Scala analysis: xen16-burt-drones-04
Scale 4 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: 160/81 1178.493710 octave - syntonic comma 11: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 81/80 21.5063 syntonic comma, Didymus comma 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: 7840/6561 308.3255 11: 81/80 21.5063 syntonic comma, Didymus comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 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: 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: 1 7840/6561 308.326 cents 1: 1 63/50 400.108 cents quasi-equal major third 2: 1 6561/6400 43.013 cents Mathieu superdiesis 2: 1 729/700 70.277 cents 2: 1 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 98/81 329.832 cents 2: 1 8000/6561 343.301 cents 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: 1 800/729 160.897 cents grave whole tone 3: 1 729/640 225.416 cents acute major second 3: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 3: 1 7840/6561 308.326 cents 3: 1 49/40 351.338 cents larger approximation to neutral third 3: 1 100/81 364.807 cents grave major third 3: 1 64/49 462.348 cents 2 septatones or septatonic major third 3: 1 6561/5000 470.385 cents 3: 1 1120/729 743.410 cents 4: 1 10/9 182.404 cents minor whole tone 4: 1 9/8 203.910 cents major whole tone 4: 1 6561/5600 274.187 cents 4: 1 98/81 329.832 cents 4: 1 8000/6561 343.301 cents 4: 1 5/4 386.314 cents major third 4: 2 6561/4900 505.361 cents two (Al-Hwarizmi's lute middle finger) 4: 1 49/36 533.742 cents Arabic lute acute fourth 4: 1 14/9 764.916 cents septimal minor sixth 4: 1 10240/6561 770.674 cents grave minor sixth 5: 1 8/7 231.174 cents septimal whole tone 5: 1 49/40 351.338 cents larger approximation to neutral third 5: 1 100/81 364.807 cents grave major third 5: 1 5/4 386.314 cents major third 5: 1 6561/4802 540.336 cents 5: 1 25/18 568.717 cents classic augmented fourth 5: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 1 63/40 786.422 cents narrow minor sixth 5: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 8/5 813.686 cents minor sixth 6: 1 5/4 386.314 cents major third 6: 1 81/64 407.820 cents Pythagorean major third 6: 1 80/63 413.578 cents wide major third 6: 2 10/7 617.488 cents Euler's tritone 6: 1 36/25 631.283 cents classic diminished fifth 6: 1 9604/6561 659.664 cents 6: 1 8/5 813.686 cents minor sixth 6: 1 81/50 835.193 cents acute minor sixth 6: 1 80/49 848.662 cents smaller approximation to neutral sixth 6: 1 7/4 968.826 cents harmonic seventh 7: 1 6561/5120 429.326 cents acute major third 7: 1 9/7 435.084 cents septimal major third, BP third 7: 1 72/49 666.258 cents Arabic lute grave fifth 7: 2 9800/6561 694.639 cents 7: 1 8/5 813.686 cents minor sixth 7: 1 6561/4000 856.699 cents 7: 1 81/49 870.168 cents two (septimal major third, BP third) 7: 1 11200/6561 925.813 cents 7: 1 16/9 