Scala analysis: xen16-burt-drones-01
Scale 1 from Drones 1994 #2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 81/80 21.506290 syntonic comma, Didymus comma 2: 9/8 203.910002 major whole tone 3: 81/70 252.680383 Al-Hwarizmi's lute middle finger 4: 98/81 329.831809 5: 100/81 364.807424 grave major third 6: 81/64 407.820003 Pythagorean major third 7: 9/7 435.084095 septimal major third, BP third 8: 81/50 835.192576 acute minor sixth 9: 81/49 870.168191 two (septimal major third, BP third) 10: 140/81 947.319617 11: 16/9 996.089998 Pythagorean minor seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 81/80 21.5063 syntonic comma, Didymus comma 2: 10/9 182.4037 minor whole tone 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 6860/6561 77.1514 5: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 6: 6561/6400 43.0126 Mathieu superdiesis 7: 64/63 27.2641 septimal comma, Archytas' comma 8: 63/50 400.1085 quasi-equal major third 9: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 10: 6860/6561 77.1514 11: 36/35 48.7704 septimal diesis, 1/4-tone 12: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 81/80 21.506 cents syntonic comma, Didymus comma 1: 1 64/63 27.264 cents septimal comma, Archytas' comma 1: 2 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 1 6561/6400 43.013 cents Mathieu superdiesis 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 6860/6561 77.151 cents 1: 1 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 1: 1 63/50 400.108 cents quasi-equal major third 2: 1 729/700 70.277 cents 2: 1 6561/6272 77.988 cents 2: 2 7000/6561 112.127 cents 2: 2 784/729 125.922 cents two (Archytas' 1/3-tone) 2: 1 9/8 203.910 cents major whole tone 2: 1 729/640 225.416 cents acute major second 2: 1 8/7 231.174 cents septimal whole tone 2: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 32/25 427.373 cents classic diminished fourth 2: 1 9/7 435.084 cents septimal major third, BP third 3: 1 729/686 105.252 cents 3: 1 35/32 155.140 cents septimal neutral second 3: 2 800/729 160.897 cents grave whole tone 3: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 3: 1 6561/5600 274.187 cents 3: 1 7840/6561 308.326 cents 3: 1 98/81 329.832 cents 3: 1 81/64 407.820 cents Pythagorean major third 3: 1 64/49 462.348 cents 2 septatones or septatonic major third 3: 1 6561/5000 470.385 cents 3: 1 980/729 512.236 cents 4: 1 10/9 182.404 cents minor whole tone 4: 1 9/8 203.910 cents major whole tone 4: 1 98/81 329.832 cents 4: 1 8000/6561 343.301 cents 4: 1 49/40 351.338 cents larger approximation to neutral third 4: 1 100/81 364.807 cents grave major third 4: 2 729/560 456.590 cents 4: 2 6561/4900 505.361 cents two (Al-Hwarizmi's lute middle finger) 4: 