Scala analysis: xen16-burt-drones-06
Scale 6 from Drones 1994 #2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 81/70 252.680383 Al-Hwarizmi's lute middle finger 3: 98/81 329.831809 4: 100/81 364.807424 grave major third 5: 14/9 764.915905 septimal minor sixth 6: 128/81 792.179997 Pythagorean minor sixth 7: 81/50 835.192576 acute minor sixth 8: 81/49 870.168191 two (septimal major third, BP third) 9: 140/81 947.319617 10: 16/9 996.089998 Pythagorean minor seventh 11: 160/81 1178.493710 octave - syntonic comma 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 81/80 21.5063 syntonic comma, Didymus comma 1: 9/8 203.9100 major whole tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 6860/6561 77.1514 4: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 5: 63/50 400.1085 quasi-equal major third 6: 64/63 27.2641 septimal comma, Archytas' comma 7: 6561/6400 43.0126 Mathieu superdiesis 8: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 9: 6860/6561 77.1514 10: 36/35 48.7704 septimal diesis, 1/4-tone 11: 10/9 182.4037 minor whole tone 12: 81/80 21.5063 syntonic comma, Didymus comma
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 : 203.9 252.7 329.8 364.8 764.9 792.2 835.2 870.2 947.3 996.1 1178.5 1200.0 203.9 : 48.8 125.9 160.9 561.0 588.3 631.3 666.3 743.4 792.2 974.6 996.1 1200.0 252.7 : 77.2 112.1 512.2 539.5 582.5 617.5 694.6 743.4 925.8 947.3 1151.2 1200.0 329.8 : 35.0 435.1 462.3 505.4 540.3 617.5 666.3 848.7 870.2 1074.1 1122.8 1200.0 364.8 : 400.1 427.4 470.4 505.4 582.5 631.3 813.7 835.2 1039.1 1087.9 1165.0 1200.0 764.9 : 27.3 70.3 105.3 182.4 231.2 413.6 435.1 639.0 687.8 764.9 799.9 1200.0 792.2 : 43.0 78.0 155.1 203.9 386.3 407.8 611.7 660.5 737.7 772.6 1172.7 1200.0 835.2 : 35.0 112.1 160.9 343.3 364.8 568.7 617.5 694.6 729.6 1129.7 1157.0 1200.0 870.2 : 77.2 125.9 308.3 329.8 533.7 582.5 659.7 694.6 1094.7 1122.0 1165.0 1200.0 947.3 : 48.8 231.2 252.7 456.6 505.4 582.5 617.5 1017.6 1044.9 1087.9 1122.8 1200.0 996.1 : 182.4 203.9 407.8 456.6 533.7 568.7 968.8 996.1 1039.1 1074.1 1151.2 1200.0 1178.5: 21.5 225.4 274.2 351.3 386.3 786.4 813.7 856.7 891.7 968.8 1017.6 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 : 108.29778 cents, oct.: 1299.57335 cents Scale is not proper Step pattern alph. order: ABCDEFGDCBHI Step pattern size order : HEFCIBDCFEGA 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 : 0.133478 Specific harmonicity : 0.073559 Fundamental : 1/793800, -19.5984 octaves, 0.0003 Hz. Guide tone : 12700800, 23.5984 octaves, 3322853979.775 Hz. Exponens Consonantiae : 1.008190E+13, 43.19683 octaves Euler's gradus suavitatis : 67 Sum of Mann's harmonic distance : 755.5, average 62.95833 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 : 37.36792, average 3.11399 Vogel's harmonic complexity : 39.00000 Wille's k value : 446512 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: -3 .. 