Scala analysis: diab19_612
diab19a in 612 et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 35.294 cents 35.294118 2: 119.608 cents 119.607843 3: 231.373 cents 231.372549 4: 266.667 cents 266.666667 5: 315.686 cents 315.686275 6: 350.980 cents 350.980392 7: 386.275 cents 386.274510 8: 498.039 cents 498.039216 9: 582.353 cents 582.352941 10: 617.647 cents 617.647059 11: 701.961 cents 701.960784 12: 813.725 cents 813.725490 13: 849.020 cents 849.019608 14: 884.314 cents 884.313725 15: 933.333 cents 933.333333 16: 968.627 cents 968.627451 17: 1080.392 cents 1080.392157 18: 1164.706 cents 1164.705882 19: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 35.2941 cents 35.2941 1: 35.2941 cents 35.2941 2: 84.3137 cents 84.3137 3: 111.7647 cents 111.7647 4: 35.2941 cents 35.2941 5: 49.0196 cents 49.0196 6: 35.2941 cents 35.2941 7: 35.2941 cents 35.2941 8: 111.7647 cents 111.7647 9: 84.3137 cents 84.3137 10: 35.2941 cents 35.2941 11: 84.3137 cents 84.3137 12: 111.7647 cents 111.7647 13: 35.2941 cents 35.2941 14: 35.2941 cents 35.2941 15: 49.0196 cents 49.0196 16: 35.2941 cents 35.2941 17: 111.7647 cents 111.7647 18: 84.3137 cents 84.3137 19: 35.2941 cents 35.2941
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 9 35.29412 cents 1: 2 49.01961 cents 1: 4 84.31373 cents 1: 4 111.76471 cents 2: 3 70.58823 cents 2: 4 84.31373 cents 2: 4 119.60784 cents 2: 4 147.05882 cents 2: 4 196.07843 cents 3: 4 119.60784 cents 3: 2 154.90196 cents 3: 2 182.35294 cents 3: 2 196.07843 cents 3: 1 203.92157 cents 3: 8 231.37255 cents 4: 2 154.90196 cents 4: 4 231.37255 cents 4: 1 239.21569 cents 4: 8 266.66667 cents 4: 2 280.39216 cents 4: 2 315.68627 cents 5: 4 266.66667 cents 5: 4 301.96078 cents 5: 6 315.68628 cents 5: 4 350.98039 cents 5: 1 427.45098 cents 6: 10 350.98039 cents 6: 2 378.43137 cents 6: 4 386.27451 cents 6: 3 462.74510 cents 7: 6 386.27451 cents 7: 4 435.29412 cents 7: 4 462.74510 cents 7: 5 498.03921 cents 8: 2 421.56863 cents 8: 4 470.58824 cents 8: 4 498.03922 cents 8: 3 533.33333 cents 8: 6 547.05882 cents 9: 2 505.88235 cents 9: 2 533.33333 cents 9: 1 568.62745 cents 9: 14 582.35294 cents 10: 14 617.64706 cents 10: 1 631.37255 cents 10: 2 666.66667 cents 10: 2 694.11765 cents 11: 6 652.94118 cents 11: 3 666.66667 cents 11: 4 701.96078 cents 11: 4 729.41176 cents 11: 2 778.43137 cents 12: 5 701.96078 cents 12: 4 737.25490 cents 12: 4 764.70588 cents 12: 6 813.72549 cents 13: 3 737.25490 cents 13: 4 813.72549 cents 13: 2 821.56863 cents 13: 10 849.01961 cents 14: 1 772.54902 cents 14: 4 849.01961 cents 14: 6 884.31372 cents 14: 4 898.03922 cents 14: 4 933.33333 cents 15: 2 884.31373 cents 15: 2 919.60784 cents 15: 8 933.33333 cents 15: 1 960.78431 cents 15: 4 968.62745 cents 15: 2 1045.09804 cents 16: 8 968.62745 cents 16: 1 996.07843 cents 16: 2 1003.92157 cents 16: 2 1017.64706 cents 16: 2 1045.09804 cents 16: 4 1080.39216 cents 17: 4 1003.92157 cents 17: 4 1052.94118 cents 17: 4 1080.39216 cents 17: 4 1115.68627 cents 17: 3 1129.41176 cents 18: 4 1088.23529 cents 18: 4 1115.68627 cents 18: 2 1150.98039 cents 18: 9 1164.70588 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.77778 = 43/9
