Scala analysis: trab19_72
72-et trab19
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 116.667 cents 116.666667 2: 200.000 cents 200.000000 3: 233.333 cents 233.333333 4: 266.667 cents 266.666667 5: 316.667 cents 316.666667 6: 383.333 cents 383.333333 7: 433.333 cents 433.333333 8: 500.000 cents 500.000000 9: 583.333 cents 583.333333 10: 616.667 cents 616.666667 11: 700.000 cents 700.000000 12: 766.667 cents 766.666667 13: 816.667 cents 816.666667 14: 883.333 cents 883.333333 15: 933.333 cents 933.333333 16: 966.667 cents 966.666667 17: 1000.000 cents 1000.000000 18: 1083.333 cents 1083.333333 19: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 116.6667 cents 116.6667 1: 116.6667 cents 116.6667 2: 83.3333 cents 83.3333 3: 33.3333 cents 33.3333 4: 33.3333 cents 33.3333 5: 50.0000 cents 50.0000 6: 66.6667 cents 66.6667 7: 50.0000 cents 50.0000 8: 66.6667 cents 66.6667 9: 83.3333 cents 83.3333 10: 33.3333 cents 33.3333 11: 83.3333 cents 83.3333 12: 66.6667 cents 66.6667 13: 50.0000 cents 50.0000 14: 66.6667 cents 66.6667 15: 50.0000 cents 50.0000 16: 33.3333 cents 33.3333 17: 33.3333 cents 33.3333 18: 83.3333 cents 83.3333 19: 116.6667 cents 116.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 33.33333 cents 1: 4 50.00000 cents 1: 4 66.66667 cents 1: 4 83.33333 cents 1: 2 116.66667 cents 2: 2 66.66667 cents 2: 2 83.33333 cents 2: 10 116.66667 cents 2: 2 150.00000 cents 2: 2 200.00000 cents 2: 1 233.33333 cents 3: 2 116.66667 cents 3: 4 150.00000 cents 3: 2 166.66667 cents 3: 4 183.33333 cents 3: 3 200.00000 cents 3: 2 233.33333 cents 3: 2 316.66667 cents 4: 2 183.33333 cents 4: 4 200.00000 cents 4: 4 233.33333 cents 4: 6 266.66667 cents 4: 2 350.00000 cents 4: 1 400.00000 cents 5: 2 233.33333 cents 5: 4 266.66667 cents 5: 2 300.00000 cents 5: 6 316.66667 cents 5: 1 333.33333 cents 5: 2 383.33333 cents 5: 2 433.33333 cents 6: 2 300.00000 cents 6: 2 316.66667 cents 6: 4 350.00000 cents 6: 6 383.33333 cents 6: 2 433.33333 cents 6: 3 466.66667 cents 7: 6 383.33333 cents 7: 5 433.33333 cents 7: 2 450.00000 cents 7: 4 500.00000 cents 7: 2 516.66667 cents 8: 2 416.66667 cents 8: 4 466.66667 cents 8: 6 500.00000 cents 8: 1 533.33333 cents 8: 4 550.00000 cents 8: 2 583.33333 cents 9: 4 500.00000 cents 9: 2 533.33333 cents 9: 2 550.00000 cents 9: 1 566.66667 cents 9: 4 583.33333 cents 9: 4 616.66667 cents 9: 2 633.33333 cents 10: 2 566.66667 cents 10: 4 583.33333 cents 10: 4 616.66667 cents 10: 1 633.33333 cents 10: 2 650.00000 cents 10: 2 666.66667 cents 10: 4 700.00000 cents 11: 2 616.66667 cents 11: 4 650.00000 cents 11: 1 666.66667 cents 11: 6 700.00000 cents 11: 4 733.33333 cents 11: 2 783.33333 cents 12: 2 683.33333 cents 12: 4 700.00000 cents 12: 2 750.00000 cents 12: 5 766.66667 cents 12: 6 816.66667 cents 13: 3 733.33333 cents 13: 2 766.66667 cents 13: 6 816.66667 cents 13: 4 850.00000 cents 13: 2 883.33333 cents 13: 2 900.00000 cents 14: 2 766.66667 cents 14: 2 816.66667 cents 14: 1 866.66667 cents 14: 6 883.33333 