6600 cents 60.6600 22: 50.8300 cents 50.8300
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 14 50.83000 cents 1: 8 60.66000 cents 2: 6 101.66000 cents 2: 16 111.49000 cents 3: 20 162.32000 cents 3: 2 172.15000 cents 4: 12 213.15000 cents 4: 10 222.98000 cents 5: 4 263.98000 cents 5: 18 273.81000 cents 6: 18 324.64000 cents 6: 4 334.47000 cents 7: 10 375.47000 cents 7: 12 385.30000 cents 8: 2 426.30000 cents 8: 20 436.13000 cents 9: 16 486.96000 cents 9: 6 496.79000 cents 10: 8 537.79000 cents 10: 14 547.62000 cents 11: 22 598.45000 cents 12: 14 649.28000 cents 12: 8 659.11000 cents 13: 6 700.11000 cents 13: 16 709.94000 cents 14: 20 760.77000 cents 14: 2 770.60000 cents 15: 12 811.60000 cents 15: 10 821.43000 cents 16: 4 862.43000 cents 16: 18 872.26000 cents 17: 18 923.09000 cents 17: 4 932.92000 cents 18: 10 973.92000 cents 18: 12 983.75000 cents 19: 2 1024.75000 cents 19: 20 1034.58000 cents 20: 16 1085.41000 cents 20: 6 1095.24000 cents 21: 8 1136.24000 cents 21: 14 1146.07000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.95238 = 41/21
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 : 50.8 111.5 162.3 213.2 273.8 324.6 385.3 436.1 487.0 547.6 598.4 649.3 709.9 760.8 811.6 872.3 923.1 983.8 1034.6 1085.4 1146.1 1196.9 50.8 : 60.7 111.5 162.3 223.0 273.8 334.5 385.3 436.1 496.8 547.6 598.4 659.1 709.9 760.8 821.4 872.3 932.9 983.8 1034.6 1095.2 1146.1 1196.9 111.5 : 50.8 101.7 162.3 213.2 273.8 324.6 375.5 436.1 487.0 537.8 598.4 649.3 700.1 760.8 811.6 872.3 923.1 973.9 1034.6 1085.4 1136.2 1196.9 162.3 : 50.8 111.5 162.3 223.0 273.8 324.6 385.3 436.1 487.0 547.6 598.4 649.3 709.9 760.8 821.4 872.3 923.1 983.8 1034.6 1085.4 1146.1 1196.9 213.2 : 60.7 111.5 172.1 223.0 273.8 334.5 385.3 436.1 496.8 547.6 598.4 659.1 709.9 770.6 821.4 872.3 932.9 983.8 1034.6 1095.2 1146.1 1196.9 273.8 : 50.8 111.5 162.3 213.2 273.8 324.6 375.5 436.1 487.0 537.8 598.4 649.3 709.9 760.8 811.6 872.3 923.1 973.9 1034.6 1085.4 1136.2 1196.9 324.6 : 60.7 111.5 162.3 223.0 273.8 324.6 385.3 436.1 487.0 547.6 598.4 659.1 709.9 760.8 821.4 872.3 923.1 983.8 1034.6 1085.4 1146.1 1196.9 385.3 : 50.8 101.7 162.3 213.2 264.0 324.6 375.5 426.3 487.0 537.8 598.4 649.3 700.1 760.8 811.6 862.4 923.1 973.9 1024.8 1085.4 1136.2 1196.9 436.1 : 50.8 111.5 162.3 213.2 273.8 324.6 375.5 436.1 487.0 547.6 598.4 649.3 709.9 760.8 811.6 872.3 923.1 973.9 1034.6 1085.4 1146.1 1196.9 487.0 : 60.7 111.5 162.3 223.0 273.8 324.6 385.3 436.1 496.8 547.6 598.4 659.1 709.9 760.8 821.4 872.3 923.1 983.8 1034.6 1095.2 1146.1 1196.9 547.6 : 50.8 101.7 162.3 213.2 264.0 324.6 375.5 436.1 487.0 537.8 598.4 649.3 700.1 760.8 811.6 862.4 923.1 973.9 1034.6 1085.4 1136.2 1196.9 598.4 : 50.8 111.5 162.3 213.2 273.8 324.6 385.3 436.1 487.0 547.6 598.4 649.3 709.9 760.8 811.6 872.3 