996.090 cents Pythagorean minor seventh 7: 1 9/5 1017.596 cents just minor seventh, BP seventh 8: 1 729/560 456.590 cents 8: 1 10000/6561 729.615 cents two (grave major third) 8: 1 49/32 737.652 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 6561/3920 891.674 cents 8: 1 140/81 947.320 cents 8: 1 1280/729 974.584 cents grave minor seventh 8: 1 729/400 1039.103 cents acute minor seventh 8: 1 64/35 1044.860 cents septimal neutral seventh 8: 1 1372/729 1094.748 cents 9: 1 14/9 764.916 cents septimal minor sixth 9: 1 25/16 772.627 cents classic augmented fifth 9: 1 6561/4000 856.699 cents 9: 1 81/49 870.168 cents two (septimal major third, BP third) 9: 1 7/4 968.826 cents harmonic seventh 9: 1 16/9 996.090 cents Pythagorean minor seventh 9: 1 729/392 1074.078 cents 9: 1 6561/3500 1087.873 cents 9: 1 12544/6561 1122.012 cents 9: 1 1400/729 1129.723 cents 9: 1 12800/6561 1156.987 cents 10: 1 100/63 799.892 cents quasi-equal minor sixth 10: 1 6561/3920 891.674 cents 10: 1 9/5 1017.596 cents just minor seventh, BP seventh 10: 1 6561/3430 1122.849 cents 10: 1 35/18 1151.230 cents septimal semi-diminished octave 10: 1 12800/6561 1156.987 cents 10: 2 49/25 1165.024 cents BP eighth 10: 1 63/32 1172.736 cents octave - septimal comma 10: 2 160/81 1178.494 cents octave - syntonic comma Highest number of different intervals for one interval class: 11 Average number of different intervals per interval class: 10.20000 = 51/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 21.5 203.9 252.7 329.8 364.8 407.8 435.1 835.2 870.2 1178.5 1200.0 21.5 : 182.4 231.2 308.3 343.3 386.3 413.6 813.7 848.7 1157.0 1178.5 1200.0 203.9 : 48.8 125.9 160.9 203.9 231.2 631.3 666.3 974.6 996.1 1017.6 1200.0 252.7 : 77.2 112.1 155.1 182.4 582.5 617.5 925.8 947.3 968.8 1151.2 1200.0 329.8 : 35.0 78.0 105.3 505.4 540.3 848.7 870.2 891.7 1074.1 1122.8 1200.0 364.8 : 43.0 70.3 470.4 505.4 813.7 835.2 856.7 1039.1 1087.9 1165.0 1200.0 407.8 : 27.3 427.4 462.3 770.7 792.2 813.7 996.1 1044.9 1122.0 1157.0 1200.0 435.1 : 400.1 435.1 743.4 764.9 786.4 968.8 1017.6 1094.7 1129.7 1172.7 1200.0 835.2 : 35.0 343.3 364.8 386.3 568.7 617.5 694.6 729.6 772.6 799.9 1200.0 870.2 : 308.3 329.8 351.3 533.7 582.5 659.7 694.6 737.7 764.9 1165.0 1200.0 1178.5: 21.5 43.0 225.4 274.2 351.3 386.3 429.3 456.6 856.7 891.7 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: 43.0126 .. 435.0841 cents 6400/5103, 392.0715 cents 729/896,-357.0959 cents 3: 105.2523 .. 743.4096 cents 768320/531441, 638.1573 cents 81/98,-329.8318 cents 4: 182.4037 .. 770.6737 cents 1024/729, 588.2700 cents 81/112,-561.0059 cents 5: 231.1741 .. 813.6863 cents 7/5, 582.5122 cents 6561/8960,-539.4996 cents 6: 386.3137 .. 968.8259 cents 7/5, 582.5122 cents 25/32,-427.3726 cents 7: 429.3263 .. 1017.5963 cents 1024/729, 588.2700 cents 6561/8960,-539.4996 cents 8: 456.5904 .. 