Scala analysis: xen16-burt-drones-12
Scale 12 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: 14/9 764.915905 septimal minor sixth 9: 128/81 792.179997 Pythagorean minor sixth 10: 81/50 835.192576 acute minor sixth 11: 81/49 870.168191 two (septimal major third, BP third) 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 98/81 329.8318 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: 98/81 329.8318 9: 64/63 27.2641 septimal comma, Archytas' comma 10: 6561/6400 43.0126 Mathieu superdiesis 11: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 12: 98/81 329.8318
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 81/80 21.506 cents syntonic comma, Didymus comma 1: 2 64/63 27.264 cents septimal comma, Archytas' comma 1: 2 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 2 6561/6400 43.013 cents Mathieu superdiesis 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 6860/6561 77.151 cents 1: 1 10/9 182.404 cents minor whole tone 1: 2 98/81 329.832 cents 2: 2 729/700 70.277 cents 2: 2 6561/6272 77.988 cents 2: 1 7000/6561 112.127 cents 2: 1 784/729 125.922 cents two (Archytas' 1/3-tone) 2: 1 9/8 203.910 cents major whole tone 2: 1 8/7 231.174 cents septimal whole tone 2: 1 49/40 351.338 cents larger approximation to neutral third 2: 2 896/729 357.096 cents 2: 1 100/81 364.807 cents grave major third 3: 2 729/686 105.252 cents 3: 1 35/32 155.140 cents septimal neutral second 3: 1 800/729 160.897 cents grave whole tone 3: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 3: 1 7840/6561 308.326 cents 3: 1 8192/6561 384.360 cents Pythagorean diminished fourth 3: 1 5/4 386.314 cents major third 3: 2 63/50 400.108 cents quasi-equal major third 3: 1 81/64 407.820 cents Pythagorean major third 3: 1 49/36 533.742 cents Arabic lute acute fourth 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: 2 32/25 427.373 cents classic diminished fourth 4: 1 6561/5120 429.326 cents acute major third 4: 3 9/7 435.084 cents septimal major third, BP third 4: 1 25/18 568.717 cents classic augmented fourth 4: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 1 8/7 231.174 cents septimal whole tone 5: 1 100/81 364.807 cents grave major third 5: 1 5/4 386.314 cents major third 5: 1 729/560 456.590 cents 5: 2 64/49 462.348 cents 2 septatones or septatonic major third 5: 1 6561/5000 470.385 cents 5: 1 980/729 512.236 cents 5: 1 729/512 611.730 cents Pythagorean tritone 5: 1 10/7 617.488 cents Euler's tritone 5: 1 9604/6561 659.664 cents 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 6561/4900 505.361 cents two (Al-Hwarizmi's lute middle finger) 6: 1 8960/6561 539.500 cents 6: 1 112/81 561.006 cents 6: 1 81/56 638.994 cents 6: 1 6561/4480 660.500 cents 6: 2 9800/6561 694.639 cents 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 6561/4802 540.336 cents 7: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 7: 1 1024/729 588.270 cents Pythagorean diminished fifth 7: 1 729/490 687.764 cents 