Scala analysis: xen16-burt-drones-05
Scale 5 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: 81/64 407.820003 Pythagorean major third 5: 9/7 435.084095 septimal major third, BP third 6: 14/9 764.915905 septimal minor sixth 7: 128/81 792.179997 Pythagorean minor sixth 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: 6561/6400 43.0126 Mathieu superdiesis 5: 64/63 27.2641 septimal comma, Archytas' comma 6: 98/81 329.8318 7: 64/63 27.2641 septimal comma, Archytas' comma 8: 35/32 155.1396 septimal neutral second 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: 2 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 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 35/32 155.140 cents septimal neutral second 1: 1 10/9 182.404 cents minor whole tone 1: 1 7840/6561 308.326 cents 1: 1 98/81 329.832 cents 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 10/9 182.404 cents minor whole tone 2: 2 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: 2 896/729 357.096 cents 3: 1 729/686 105.252 cents 3: 1 729/640 225.416 cents acute major second 3: 1 8/7 231.174 cents septimal whole tone 3: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 3: 1 49/40 351.338 cents larger approximation to neutral third 3: 1 100/81 364.807 cents grave major third 3: 1 8192/6561 384.360 cents Pythagorean diminished fourth 3: 2 5/4 386.314 cents major third 3: 1 63/50 400.108 cents quasi-equal major third 3: 1 980/729 512.236 cents 4: 1 6561/5600 274.187 cents 4: 1 5/4 386.314 cents major third 4: 2 81/64 407.820 cents Pythagorean major third 4: 2 80/63 413.578 cents wide major third 4: 1 32/25 427.373 cents classic diminished fourth 4: 1 9/7 435.084 cents septimal major third, BP third 4: 1 49/36 533.742 cents Arabic lute acute fourth 4: 1 8960/6561 539.500 cents 4: 1 112/81 561.006 cents 5: 2 6561/5120 429.326 cents acute major third 5: 2 9/7 435.084 cents septimal major third, BP third 5: 1 64/49 462.348 cents 2 septatones or septatonic major third 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 1024/729 588.270 cents Pythagorean diminished fifth 5: 2 1120/729 743.410 cents 6: 2 729/560 456.590 cents 6: 1 729/512 611.730 cents Pythagorean tritone 6: 2 10/7 617.488 cents Euler's tritone 6: 1 36/25 631.283 cents classic diminished fifth 6: 1 49/32 737.652 cents 6: 2 14/9 764.916 cents septimal minor sixth 6: 2 10240/6561 770.674 cents grave minor sixth 7: 1 81/56 638.994 cents 7: 1 6561/4480 660.500 cents 7: 1 72/49 666.258 cents Arabic lute grave fifth 7: 1 14/9 764.916 cents septimal minor sixth 7: 1 25/16 772.627 cents classic augmented fifth 7: 2 63/40 786.422 cents narrow minor sixth 7: 2 128/81 792.180 cents Pythagorean minor sixth 7: 1 8/5 813.686 cents minor sixth 7: 1 11200/6561 925.813 cents 8: 1 729/490 687.764 cents 8: 1 100/63 799.892 cents quasi-equal minor sixth 8: 2 8/5 813.686 cents minor sixth 8: 1 6561/4096 815.640 cents Pythagorean