1094.7477 cents 768320/531441, 638.1573 cents 81/112,-561.0059 cents 9: 764.9159 .. 1156.9874 cents 6400/5103, 392.0715 cents 81/98,-329.8318 cents 10: 799.8915 .. 1178.4937 cents 56/45, 378.6022 cents 729/896,-357.0959 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 81/80, 21.5063 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 63/50, 400.1085 cents Average / Smallest step : 5.072512 Largest / Average step : 3.667661 Largest / Smallest step : 18.604254 Median interval of one step : 6561/6400, 43.0126 cents, amount: 1 Least squares average step : 97.47279 cents, oct.: 1072.20069 cents Scale is not proper Step pattern alph. order: ABCDEFGHEIA Step pattern size order : AGEFCDBICHA Scale is not a Constant Structure Scale diversity : 1.685643 Lumma stability : 0.035844 Lumma impropriety factor : 0.928312 Rothenberg efficiency : 0.234160 redundancy: 0.765840 Efficiency x scale size : 2.575758 Number of different interval sizes : 78 = 7.80000 / class Number of one step interval sizes : 9 Highest interval variety : 11 Mean interval variety : 10.20000 = 51/5 Median interval variety : 9.5 Lowest interval variety : 9 Smallest interval difference : 43046721/43025920, 0.8368 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 3 Most common triad is 0.0 386.314 813.686 cents, amount: 1 Number of recognisable fifths : 2, average 694.6392 cents Scale contains a complete diamond : 5 81 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 63.6364% -- Rational properties -- Prime limit : 7 Odd number limit : 6561 (O: 6561 U: 6561) Highest odd numerator or denominator: 81 Scale harmonicity : 0.010093 Average absolute harmonicity : 0.137750 Specific harmonicity : 0.074377 Fundamental : 1/6350400, -22.5984 octaves, 0.0000 Hz. Guide tone : 3175200, 21.5984 octaves, 830713494.944 Hz. Exponens Consonantiae : 2.016379E+13, 44.19683 octaves Euler's gradus suavitatis : 68 Sum of Mann's harmonic distance : 677.5, average 61.59091 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 17.17637, average 1.56149 Sum of Tenney's harmonic distance : 34.36446, average 3.12404 Vogel's harmonic complexity : 43.00000 Wille's k value : 4018612 Wilson's harmonic complexity : 72 Rectangular lattice diameter : 16 Triangular lattice diameter : 8 Lattice compactness : 384.96124, average 5.83275 Lattice compactness (without 2's) : 289.97881, average 4.39362 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -6 .. 5 -0.54545 24 1 3: -4 .. 4 1.09091 36 2 5: -2 .. 2 -0.09091 7 4 7: -2 .. 2 -0.18182 6 4 Average exponent except 2's : 9 / 11 = 0.81818 Average absolute exponent except 2's: 49 / 11 = 4.45455
FIT/MODE