7: 1 10000/6561 729.615 cents two (grave major third) 7: 2 49/32 737.652 cents 7: 1 1120/729 743.410 cents 7: 1 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 10/7 617.488 cents Euler's tritone 8: 1 36/25 631.283 cents classic diminished fifth 8: 3 14/9 764.916 cents septimal minor sixth 8: 1 10240/6561 770.674 cents grave minor sixth 8: 2 25/16 772.627 cents classic augmented fifth 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 72/49 666.258 cents Arabic lute grave fifth 9: 1 128/81 792.180 cents Pythagorean minor sixth 9: 2 100/63 799.892 cents quasi-equal minor sixth 9: 1 8/5 813.686 cents minor sixth 9: 1 6561/4096 815.640 cents Pythagorean augmented fifth 9: 1 6561/3920 891.674 cents 9: 1 140/81 947.320 cents 9: 1 729/400 1039.103 cents acute minor seventh 9: 1 64/35 1044.860 cents septimal neutral seventh 9: 2 1372/729 1094.748 cents 10: 1 81/50 835.193 cents acute minor sixth 10: 2 729/448 842.904 cents 10: 1 80/49 848.662 cents smaller approximation to neutral sixth 10: 1 7/4 968.826 cents harmonic seventh 10: 1 16/9 996.090 cents Pythagorean minor seventh 10: 1 729/392 1074.078 cents 10: 1 6561/3500 1087.873 cents 10: 2 12544/6561 1122.012 cents 10: 2 1400/729 1129.723 cents 11: 2 81/49 870.168 cents two (septimal major third, BP third) 11: 1 9/5 1017.596 cents just minor seventh, BP seventh 11: 1 6561/3430 1122.849 cents 11: 1 35/18 1151.230 cents septimal semi-diminished octave 11: 2 12800/6561 1156.987 cents 11: 2 49/25 1165.024 cents BP eighth 11: 2 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: 9.45455 = 104/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 21.5 203.9 252.7 329.8 364.8 407.8 435.1 764.9 792.2 835.2 870.2 1200.0 21.5 : 182.4 231.2 308.3 343.3 386.3 413.6 743.4 770.7 813.7 848.7 1178.5 1200.0 203.9 : 48.8 125.9 160.9 203.9 231.2 561.0 588.3 631.3 666.3 996.1 1017.6 1200.0 252.7 : 77.2 112.1 155.1 182.4 512.2 539.5 582.5 617.5 947.3 968.8 1151.2 1200.0 329.8 : 35.0 78.0 105.3 435.1 462.3 505.4 540.3 870.2 891.7 1074.1 1122.8 1200.0 364.8 : 43.0 70.3 400.1 427.4 470.4 505.4 835.2 856.7 1039.1 1087.9 1165.0 1200.0 407.8 : 27.3 357.1 384.4 427.4 462.3 792.2 813.7 996.1 1044.9 1122.0 1157.0 1200.0 435.1 : 329.8 357.1 400.1 435.1 764.9 786.4 968.8 1017.6 1094.7 1129.7 1172.7 1200.0 764.9 : 27.3 70.3 105.3 435.1 456.6 639.0 687.8 764.9 799.9 842.9 870.2 1200.0 792.2 : 43.0 78.0 407.8 429.3 611.7 660.5 737.7 772.6 815.6 842.9 1172.7 1200.0 835.2 : 35.0 364.8 386.3 568.7 617.5 694.6 729.6 772.6 799.9 1129.7 1157.0 1200.0 870.2 : 329.8 351.3 533.7 582.5 659.7 694.6 737.7 764.9 1094.7 1122.0 1165.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 329.8318 cents 7840/6561, 308.3255 cents 81/80, 21.5063 cents 2: 70.2767 .. 364.8074 cents 70000/59049, 294.5308 cents 59049/68600,-259.5551 cents 3: 105.2523 .. 533.7418 cents 16807/13122, 428.4895 cents 59049/68600,-259.5551 cents 4: 182.4037 .. 582.5122 cents 63/50, 400.1085 cents 40/49,-351.3381 cents 5: 231.1741 .. 