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 : 35.3 119.6 231.4 266.7 315.7 351.0 386.3 498.0 582.4 617.6 702.0 813.7 849.0 884.3 933.3 968.6 1080.4 1164.7 1200.0 35.3 : 84.3 196.1 231.4 280.4 315.7 351.0 462.7 547.1 582.4 666.7 778.4 813.7 849.0 898.0 933.3 1045.1 1129.4 1164.7 1200.0 119.6 : 111.8 147.1 196.1 231.4 266.7 378.4 462.7 498.0 582.4 694.1 729.4 764.7 813.7 849.0 960.8 1045.1 1080.4 1115.7 1200.0 231.4 : 35.3 84.3 119.6 154.9 266.7 351.0 386.3 470.6 582.4 617.6 652.9 702.0 737.3 849.0 933.3 968.6 1003.9 1088.2 1200.0 266.7 : 49.0 84.3 119.6 231.4 315.7 351.0 435.3 547.1 582.4 617.6 666.7 702.0 813.7 898.0 933.3 968.6 1052.9 1164.7 1200.0 315.7 : 35.3 70.6 182.4 266.7 302.0 386.3 498.0 533.3 568.6 617.6 652.9 764.7 849.0 884.3 919.6 1003.9 1115.7 1151.0 1200.0 351.0 : 35.3 147.1 231.4 266.7 351.0 462.7 498.0 533.3 582.4 617.6 729.4 813.7 849.0 884.3 968.6 1080.4 1115.7 1164.7 1200.0 386.3 : 111.8 196.1 231.4 315.7 427.5 462.7 498.0 547.1 582.4 694.1 778.4 813.7 849.0 933.3 1045.1 1080.4 1129.4 1164.7 1200.0 498.0 : 84.3 119.6 203.9 315.7 351.0 386.3 435.3 470.6 582.4 666.7 702.0 737.3 821.6 933.3 968.6 1017.6 1052.9 1088.2 1200.0 582.4 : 35.3 119.6 231.4 266.7 302.0 351.0 386.3 498.0 582.4 617.6 652.9 737.3 849.0 884.3 933.3 968.6 1003.9 1115.7 1200.0 617.6 : 84.3 196.1 231.4 266.7 315.7 351.0 462.7 547.1 582.4 617.6 702.0 813.7 849.0 898.0 933.3 968.6 1080.4 1164.7 1200.0 702.0 : 111.8 147.1 182.4 231.4 266.7 378.4 462.7 498.0 533.3 617.6 729.4 764.7 813.7 849.0 884.3 996.1 1080.4 1115.7 1200.0 813.7 : 35.3 70.6 119.6 154.9 266.7 351.0 386.3 421.6 505.9 617.6 652.9 702.0 737.3 772.5 884.3 968.6 1003.9 1088.2 1200.0 849.0 : 35.3 84.3 119.6 231.4 315.7 351.0 386.3 470.6 582.4 617.6 666.7 702.0 737.3 849.0 933.3 968.6 1052.9 1164.7 1200.0 884.3 : 49.0 84.3 196.1 280.4 315.7 351.0 435.3 547.1 582.4 631.4 666.7 702.0 813.7 898.0 933.3 1017.6 1129.4 1164.7 1200.0 933.3 : 35.3 147.1 231.4 266.7 302.0 386.3 498.0 533.3 582.4 617.6 652.9 764.7 849.0 884.3 968.6 1080.4 1115.7 1151.0 1200.0 968.6 : 111.8 196.1 231.4 266.7 351.0 462.7 498.0 547.1 582.4 617.6 729.4 813.7 849.0 933.3 1045.1 1080.4 1115.7 1164.7 1200.0 1080.4: 84.3 119.6 154.9 239.2 351.0 386.3 435.3 470.6 505.9 617.6 702.0 737.3 821.6 933.3 968.6 1003.9 1052.9 1088.2 1200.0 1164.7: 35.3 70.6 154.9 266.7 302.0 351.0 386.3 421.6 533.3 617.6 652.9 737.3 849.0 884.3 919.6 968.6 1003.9 1115.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.2941 .. 111.7647 cents 76.47059 cents 35.29412 cents 2: 70.5882 .. 196.0784 cents 125.49020 cents -41.17647 cents 3: 119.6078 .. 