7 1.50000 28 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: 2 1 0 1 4 0 0 1 1 0 2 0 N SD: 30.3541 c. M:-52.6804 c. 13: 2 1 1 0 4 1 0 0 1 1 2 0 N SD: 25.3561 c. M: 39.3990 c. 14: 2 1 1 0 5 0 1 0 1 1 2 0 N SD: 19.1233 c. M:-32.4814 c. 17: 3 1 1 0 6 0 1 0 1 1 3 0 N SD: 18.4319 c. M: 29.6726 c. 18: 3 1 1 0 6 1 1 0 1 1 3 0 N SD: 18.1400 c. M: 31.5826 c. 19: 3 1 1 1 6 1 0 1 1 1 3 0 N SD: 14.5960 c. M:-28.8726 c. 22: 4 1 1 1 7 1 0 1 1 1 4 0 N SD: 15.6610 c. M:-26.0018 c. 23: 4 1 1 1 8 0 1 1 1 1 4 0 N SD: 11.5871 c. M:-21.5063 c. 29: 5 1 2 1 9 1 1 1 2 1 4 1 N SD: 9.1715 c. M: 20.0883 c. 30: 5 1 2 1 10 1 1 1 2 1 4 1 N SD: 9.2152 c. M: 18.4937 c. 33: 6 1 2 1 11 1 1 1 2 1 5 1 N SD: 7.7120 c. M: 14.8573 c. 36: 6 2 2 1 12 1 1 1 2 2 5 1 N SD: 7.4012 c. M: 13.9863 c. 37: 6 2 2 1 13 0 2 1 2 2 5 1 N SD: 8.8828 c. M: 13.8016 c. 39: 7 1 3 1 13 1 1 1 3 1 6 1 N SD: 7.6495 c. M:-11.4746 c. 42: 7 2 3 1 14 1 1 1 3 2 6 1 N SD: 7.3648 c. M: 13.0253 c. 43: 7 2 3 1 14 1 2 1 3 2 6 1 N SD: 6.4436 c. M: 11.4275 c. 46: 8 2 3 1 15 1 2 1 3 2 7 1 N SD: 6.6849 c. M: 9.5713 c. 47: 8 2 3 1 16 1 2 1 3 2 7 1 N SD: 3.5233 c. M: 7.3606 c. 66: 11 3 4 2 22 2 2 2 4 3 10 1 N SD: 3.2560 c. M:-7.8200 c. 70: 12 3 4 2 24 1 3 2 4 3 11 1 N SD: 4.0921 c. M:-6.5127 c. 72: 12 3 5 2 24 2 2 2 5 3 11 1 N SD: 3.6971 c. M:-7.8200 c. 76: 13 3 5 2 25 2 3 2 5 3 12 1 N SD: 2.9512 c. M: 7.0212 c. 77: 13 3 5 2 26 2 3 2 5 3 12 1 N SD: 3.6897 c. M: 6.3659 c. 89: 15 4 5 3 30 2 3 3 5 4 13 2 N SD: 3.6852 c. M: 6.2363 c. 94: 16 4 6 3 31 2 3 3 6 4 14 2 N SD: 2.8729 c. M: 5.4053 c. 95: 16 4 6 3 32 2 3 3 6 4 14 2 N SD: 2.4777 c. M:-5.6104 c. 99: 17 4 6 3 33 2 4 3 6 4 15 2 N SD: 2.2299 c. M: 4.3012 c. 105: 18 4 7 3 35 2 4 3 7 4 16 2 N SD: 1.6297 c. M: 3.6086 c. 124: 21 5 8 4 41 3 4 4 8 5 19 2 N SD: 1.5378 c. M: 2.9345 c. 148: 25 6 10 4 49 4 5 4 10 6 22 3 N SD: 1.8560 c. M: 2.8180 c. 152: 26 6 10 4 51 3 6 4 10 6 23 3 N SD: 1.5287 c. M: 2.7063 c. 165: 28 7 10 5 55 4 6 5 10 7 25 3 N SD: 1.4428 c. M: 2.5591 c. 171: 29 7 11 5 57 4 6 5 11 7 26 3 N SD: 0.3160 c. M:-0.8025 c. 389: 66 16 25 11 130 9 14 11 25 16 59 7 N SD: 0.4229 c. M: 0.7971 c. 441: 75 18 28 13 147 10 16 13 28 18 67 8 N SD: 0.3365 c. M: 0.5801 c. 447: 76 18 29 13 149 10 16 13 29 18 68 8 N SD: 0.2552 c. M: 0.3695 c. 612: 104 25 39 18 204 14 22 18 39 25 93 11 N SD: 0.2157 c. M: 0.4200 c. 618: 105 25 40 18 206 14 22 18 40 25 94 11 N SD: 0.1890 c. M:-0.2653 c. 783: 133 32 50 23 261 18 28 23 50 32 119 14 N SD: 0.1745 c. M: 0.3299 c. 789: 134 32 51 23 263 18 28 23 51 32 120 14 N SD: 0.1797 c. M:-0.2154 c. 836: 142 34 54 24 279 19 30 24 54 34 127 15 N SD: 0.1723 c. M: 0.3117 c. 888: 151 36 57 26 296 20 32 26 57 36 135 16 N SD: 0.1186 c. M: 0.2881 c. 1059: 180 43 68 31 353 24 38 31 68 43 161 19 N SD: 0.0612 c. M: 0.1120 c. 1230: 209 50 79 36 410 28 44 36 79 50 187 22 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 3 x x x x x x 4 S SD: 31.4805 cents 3 x x x 4 x x x 5 x x x 6 S SD: 44.6637 cents 4 x x x 5:6 x x x 7 x x 8 S SD: 17.4806 cents 5 x x 6 x x x 8 x x 9 x 10 S SD: 8.3905 cents 6 x 7 x x 9 x x 10 x 11 x 12 SD: 16.9762 cents 7 x 8 x 9 x 11 x x 12 x x 14 SD: 15.0951 cents 8:9 x x 10:12 x 13 x 14 x x 16 S SD: 11.6876 