Scala analysis: xen16-burt-drones-07
Scale 7 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: 98/81 329.831809 3: 100/81 364.807424 grave major third 4: 14/9 764.915905 septimal minor sixth 5: 128/81 792.179997 Pythagorean minor sixth 6: 81/50 835.192576 acute minor sixth 7: 81/49 870.168191 two (septimal major third, BP third) 8: 140/81 947.319617 9: 16/9 996.089998 Pythagorean minor seventh 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: 7840/6561 308.3255 3: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 4: 63/50 400.1085 quasi-equal major third 5: 64/63 27.2641 septimal comma, Archytas' comma 6: 6561/6400 43.0126 Mathieu superdiesis 7: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 8: 6860/6561 77.1514 9: 36/35 48.7704 septimal diesis, 1/4-tone 10: 10/9 182.4037 minor whole tone 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 : 21.5 329.8 364.8 764.9 792.2 835.2 870.2 947.3 996.1 1178.5 1200.0 21.5 : 308.3 343.3 743.4 770.7 813.7 848.7 925.8 974.6 1157.0 1178.5 1200.0 329.8 : 35.0 435.1 462.3 505.4 540.3 617.5 666.3 848.7 870.2 891.7 1200.0 364.8 : 400.1 427.4 470.4 505.4 582.5 631.3 813.7 835.2 856.7 1165.0 1200.0 764.9 : 27.3 70.3 105.3 182.4 231.2 413.6 435.1 456.6 764.9 799.9 1200.0 792.2 : 43.0 78.0 155.1 203.9 386.3 407.8 429.3 737.7 772.6 1172.7 1200.0 835.2 : 35.0 112.1 160.9 343.3 364.8 386.3 694.6 729.6 1129.7 1157.0 1200.0 870.2 : 77.2 125.9 308.3 329.8 351.3 659.7 694.6 1094.7 1122.0 1165.0 1200.0 947.3 : 48.8 231.2 252.7 274.2 582.5 617.5 1017.6 1044.9 1087.9 1122.8 1200.0 996.1 : 182.4 203.9 225.4 533.7 568.7 968.8 996.1 1039.1 1074.1 1151.2 1200.0 1178.5: 21.5 43.0 351.3 386.3 786.4 813.7 856.7 891.7 968.8 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: 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 : 121.39682 cents, oct.: 1335.36506 cents Scale is not proper Step pattern alph. order: ABCDEFCGHIA Step pattern size order : AHCIBDCFEGA 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 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 : 0.135813 Specific harmonicity : 0.074377 Fundamental : 1/1587600, -20.5984 octaves, 0.0002 Hz. Guide tone : 12700800, 23.5984 octaves, 3322853979.775 Hz. Exponens Consonantiae : 2.016379E+13, 44.19683 octaves Euler's gradus suavitatis : 68 Sum of Mann's harmonic distance : 752.0, average 68.36364 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 : 35.56858, average 3.23351 Vogel's harmonic complexity : 40.09091 Wille's k value : 803722 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: -4 .. 7 1.63636 28 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 3 0 4 0 1 0 1 0 2 0 N SD: 23.2888 c. M: 37.5347 c. 14: 0 4 0 5 0 1 0 1 1 2 0 N SD: 18.5276 c. M:-32.4814 c. 17: 0 5 0 6 0 1 0 1 1 3 0 N SD: 18.0836 c. M: 29.6726 c. 19: 0 5 1 6 1 0 1 1 1 3 0 N G SD: 15.9847 c. M:-28.8726 c. 21: 0 6 0 7 1 1 0 2 0 4 0 N SD: 18.9860 c. M: 24.6614 c. 22: 0 6 0 8 0 1 1 1 1 3 1 N SD: 20.6428 c. M: 37.5347 c. 23: 0 6 1 8 0 1 1 1 1 4 0 N SD: 13.4289 c. M:-21.5063 c. 27: 0 7 1 9 1 1 0 2 1 4 1 N SD: 16.1013 c. M: 25.7237 c. 28: 