11: 0 2 0 1 0 1 0 4 0 3 0 N SD: 23.2888 c. M: 37.5347 c. 14: 0 2 1 1 0 1 0 5 0 4 0 N SD: 18.5276 c. M: 32.4814 c. 17: 0 3 1 1 0 1 0 6 0 5 0 N SD: 18.0836 c. M:-29.6726 c. 19: 0 3 1 1 1 0 1 6 1 5 0 N G SD: 15.9847 c. M: 28.8726 c. 22: 0 4 1 1 1 0 1 7 1 6 0 N SD: 15.9550 c. M: 26.0018 c. 23: 0 4 1 1 1 1 0 8 1 6 0 N SD: 13.4289 c. M:-21.5063 c. 29: 1 4 1 2 1 1 1 9 1 8 0 N SD: 11.4559 c. M:-21.5063 c. 30: 0 5 1 2 1 1 1 10 1 7 1 N SD: 10.8941 c. M: 21.5063 c. 33: 1 5 1 2 1 1 1 11 1 8 1 N SD: 8.1312 c. M:-14.8573 c. 36: 1 5 2 2 1 1 1 12 1 9 1 N SD: 7.3008 c. M:-13.9863 c. 37: 1 5 2 2 1 2 0 13 1 9 1 N SD: 9.2122 c. M:-13.8016 c. 39: 1 6 1 3 1 1 1 13 1 10 1 N SD: 7.4694 c. M:-11.4746 c. 43: 1 6 2 3 1 2 1 14 1 11 1 N SD: 6.4920 c. M:-11.4275 c. 46: 1 7 2 3 1 2 1 15 1 12 1 N SD: 6.5176 c. M:-9.5713 c. 47: 1 7 2 3 1 2 1 16 1 12 1 N SD: 3.7910 c. M: 7.3606 c. 59: 1 9 2 4 2 2 1 20 2 15 1 N SD: 4.0890 c. M: 8.6126 c. 65: 1 10 3 4 2 2 2 21 2 17 1 N SD: 3.9394 c. M:-7.9928 c. 66: 1 10 3 4 2 2 2 22 2 17 1 N SD: 3.2960 c. M: 7.8200 c. 70: 1 11 3 4 2 3 1 24 2 18 1 N SD: 4.2299 c. M: 6.5127 c. 72: 1 11 3 5 2 2 2 24 2 19 1 N SD: 3.8726 c. M: 7.8200 c. 76: 1 12 3 5 2 3 2 25 2 20 1 N SD: 3.5080 c. M:-7.0212 c. 79: 1 12 4 5 2 3 2 26 2 21 1 N SD: 4.5194 c. M: 6.4416 c. 80: 1 13 3 5 2 3 2 27 2 21 1 N SD: 4.0606 c. M:-6.5063 c. 86: 2 13 3 6 2 3 2 29 2 22 2 N SD: 4.1442 c. M:-6.4007 c. 88: 2 13 4 5 3 3 2 29 3 22 2 N SD: 3.6572 c. M:-6.4105 c. 91: 2 13 4 6 3 3 2 30 3 23 2 N SD: 3.4293 c. M: 6.1078 c. 94: 2 14 4 6 3 3 2 31 3 24 2 N SD: 3.1359 c. M: 5.4053 c. 95: 2 14 4 6 3 3 2 32 3 24 2 N SD: 2.7720 c. M: 5.6104 c. 99: 2 15 4 6 3 4 2 33 3 25 2 N SD: 2.3170 c. M:-4.3012 c. 105: 2 16 4 7 3 4 2 35 3 27 2 N SD: 1.6202 c. M:-3.6086 c. 124: 2 19 5 8 4 4 3 41 4 32 2 N SD: 1.6895 c. M: 2.9345 c. 148: 3 22 6 10 4 5 4 49 4 38 3 N SD: 2.0461 c. M:-2.8180 c. 152: 3 23 6 10 4 6 3 51 4 39 3 N SD: 1.6775 c. M:-2.7063 c. 157: 3 24 6 10 5 5 4 52 5 40 3 N SD: 1.6345 c. M: 2.7245 c. 161: 3 24 7 10 5 6 3 54 5 41 3 N SD: 1.6175 c. M: 2.7860 c. 165: 3 25 7 10 5 6 4 55 5 42 3 N SD: 1.3989 c. M: 2.5591 c. 171: 3 26 7 11 5 6 4 57 5 44 3 N SD: 0.3359 c. M: 0.8025 c. 389: 7 59 16 25 11 14 9 130 11 100 7 N SD: 0.4244 c. M: 0.7971 c. 441: 8 67 18 28 13 16 10 147 13 113 8 N SD: 0.3375 c. M: 0.5801 c. 447: 8 68 18 29 13 16 10 149 13 115 8 N SD: 0.2448 c. M: 0.3695 c. 612: 11 93 25 39 18 22 14 204 18 157 11 N SD: 0.2119 c. M: 0.4200 c. 618: 11 94 25 40 18 22 14 206 18 159 11 N SD: 0.1872 c. M:-0.2653 c. 783: 14 119 32 50 23 28 18 261 23 201 14 N SD: 0.1718 c. M: 0.3299 c. 789: 14 120 32 51 23 28 18 263 23 203 14 N SD: 0.1854 c. M: 0.2154 c. 836: 15 127 34 54 24 30 19 279 24 215 15 N SD: 0.1778 c. M: 0.3117 c. 888: 16 135 36 57 26 32 20 296 26 228 16 N SD: 0.1209 c. M:-0.2881 c. 1059: 19 161 43 68 31 38 24 353 31 272 19 N SD: 0.0620 c. M:-0.1120 c. 1230: 22 187 50 79 36 44 28 410 36 316 22 N SD: 0.0494 c. M: 0.0757 c. 1895: 34 288 77 122 55 68 43 632 55 487 34 N SD: 0.0487 c. M: 0.0890 c. 2066: 37 314 84 133 60 74 47 689 60 531 37 N SD: 0.0493 c. M:-0.0811 c. 2289: 41 348 93 147 67 82 52 763 67 588 41 N SD: 0.0493 c. M: 0.0808 c.