augmented fifth 8: 1 81/50 835.193 cents acute minor sixth 8: 1 80/49 848.662 cents smaller approximation to neutral sixth 8: 1 140/81 947.320 cents 8: 1 7/4 968.826 cents harmonic seventh 8: 1 1280/729 974.584 cents grave minor seventh 8: 1 1372/729 1094.748 cents 9: 2 729/448 842.904 cents 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: 2 16/9 996.090 cents Pythagorean minor seventh 9: 1 9/5 1017.596 cents just minor seventh, BP seventh 9: 1 12544/6561 1122.012 cents 9: 1 1400/729 1129.723 cents 9: 1 12800/6561 1156.987 cents 10: 1 81/49 870.168 cents two (septimal major third, BP third) 10: 1 6561/3920 891.674 cents 10: 1 9/5 1017.596 cents just minor seventh, BP seventh 10: 1 64/35 1044.860 cents septimal neutral seventh 10: 1 35/18 1151.230 cents septimal semi-diminished octave 10: 1 12800/6561 1156.987 cents 10: 1 49/25 1165.024 cents BP eighth 10: 2 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: 10 Average number of different intervals per interval class: 8.80000 = 44/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 21.5 329.8 364.8 407.8 435.1 764.9 792.2 947.3 996.1 1178.5 1200.0 21.5 : 308.3 343.3 386.3 413.6 743.4 770.7 925.8 974.6 1157.0 1178.5 1200.0 329.8 : 35.0 78.0 105.3 435.1 462.3 617.5 666.3 848.7 870.2 891.7 1200.0 364.8 : 43.0 70.3 400.1 427.4 582.5 631.3 813.7 835.2 856.7 1165.0 1200.0 407.8 : 27.3 357.1 384.4 539.5 588.3 770.7 792.2 813.7 1122.0 1157.0 1200.0 435.1 : 329.8 357.1 512.2 561.0 743.4 764.9 786.4 1094.7 1129.7 1172.7 1200.0 764.9 : 27.3 182.4 231.2 413.6 435.1 456.6 764.9 799.9 842.9 870.2 1200.0 792.2 : 155.1 203.9 386.3 407.8 429.3 737.7 772.6 815.6 842.9 1172.7 1200.0 947.3 : 48.8 231.2 252.7 274.2 582.5 617.5 660.5 687.8 1017.6 1044.9 1200.0 996.1 : 182.4 203.9 225.4 533.7 568.7 611.7 639.0 968.8 996.1 1151.2 1200.0 1178.5: 21.5 43.0 351.3 386.3 429.3 456.6 786.4 813.7 968.8 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 329.8318 cents 7840/6561, 308.3255 cents 81/80, 21.5063 cents 2: 43.0126 .. 357.0959 cents 5734400/4782969, 314.0833 cents 531441/627200,-286.8192 cents 3: 105.2523 .. 512.2355 cents 672280/531441, 406.9832 cents 531441/614656,-251.8436 cents 4: 274.1867 .. 561.0059 cents 627200/531441, 286.8192 cents 4782969/5488000,-238.0488 cents 5: 429.3263 .. 743.4096 cents 5734400/4782969, 314.0833 cents 531441/573440,-131.6796 cents 6: 456.5904 .. 770.6737 cents 5734400/4782969, 314.0833 cents 531441/627200,-286.8192 cents 7: 638.9941 .. 925.8133 cents 627200/531441, 286.8192 cents 531441/573440,-131.6796 cents 8: 687.7645 .. 1094.7477 cents 672280/531441, 406.9832 cents 4782969/5488000,-238.0488 cents 9: 842.9041 .. 1156.9874 cents 5734400/4782969, 314.0833 cents 531441/614656,-251.8436 cents 10: 870.1682 .. 