Scala analysis: mothra16br4
Mothra[16] with a brat of 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 156.687 cents 156.687485 2: 194.557 cents 194.556810 3: 232.426 cents 232.426135 4: 389.114 cents 389.113620 5: 426.983 cents 426.982945 6: 464.852 cents 464.852270 7: 621.540 cents 621.539755 8: 659.409 cents 659.409080 9: 697.278 cents 697.278405 10: 853.966 cents 853.965890 11: 891.835 cents 891.835215 12: 929.705 cents 929.704540 13: 1086.392 cents 1086.392025 14: 1124.261 cents 1124.261350 15: 1162.131 cents 1162.130675 16: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 37.8693 cents 37.8693 1: 156.6875 cents 156.6875 2: 37.8693 cents 37.8693 3: 37.8693 cents 37.8693 4: 156.6875 cents 156.6875 5: 37.8693 cents 37.8693 6: 37.8693 cents 37.8693 7: 156.6875 cents 156.6875 8: 37.8693 cents 37.8693 9: 37.8693 cents 37.8693 10: 156.6875 cents 156.6875 11: 37.8693 cents 37.8693 12: 37.8693 cents 37.8693 13: 156.6875 cents 156.6875 14: 37.8693 cents 37.8693 15: 37.8693 cents 37.8693 16: 37.8693 cents 37.8693
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 11 37.86933 cents 1: 5 156.68748 cents 2: 6 75.73865 cents 2: 10 194.55681 cents 3: 1 113.60798 cents 3: 15 232.42613 cents 4: 12 270.29546 cents 4: 4 389.11362 cents 5: 7 308.16479 cents 5: 9 426.98294 cents 6: 2 346.03411 cents 6: 14 464.85227 cents 7: 13 502.72160 cents 7: 3 621.53975 cents 8: 8 540.59092 cents 8: 8 659.40908 cents 9: 3 578.46025 cents 9: 13 697.27840 cents 10: 14 735.14773 cents 10: 2 853.96589 cents 11: 9 773.01706 cents 11: 7 891.83521 cents 12: 4 810.88638 cents 12: 12 929.70454 cents 13: 15 967.57387 cents 13: 1 1086.39202 cents 14: 10 1005.44319 cents 14: 6 1124.26135 cents 15: 5 1043.31252 cents 15: 11 1162.13067 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 0.0 : 156.7 194.6 232.4 389.1 427.0 464.9 621.5 659.4 697.3 854.0 891.8 929.7 1086.4 1124.3 1162.1 1200.0 156.7 : 37.9 75.7 232.4 270.3 308.2 464.9 502.7 540.6 697.3 735.1 773.0 929.7 967.6 1005.4 1043.3 1200.0 194.6 : 37.9 194.6 232.4 270.3 427.0 464.9 502.7 659.4 697.3 735.1 891.8 929.7 967.6 1005.4 1162.1 1200.0 232.4 : 156.7 194.6 232.4 389.1 427.0 464.9 621.5 659.4 697.3 854.0 891.8 929.7 967.6 1124.3 1162.1 1200.0 389.1 : 37.9 75.7 232.4 270.3 308.2 464.9 502.7 540.6 697.3 735.1 773.0 810.9 967.6 1005.4 1043.3 1200.0 427.0 : 37.9 194.6 232.4 270.3 427.0 464.9 502.7 659.4 697.3 735.1 773.0 929.7 967.6 1005.4 1162.1 1200.0 464.9 : 156.7 194.6 232.4 389.1 427.0 464.9 621.5 659.4 697.3 735.1 891.8 929.7 967.6 1124.3 1162.1 1200.0 621.5 : 37.9 75.7 232.4 270.3 308.2 464.9 502.7 540.6 578.5 735.1 773.0 810.9 967.6 1005.4 1043.3 1200.0 659.4 : 37.9 194.6 232.4 270.3 427.0 464.9 502.7 