0 7 1 10 0 1 1 2 1 4 1 N SD: 17.8313 c. M: 29.8318 c. 29: 0 8 1 9 1 1 1 2 1 4 1 N SD: 11.4559 c. M: 21.5063 c. 30: 1 7 1 10 1 1 1 2 1 5 0 N SD: 10.8941 c. M:-21.5063 c. 33: 1 8 1 11 1 1 1 2 1 5 1 N SD: 8.1312 c. M:-14.8573 c. 35: 1 9 1 11 1 1 1 3 1 5 1 N SD: 10.7040 c. M: 13.0253 c. 36: 1 9 1 12 1 1 1 2 2 5 1 N SD: 7.3008 c. M: 13.9863 c. 39: 1 10 1 13 1 1 1 3 1 6 1 N SD: 7.4694 c. M: 11.4746 c. 43: 1 11 1 14 1 2 1 3 2 6 1 N SD: 6.4920 c. M: 11.4275 c. 46: 1 11 2 15 1 2 1 3 2 7 1 N SD: 7.7615 c. M: 16.7883 c. 47: 1 12 1 16 1 2 1 3 2 7 1 N SD: 3.7910 c. M: 7.3606 c. 59: 1 15 2 20 1 2 2 4 2 9 1 N SD: 4.0890 c. M:-8.6126 c. 65: 1 17 2 21 2 2 2 4 3 10 1 N SD: 3.9394 c. M: 7.9928 c. 66: 1 17 2 22 2 2 2 4 3 10 1 N SD: 3.2960 c. M:-7.8200 c. 70: 1 18 2 24 1 3 2 4 3 11 1 N SD: 4.2299 c. M:-6.5127 c. 72: 1 19 2 24 2 2 2 5 3 11 1 N SD: 3.8726 c. M:-7.8200 c. 76: 1 20 2 25 2 3 2 5 3 12 1 N SD: 3.5080 c. M: 7.0212 c. 77: 1 20 2 26 2 3 2 5 3 12 1 N SD: 4.1079 c. M: 6.3659 c. 88: 1 23 3 29 2 3 3 5 4 13 2 N SD: 3.9978 c. M: 7.8699 c. 89: 2 22 3 30 2 3 3 5 4 13 2 N SD: 4.0200 c. M: 6.2363 c. 90: 2 23 2 30 2 4 2 6 4 13 2 N SD: 4.2026 c. M: 5.5133 c. 91: 2 23 3 30 2 3 3 6 4 13 2 N SD: 3.4293 c. M:-6.1078 c. 92: 2 23 3 31 2 3 3 6 3 14 2 N SD: 3.6987 c. M:-4.8543 c. 94: 2 24 3 31 2 3 3 6 4 14 2 N SD: 3.1359 c. M: 5.4053 c. 95: 2 24 3 32 2 3 3 6 4 14 2 N SD: 2.7720 c. M:-5.6104 c. 96: 2 24 3 32 2 4 3 6 4 14 2 N SD: 3.4636 c. M: 4.8318 c. 98: 2 25 3 32 3 3 3 6 4 15 2 N SD: 3.2580 c. M: 5.7322 c. 99: 2 25 3 33 2 4 3 6 4 15 2 N SD: 2.3170 c. M: 4.3012 c. 105: 2 27 3 35 2 4 3 7 4 16 2 N SD: 1.6202 c. M: 3.6086 c. 124: 2 32 4 41 3 4 4 8 5 19 2 N SD: 1.6895 c. M: 2.9345 c. 148: 3 38 4 49 4 5 4 10 6 22 3 N SD: 2.0461 c. M:-2.8180 c. 152: 3 39 4 51 3 6 4 10 6 23 3 N SD: 1.6775 c. M: 2.7063 c. 157: 3 40 5 52 4 5 5 10 6 24 3 N SD: 1.6345 c. M:-2.7245 c. 161: 3 41 5 54 3 6 5 10 7 24 3 N SD: 1.6175 c. M:-2.7860 c. 165: 3 42 5 55 4 6 5 10 7 25 3 N SD: 1.3989 c. M: 2.5591 c. 171: 3 44 5 57 4 6 5 11 7 26 3 N SD: 0.3359 c. M:-0.8025 c. 389: 7 100 11 130 9 14 11 25 16 59 7 N SD: 0.4244 c. M: 0.7971 c. 441: 8 113 13 147 10 16 13 28 18 67 8 N SD: 0.3375 c. M: 0.5801 c. 447: 8 115 13 149 10 16 13 29 18 68 8 N SD: 0.2448 c. M: 0.3695 c. 612: 11 157 18 204 14 22 18 39 25 93 11 N SD: 0.2119 c. M: 0.4200 c. 618: 11 159 18 206 14 22 18 40 25 94 11 N SD: 0.1872 c. M:-0.2653 c. 783: 14 201 23 261 18 28 23 50 32 119 14 N SD: 0.1718 c. M: 0.3299 c. 789: 14 203 23 263 18 28 23 51 32 120 14 N SD: 0.1854 c. M:-0.2154 c. 836: 15 215 24 279 19 30 24 54 34 127 15 N SD: 0.1778 c. M: 0.3117 c. 888: 16 228 26 296 20 32 26 57 36 135 16 N SD: 0.1209 c. M: 0.2881 c. 1059: 19 272 31 353 24 38 31 68 43 161 19 N SD: 0.0620 c. M: 0.1120 c. 1230: 22 316 36 410 28 44 36 79 50 187 22 N SD: 0.0494 c. M: 0.0757 c. 1895: 34 487 55 632 43 68 55 122 77 288 34 N SD: 0.0487 c. M: 0.0890 c. 2066: 37 531 60 689 47 74 60 133 84 314 37 N SD: 0.0493 c. M:-0.0811 c. 2289: 41 588 67 763 52 82 67 147 93 348 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 3 x x x x x x 4 S SD: 31.4805 cents 