cents 9:10 x x 11:14 x x 15 x 16 x 18 SD: 5.1818 cents 10:11 x 12 x x x 16 x 17:18 x 20 S SD: 9.8072 cents 11:12:13 x 14:17 x 18 x 19:20 x 22 SD: 11.7889 cents 12 x 14 x 15 x 19 x 20:21 x x 24 SD: 6.0992 cents 13 x 15 x 16:20 x 21 x 22:23 x 26 SD: 6.1399 cents 14 x 16:17 x x 22 x 23:24:25 x 28 SD: 4.4534 cents 15:17 x 18:19:23 x 24:25:26:27 x 30 SD: 7.1238 cents 16:18 x 19:20:25 x 26 x 28 x x 32 S SD: 6.4799 cents 17:19:20 x 21:26:27 x 28:29:30 x 34 SD: 5.6739 cents 18:20:21 x 22:28 x 29:30:31:32 x 36 SD: 4.0017 cents 19:21:22:23 x x 30:31 x 33:34 x 38 SD: 4.4987 cents 20 x 23:24:25:31 x 32:33:35:36 x 40 SD: 5.2293 cents 21 x 24:25:26 x 33:34:35:36:37:41:42 SD: 4.9167 cents 22:25 x x 27:34:35:36 x 38:39:43:44 SD: 4.0577 cents 23:26:27:28 x 36 x 37:38:40:41:45:46 SD: 3.8451 cents 24:27:28:29:30:37:38:39:40:41:43:47:48 SD: 3.6935 cents 25:28:29:30:31:39 x x 41:43:44:49:50 SD: 3.3242 cents 26:29:30:31:32:40:41:42:43:45:46:51:52 SD: 3.2716 cents 27:30:31 x 33:42:43:44:45:47:48:53:54 SD: 3.7544 cents 28 x 32:34:35 x 44:45:46:48:50:55:56 SD: 4.1454 cents 29:33:34:35:36:45:46:47:48:50:52:57:58 SD: 3.1123 cents 30:34:35:36:37:47 x 49:50:52:53:59:60 SD: 3.3071 cents 31:35:36 x 38:48:49:50:51:54:55:61:62 SD: 2.3325 cents 34:38:39:41:42:53:54:55:56:59:60:67:68 SD: 2.2908 cents 36:41:42 x 44:56:57:58:60:62:64:71:72 SD: 3.2835 cents 37:42:43:45:46:58 x 60:61:64:66:73:74 SD: 2.5192 cents 38:43:44:46:47:59:60:62:63:66:68:75:76 SD: 1.8755 cents 43:48:50:52:53:67:68:70:71:74:76:85:86 SD: 1.8739 cents 47:53:54:57:58:73:74:76:78:81:84:93:94 SD: 1.6836 cents 55:62:64:67:68:86:87:89:91:95:98:109:110 SD: 1.6487 cents 56:63:65:68:69:87:88:91:93:97:100:111:112 SD: 1.6248 cents 57:64:66:69:70:89:90:92:94:99:101:113:114 SD: 1.5410 cents 58:65:67:70:72:90:92:94:96:100:103:115:116 SD: 1.4244 cents 63:71:73:76:78:98:100:102:104:109:112:124:126 SD: 1.0946 cents 72:81:83:87:89:112:114:117:119:124:128:142:144 SD: 0.9790 cents 77:87:89:93:95:120:122:125:127:133:137:152:154 SD: 0.9633 cents 81:91:94:98:100:126:128:131:134:140:144:160:162 SD: 0.5329 cents 152:171:176:184:188:236:240:246:251:263:270:300:304 SD: 0.5182 cents 153:172:177:185:189:238:242:248:253:264:272:302:306 SD: 0.3513 cents 210:236:243:254:259:327:332:340:347:363:373:415:420 SD: 0.3216 cents 234:263:271:283:289:364:370:379:387:404:416:462:468 SD: 0.2881 cents 243:273:281:294:300:378:384:394:402:420:432:480:486 SD: 0.2755 cents 247:278:286:299:305:384:390:400:408:427:439:488:494 SD: 0.2412 cents 248:279:287:300:306:386:392:402:410:429:441:490:496 SD: 0.2010 cents 319:359:369:386:394:496:504:517:527:551:567:630:638 SD: 0.1911 cents 329:370:381:398:406:512:520:533:544:569:585:650:658 SD: 0.1878 cents 376:423:435:455:464:585:594:609:622:650:668:743:752 SD: 0.1803 cents 400:450:463:484:494:622:632:648:661:691:711:790:800 SD: 0.1300 cents 490:551:567:593:605:762:774:794:810:847:871:968:980 SD: 0.1160 cents 553:622:640:669:683:860:874:896:914:956:983:1092:1106 SD: 0.1058 cents 567:638:656:686:700:882:896:919:937:980:1008:1120:1134 SD: 0.0918 cents