540.6 697.3 735.1 773.0 929.7 967.6 1005.4 1162.1 1200.0 697.3 : 156.7 194.6 232.4 389.1 427.0 464.9 502.7 659.4 697.3 735.1 891.8 929.7 967.6 1124.3 1162.1 1200.0 854.0 : 37.9 75.7 232.4 270.3 308.2 346.0 502.7 540.6 578.5 735.1 773.0 810.9 967.6 1005.4 1043.3 1200.0 891.8 : 37.9 194.6 232.4 270.3 308.2 464.9 502.7 540.6 697.3 735.1 773.0 929.7 967.6 1005.4 1162.1 1200.0 929.7 : 156.7 194.6 232.4 270.3 427.0 464.9 502.7 659.4 697.3 735.1 891.8 929.7 967.6 1124.3 1162.1 1200.0 1086.4: 37.9 75.7 113.6 270.3 308.2 346.0 502.7 540.6 578.5 735.1 773.0 810.9 967.6 1005.4 1043.3 1200.0 1124.3: 37.9 75.7 232.4 270.3 308.2 464.9 502.7 540.6 697.3 735.1 773.0 929.7 967.6 1005.4 1162.1 1200.0 1162.1: 37.9 194.6 232.4 270.3 427.0 464.9 502.7 659.4 697.3 735.1 891.8 929.7 967.6 1124.3 1162.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 37.8693 .. 156.6875 cents 118.81816 cents 37.86933 cents 2: 75.7387 .. 194.5568 cents 118.81816 cents -80.94883 cents 3: 113.6080 .. 232.4261 cents 118.81816 cents -80.94883 cents 4: 270.2955 .. 389.1136 cents 118.81816 cents 37.86933 cents 5: 308.1648 .. 426.9829 cents 118.81816 cents -80.94883 cents 6: 346.0341 .. 464.8523 cents 118.81816 cents -80.94883 cents 7: 502.7216 .. 621.5398 cents 118.81816 cents 37.86933 cents 8: 540.5909 .. 659.4091 cents 118.81816 cents -80.94883 cents 9: 578.4602 .. 697.2784 cents 118.81816 cents -80.94883 cents 10: 735.1477 .. 853.9659 cents 118.81816 cents 37.86933 cents 11: 773.0171 .. 891.8352 cents 118.81816 cents -80.94883 cents 12: 810.8864 .. 929.7045 cents 118.81816 cents -80.94883 cents 13: 967.5739 .. 1086.3920 cents 118.81816 cents 37.86933 cents 14: 1005.4432 .. 1124.2613 cents 118.81816 cents -80.94883 cents 15: 1043.3125 .. 1162.1307 cents 118.81816 cents -80.94883 cents
SHOW DATA
Number of notes : 16 -- Interval properties -- Smallest interval : 37.86933 cents, class 1 Average step (divided formal octave): 75.0000 cents Largest one step interval : 156.68748 cents Average / Smallest step : 1.980495 Largest / Average step : 2.089166 Largest / Smallest step : 4.137583 Median interval of one step : 37.86933 cents, amount: 11 Most common interval of one step : 37.86933 cents, amount: 11 Least squares average step : 79.96399 cents, oct.: 1279.42390 cents Scale is not proper Scale has Myhill's property chromas: 118.81816 cents and 80.94883 cents, ratio: 1.467818 generators: 3 of 232.42613 cents and 967.57387 cents ET pair of linear temperament : 31&222 Scale is distributional even Scale is a mode of a 1616-tone equal temperament with octave 1200.000 cents degrees: 211 262 313 524 575 626 837 888 939 1150 1201 1252 1463 1514 1565 1616 generators: 313 and 1303 