3 x x 4 x x x 5 x x x 6 S SD: 44.6637 cents 4 x x 5:6 x x x 7 x x 8 S SD: 17.4806 cents 5 x 6 x x x 8 x x 9 x 10 S SD: 8.3905 cents 6 x 7 x 9 x x 10 x 11 x 12 SD: 20.9452 cents 7 x 8:9 x 11 x x 12 x x 14 SD: 24.4683 cents 8 x x 10:12 x 13 x 14 x x 16 S SD: 14.0251 cents 9 x x 11:14 x x 15 x 16 x 18 SD: 4.4905 cents 10:11:12 x x x 16 x 17:18 x 20 S SD: 25.0225 cents 11:12:13:14:17 x 18 x 19:20 x 22 SD: 18.9766 cents 12:13 x 15 x 19 x 20:21 x x 24 SD: 20.3049 cents 13:14 x 16:20 x 21 x 22:23 x 26 SD: 16.4300 cents 14:15:17 x x 22 x 23:24:25 x 28 SD: 14.3576 cents 15:16:18:19:23 x 24:25:26:27 x 30 SD: 12.2161 cents 16:17:19:20:25 x 26 x 28 x x 32 SD: 13.5686 cents 17:18 x 21:26:27 x 28:29:30 x 34 SD: 10.9363 cents 18:19 x 22:28 x 29:30:31:32 x 36 SD: 9.5452 cents 19:20:23 x x 30:31 x 33:34 x 38 SD: 9.9832 cents 20:21:24:25:31 x 32:33:35:36 x 40 SD: 8.6525 cents 21:22:25:26 x 33:34:35:36:37:41:42 SD: 7.3753 cents 22:23 x 27:34:35:36 x 38:39:43:44 SD: 7.1195 cents 23:24:28 x 36 x 37:38:40:41:45:46 SD: 6.5833 cents 24:25:29:30:37:38:39:40:41:43:47:48 SD: 5.8778 cents 25:26:30:31:39 x x 41:43:44:49:50 SD: 6.2655 cents 26:27:31:32:40:41:42:43:45:46:51:52 SD: 5.1564 cents 27:28 x 33:42:43:44:45:47:48:53:54 SD: 5.2717 cents 28:29:34:35 x 44:45:46:48:50:55:56 SD: 5.2878 cents 29:30:35:36:45:46:47:48:50:52:57:58 SD: 3.9322 cents 30:31:36:37:47 x 49:50:52:53:59:60 SD: 4.6926 cents 31:32 x 38:48:49:50:51:54:55:61:62 SD: 4.1244 cents 33:34:40:41:51:52:53:55:57:59:65:66 SD: 3.7920 cents 34:35:41:42:53:54:55:56:59:60:67:68 SD: 3.1748 cents 36:37 x 44:56:57:58:60:62:64:71:72 SD: 3.6390 cents 37:38:45:46:58 x 60:61:64:66:73:74 SD: 3.2847 cents 38:39:46:47:59:60:62:63:66:68:75:76 SD: 2.8078 cents 42:43:51:52:65:66:68:69:73:75:83:84 SD: 2.6907 cents 43:44:52:53:67:68:70:71:74:76:85:86 SD: 2.2040 cents 47:48:57:58:73:74:76:78:81:84:93:94 SD: 1.9559 cents 52:53:63:64:81:82:84:86:90:92:103:104 SD: 1.5949 cents 58:59:70:72:90:92:94:96:100:103:115:116 SD: 1.5869 cents 63:64:76:78:98:100:102:104:109:112:124:126 SD: 1.2555 cents 67:68:81:83:104:106:109:111:116:119:132:134 SD: 1.1918 cents 72:73:87:89:112:114:117:119:124:128:142:144 SD: 0.9129 cents 76:77:92:94:118:120:123:126:131:135:150:152 SD: 0.8116 cents 77:78:93:95:120:122:125:127:133:137:152:154 SD: 0.7852 cents 81:82:98:100:126:128:131:134:140:144:160:162 SD: 0.2910 cents 234:237:283:289:364:370:379:387:404:416:462:468 SD: 0.2475 cents 239:242:289:295:372:378:387:395:413:425:472:478 SD: 0.2140 cents 243:246:294:300:378:384:394:402:420:432:480:486 SD: 0.1828 cents 324:328:392:400:504:512:525:536:560:576:640:648 SD: 0.1275 cents 405:410:490:500:630:640:656:669:700:720:800:810 SD: 0.1201 cents 481:487:582:594:748:760:779:795:831:855:950:962 SD: 0.1135 cents 482:488:583:595:750:762:781:797:833:857:952:964 SD: 0.1129 cents 486:492:588:600:756:768:787:803:840:864:960:972 SD: 0.1022 cents 563:570:681:695:876:890:912:931:973:1001:1112:1126 SD: 0.1017 cents 567:574:686:700:882:896:919:937:980:1008:1120:1134 SD: 0.0953 cents 571:578:691:705:888:902:925:944:987:1015:1128:1142 SD: 0.0927 cents