1178.4937 cents 7840/6561, 308.3255 cents 531441/627200,-286.8192 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 : 98/81, 329.8318 cents Average / Smallest step : 5.072512 Largest / Average step : 3.023458 Largest / Smallest step : 15.336528 Median interval of one step : 6561/6400, 43.0126 cents, amount: 1 Least squares average step : 113.13311 cents, oct.: 1244.46418 cents Scale is not proper Step pattern alph. order: ABCDEFEGHIA Step pattern size order : AHCDBIBFEGA Scale is not a Constant Structure Scale diversity : 1.631523 Lumma stability : 0.035844 Lumma impropriety factor : 0.928312 Rothenberg efficiency : 0.236915 redundancy: 0.763085 Efficiency x scale size : 2.606061 Number of different interval sizes : 76 = 7.60000 / class Number of one step interval sizes : 9 Highest interval variety : 10 Mean interval variety : 8.80000 = 44/5 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 32805/32768, 1.9537 cents Most common triad is 0.0 435.084 764.916 cents, amount: 2 Number of recognisable fifths : 1, average 687.7645 cents Number of appreciable fifths : 0 Scale contains a complete diamond : 1 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 : 0.011850 Average absolute harmonicity : 0.140462 Specific harmonicity : 0.084378 Fundamental : 1/181440, -17.4691 octaves, 0.0014 Hz. Guide tone : 12700800, 23.5984 octaves, 3322853979.775 Hz. Exponens Consonantiae : 2.304433E+12, 41.06755 octaves Euler's gradus suavitatis : 60 Sum of Mann's harmonic distance : 702.0, average 63.81818 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 16.22212, average 1.47474 Sum of Tenney's harmonic distance : 33.87645, average 3.07968 Vogel's harmonic complexity : 30.63636 Wille's k value : 114817 Wilson's harmonic complexity : 60 Rectangular lattice diameter : 14 Triangular lattice diameter : 8 Lattice compactness : 394.96164, average 5.98427 Lattice compactness (without 2's) : 266.13457, average 4.03234 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -6 .. 7 1.18182 33 1 3: -4 .. 4 -1.27273 34 3 5: -1 .. 2 0.27273 5 3 7: -1 .. 2 0.27273 5 4 Average exponent except 2's :-8 / 11 =-0.72727 Average absolute exponent except 2's: 44 / 11 = 4.00000 Scale is weakly epimorphic with val: <11 15 25 34|
FIT/MODE
11: 0 3 0 1 0 3 0 2 0 2 0 N SD: 22.0887 c. M: 37.5347 c. 14: 0 4 0 1 0 4 0 2 1 2 0 N SD: 18.0845 c. M:-32.4814 c. 17: 0 5 0 1 0 5 0 2 1 3 0 N SD: 17.3274 c. M: 29.6726 c. 19: 0 5 1 0 1 5 1 2 1 3 0 N SD: 17.3111 c. M: 28.8726 c. 21: 0 6 0 1 1 5 1 3 0 4 0 N SD: 18.7360 c. M: 24.6614 c. 22: 0 6 0 1 1 6 0 3 1 3 1 N SD: 21.4671 c. M: 37.5347 c. 23: 0 6 1 1 0 6 1 3 1 3 1 N SD: 17.7360 c. M: 34.4811 c. 24: 0 7 0 1 1 6 1 3 1 4 0 N SD: 13.9506 c. M:-21.5063 c. 29: 1 7 1 1 1 8 0 4 1 5 0 N SD: 13.0498 c. M:-21.5063 c. 30: 1 7 1 1 1 8 1 4 1 4 1 N SD: 10.2271 c. M:-18.4937 c. 33: 0 9 1 1 1 9 1 4 1 5 1 N SD: 9.6480 c. M: 21.5063 c. 36: 1 9 1 1 1 10 1 4 2 5 1 N SD: 7.5967 c. M: 13.9863 c. 37: 1 9 1 2 0 11 0 5 2 5 1 N SD: 10.4885 c. M:-13.8016 c. 38: 1 9 2 1 1 10 1 5 2 5 1 N SD: 9.1537 c. M:-14.4363 c. 39: 1 10 1 1 1 11 1 5 1 6 1 N SD: 7.3821 