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABBABBABBABBB Step pattern size order : LSSLSSLSSLSSLSSS Scale is a Constant Structure, by a margin of 37.86933 cents Scale diversity : 1.237666 Lumma stability : 0.189347 Lumma impropriety factor : 0.495076 Rothenberg efficiency : 0.708333 redundancy: 0.291667 Efficiency x scale size : 11.333333 Number of different interval sizes : 30 = 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 : 37.86933 cents Most common intervals : 232.42613 cents & inv., amount: 15 Scale is a chain of 8 triads 0.0 426.983 967.574 cents Most common triad is 0.0 232.426 967.574 cents, amount: 14 Number of recognisable fifths : 13, average 697.2784 cents Scale contains two identical disjunct heptachords Formal octave complements present : 1 = 6.2500% Limited inverse transpositions : 13 Inversional symmetry on intervals : 6-7 14-15 -- Rational properties --
FIT/MODE
16: 2 0 1 2 0 1 2 1 0 2 1 0 2 1 0 1 N D3 SD: 26.1034 c. M: 51.9829 c. 18: 2 1 0 3 0 1 2 1 0 3 0 1 2 1 0 1 N SD: 19.4273 c. M: 32.4261 c. 19: 2 1 1 2 1 0 3 0 1 2 1 1 2 1 0 1 N SD: 18.5413 c. M: 32.9133 c. 21: 3 0 1 3 0 1 3 1 0 3 1 0 3 1 0 1 N D3 SD: 15.8466 c. M: 26.9829 c. 22: 3 1 0 3 1 1 2 1 1 3 0 1 3 1 0 1 N SD: 15.2630 c. M:-26.0568 c. 23: 3 1 0 3 1 1 3 0 1 3 1 1 3 0 1 1 N SD: 16.8273 c. M: 33.3221 c. 24: 3 1 1 3 1 0 3 1 1 3 1 1 3 0 1 1 N SD: 14.2022 c. M: 24.2613 c. 25: 3 1 1 3 1 1 3 1 1 3 1 0 4 0 1 1 N SD: 13.3005 c. M:-22.7216 c. 26: 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 1 N M DE SD: 14.5864 c. M: 24.8536 c. 28: 4 1 0 4 1 1 4 0 1 4 1 1 3 1 1 1 N SD: 12.3822 c. M:-21.3174 c. 29: 4 1 1 3 1 1 4 1 1 4 1 0 4 1 1 1 N SD: 11.6960 c. M: 19.3597 c. 31: 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 1 N M DE SD: 1.4796 c. M: 2.5211 c. 129: 17 4 4 17 4 4 17 4 4 17 4 4 17 4 4 4 N M DE SD: 1.1621 c. M:-1.9801 c. 160: 21 5 5 21 5 5 21 5 5 21 5 5 21 5 5 5 N M DE SD: 0.6503 c. M:-1.1080 c. 191: 25 6 6 25 6 6 25 6 6 25 6 6 25 6 6 6 N M DE SD: 0.3046 c. M:-0.5190 c. 222: 29 7 7 29 7 7 29 7 7 29 7 7 29 7 7 7 N M DE SD: 0.0554 c. M:-0.0945 c. 475: 62 15 15 62 15 15 62 15 15 62 15 15 62 15 15 15 N M DE SD: 0.0447 c. M: 0.0762 c. 697: 91 22 22 91 22 22 91 22 22 91 22 22 91 22 22 22 N M DE SD: 0.0128 c. M: 0.0219 c. 919: 120 29 29 120 29 29 120 29 29 120 29 29 120 29 29 29 N M DE SD: 0.0037 c. M:-0.0062 c. 1616: 211 51 51 211 51 51 211 51 51 211 51 51 211 51 51 51 N M DE SD: 0.0035 c. M: 0.0059 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 2.3383 cents 3 .. 6 match: 3 H SD: 11.3414 cents 4 .. 8 match: 4 H SD: 9.8748 cents 5 .. 10 match: 5 H SD: 23.0449 cents 6 .. 12 match: 6 H SD: 10.1887 cents 7 .. 14 match: 7 H SD: 10.5169 cents 8 .. 