FIT/HARMONIC
1 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 4 S SD: 66.6188 cents 3 x x x x x x 4 x 5 x 6 S SD: 21.5134 cents 4 x x x x x 5 x 6:7 x 8 S SD: 41.7942 cents 5 x x x 6 x x x 8 x x 10 S SD: 8.5887 cents 6 x x 7 x x x 8 x 10 x 12 S SD: 16.5205 cents 7 x x 8 x x x 9:11:12 x 14 SD: 16.9752 cents 8 x 9 x x x 10 x 13 x x 16 SD: 5.5395 cents 9 x 10 x x 11 x 12 x 15 x 18 S SD: 14.0438 cents 10 x 11 x 12 x x 13:16:17 x 20 SD: 11.6585 cents 11 x 12:13 x x 14 x 18 x x 22 SD: 13.5189 cents 12 x x 14 x x 15 x 19:20 x 24 SD: 9.8715 cents 13 x x 15 x 16 x 17:21 x x 26 SD: 6.1264 cents 14 x x 16:17 x x 18 x 23 x 28 SD: 4.9683 cents 15:16:17 x 18 x 19 x 24:25 x 30 SD: 13.6808 cents 16:17:18 x 19 x 20:21:26 x x 32 SD: 14.1230 cents 17:18:19:20 x 21 x 22 x 28 x 34 SD: 12.0521 cents 18:19:20:21 x 22 x 23:29:30 x 36 SD: 10.1332 cents 19:20:21:22:23 x 24 x 31 x x 38 SD: 10.7219 cents 20:21 x 23:24 x 25:26:32:33 x 40 SD: 9.3388 cents 21:22 x 24:25:26 x 27:34:35:41:42 SD: 8.1390 cents 22:23:25 x x 27:28 x 36 x 43:44 SD: 9.2736 cents 23:24:26:27:28 x 29:30:37:38:45:46 SD: 6.7910 cents 24:25:27:28:29 x 30:31:39:40:47:48 SD: 6.0026 cents 25:26:28:29:30:31 x 32 x 41:49:50 SD: 6.0028 cents 26:27:29:30:31:32:33 x 42:43:51:52 SD: 5.5065 cents 27:28:30:31 x 33:34:35:44:45:53:54 SD: 5.8037 cents 28:29 x 32:34 x 35:36:45:46:55:56 SD: 5.9876 cents 29:30:33:34:35:36 x 37:47:48:57:58 SD: 5.1528 cents 30:31:34:35:36:37:38:39:49:50:59:60 SD: 4.6716 cents 31:32:35:36 x 38:39:40:50:51:61:62 SD: 4.0803 cents 32:33:36:37:39 x x 41:52:53:63:64 SD: 3.9752 cents 33:34:37:38:40:41:42 x 53:55:65:66 SD: 4.1111 cents 34:35:38:39:41:42:43:44:55:56:67:68 SD: 3.4096 cents 36:37:41:42 x 44 x 46:58:60:71:72 SD: 5.0209 cents 37:38:42:43:45:46:47:48:60:61:73:74 SD: 3.4548 cents 38:39:43:44:46:47:48:49:62:63:75:76 SD: 2.6988 cents 40:41:45:46:48:49:51 x 65:66:79:80 SD: 3.3927 cents 41:42:46:47:50:51:52:53:66:68:81:82 SD: 3.2868 cents 42:43:47:49:51:52:53:54:68:69:83:84 SD: 2.6692 cents 46:47:52:53:56:57:58:59:75:76:91:92 SD: 2.4380 cents 48:49:54:56:58:59:61:62:78:79:95:96 SD: 2.3657 cents 49:50:55:57:59:60:62:63:79:81:97:98 SD: 2.2891 cents 52:53:59:60:63:64:66:67:84:86:103:104 SD: 2.0185 cents 56:57:63:65:68:69:71:72:91:93:111:112 SD: 1.5763 cents 63:64:71:73:76:78:80:81:102:104:124:126 SD: 1.2069 cents 71:72:80:82:86:88:90:91:115:117:140:142 SD: 1.1196 cents 81:82:91:94:98:100:103:104:131:134:160:162 SD: 0.9672 cents 90:91:101:104:109:111:114:116:146:149:178:180 SD: 0.7773 cents 95:96:107:110:115:117:120:122:154:157:188:190 SD: 0.7180 cents 144:146:162:167:174:178:182:185:233:238:284:288 SD: 0.6378 cents 152:154:171:176:184:188:192:195:246:251:300:304 SD: 0.6274 cents 153:155:172:177:185:189:194:197:248:253:302:306 SD: 0.4485 cents 158:160:178:183:191:195:200:203:256:261:312:316 SD: 0.3456 cents 234:237:263:271:283:289:296:301:379:387:462:468 SD: 0.2736 cents 248:251:279:287:300:306:314:319:402:410:490:496 SD: 0.1797 cents 400:405:450:463:484:494:506:514:648:661:790:800 SD: 0.1510 cents 482:488:542:558:583:595:610:620:781:797:952:964 SD: 0.1461 cents 490:496:551:567:593:605:620:630:794:810:968:980 SD: 0.1102 cents 553:560:622:640:669:683:700:711:896:914:1092:1106 SD: 0.1049 cents