c. M: 11.4746 c. 41: 1 10 1 2 1 11 1 5 2 6 1 N SD: 6.8883 c. M: 13.5879 c. 43: 1 11 1 2 1 11 1 6 2 6 1 N SD: 7.8678 c. M: 11.4275 c. 44: 1 11 1 2 1 12 1 6 2 6 1 N SD: 6.0760 c. M:-13.0009 c. 46: 1 12 1 2 1 12 1 6 2 7 1 N SD: 7.0240 c. M:-9.5713 c. 47: 1 12 1 2 1 13 1 6 2 7 1 N SD: 3.0322 c. M: 7.3606 c. 70: 1 18 2 3 1 20 1 9 3 11 1 N SD: 4.3920 c. M: 6.5127 c. 71: 1 19 2 2 2 19 2 9 3 11 1 N SD: 4.3513 c. M:-8.1964 c. 76: 1 20 2 3 2 20 2 10 3 12 1 N SD: 4.1144 c. M: 7.0212 c. 77: 1 20 2 3 2 21 2 10 3 12 1 N SD: 3.6566 c. M: 6.3659 c. 91: 2 23 3 3 2 25 2 12 4 13 2 N SD: 3.1726 c. M:-6.1078 c. 92: 2 23 3 3 2 26 2 12 3 14 2 N SD: 3.9309 c. M:-4.8543 c. 94: 2 24 3 3 2 26 2 12 4 14 2 N SD: 2.6315 c. M:-5.4053 c. 96: 2 24 3 4 2 26 2 13 4 14 2 N SD: 3.4514 c. M: 4.8318 c. 99: 2 25 3 4 2 27 2 13 4 15 2 N SD: 2.5454 c. M:-4.3012 c. 105: 2 27 3 4 2 29 2 14 4 16 2 N SD: 1.8869 c. M:-3.6086 c. 118: 2 30 4 4 3 32 3 15 5 18 2 N SD: 1.8685 c. M: 4.4081 c. 124: 2 32 4 4 3 34 3 16 5 19 2 N SD: 1.4826 c. M:-2.9345 c. 148: 3 38 4 5 4 40 4 19 6 22 3 N SD: 2.1888 c. M:-2.8180 c. 152: 3 39 4 6 3 42 3 20 6 23 3 N SD: 1.7391 c. M:-2.7063 c. 157: 3 40 5 5 4 43 4 20 6 24 3 N SD: 1.6921 c. M:-2.7245 c. 165: 3 42 5 6 4 45 4 21 7 25 3 N SD: 1.1886 c. M: 2.5591 c. 171: 3 44 5 6 4 47 4 22 7 26 3 N SD: 0.4127 c. M: 0.8025 c. 389: 7 100 11 14 9 107 9 50 16 59 7 N SD: 0.3917 c. M: 0.7971 c. 441: 8 113 13 16 10 121 10 57 18 67 8 N SD: 0.3142 c. M: 0.5801 c. 447: 8 115 13 16 10 123 10 58 18 68 8 N SD: 0.2185 c. M:-0.3695 c. 612: 11 157 18 22 14 168 14 79 25 93 11 N SD: 0.1789 c. M: 0.4200 c. 618: 11 159 18 22 14 170 14 80 25 94 11 N SD: 0.1588 c. M:-0.2653 c. 783: 14 201 23 28 18 215 18 101 32 119 14 N SD: 0.1550 c. M: 0.3299 c. 789: 14 203 23 28 18 217 18 102 32 120 14 N SD: 0.1778 c. M:-0.2154 c. 836: 15 215 24 30 19 230 19 108 34 127 15 N SD: 0.1526 c. M:-0.3117 c. 888: 16 228 26 32 20 244 20 115 36 135 16 N SD: 0.1455 c. M:-0.2881 c. 1059: 19 272 31 38 24 291 24 137 43 161 19 N SD: 0.0639 c. M:-0.1120 c. 1230: 22 316 36 44 28 338 28 159 50 187 22 N SD: 0.0402 c. M: 0.0757 c. 1895: 34 487 55 68 43 521 43 245 77 288 34 N SD: 0.0392 c. M:-0.0890 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 3 x x x x 4 S SD: 31.4805 cents 3 x x x x 4 x x 5 x x 6 S SD: 29.6801 cents 4 x x x 5 x 6 x 7 x x 8 S SD: 17.4806 cents 5 x 6 x x x x 8 x 9 x 10 S SD: 8.3905 cents 6 x 7 x x 8:9 x 10:11 x 12 S SD: 22.7879 cents 7 x 8 x x 9 x 11:12 x x 14 SD: 20.0286 cents 8 x x x 10 x 12:13:14 x x 16 S SD: 17.0019 cents 9 x x 11 x 12:14 x x 16 x 18 SD: 13.0642 cents 10:11:12 x x 13 x 16:17:18 x 20 SD: 21.6213 cents 11:12:13 x 14 x 17 x 19:20 x 22 SD: 20.2338 cents 12:13 x x 15 x x 19:21 x x 24 SD: 24.2000 cents 13:14 x 16 x 17:20:21:22:23 x 26 SD: 15.5692 cents 14:15:17 x x 18 x 22:24:25 x 28 SD: 14.2757 cents 15:16:18 x 19 x 23:24:26:27 x 30 SD: 12.4461 cents 16:17:19 x 20:21:25 x 28 x x 32 SD: 14.4752 cents 