cents 14: 2 900.00000 cents 14: 4 933.33333 cents 14: 2 966.66667 cents 15: 1 800.00000 cents 15: 2 850.00000 cents 15: 6 933.33333 cents 15: 4 966.66667 cents 15: 4 1000.00000 cents 15: 2 1016.66667 cents 16: 2 883.33333 cents 16: 2 966.66667 cents 16: 3 1000.00000 cents 16: 4 1016.66667 cents 16: 2 1033.33333 cents 16: 4 1050.00000 cents 16: 2 1083.33333 cents 17: 1 966.66667 cents 17: 2 1000.00000 cents 17: 2 1050.00000 cents 17: 10 1083.33333 cents 17: 2 1116.66667 cents 17: 2 1133.33333 cents 18: 2 1083.33333 cents 18: 4 1116.66667 cents 18: 4 1133.33333 cents 18: 4 1150.00000 cents 18: 5 1166.66667 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.11111 = 55/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0.0 : 116.7 200.0 233.3 266.7 316.7 383.3 433.3 500.0 583.3 616.7 700.0 766.7 816.7 883.3 933.3 966.7 1000.0 1083.3 1200.0 116.7 : 83.3 116.7 150.0 200.0 266.7 316.7 383.3 466.7 500.0 583.3 650.0 700.0 766.7 816.7 850.0 883.3 966.7 1083.3 1200.0 200.0 : 33.3 66.7 116.7 183.3 233.3 300.0 383.3 416.7 500.0 566.7 616.7 683.3 733.3 766.7 800.0 883.3 1000.0 1116.7 1200.0 233.3 : 33.3 83.3 150.0 200.0 266.7 350.0 383.3 466.7 533.3 583.3 650.0 700.0 733.3 766.7 850.0 966.7 1083.3 1166.7 1200.0 266.7 : 50.0 116.7 166.7 233.3 316.7 350.0 433.3 500.0 550.0 616.7 666.7 700.0 733.3 816.7 933.3 1050.0 1133.3 1166.7 1200.0 316.7 : 66.7 116.7 183.3 266.7 300.0 383.3 450.0 500.0 566.7 616.7 650.0 683.3 766.7 883.3 1000.0 1083.3 1116.7 1150.0 1200.0 383.3 : 50.0 116.7 200.0 233.3 316.7 383.3 433.3 500.0 550.0 583.3 616.7 700.0 816.7 933.3 1016.7 1050.0 1083.3 1133.3 1200.0 433.3 : 66.7 150.0 183.3 266.7 333.3 383.3 450.0 500.0 533.3 566.7 650.0 766.7 883.3 966.7 1000.0 1033.3 1083.3 1150.0 1200.0 500.0 : 83.3 116.7 200.0 266.7 316.7 383.3 433.3 466.7 500.0 583.3 700.0 816.7 900.0 933.3 966.7 1016.7 1083.3 1133.3 1200.0 583.3 : 33.3 116.7 183.3 233.3 300.0 350.0 383.3 416.7 500.0 616.7 733.3 816.7 850.0 883.3 933.3 1000.0 1050.0 1116.7 1200.0 616.7 : 83.3 150.0 200.0 266.7 316.7 350.0 383.3 466.7 583.3 700.0 783.3 816.7 850.0 900.0 966.7 1016.7 1083.3 1166.7 1200.0 700.0 : 66.7 116.7 183.3 233.3 266.7 300.0 383.3 500.0 616.7 700.0 733.3 766.7 816.7 883.3 933.3 1000.0 1083.3 1116.7 1200.0 766.7 : 50.0 116.7 166.7 200.0 233.3 316.7 433.3 550.0 633.3 666.7 700.0 750.0 816.7 866.7 933.3 1016.7 1050.0 1133.3 1200.0 816.7 : 66.7 116.7 150.0 183.3 266.7 383.3 500.0 583.3 616.7 650.0 700.0 766.7 816.7 883.3 966.7 1000.0 1083.3 1150.0 1200.0 883.3 : 50.0 83.3 116.7 200.0 316.7 433.3 516.7 550.0 583.3 633.3 700.0 750.0 816.7 900.0 933.3 1016.7 1083.3 1133.3 1200.0 933.3 : 33.3 66.7 150.0 266.7 383.3 466.7 500.0 533.3 583.3 650.0 700.0 766.7 850.0 883.3 966.7 1033.3 1083.3 1150.0 1200.0 966.7 : 33.3 116.7 233.3 350.0 433.3 466.7 500.0 550.0 616.7 666.7 733.3 816.7 850.0 933.3 1000.0 1050.0 1116.7 1166.7 1200.0 1000.0: 83.3 200.0 316.7 400.0 433.3 466.7 516.7 583.3 633.3 700.0 783.3 816.7 900.0 966.7 1016.7 1083.3 1133.3 1166.7 1200.0 1083.3: 116.7 233.3 316.7 350.0 383.3 433.3 500.0 550.0 616.7 700.0 733.3 816.7 883.3 933.3 1000.0 1050.0 1083.3 1116.