923.1 983.8 1034.6 1085.4 1146.1 1196.9 649.3 : 60.7 111.5 162.3 223.0 273.8 334.5 385.3 436.1 496.8 547.6 598.4 659.1 709.9 760.8 821.4 872.3 932.9 983.8 1034.6 1095.2 1146.1 1196.9 709.9 : 50.8 101.7 162.3 213.2 273.8 324.6 375.5 436.1 487.0 537.8 598.4 649.3 700.1 760.8 811.6 872.3 923.1 973.9 1034.6 1085.4 1136.2 1196.9 760.8 : 50.8 111.5 162.3 223.0 273.8 324.6 385.3 436.1 487.0 547.6 598.4 649.3 709.9 760.8 821.4 872.3 923.1 983.8 1034.6 1085.4 1146.1 1196.9 811.6 : 60.7 111.5 172.1 223.0 273.8 334.5 385.3 436.1 496.8 547.6 598.4 659.1 709.9 770.6 821.4 872.3 932.9 983.8 1034.6 1095.2 1146.1 1196.9 872.3 : 50.8 111.5 162.3 213.2 273.8 324.6 375.5 436.1 487.0 537.8 598.4 649.3 709.9 760.8 811.6 872.3 923.1 973.9 1034.6 1085.4 1136.2 1196.9 923.1 : 60.7 111.5 162.3 223.0 273.8 324.6 385.3 436.1 487.0 547.6 598.4 659.1 709.9 760.8 821.4 872.3 923.1 983.7 1034.6 1085.4 1146.1 1196.9 983.8 : 50.8 101.7 162.3 213.2 264.0 324.6 375.5 426.3 487.0 537.8 598.4 649.3 700.1 760.8 811.6 862.4 923.1 973.9 1024.8 1085.4 1136.2 1196.9 1034.6: 50.8 111.5 162.3 213.2 273.8 324.6 375.5 436.1 487.0 547.6 598.4 649.3 709.9 760.8 811.6 872.3 923.1 973.9 1034.6 1085.4 1146.1 1196.9 1085.4: 60.7 111.5 162.3 223.0 273.8 324.6 385.3 436.1 496.8 547.6 598.4 659.1 709.9 760.8 821.4 872.3 923.1 983.8 1034.6 1095.2 1146.1 1196.9 1146.1: 50.8 101.7 162.3 213.2 264.0 324.6 375.5 436.1 487.0 537.8 598.4 649.3 700.1 760.8 811.6 862.4 923.1 973.9 1034.6 1085.4 1136.2 1196.9 1196.9
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 50.8300 .. 60.6600 cents 9.83000 cents 50.83000 cents 2: 101.6600 .. 111.4900 cents 9.83000 cents 41.00000 cents 3: 162.3200 .. 172.1500 cents 9.83000 cents 50.83000 cents 4: 213.1500 .. 222.9800 cents 9.83000 cents 41.00000 cents 5: 263.9800 .. 273.8100 cents 9.83000 cents 41.00000 cents 6: 324.6400 .. 334.4700 cents 9.83000 cents 50.83000 cents 7: 375.4700 .. 385.3000 cents 9.83000 cents 41.00000 cents 8: 426.3000 .. 436.1300 cents 9.83000 cents 41.00000 cents 9: 486.9600 .. 496.7900 cents 9.83000 cents 50.83000 cents 10: 537.7900 .. 547.6200 cents 9.83000 cents 41.00000 cents 11: 598.4500 .. 598.4500 cents 1/1, 0.0000 cents 50.83000 cents 12: 649.2800 .. 659.1100 cents 9.83000 cents 50.83000 cents 13: 700.1100 .. 709.9400 cents 9.83000 cents 41.00000 cents 14: 760.7700 .. 770.6000 cents 9.83000 cents 50.83000 cents 15: 811.6000 .. 821.4300 cents 9.83000 cents 41.00000 cents 16: 862.4300 .. 872.2600 cents 9.83000 cents 41.00000 cents 17: 923.0900 .. 932.9200 cents 9.83000 cents 50.83000 cents 18: 973.9200 .. 983.7500 cents 9.83000 cents 41.00000 cents 19: 1024.7500 .. 1034.5800 cents 9.83000 cents 41.00000 cents 20: 1085.4100 .. 1095.2400 cents 9.83000 cents 50.83000 cents 21: 1136.2400 .. 1146.0700 cents 9.83000 cents 41.00000 cents