764.9159 cents 49/36, 533.7418 cents 40/49,-351.3381 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: 617.4878 .. 1017.5963 cents 63/50, 400.1085 cents 40/49,-351.3381 cents 9: 666.2582 .. 1094.7477 cents 16807/13122, 428.4895 cents 40/49,-351.3381 cents 10: 835.1926 .. 1129.7233 cents 70000/59049, 294.5308 cents 59049/68600,-259.5551 cents 11: 870.1682 .. 1178.4937 cents 7840/6561, 308.3255 cents 59049/68600,-259.5551 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 : 98/81, 329.8318 cents Average / Smallest step : 4.649803 Largest / Average step : 3.298318 Largest / Smallest step : 15.336528 Median interval of one step : 6561/6400, 43.0126 cents, amount: 2 Least squares average step : 85.22456 cents, oct.: 1022.69471 cents Scale is not proper Step pattern alph. order: ABCDEFGHGFEH Step pattern size order : AGEFCDBHBDCH Scale is not a Constant Structure Scale diversity : 1.607252 Lumma stability : 0.035844 Lumma impropriety factor : 0.882872 Rothenberg efficiency : 0.223948 redundancy: 0.776052 Efficiency x scale size : 2.687374 Number of different interval sizes : 86 = 7.81818 / class Number of one step interval sizes : 8 Highest interval variety : 11 Mean interval variety : 9.45455 = 104/11 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 43046721/43025920, 0.8368 cents Most common intervals : 9/7, 435.0841 cents & inv., amount: 4 Most common triad is 0.0 435.084 764.916 cents, amount: 3 Number of recognisable fifths : 3, average 692.3476 cents Number of appreciable fifths : 2, average 694.6392 cents Scale contains a complete diamond : 7 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 : 0.009894 Average absolute harmonicity : 0.132225 Specific harmonicity : 0.074730 Fundamental : 1/6350400, -22.5984 octaves, 0.0000 Hz. Guide tone : 12700800, 23.5984 octaves, 3322853979.775 Hz. Exponens Consonantiae : 8.065516E+13, 46.19683 octaves Euler's gradus suavitatis : 70 Sum of Mann's harmonic distance : 673.0, average 56.08333 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 : 36.36792, average 3.03066 Vogel's harmonic complexity : 42.83333 Wille's k value : 4018612 Wilson's harmonic complexity : 72 Rectangular lattice diameter : 16 Triangular lattice diameter : 8 Lattice compactness : 465.52903, average 5.96832 Lattice compactness (without 2's) : 341.84625, average 4.38264 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -6 .. 7 -0.25000 27 1 3: -4 .. 4 0.83333 38 3 5: -2 .. 2 -0.16667 6 3 7: -2 .. 2 -0.08333 7 5 Average exponent except 2's : 7 / 12 = 0.58333 Average absolute exponent except 2's: 51 / 12 = 4.25000
FIT/MODE