1 8960/6561 539.500 cents 4: 1 112/81 561.006 cents 5: 1 8/7 231.174 cents septimal whole tone 5: 1 100/81 364.807 cents grave major third 5: 2 5/4 386.314 cents major third 5: 1 6561/4900 505.361 cents two (Al-Hwarizmi's lute middle finger) 5: 2 49/36 533.742 cents Arabic lute acute fourth 5: 1 6561/4802 540.336 cents 5: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 1 1024/729 588.270 cents Pythagorean diminished fifth 5: 1 14/9 764.916 cents septimal minor sixth 6: 1 81/64 407.820 cents Pythagorean major third 6: 1 80/63 413.578 cents wide major third 6: 2 25/18 568.717 cents classic augmented fourth 6: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 2 10/7 617.488 cents Euler's tritone 6: 2 36/25 631.283 cents classic diminished fifth 6: 1 63/40 786.422 cents narrow minor sixth 6: 1 128/81 792.180 cents Pythagorean minor sixth 7: 1 9/7 435.084 cents septimal major third, BP third 7: 1 729/512 611.730 cents Pythagorean tritone 7: 2 10/7 617.488 cents Euler's tritone 7: 1 9604/6561 659.664 cents 7: 2 72/49 666.258 cents Arabic lute grave fifth 7: 1 9800/6561 694.639 cents 7: 2 8/5 813.686 cents minor sixth 7: 1 81/50 835.193 cents acute minor sixth 7: 1 7/4 968.826 cents harmonic seventh 8: 1 81/56 638.994 cents 8: 1 6561/4480 660.500 cents 8: 2 9800/6561 694.639 cents 8: 2 1120/729 743.410 cents 8: 1 81/50 835.193 cents acute minor sixth 8: 1 80/49 848.662 cents smaller approximation to neutral sixth 8: 1 6561/4000 856.699 cents 8: 1 81/49 870.168 cents two (septimal major third, BP third) 8: 1 16/9 996.090 cents Pythagorean minor seventh 8: 1 9/5 1017.596 cents just minor seventh, BP seventh 9: 1 729/490 687.764 cents 9: 1 10000/6561 729.615 cents two (grave major third) 9: 1 49/32 737.652 cents 9: 1 128/81 792.180 cents Pythagorean minor sixth 9: 1 81/49 870.168 cents two (septimal major third, BP third) 9: 1 6561/3920 891.674 cents 9: 1 11200/6561 925.813 cents 9: 1 140/81 947.320 cents 9: 2 729/400 1039.103 cents acute minor seventh 9: 1 64/35 1044.860 cents septimal neutral seventh 9: 1 1372/729 1094.748 cents 10: 1 14/9 764.916 cents septimal minor sixth 10: 1 25/16 772.627 cents classic augmented fifth 10: 1 140/81 947.320 cents 10: 1 7/4 968.826 cents harmonic seventh 10: 1 1280/729 974.584 cents grave minor seventh 10: 1 16/9 996.090 cents Pythagorean minor seventh 10: 2 729/392 1074.078 cents 10: 2 6561/3500 1087.873 cents 10: 1 12544/6561 1122.012 cents 10: 1 1400/729 1129.723 cents 11: 1 100/63 799.892 cents quasi-equal minor sixth 11: 1 16/9 996.090 cents Pythagorean minor seventh 11: 1 9/5 1017.596 cents just minor seventh, BP seventh 11: 2 6561/3430 1122.849 cents 11: 2 35/18 1151.230 cents septimal semi-diminished octave 11: 1 12800/6561 