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.3333 .. 116.6667 cents 83.33333 cents 33.33333 cents 2: 66.6667 .. 233.3333 cents 166.66667 cents -50.00000 cents 3: 116.6667 .. 316.6667 cents 200.00000 cents -116.66667 cents 4: 183.3333 .. 400.0000 cents 216.66667 cents -133.33333 cents 5: 233.3333 .. 433.3333 cents 200.00000 cents -166.66667 cents 6: 300.0000 .. 466.6667 cents 166.66667 cents -133.33333 cents 7: 383.3333 .. 516.6667 cents 133.33333 cents -83.33333 cents 8: 416.6667 .. 583.3333 cents 166.66667 cents -100.00000 cents 9: 500.0000 .. 633.3333 cents 133.33333 cents -83.33333 cents 10: 566.6667 .. 700.0000 cents 133.33333 cents -66.66667 cents 11: 616.6667 .. 783.3333 cents 166.66667 cents -83.33333 cents 12: 683.3333 .. 816.6667 cents 133.33333 cents -100.00000 cents 13: 733.3333 .. 900.0000 cents 166.66667 cents -83.33333 cents 14: 766.6667 .. 966.6667 cents 200.00000 cents -133.33333 cents 15: 800.0000 .. 1016.6667 cents 216.66667 cents -166.66667 cents 16: 883.3333 .. 1083.3333 cents 200.00000 cents -133.33333 cents 17: 966.6667 .. 1133.3333 cents 166.66667 cents -116.66667 cents 18: 1083.3333 .. 1166.6667 cents 83.33333 cents -50.00000 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 33.33333 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 116.66667 cents Average / Smallest step : 1.894737 Largest / Average step : 1.847222 Largest / Smallest step : 3.500000 Median interval of one step : 66.66667 cents, amount: 4 Most common interval of one step : 33.33333 cents, amount: 5 Least squares average step : 62.05128 cents, oct.: 1178.97436 cents Scale is not proper Scale is a mode of a 72-tone equal temperament with octave 1200.000 cents degrees: 7 12 14 16 19 23 26 30 35 37 42 46 49 53 56 58 60 65 72 Least number of segments generator : 49 of 816.667 cents and inv. number of contiguous generator circle segments: 2 Shortest superset generator : 65 of 1083.333 cents and inv. generated superset size: 29 = 10 more = 152.632% Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 72-tone equal temperament Step pattern alph. order: ABCCDEDEBCBEDEDCCBA Step pattern size order : EDAABCBCDADCBCBAADE Interval vector is [ 0 5 4 6 6 0 14 0 6 2 6 9 0 9 0 10 0 4 10 1 6 0 14 1 2 9 2 7 0 14 2 3 6 3 10 0 ] Scale is not a Constant Structure Scale diversity : 1.321098 Lumma stability : 0.055556 Lumma impropriety factor : 0.888889 Number of different interval sizes : 54 = 3.00000 / class Number of one step interval sizes : 5 Highest interval variety : 7 Mean interval variety : 6.11111 = 55/9 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 16.66667 cents Number of recognisable fifths : 14, average 700.0000 cents Formal octave complements present : 19 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 9-10 -- Rational properties --
FIT/MODE