SHOW DATA
Number of notes : 22 -- Interval properties -- Smallest interval : 50.83000 cents, class 1 Average step (divided formal octave): 54.4045 cents Largest one step interval : 60.66000 cents Average / Smallest step : 1.070324 Largest / Average step : 1.114980 Largest / Smallest step : 1.193390 Median interval of one step : 50.83000 cents, amount: 14 Most common interval of one step : 50.83000 cents, amount: 14 Least squares average step : 54.42009 cents, oct.: 1197.24191 cents Scale is strictly proper Scale has 2 repeating blocks of 11 notes Blocks have Myhill's property chromas: 9.83000 cents and 41.00000 cents, ratio: 4.170905 generators: 3 of 162.32000 cents and 8 of 436.13000 cents ET pair of linear temperament : 22&118 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 730-tone equal temperament with octave 1196.900 cents degrees: 31 68 99 130 167 198 235 266 297 334 365 396 433 464 495 532 563 600 631 662 699 730 Least number of segments generator : 367 of 601.729 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 631 of 1034.581 cents and inv. generated superset size: 376 = 354 more = 1709.091% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABABAABAABAABABAABA Step pattern size order : SLSSLSLSSLSSLSSLSLSSLS Scale is a Constant Structure, by a margin of 41.00000 cents Scale diversity : 1.101124 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.835742 Number of different interval sizes : 41 = 1.95238 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.95238 = 41/21 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 9.83000 cents Most common intervals : 598.45000 cents & inv., amount: 22 Number of recognisable fifths : 22, average 707.2591 cents Number of recognisable fourths : 22, average 489.6409 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 : 22 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 11 Limited inverse transpositions : 11 Inversional symmetry on degrees : 0 11 Inversional symmetry on intervals : 5-6 16-17 -- 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: 2.8259 c. M:-4.4682 c. 74: 3 4 3 3 4 3 4 3 3 4 3 3 4 3 3 4 3 4 3 3 4 3 SP B ME I SD: 1.8239 c. M:-2.8838 c. 96: 4 5 4 4 5 4 5 4 4 5 4 4 5 4 4 5 4 5 4 4 5 4 SP B ME I SD: 0.7583 c. M: 1.1990 c. 118: 5 6 5 5 6 5 6 5 5 6 5 5 6 5 5 6 5 6 5 5 6 5 SP B ME I SD: 0.0900 c. M: 0.1424 c. 376: 16 19 16 16 19 16 19 16 16 19 16 16 19 16 16 19 16 19 16 16 19 16 SP B DE I SD: 0.0806 c. M: 0.1274 c. 494: 21 25 21 21 25 21 25 21 21 25 21 21 25 21 21 25 21 25 21 21 25 21 SP B DE I SD: 0.0398 c. M:-0.0630 c. 612: 26 31 26 26 31 26 31 26 26 31 26 26 31 26 26 31 26 31 26 26 31 26 SP B DE I SD: 0.0148 c. M: 0.0234 c. 730: 31 37 31 31 37 31 37 31 31 37 31 31 37 31 31 37 31 37 31 31 37 31 SP B DE I SD: 0.0022 c. M:-0.0034 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 3.1000 cents 2 .. 