1156.987 cents 11: 2 49/25 1165.024 cents BP eighth 11: 1 63/32 1172.736 cents octave - septimal comma 11: 1 160/81 1178.494 cents octave - syntonic comma Highest number of different intervals for one interval class: 11 Average number of different intervals per interval class: 9.63636 = 106/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 21.5 203.9 252.7 329.8 364.8 407.8 435.1 835.2 870.2 947.3 996.1 1200.0 21.5 : 182.4 231.2 308.3 343.3 386.3 413.6 813.7 848.7 925.8 974.6 1178.5 1200.0 203.9 : 48.8 125.9 160.9 203.9 231.2 631.3 666.3 743.4 792.2 996.1 1017.6 1200.0 252.7 : 77.2 112.1 155.1 182.4 582.5 617.5 694.6 743.4 947.3 968.8 1151.2 1200.0 329.8 : 35.0 78.0 105.3 505.4 540.3 617.5 666.3 870.2 891.7 1074.1 1122.8 1200.0 364.8 : 43.0 70.3 470.4 505.4 582.5 631.3 835.2 856.7 1039.1 1087.9 1165.0 1200.0 407.8 : 27.3 427.4 462.3 539.5 588.3 792.2 813.7 996.1 1044.9 1122.0 1157.0 1200.0 435.1 : 400.1 435.1 512.2 561.0 764.9 786.4 968.8 1017.6 1094.7 1129.7 1172.7 1200.0 835.2 : 35.0 112.1 160.9 364.8 386.3 568.7 617.5 694.6 729.6 772.6 799.9 1200.0 870.2 : 77.2 125.9 329.8 351.3 533.7 582.5 659.7 694.6 737.7 764.9 1165.0 1200.0 947.3 : 48.8 252.7 274.2 456.6 505.4 582.5 617.5 660.5 687.8 1087.9 1122.8 1200.0 996.1 : 203.9 225.4 407.8 456.6 533.7 568.7 611.7 639.0 1039.1 1074.1 1151.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 400.1085 cents 56/45, 378.6022 cents 81/80, 21.5063 cents 2: 70.2767 .. 435.0841 cents 100/81, 364.8074 cents 81/98,-329.8318 cents 3: 105.2523 .. 512.2355 cents 672280/531441, 406.9832 cents 81/98,-329.8318 cents 4: 182.4037 .. 561.0059 cents 56/45, 378.6022 cents 81/98,-329.8318 cents 5: 231.1741 .. 764.9159 cents 49/36, 533.7418 cents 81/98,-329.8318 cents 6: 407.8200 .. 792.1800 cents 8192/6561, 384.3600 cents 729/896,-357.0959 cents 7: 435.0841 .. 968.8259 cents 49/36, 533.7418 cents 729/896,-357.0959 cents 8: 638.9941 .. 1017.5963 cents 56/45, 378.6022 cents 81/98,-329.8318 cents 9: 687.7645 .. 1094.7477 cents 672280/531441, 406.9832 cents 81/98,-329.8318 cents 10: 764.9159 .. 1129.7233 cents 100/81, 364.8074 cents 81/98,-329.8318 cents 11: 799.8915 .. 1178.4937 cents 56/45, 378.6022 cents 81/98,-329.8318 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 81/80, 21.5063 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 63/50, 400.1085 cents Average / Smallest step : 4.649803 Largest / Average step : 4.001085 Largest / Smallest step : 18.604254 Median interval of one step : 36/35, 48.7704 cents, amount: 2 Least squares average step : 91.02536 cents, oct.: 1092.30426 cents Scale is not proper Step pattern alph. order: ABCDEFGHEDCI Step pattern size order : AGEFCDBICFEH Scale is not a Constant Structure Scale diversity : 1.656501 Lumma stability : 0.035844 Lumma impropriety factor : 0.882872 Rothenberg efficiency : 0.227104 redundancy: 0.772896 Efficiency x scale size : 2.725253 Number of different interval sizes : 84 = 7.63636 / class Number of one step interval sizes : 9 Highest interval variety : 11 Mean interval variety : 9.63636 = 106/11 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 43046721/43025920, 0.8368 cents Most common intervals : 7/5, 582.5122 cents & inv., amount: 4 Most common triad is 0.0 582.512 617.488 cents, amount: 2 Number of recognisable fifths : 4, average 692.9205 cents Number of appreciable fifths : 3, average 694.6392 cents Scale contains a complete diamond : 1 9 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 9 = 75.0000% -- Rational properties -- Prime limit : 7 Odd number limit : 6561 (O: 6561 U: 6561) Highest odd numerator or denominator: 81 Scale harmonicity : 0.010196 Average absolute harmonicity : 0.134262 Specific harmonicity : 0.073559 Fundamental : 1/6350400, -22.5984 octaves, 0.0000 Hz. Guide tone : 1587600, 20.5984 octaves, 415356747.472 Hz. Exponens Consonantiae : 1.008190E+13, 43.19683 octaves Euler's gradus suavitatis : 67 Sum of Mann's harmonic distance : 680.0, average 56.66667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 18.13061, average 1.51088 Sum of Tenney's harmonic distance : 36.46483, average 3.03874 Vogel's harmonic complexity : 43.08333 Wille's k value : 4018612 Wilson's harmonic complexity : 72 Rectangular lattice diameter : 16 Triangular lattice diameter : 8 Lattice compactness : 444.03713, average 5.69278 Lattice compactness (without 2's) : 341.91121, average 4.38348 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -6 .. 4 -0.41667 25 1 3: -4 .. 4 0.83333 38 3 5: -2 .. 2 -0.08333 7 3 7: -2 .. 2 -0.08333 7 5 Average exponent except 2's : 8 / 12 = 0.66667 Average absolute exponent except 2's: 52 / 12 = 4.33333
FIT/MODE
12: 0 2 0 1 0 1 0 4 0 1 1 2 N SD: 38.7852 c. M: 70.1682 c. 13: 0 2 1 1 0 0 1 4 0 1 1 2 N SD: 25.3561 c. M: 39.3990 c. 14: 0 2 1 1 0 1 0 5 0 1 1 2 N SD: 19.1233 c. M:-32.4814 c. 17: 0 3 1 1 0 1 0 6 0 1 1 3 N SD: 18.4319 c. M: 29.6726 c. 18: 0 3 1 1 0 1 1 6 0 1 1 3 N SD: 18.1400 c. M:-31.5826 c. 19: 0 3 1 1 1 0 1 6 1 1 1 3 N SD: 14.5960 c. M: 28.8726 c. 21: 0 4 0 2 0 1 1 7 0 2 0 4 N SD: 19.7739 c. M:-24.6614 c. 23: 0 4 1 1 1 1 0 8 1 1 1 4 N SD: 11.5871 c. M: 21.5063 c. 29: 1 4 1 2 1 1 1 9 1 2 1 5 N SD: 9.1715 c. M:-20.0883 c. 30: 1 4 1 2 1 1 1 10 1 2 1 5 N SD: 9.2152 c. M:-18.4937 c. 33: 1 5 1 2 1 1 1 11 1 2 1 6 N SD: 7.7120 c. M:-14.8573 c. 36: 1 5 2 2 1 1 1 12 1 2 2 6 N SD: 7.4012 c. M: 13.9863 c. 39: 1 6 1 3 1 1 1 13 1 3 1 7 N SD: 7.6495 c. M:-11.4746 c. 43: 1 6 2 3 1 2 1 14 1 3 2 7 