231.3725 cents 111.76471 cents -76.47059 cents 4: 154.9020 .. 315.6863 cents 160.78431 cents -76.47059 cents 5: 266.6667 .. 427.4510 cents 160.78431 cents -49.01961 cents 6: 350.9804 .. 462.7451 cents 111.76471 cents -76.47059 cents 7: 386.2745 .. 498.0392 cents 111.76470 cents -76.47059 cents 8: 421.5686 .. 547.0588 cents 125.49020 cents -76.47059 cents 9: 505.8824 .. 582.3529 cents 76.47059 cents -41.17647 cents 10: 617.6471 .. 694.1176 cents 76.47059 cents 35.29412 cents 11: 652.9412 .. 778.4314 cents 125.49020 cents -41.17647 cents 12: 701.9608 .. 813.7255 cents 111.76471 cents -76.47059 cents 13: 737.2549 .. 849.0196 cents 111.76471 cents -76.47059 cents 14: 772.5490 .. 933.3333 cents 160.78431 cents -76.47059 cents 15: 884.3137 .. 1045.0980 cents 160.78431 cents -49.01961 cents 16: 968.6275 .. 1080.3922 cents 111.76471 cents -76.47059 cents 17: 1003.9216 .. 1129.4118 cents 125.49020 cents -76.47059 cents 18: 1088.2353 .. 1164.7059 cents 76.47059 cents -41.17647 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 35.29412 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 111.76471 cents Average / Smallest step : 1.789474 Largest / Average step : 1.769608 Largest / Smallest step : 3.166667 Median interval of one step : 49.01961 cents, amount: 2 Most common interval of one step : 35.29412 cents, amount: 9 Least squares average step : 63.30317 cents, oct.: 1202.76018 cents Scale is not proper Scale is a mode of a 612-tone equal temperament with octave 1200.000 cents degrees: 18 61 118 136 161 179 197 254 297 315 358 415 433 451 476 494 551 594 612 Least number of segments generator : 311 of 609.804 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 533 of 1045.098 cents and inv. generated superset size: 191 = 172 more = 1005.263% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCADAACBABCAADACBA Step pattern size order : ACDABAADCACDAABADCA Scale is not a Constant Structure Scale diversity : 1.329017 Lumma stability : 0.088235 Lumma impropriety factor : 0.650327 Number of different interval sizes : 62 = 3.44444 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.77778 = 43/9 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 5.88235 cents Number of recognisable fifths : 11, average 700.5348 cents Formal octave complements present : 19 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 9-10 -- Rational properties --
FIT/MODE
19: 1 1 2 0 1 1 0 2 1 1 1 2 0 1 1 0 2 1 1 N I SD: 16.3914 c. M: 27.9670 c. 21: 1 1 2 1 1 0 1 2 1 1 1 2 1 0 1 1 2 1 1 N T3 I SD: 15.3974 c. M: 27.1709 c. 22: 1 1 2 1 1 0 1 2 2 0 2 2 1 0 1 1 2 1 1 N I SD: 13.6511 c. M: 23.7077 c. 23: 1 1 2 1 1 1 0 3 1 1 1 3 0 1 1 1 2 1 1 N I SD: 15.7334 c. M:-23.6999 c. 24: 1 1 3 0 1 1 1 2 2 0 2 2 1 1 1 0 3 1 1 N I SD: 14.4228 c. M: 19.6078 c. 27: 1 2 2 1 1 1 1 2 2 1 2 2 1 1 1 1 2 2 1 N I SD: 8.5271 c. M: 13.7255 c. 31: 1 2 3 1 1 1 1 3 2 