4 match: 2 H SD: 4.2828 cents 3 .. 6 match: 3 H SD: 5.5664 cents 4 .. 8 match: 4 H SD: 4.3093 cents 5 .. 10 match: 5 H SD: 5.0494 cents 6 .. 12 match: 6 H SD: 4.1140 cents 7 .. 14 match: 7 H SD: 5.4559 cents 8 .. 16 match: 8 H SD: 4.4038 cents 9 .. 18 match: 9 H SD: 4.6810 cents 10 .. 20 match: 10 H SD: 4.1476 cents 11 .. 22 match: 11 H SD: 4.5671 cents 12 .. 24 match: 12 H SD: 3.7870 cents 13 .. 26 match: 13 H SD: 4.8433 cents 14 .. 28 match: 14 H SD: 3.7278 cents 15 .. 30 match: 15 H SD: 3.6578 cents 16 .. 32 match: 16 H SD: 3.4302 cents 17 .. 34 match: 17 H SD: 3.2288 cents 18 .. 36 match: 18 H SD: 3.3141 cents 19 .. 38 match: 18 S SD: 4.2116 cents 20 .. 40 match: 19 SD: 3.4161 cents 21 .. 42 match: 20 SD: 3.6214 cents 22 .. 44 match: 20 SD: 3.1597 cents 23 .. 46 match: 19 SD: 3.5134 cents 24 .. 48 match: 21 SD: 2.4742 cents 25 .. 50 match: 21 SD: 3.0047 cents 26 .. 52 match: 21 SD: 3.5572 cents 27 .. 54 match: 22 SD: 2.8477 cents 28 .. 56 match: 22 SD: 2.5115 cents 29 .. 58 match: 22 SD: 1.9786 cents 38 .. 76 match: 22 SD: 1.9663 cents 39 .. 78 match: 22 SD: 1.9497 cents 40 .. 80 match: 22 SD: 1.6668 cents 43 .. 86 match: 22 SD: 1.6580 cents 44 .. 88 match: 22 SD: 1.6435 cents 48 .. 96 match: 22 SD: 1.5364 cents 52 .. 104 match: 22 SD: 1.5130 cents 53 .. 106 match: 22 SD: 1.3386 cents 59 .. 118 match: 22 SD: 1.1100 cents 63 .. 126 match: 22 SD: 1.0723 cents 64 .. 128 match: 22 SD: 1.0428 cents 70 .. 140 match: 22 SD: 0.9997 cents 72 .. 144 match: 22 SD: 0.9957 cents 73 .. 146 match: 22 SD: 0.9759 cents 77 .. 154 match: 22 SD: 0.8203 cents 92 .. 184 match: 22 SD: 0.6077 cents 105 .. 210 match: 22 SD: 0.5777 cents 121 .. 242 match: 22 SD: 0.5658 cents 130 .. 260 match: 22 SD: 0.5641 cents 132 .. 264 match: 22 SD: 0.4527 cents 136 .. 272 match: 22 SD: 0.4333 cents 163 .. 325 match: 22 SD: 0.4317 cents 164 .. 327 match: 22 SD: 0.4254 cents 165 .. 329 match: 22 SD: 0.3835 cents 169 .. 337 match: 22 SD: 0.3690 cents 192 .. 383 match: 22 SD: 0.3553 cents 193 .. 385 match: 22 SD: 0.3456 cents 194 .. 387 match: 22 SD: 0.3440 cents 196 .. 391 match: 22 SD: 0.3408 cents 199 .. 397 match: 22 SD: 0.3385 cents 209 .. 417 match: 22 SD: 0.2899 cents 237 .. 473 match: 22 SD: 0.2395 cents 268 .. 535 match: 22 SD: 0.2221 cents 296 .. 591 match: 22 SD: 0.2042 cents 304 .. 607 match: 22 SD: 0.1970 cents 314 .. 627 match: 22 SD: 0.1831 cents 345 .. 689 match: 22 SD: 0.1588 cents 373 .. 745 match: 22 SD: 0.1377 cents 468 .. 934 match: 22 SD: 0.1354 cents 495 .. 988 match: 22 SD: 0.1317 cents 510 .. 1018 match: 22 SD: 0.1277 cents 527 .. 1052 match: 22 SD: 0.1190 cents 537 .. 1072 match: 22 SD: 0.1172 cents 538 .. 1074 match: 22 SD: 0.1066 cents 542 .. 1082 match: 22 SD: 0.1019 cents 572 .. 1142 match: 22 SD: 0.0914 cents