N SD: 6.4436 c. M:-11.4275 c. 46: 1 7 2 3 1 2 1 15 1 3 2 8 N SD: 6.6849 c. M:-9.5713 c. 47: 1 7 2 3 1 2 1 16 1 3 2 8 N SD: 3.5233 c. M: 7.3606 c. 66: 1 10 3 4 2 2 2 22 2 4 3 11 N SD: 3.2560 c. M: 7.8200 c. 70: 1 11 3 4 2 3 1 24 2 4 3 12 N SD: 4.0921 c. M: 6.5127 c. 72: 1 11 3 5 2 2 2 24 2 5 3 12 N SD: 3.6971 c. M: 7.8200 c. 76: 1 12 3 5 2 3 2 25 2 5 3 13 N SD: 2.9512 c. M:-7.0212 c. 77: 1 12 3 5 2 3 2 26 2 5 3 13 N SD: 3.6897 c. M: 6.3659 c. 91: 2 14 3 6 3 3 2 30 3 6 4 15 N SD: 3.6552 c. M:-7.0790 c. 94: 2 14 4 6 3 3 2 31 3 6 4 16 N SD: 2.8729 c. M: 5.4053 c. 95: 2 14 4 6 3 3 2 32 3 6 4 16 N SD: 2.4777 c. M: 5.6104 c. 99: 2 15 4 6 3 4 2 33 3 6 4 17 N SD: 2.2299 c. M:-4.3012 c. 105: 2 16 4 7 3 4 2 35 3 7 4 18 N SD: 1.6297 c. M:-3.6086 c. 124: 2 19 5 8 4 4 3 41 4 8 5 21 N SD: 1.5378 c. M: 2.9345 c. 148: 3 22 6 10 4 5 4 49 4 10 6 25 N SD: 1.8560 c. M:-2.8180 c. 152: 3 23 6 10 4 6 3 51 4 10 6 26 N SD: 1.5287 c. M:-2.7063 c. 165: 3 25 7 10 5 6 4 55 5 10 7 28 N SD: 1.4428 c. M: 2.5591 c. 171: 3 26 7 11 5 6 4 57 5 11 7 29 N SD: 0.3160 c. M: 0.8025 c. 389: 7 59 16 25 11 14 9 130 11 25 16 66 N SD: 0.4229 c. M: 0.7971 c. 441: 8 67 18 28 13 16 10 147 13 28 18 75 N SD: 0.3365 c. M: 0.5801 c. 447: 8 68 18 29 13 16 10 149 13 29 18 76 N SD: 0.2552 c. M: 0.3695 c. 612: 11 93 25 39 18 22 14 204 18 39 25 104 N SD: 0.2157 c. M: 0.4200 c. 618: 11 94 25 40 18 22 14 206 18 40 25 105 N SD: 0.1890 c. M:-0.2653 c. 783: 14 119 32 50 23 28 18 261 23 50 32 133 N SD: 0.1745 c. M: 0.3299 c. 789: 14 120 32 51 23 28 18 263 23 51 32 134 N SD: 0.1797 c. M: 0.2154 c. 836: 15 127 34 54 24 30 19 279 24 54 34 142 N SD: 0.1723 c. M: 0.3117 c. 888: 16 135 36 57 26 32 20 296 26 57 36 151 N SD: 0.1186 c. M:-0.2881 c. 1059: 19 161 43 68 31 38 24 353 31 68 43 180 N SD: 0.0612 c. M:-0.1120 c. 1230: 22 187 50 79 36 44 28 410 36 79 50 209 N SD: 0.0457 c. M: 0.0757 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x x 3 x x x 4 S SD: 66.6188 cents 3 x x x x x x 4 x 5 x x 6 S SD: 21.5134 cents 4 x x x x x 5 x 6 x 7 x 8 S SD: 34.1662 cents 5 x x x 6 x x x 8 x x 9:10 S SD: 8.3905 cents 6 x x 7 x x x 8 x 10 x 11:12 S SD: 16.9762 cents 7 x x 8 x x x 9:11 x 12 x 14 SD: 11.7324 cents 8 x 9 x x x 10 x 13 x 14 x 16 SD: 6.1758 cents 9 x 10 x x 11 x 12 x 15 x 16:18 S SD: 11.7032 cents 10 x 11 x 12 x x 13:16 x 17:18:20 SD: 8.8392 cents 11 x 12:13 x x 14 x 18 x 19:20:22 SD: 11.1428 cents 12 x x 14 x x 15 x 19:20:21 x 24 SD: 8.9732 cents 13 x x 15 x 16 x 17:21 x 22:23:26 SD: 6.9139 cents 14 x x 16:17 x x 18 x 23:24:25:28 SD: 4.2328 cents 15:16:17 x 18 x 19 x 24:25:26:27:30 SD: 10.9195 cents 16:17:18 x 19 x 20:21:26 x 28 x 32 SD: 12.6467 cents 17:18:19:20 x 21 x 22 x 28:29:30:34 SD: 9.8105 cents 18:19:20:21 x 22 x 23:29:30:31:32:36 