16 match: 8 H SD: 10.2796 cents 9 .. 18 match: 7 SD: 8.4356 cents 10 .. 20 match: 8 SD: 7.5445 cents 11 .. 22 match: 8 SD: 7.6676 cents 12 .. 24 match: 11 S SD: 7.0133 cents 13 .. 26 match: 10 SD: 5.9413 cents 14 .. 28 match: 10 SD: 4.3744 cents 15 .. 30 match: 11 SD: 7.1065 cents 16 .. 32 match: 10 SD: 2.9511 cents 17 .. 34 match: 10 SD: 4.4140 cents 18 .. 36 match: 12 SD: 5.2788 cents 19 .. 38 match: 12 SD: 4.2571 cents 20 .. 40 match: 12 SD: 3.2461 cents 21 .. 42 match: 13 SD: 2.9250 cents 22 .. 44 match: 13 SD: 2.4436 cents 23 .. 46 match: 12 SD: 3.1541 cents 24 .. 48 match: 14 SD: 2.6146 cents 25 .. 50 match: 15 SD: 3.2171 cents 26 .. 52 match: 14 SD: 3.3947 cents 27 .. 54 match: 13 SD: 3.0584 cents 28 .. 56 match: 15 SD: 2.3585 cents 29 .. 58 match: 14 SD: 3.3812 cents 30 .. 60 match: 14 SD: 2.5392 cents 31 .. 62 match: 15 SD: 2.8313 cents 32 .. 64 match: 16 SD: 2.1742 cents 34 .. 68 match: 15 SD: 2.4567 cents 35 .. 70 match: 16 SD: 2.1666 cents 37 .. 74 match: 15 SD: 2.5682 cents 38 .. 76 match: 15 SD: 2.7833 cents 39 .. 78 match: 16 SD: 1.9790 cents 42 .. 84 match: 16 SD: 1.6716 cents 49 .. 98 match: 16 SD: 1.4296 cents 56 .. 112 match: 16 SD: 1.3036 cents 61 .. 122 match: 16 SD: 1.2495 cents 64 .. 128 match: 16 SD: 1.2479 cents 65 .. 130 match: 16 SD: 1.1776 cents 69 .. 138 match: 16 SD: 1.1703 cents 71 .. 142 match: 16 SD: 1.0517 cents 75 .. 150 match: 16 SD: 0.9477 cents 83 .. 166 match: 16 SD: 0.8409 cents 91 .. 182 match: 16 SD: 0.8292 cents 93 .. 186 match: 16 SD: 0.7759 cents 97 .. 194 match: 16 SD: 0.7750 cents 103 .. 206 match: 16 SD: 0.7624 cents 104 .. 208 match: 16 SD: 0.6493 cents 107 .. 214 match: 16 SD: 0.6400 cents 117 .. 234 match: 16 SD: 0.6222 cents 118 .. 236 match: 16 SD: 0.5806 cents 119 .. 238 match: 16 SD: 0.5695 cents 127 .. 254 match: 16 SD: 0.5280 cents 139 .. 278 match: 16 SD: 0.5260 cents 151 .. 302 match: 16 SD: 0.5141 cents 158 .. 316 match: 16 SD: 0.5013 cents 159 .. 318 match: 16 SD: 0.4245 cents 160 .. 320 match: 16 SD: 0.3930 cents 179 .. 358 match: 16 SD: 0.3653 cents 201 .. 402 match: 16 SD: 0.3361 cents 210 .. 420 match: 16 SD: 0.3241 cents 211 .. 422 match: 16 SD: 0.2766 cents 243 .. 486 match: 16 SD: 0.2627 cents 276 .. 552 match: 16 SD: 0.2363 cents 285 .. 570 match: 16 SD: 0.2199 cents 325 .. 650 match: 16 SD: 0.2133 cents 326 .. 652 match: 16 SD: 0.2088 cents 328 .. 656 match: 16 SD: 0.1790 cents 361 .. 722 match: 16 SD: 0.1543 cents 412 .. 824 match: 16 SD: 0.1392 cents 444 .. 888 match: 16 SD: 0.1351 cents 464 .. 928 match: 16 SD: 0.1307 cents 516 .. 1032 match: 16 SD: 0.1283 cents 528 .. 1056 match: 16 SD: 0.1183 cents 571 .. 1142 match: 16 SD: 0.1060 cents 591 .. 1182 match: 16 SD: 0.1014 cents