12: 0 2 1 0 1 0 0 4 0 0 1 3 N SD: 28.2223 c. M:-47.3196 c. 14: 0 2 1 1 0 1 0 4 0 1 0 4 N SD: 17.7635 c. M: 32.4814 c. 17: 0 3 1 1 0 1 0 5 0 1 0 5 N SD: 17.1147 c. M:-29.6726 c. 19: 0 3 1 1 1 0 1 5 0 1 1 5 N SD: 17.2551 c. M: 34.2853 c. 20: 0 3 1 1 1 1 0 6 0 1 0 6 N SD: 17.7788 c. M: 30.1682 c. 21: 0 4 0 2 0 1 1 5 1 1 0 6 N SD: 18.3720 c. M:-24.6614 c. 22: 0 4 1 1 1 0 1 6 1 0 1 6 N SD: 15.8519 c. M:-26.0018 c. 23: 0 4 1 1 1 1 0 7 0 1 1 6 N SD: 12.6682 c. M: 21.5063 c. 29: 1 4 1 2 1 1 1 8 0 1 1 8 N SD: 11.0682 c. M:-21.2910 c. 30: 1 4 1 2 1 1 1 8 1 1 1 8 N SD: 8.7953 c. M:-18.4937 c. 33: 1 5 1 2 1 1 1 9 1 1 1 9 N SD: 6.8879 c. M:-14.8573 c. 36: 1 5 2 2 1 1 1 10 1 1 1 10 N SD: 6.5234 c. M:-13.9863 c. 39: 1 6 1 3 1 1 1 11 1 1 1 11 N SD: 7.1162 c. M:-11.4746 c. 43: 1 6 2 3 1 2 1 11 1 2 1 12 N SD: 7.4696 c. M: 11.4275 c. 44: 1 6 2 3 1 2 1 12 1 2 1 12 N SD: 6.3555 c. M: 13.0009 c. 46: 1 7 2 3 1 2 1 12 1 2 1 13 N SD: 7.1201 c. M:-9.5713 c. 47: 1 7 2 3 1 2 1 13 1 2 1 13 N SD: 3.4574 c. M: 7.3606 c. 70: 1 11 3 4 2 3 1 20 1 3 2 19 N SD: 4.4084 c. M: 6.5127 c. 72: 1 11 3 5 2 2 2 20 1 3 2 20 N SD: 4.3096 c. M: 8.8467 c. 76: 1 12 3 5 2 3 1 21 2 3 2 21 N SD: 3.9464 c. M: 8.7683 c. 80: 1 13 3 5 2 3 2 22 2 3 2 22 N SD: 3.5000 c. M: 6.5063 c. 86: 2 13 3 6 2 3 2 24 2 3 2 24 N SD: 3.7010 c. M:-6.4007 c. 88: 2 13 4 5 3 3 2 24 2 3 3 24 N SD: 3.1242 c. M:-6.4105 c. 91: 2 13 4 6 3 3 2 25 2 3 3 25 N SD: 2.9808 c. M: 6.1078 c. 92: 2 14 3 6 3 3 2 26 2 3 3 25 N SD: 3.6876 c. M: 4.8543 c. 94: 2 14 4 6 3 3 2 26 2 3 3 26 N SD: 2.7917 c. M: 5.4053 c. 96: 2 14 4 6 3 4 2 26 2 4 3 26 N SD: 3.5059 c. M: 4.8318 c. 99: 2 15 4 6 3 4 2 27 2 4 3 27 N SD: 2.4445 c. M:-4.3012 c. 105: 2 16 4 7 3 4 2 29 2 4 3 29 N SD: 1.8419 c. M:-3.6086 c. 124: 2 19 5 8 4 4 3 34 3 4 4 34 N SD: 1.5493 c. M: 2.9345 c. 148: 3 22 6 10 4 5 4 40 4 5 4 41 N SD: 2.0721 c. M:-2.8180 c. 152: 3 23 6 10 4 6 3 42 3 6 4 42 N SD: 1.6906 c. M:-2.7063 c. 165: 3 25 7 10 5 6 4 45 4 6 5 45 N SD: 1.3954 c. M: 2.5591 c. 168: 3 26 6 11 5 6 4 46 4 6 5 46 N SD: 1.3867 c. M:-3.2329 c. 171: 3 26 7 11 5 6 4 47 4 6 5 47 N SD: 0.3741 c. M: 0.8025 c. 389: 7 59 16 25 11 14 9 107 9 14 11 107 N SD: 0.4449 c. M: 0.7971 c. 441: 8 67 18 28 13 16 10 121 10 16 13 121 N SD: 0.3399 c. M: 0.5801 c. 447: 8 68 18 29 13 16 10 123 10 16 13 123 N SD: 0.2495 c. M: 0.3695 c. 612: 11 93 25 39 18 22 14 168 14 22 18 168 N SD: 0.2111 c. M: 0.4200 c. 618: 11 94 25 40 18 22 14 170 14 22 18 170 N SD: 0.1789 c. M:-0.2653 c. 783: 14 119 32 50 23 28 18 215 18 28 23 215 N SD: 0.1765 c. M: 0.3299 c. 789: 14 120 32 51 23 28 18 217 18 28 23 217 N SD: 0.1802 c. M:-0.2154 c. 888: 16 135 36 57 26 32 20 244 20 32 26 244 N SD: 0.1394 c. M:-0.2881 c. 1059: 19 161 43 68 31 38 24 291 24 38 31 291 N SD: 0.0684 c. M:-0.1120 c. 1230: 22 187 50 79 36 44 28 338 28 44 36 338 N SD: 0.0471 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: 31.4805 cents 3 x x x x x x 4 x x x 5:6 S SD: 21.5134 cents 4 x x x x x 5 x 6 x x 7:8 S SD: 29.7489 cents 5 x x x 6 x x x x x 8 x 10 S SD: 8.5887 cents 6 x x 7 x x x 8:9 x x 10:12 S SD: 18.2547 cents 7 x x 8 x x x 9 x 11 x 12:14 SD: 13.4469 cents 8 x 9 x x x 10 x 12 x 13 x 16 SD: 13.3492 cents 9 x 10 x x 11 x 12:14 x x 15:18 S SD: 11.7032 cents 10 x 11 x 12 x x 13 x x 16:17:20 SD: 11.6585 cents 11 x 12:13 x x 14 x 17 x 18 x 22 SD: 11.4215 