1 2 3 1 1 1 1 3 2 1 N I SD: 3.5000 c. M: 6.0089 c. 68: 2 5 6 2 3 2 2 6 5 2 5 6 2 2 3 2 6 5 2 N I SD: 2.2937 c. M:-3.9216 c. 72: 2 5 7 2 3 2 2 7 5 2 5 7 2 2 3 2 7 5 2 N I SD: 1.8272 c. M:-2.9412 c. 99: 3 7 9 3 4 3 3 9 7 3 7 9 3 3 4 3 9 7 3 N I SD: 0.9967 c. M: 1.6043 c. 140: 4 10 13 4 6 4 4 13 10 4 10 13 4 4 6 4 13 10 4 N I SD: 0.7797 c. M: 1.4566 c. 171: 5 12 16 5 7 5 5 16 12 5 12 16 5 5 7 5 16 12 5 N I SD: 0.1923 c. M:-0.3096 c. 441: 13 31 41 13 18 13 13 41 31 13 31 41 13 13 18 13 41 31 13 N I SD: 0.0746 c. M: 0.1200 c. 612: 18 43 57 18 25 18 18 57 43 18 43 57 18 18 25 18 57 43 18 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: 0.0029 cents 3 .. 6 match: 3 H SD: 0.0151 cents 4 .. 8 match: 4 H SD: 0.0506 cents 5 .. 10 match: 5 H SD: 9.7938 cents 6 .. 12 match: 6 H SD: 5.1717 cents 7 .. 14 match: 7 H SD: 8.3709 cents 8 .. 16 match: 8 H SD: 5.3787 cents 9 .. 18 match: 9 H SD: 8.8427 cents 10 .. 20 match: 10 H SD: 8.6858 cents 11 .. 22 match: 10 SD: 9.6431 cents 12 .. 24 match: 11 S SD: 3.9282 cents 13 .. 26 match: 13 H SD: 6.8557 cents 14 .. 28 match: 14 H SD: 5.8488 cents 15 .. 30 match: 13 SD: 4.2608 cents 16 .. 32 match: 14 S SD: 4.5758 cents 17 .. 34 match: 14 SD: 5.3032 cents 18 .. 36 match: 15 SD: 4.3468 cents 19 .. 38 match: 14 SD: 4.9756 cents 20 .. 40 match: 15 SD: 3.8250 cents 21 .. 42 match: 15 SD: 4.0429 cents 22 .. 44 match: 16 SD: 4.5788 cents 23 .. 46 match: 17 SD: 4.0971 cents 24 .. 48 match: 17 SD: 3.3415 cents 25 .. 50 match: 17 SD: 3.2669 cents 26 .. 52 match: 16 SD: 3.8660 cents 27 .. 54 match: 18 SD: 2.9680 cents 28 .. 56 match: 18 SD: 2.4307 cents 29 .. 58 match: 17 SD: 2.9988 cents 30 .. 60 match: 19 SD: 2.3339 cents 32 .. 64 match: 18 SD: 2.4294 cents 33 .. 66 match: 17 SD: 2.6524 cents 35 .. 70 match: 19 SD: 2.1387 cents 36 .. 72 match: 19 SD: 1.9793 cents 39 .. 78 match: 18 SD: 2.1101 cents 40 .. 80 match: 19 SD: 1.5687 cents 44 .. 88 match: 19 SD: 1.5453 cents 48 .. 96 match: 19 SD: 1.4384 cents 54 .. 108 match: 19 SD: 1.3250 cents 55 .. 110 match: 19 SD: 1.2715 cents 60 .. 120 match: 19 SD: 1.0850 cents 72 .. 144 match: 19 SD: 1.0390 cents 80 .. 160 match: 19 SD: 0.9224 cents 84 .. 168 match: 19 SD: 0.6139 cents 112 .. 224 match: 19 SD: 0.5875 cents 120 .. 240 match: 19 SD: 0.5436 cents 140 .. 280 match: 19 SD: 0.4347 cents 155 .. 310 match: 19 SD: 0.4340 cents 156 .. 312 match: 19 SD: 0.3870 cents 168 .. 336 match: 19 SD: 0.3810 cents 180 .. 360 match: 19 SD: 0.3092 cents 196 .. 392 match: 19 SD: 0.2859 cents 210 .. 420 match: 19 SD: 0.2801 cents 240 .. 480 match: 19 SD: 0.1787 cents 336 .. 672 match: 19 SD: 0.1754 cents 348 .. 696 match: 19 SD: 0.1651 cents 390 .. 780 match: 19 SD: 0.1539 cents 392 .. 784 match: 19 SD: 0.1457 cents 420 .. 840 match: 19 SD: 0.1074 cents 480 .. 960 match: 19 SD: 0.1047 cents 588 .. 1176 match: 19 SD: 0.0816 cents 600 .. 1200 match: 19 SD: 0.0801 cents