17:18 x 21 x 22:26:27:29:30 x 34 SD: 10.9987 cents 18:19 x 22 x 23:28 x 31:32 x 36 SD: 10.7418 cents 19:20:23 x 24 x x 30:33:34 x 38 SD: 9.8384 cents 20:21:24 x 25:26:31:32:35:36 x 40 SD: 8.9027 cents 21:22:25:26 x 27 x 33:36:37:41:42 SD: 8.0408 cents 22:23 x 27:28 x 34:35:38:39:43:44 SD: 6.9360 cents 23:24:28 x 29:30:36 x 40:41:45:46 SD: 7.0498 cents 24:25:29 x 30:31:37:38:41:43:47:48 SD: 6.3360 cents 25:26:30:31 x 32:39:40:43:44:49:50 SD: 5.9272 cents 26:27:31:32:33 x 40:41:45:46:51:52 SD: 5.6713 cents 27:28 x 33:34:35:42:43:47:48:53:54 SD: 5.2440 cents 28:29:34 x 35:36 x 44:48:50:55:56 SD: 5.5454 cents 29:30:35:36 x 37:45:46:50:52:57:58 SD: 4.5198 cents 30:31:36:37:38:39:47 x 52:53:59:60 SD: 4.6554 cents 31:32 x 38:39:40:48:49:54:55:61:62 SD: 4.1478 cents 32:33:39 x x 41:50:51:55:57:63:64 SD: 4.4725 cents 33:34:40:41:42 x 51:52:57:59:65:66 SD: 3.7531 cents 34:35:41:42:43:44:53:54:59:60:67:68 SD: 3.2808 cents 36:37 x 44 x 46:56:57:62:64:71:72 SD: 3.7631 cents 37:38:45:46:47:48:58 x 64:66:73:74 SD: 3.6549 cents 38:39:46:47:48:49:59:60:66:68:75:76 SD: 2.5926 cents 40:41:48:49:51 x 62:63:69:71:79:80 SD: 3.2982 cents 41:42:50:51:52:53:64:65:71:73:81:82 SD: 2.8074 cents 42:43:51:52:53:54:65:66:73:75:83:84 SD: 2.5488 cents 43:44:52:53:54:55:67:68:74:76:85:86 SD: 2.5304 cents 45:46:54:56:57:58:70:71:78:80:89:90 SD: 2.4428 cents 48:49:58:59:61:62:75:76:83:85:95:96 SD: 2.0473 cents 52:53:63:64:66:67:81:82:90:92:103:104 SD: 1.6278 cents 59:60:71:73:75:76:92:93:102:105:117:118 SD: 1.6082 cents 60:61:73:74:76:77:93:95:104:107:119:120 SD: 1.6067 cents 63:64:76:78:80:81:98:100:109:112:124:126 SD: 1.3398 cents 67:68:81:83:85:86:104:106:116:119:132:134 SD: 1.0327 cents 76:77:92:94:96:98:118:120:131:135:150:152 SD: 0.8541 cents 81:82:98:100:103:104:126:128:140:144:160:162 SD: 0.7731 cents 90:91:109:111:114:116:140:142:156:160:178:180 SD: 0.7520 cents 129:131:156:159:163:166:201:204:223:229:255:258 SD: 0.7213 cents 133:135:161:164:168:171:207:210:230:236:263:266 SD: 0.6635 cents 140:142:169:173:177:180:218:221:242:249:277:280 SD: 0.6157 cents 144:146:174:178:182:185:224:228:249:256:284:288 SD: 0.5889 cents 148:150:179:183:187:190:230:234:256:263:292:296 SD: 0.5443 cents 153:155:185:189:194:197:238:242:264:272:302:306 SD: 0.5168 cents 157:159:190:194:199:202:244:248:271:279:310:314 SD: 0.4072 cents 158:160:191:195:200:203:246:250:273:281:312:316 SD: 0.3215 cents 162:164:196:200:205:208:252:256:280:288:320:324 SD: 0.2187 cents 315:319:381:389:399:405:490:498:544:560:622:630 SD: 0.2155 cents 319:323:386:394:404:410:496:504:551:567:630:638 SD: 0.1929 cents 324:328:392:400:410:417:504:512:560:576:640:648 SD: 0.1654 cents 396:401:479:489:501:509:616:626:684:704:782:792 SD: 0.1549 cents 410:415:496:506:519:527:638:648:709:729:810:820 SD: 0.1381 cents 482:488:583:595:610:620:750:762:833:857:952:964 SD: 0.1227 cents 486:492:588:600:615:625:756:768:840:864:960:972 SD: 0.0495 cents