cents 12 x x 14 x x 15 x x 19 x 20:24 SD: 5.9217 cents 13 x x 15 x 16 x 17:20 x 21 x 26 SD: 6.0191 cents 14 x x 16:17 x x 18 x 22 x 23:28 SD: 4.4439 cents 15:16:17 x 18 x 19 x 23 x 24:25:30 SD: 12.3691 cents 16:17:18 x 19 x 20:21:25 x 26 x 32 SD: 12.3952 cents 17:18:19:20 x 21 x 22:26:27 x 28:34 SD: 9.9720 cents 18:19:20:21 x 22 x 23:28 x 29:30:36 SD: 9.0073 cents 19:20:21:22:23 x 24 x x 30:31 x 38 SD: 9.3834 cents 20:21 x 23:24 x 25:26:31 x 32:33:40 SD: 8.3296 cents 21:22 x 24:25:26 x 27 x 33:34:35:42 SD: 7.8967 cents 22:23:25 x x 27:28 x 34:35:36 x 44 SD: 8.0449 cents 23:24:26:27:28 x 29:30:36 x 37:38:46 SD: 6.6730 cents 24:25:27:28:29 x 30:31:37:38:39:40:48 SD: 5.4790 cents 25:26:28:29:30:31 x 32:39 x x 41:50 SD: 5.8391 cents 26:27:29:30:31:32:33 x 40:41:42:43:52 SD: 5.1943 cents 27:28:30:31 x 33:34:35:42:43:44:45:54 SD: 5.3258 cents 28:29 x 32:34 x 35:36 x 44:45:46:56 SD: 5.9876 cents 29:30:33:34:35:36 x 37:45:46:47:48:58 SD: 4.6726 cents 30:31:34:35:36:37:38:39:47 x 49:50:60 SD: 4.7542 cents 31:32:35:36 x 38:39:40:48:49:50:51:62 SD: 3.7315 cents 32:33:36:37:39 x x 41:50:51:52:53:64 SD: 3.9029 cents 33:34:37:38:40:41:42 x 51:52:53:55:66 SD: 3.8755 cents 34:35:38:39:41:42:43:44:53:54:55:56:68 SD: 3.2047 cents 36:37:41:42 x 44 x 46:56:57:58:60:72 SD: 4.5233 cents 37:38:42:43:45:46:47:48:58 x 60:61:74 SD: 3.6561 cents 38:39:43:44:46:47:48:49:59:60:62:63:76 SD: 2.4887 cents 40:41:45:46:48:49:51 x 62:63:65:66:80 SD: 3.1785 cents 41:42:46:47:50:51:52:53:64:65:66:68:82 SD: 3.0898 cents 42:43:47:49:51:52:53:54:65:66:68:69:84 SD: 2.6794 cents 43:44:48:50:52:53:54:55:67:68:70:71:86 SD: 2.5586 cents 46:47:52:53:56:57:58:59:72:73:75:76:92 SD: 2.4738 cents 47:48:53:54:57:58:59:60:73:74:76:78:94 SD: 2.4513 cents 48:49:54:56:58:59:61:62:75:76:78:79:96 SD: 2.2617 cents 50:51:56:58:60:62:63:64:78:79:81:83:100 SD: 2.1986 cents 52:53:59:60:63:64:66:67:81:82:84:86:104 SD: 1.8430 cents 56:57:63:65:68:69:71:72:87:88:91:93:112 SD: 1.5891 cents 57:58:64:66:69:70:72:73:89:90:92:94:114 SD: 1.5143 cents 63:64:71:73:76:78:80:81:98:100:102:104:126 SD: 1.1707 cents 72:73:81:83:87:89:91:93:112:114:117:119:144 SD: 1.0787 cents 81:82:91:94:98:100:103:104:126:128:131:134:162 SD: 0.8866 cents 90:91:101:104:109:111:114:116:140:142:146:149:180 SD: 0.7253 cents 95:96:107:110:115:117:120:122:148:150:154:157:190 SD: 0.6510 cents 144:146:162:167:174:178:182:185:224:228:233:238:288 SD: 0.6084 cents 153:155:172:177:185:189:194:197:238:242:248:253:306 SD: 0.4187 cents 158:160:178:183:191:195:200:203:246:250:256:261:316 SD: 0.3868 cents 230:233:259:266:278:284:291:296:358:363:373:380:460 SD: 0.3799 cents 234:237:263:271:283:289:296:301:364:370:379:387:468 SD: 0.2561 cents 248:251:279:287:300:306:314:319:386:392:402:410:496 SD: 0.1845 cents 400:405:450:463:484:494:506:514:622:632:648:661:800 SD: 0.1477 cents 490:496:551:567:593:605:620:630:762:774:794:810:980 SD: 0.1238 cents 553:560:622:640:669:683:700:711:860:874:896:914:1106 SD: 0.0947 cents