SD: 8.1302 cents 19:20:21:22:23 x 24 x 31 x 33:34:38 SD: 8.4861 cents 20:21 x 23:24 x 25:26:32:33:35:36:40 SD: 8.0664 cents 21:22 x 24:25:26 x 27:34:35:36:37:42 SD: 7.3482 cents 22:23:25 x x 27:28 x 36 x 38:39:44 SD: 7.8111 cents 23:24:26:27:28 x 29:30:37:38:40:41:46 SD: 6.0814 cents 24:25:27:28:29 x 30:31:39:40:41:43:48 SD: 5.7279 cents 25:26:28:29:30:31 x 32 x 41:43:44:50 SD: 5.5777 cents 26:27:29:30:31:32:33 x 42:43:45:46:52 SD: 4.9466 cents 27:28:30:31 x 33:34:35:44:45:47:48:54 SD: 5.3027 cents 28:29 x 32:34 x 35:36:45:46:48:50:56 SD: 5.5416 cents 29:30:33:34:35:36 x 37:47:48:50:52:58 SD: 4.8278 cents 30:31:34:35:36:37:38:39:49:50:52:53:60 SD: 4.3503 cents 31:32:35:36 x 38:39:40:50:51:54:55:62 SD: 3.8735 cents 32:33:36:37:39 x x 41:52:53:55:57:64 SD: 3.6771 cents 33:34:37:38:40:41:42 x 53:55:57:59:66 SD: 3.8175 cents 34:35:38:39:41:42:43:44:55:56:59:60:68 SD: 3.3337 cents 36:37:41:42 x 44 x 46:58:60:62:64:72 SD: 4.5530 cents 37:38:42:43:45:46:47:48:60:61:64:66:74 SD: 3.2015 cents 38:39:43:44:46:47:48:49:62:63:66:68:76 SD: 2.7378 cents 40:41:45:46:48:49:51 x 65:66:69:71:80 SD: 3.1094 cents 41:42:46:47:50:51:52:53:66:68:71:73:82 SD: 3.0334 cents 42:43:47:49:51:52:53:54:68:69:73:75:84 SD: 2.6547 cents 45:46:51:52:54:56:57:58:73:74:78:80:90 SD: 2.5906 cents 46:47:52:53:56:57:58:59:75:76:80:82:92 SD: 2.4289 cents 48:49:54:56:58:59:61:62:78:79:83:85:96 SD: 2.2240 cents 49:50:55:57:59:60:62:63:79:81:85:87:98 SD: 2.1482 cents 52:53:59:60:63:64:66:67:84:86:90:92:104 SD: 1.9462 cents 55:56:62:64:67:68:70:71:89:91:95:98:110 SD: 1.8856 cents 56:57:63:65:68:69:71:72:91:93:97:100:112 SD: 1.5330 cents 63:64:71:73:76:78:80:81:102:104:109:112:126 SD: 0.9895 cents 81:82:91:94:98:100:103:104:131:134:140:144:162 SD: 0.8866 cents 90:91:101:104:109:111:114:116:146:149:156:160:180 SD: 0.8029 cents 95:96:107:110:115:117:120:122:154:157:164:169:190 SD: 0.6339 cents 144:146:162:167:174:178:182:185:233:238:249:256:288 SD: 0.5432 cents 153:155:172:177:185:189:194:197:248:253:264:272:306 SD: 0.4654 cents 158:160:178:183:191:195:200:203:256:261:273:281:316 SD: 0.3219 cents 234:237:263:271:283:289:296:301:379:387:404:416:468 SD: 0.2885 cents 242:245:272:280:293:299:306:311:392:400:418:430:484 SD: 0.2797 cents 248:251:279:287:300:306:314:319:402:410:429:441:496 SD: 0.2041 cents 392:397:441:454:474:484:496:504:635:648:678:697:784 SD: 0.1909 cents 395:400:444:457:478:488:500:508:640:653:683:702:790 SD: 0.1887 cents 400:405:450:463:484:494:506:514:648:661:691:711:800 SD: 0.1573 cents 482:488:542:558:583:595:610:620:781:797:833:857:964 SD: 0.1352 cents 490:496:551:567:593:605:620:630:794:810:847:871:980 SD: 0.1027 cents 553:560:622:640:669:683:700:711:896:914:956:983:1106 SD: 0.0912 cents