19: 2 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 2 N I SD: 10.8596 c. M:-19.2982 c. 22: 2 2 0 1 1 1 1 1 2 0 2 1 1 1 1 1 0 2 2 N I SD: 10.9480 c. M:-18.1818 c. 31: 3 2 1 1 1 2 1 2 2 1 2 2 1 2 1 1 1 2 3 N I SD: 4.5753 c. M:-7.5269 c. 41: 4 3 1 1 2 2 2 2 3 1 3 2 2 2 2 1 1 3 4 N I SD: 3.4594 c. M:-5.6911 c. 72: 7 5 2 2 3 4 3 4 5 2 5 4 3 4 3 2 2 5 7 N I SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.9775 cents 3 .. 6 match: 3 H SD: 0.7359 cents 4 .. 8 match: 4 H SD: 1.0418 cents 5 .. 10 match: 5 H SD: 3.5790 cents 6 .. 12 match: 6 H SD: 5.6831 cents 7 .. 14 match: 7 H SD: 2.8363 cents 8 .. 16 match: 8 H SD: 5.0796 cents 9 .. 18 match: 9 H SD: 4.9562 cents 10 .. 20 match: 10 H SD: 5.4563 cents 11 .. 22 match: 11 H SD: 8.1885 cents 12 .. 24 match: 11 S SD: 4.3489 cents 13 .. 26 match: 12 S SD: 6.2703 cents 14 .. 28 match: 13 S SD: 3.6018 cents 15 .. 30 match: 14 S SD: 4.2248 cents 16 .. 32 match: 15 S SD: 4.5028 cents 17 .. 34 match: 15 S SD: 4.6766 cents 18 .. 36 match: 16 S SD: 3.4011 cents 19 .. 38 match: 14 SD: 5.2807 cents 20 .. 40 match: 18 SD: 3.9602 cents 21 .. 42 match: 16 SD: 3.8897 cents 22 .. 44 match: 15 SD: 4.4012 cents 23 .. 46 match: 18 SD: 3.6977 cents 24 .. 48 match: 17 SD: 2.5080 cents 25 .. 50 match: 18 SD: 2.7195 cents 26 .. 52 match: 17 SD: 3.5463 cents 27 .. 54 match: 18 SD: 2.9610 cents 28 .. 56 match: 19 SD: 2.5211 cents 29 .. 58 match: 17 SD: 2.6793 cents 30 .. 60 match: 18 SD: 2.4667 cents 31 .. 62 match: 18 SD: 2.4892 cents 32 .. 64 match: 18 SD: 2.0601 cents 33 .. 66 match: 18 SD: 2.3582 cents 35 .. 70 match: 19 SD: 2.1877 cents 36 .. 72 match: 19 SD: 2.1474 cents 37 .. 74 match: 18 SD: 2.6008 cents 38 .. 76 match: 18 SD: 2.2002 cents 39 .. 78 match: 18 SD: 2.1115 cents 40 .. 80 match: 19 SD: 1.6831 cents 42 .. 84 match: 19 SD: 1.5592 cents 45 .. 90 match: 18 SD: 1.6723 cents 48 .. 96 match: 19 SD: 1.4492 cents 54 .. 108 match: 19 SD: 1.3880 cents 56 .. 112 match: 19 SD: 1.0424 cents 60 .. 120 match: 19 SD: 0.9638 cents 83 .. 166 match: 19 SD: 0.9184 cents 84 .. 168 match: 19 SD: 0.6269 cents 113 .. 226 match: 19 SD: 0.6002 cents 120 .. 240 match: 19 SD: 0.5748 cents 129 .. 258 match: 19 SD: 0.5678 cents 131 .. 262 match: 19 SD: 0.5322 cents 138 .. 276 match: 19 SD: 0.4463 cents 155 .. 310 match: 19 SD: 0.4376 cents 161 .. 322 match: 19 SD: 0.4157 cents 173 .. 346 match: 19 SD: 0.3709 cents 185 .. 370 match: 19 SD: 0.3669 cents 189 .. 378 match: 19 SD: 0.3647 cents 194 .. 388 match: 19 SD: 0.3479 cents 203 .. 406 match: 19 SD: 0.3227 cents 214 .. 428 match: 19 SD: 0.3139 cents 215 .. 430 match: 19 SD: 0.2593 cents 229 .. 458 match: 19 SD: 0.2455 cents 269 .. 538 match: 19 SD: 0.2227 cents 299 .. 598 match: 19 SD: 0.2006 cents 344 .. 688 match: 19 SD: 0.1890 cents 359 .. 718 match: 19 SD: 0.1712 cents 400 .. 800 match: 19 SD: 0.1568 cents 415 .. 830 match: 19 SD: 0.1559 cents 444 .. 888 match: 19 SD: 0.1419 cents 472 .. 944 match: 19 SD: 0.1326 cents 499 .. 998 match: 19 SD: 0.1205 cents 574 .. 1148 match: 19 SD: 0.1128 cents 589 .. 1178 match: 19 SD: 0.1108 cents