Scala analysis: xen16-burt-drones-09
Scale 9 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: 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: 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: 63/50 400.1085 quasi-equal major third 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: 1 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 6860/6561 77.151 cents 1: 1 35/32 155.140 cents septimal neutral second 1: 2 10/9 182.404 cents minor whole tone 1: 1 63/50 400.108 cents quasi-equal major third 2: 1 6561/6400 43.013 cents Mathieu superdiesis 2: 1 7000/6561 112.127 cents 2: 1 784/729 125.922 cents two (Archytas' 1/3-tone) 2: 1 10/9 182.404 cents minor whole tone 2: 3 9/8 203.910 cents major whole tone 2: 2 8/7 231.174 cents septimal whole tone 2: 1 32/25 427.373 cents classic diminished fourth 2: 1 9/7 435.084 cents septimal major third, BP third 3: 1 800/729 160.897 cents grave whole tone 3: 2 729/640 225.416 cents acute major second 3: 1 8/7 231.174 cents septimal whole tone 3: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 3: 1 7840/6561 308.326 cents 3: 1 5/4 386.314 cents major third 3: 1 64/49 462.348 cents 2 septatones or septatonic major third 3: 1 980/729 512.236 cents 3: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 2 6561/5600 274.187 cents 4: 1 98/81 329.832 cents 4: 1 8000/6561 343.301 cents 4: 2 81/64 407.820 cents Pythagorean major third 4: 1 80/63 413.578 cents wide major third 4: 1 8960/6561 539.500 cents 4: 1 112/81 561.006 cents 4: 1 10/7 617.488 cents Euler's tritone 4: 1 36/25 631.283 cents classic diminished fifth 5: 1 49/40 351.338 cents larger approximation to neutral third 5: 1 100/81 364.807 cents grave major third 5: 1 6561/5120 429.326 cents acute major third 5: 1 9/7 435.084 cents septimal major third, BP third 5: 2 729/560 456.590 cents 5: 1 1024/729 588.270 cents Pythagorean diminished fifth 5: 1 72/49 666.258 cents Arabic lute grave fifth 5: 1 9800/6561 694.639 cents 5: 1 1120/729 743.410 cents 5: 1 8/5 813.686 cents minor sixth 6: 1 5/4 386.314 cents major third 6: 1 729/560 456.590 cents 6: 1 6561/4900 505.361 cents two (Al-Hwarizmi's lute middle finger) 6: 1 49/36 533.742 cents Arabic lute acute fourth 6: 1 729/512 611.730 cents Pythagorean tritone 6: 2 1120/729 743.410 cents 6: 1 14/9 764.916 cents septimal minor sixth 6: 1 10240/6561 770.674 cents grave minor sixth 6: 1 81/50 835.193 cents acute minor sixth 6: 1 80/49 848.662 cents smaller approximation to neutral sixth 7: 1 25/18 568.717 cents classic augmented fourth 7: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 7: 1 81/56 638.994 cents 7: 1 6561/4480 660.500 cents 7: 1 63/40 786.422 cents narrow minor sixth 7: 2 128/81 792.180 cents Pythagorean minor sixth 7: 1 6561/4000 856.699 cents 7: 1 81/49 870.168 cents two (septimal major third, BP third) 7: 2 11200/6561 925.813 cents 8: 1 10/7 617.488 cents Euler's tritone 8: 1 729/490 687.764 cents 8: 1 49/32 737.652 cents 8: 1 8/5 813.686 cents minor sixth 8: 1 6561/3920 891.674 cents 8: 2 140/81 947.320 cents 8: 1 7/4 968.826 cents harmonic seventh 8: 2 1280/729 974.584 cents grave minor seventh 8: 1 729/400 1039.103 cents acute minor seventh 9: 1 14/9 764.916 cents septimal minor sixth 9: 1 25/16 772.627 cents classic augmented fifth 9: 2 7/4 968.826 cents harmonic seventh 9: 3 16/9 996.090 cents Pythagorean minor seventh 9: 1 9/5 1017.596 cents just minor seventh, BP seventh 9: 1 729/392 1074.078 cents 9: 1 6561/3500 1087.873 cents 9: 1 12800/6561 1156.987 cents 10: 1 100/63 799.892 cents quasi-equal minor sixth 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 10: 1 64/35 1044.860 cents septimal neutral seventh 10: 1 6561/3430 1122.849 cents 10: 2 35/18 1151.230 cents septimal semi-diminished octave 10: 1 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: 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 : 21.5 203.9 252.7 329.8 364.8 764.9 792.2 947.3 996.1 1178.5 1200.0 21.5 : 182.4 231.2 308.3 343.3 743.4 770.7 925.8 974.6 1157.0 1178.5 1200.0 203.9 : 48.8 125.9 160.9 561.0 588.3 743.4 792.2 974.6 996.1 1017.6 1200.0 252.7 : 77.2 112.1 512.2 539.5 694.6 743.4 925.8 947.3 968.8 1151.2 1200.0 329.8 : 35.0 435.1 462.3 617.5 666.3 848.7 870.2 891.7 1074.1 1122.8 1200.0 364.8 : 400.1 427.4 582.5 631.3 813.7 835.2 856.7 1039.1 1087.9 1165.0 1200.0 764.9 : 27.3 182.4 231.2 413.6 435.1 456.6 639.0 687.8 764.9 799.9 1200.0 792.2 : 155.1 203.9 386.3 407.8 429.3 611.7 660.5 737.7 772.6 1172.7 1200.0 947.3 : 48.8 231.2 252.7 274.2 456.6 505.4 582.5 617.5 1017.6 1044.9 1200.0 996.1 : 182.4 203.9 225.4 407.8 456.6 533.7 568.7 968.8 996.1 1151.2 1200.0 1178.5: 21.5 43.0 225.4 274.2 351.3 386.3 786.4 813.7 968.8 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 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: 160.8974 .. 582.5122 cents 5103/4000, 421.6148 cents 5600/6561,-274.1867 cents 4: 274.1867 .. 631.2826 cents 896/729, 357.0959 cents 6561/7840,-308.3255 cents 5: 351.3381 .. 813.6863 cents 64/49, 462.3482 cents 245/288,-279.9445 cents 6: 386.3137 .. 848.6619 cents 64/49, 462.3482 cents 25/32,-427.3726 cents 7: 568.7174 .. 925.8133 cents 896/729, 357.0959 cents 245/288,-279.9445 cents 8: 617.4878 .. 1039.1026 cents 5103/4000, 421.6148 cents 6561/7840,-308.3255 cents 9: 764.9159 .. 1156.9874 cents 6400/5103, 392.0715 cents 5600/6561,-274.1867 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 : 36/35, 48.7704 cents, amount: 2 Least squares average step : 110.65967 cents, oct.: 1217.25633 cents Scale is not proper Step pattern alph. order: ABCDEFGHCBA Step pattern size order : AGDECHBFDGA Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.672749 Lumma stability : 0.035844 Lumma impropriety factor : 0.928312 Rothenberg efficiency : 0.235813 redundancy: 0.764187 Efficiency x scale size : 2.593939 Number of different interval sizes : 76 = 7.60000 / class Number of one step interval sizes : 8 Highest interval variety : 10 Mean interval variety : 8.80000 = 44/5 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 32805/32768, 1.9537 cents Number of recognisable fifths : 2, average 691.2019 cents Number of appreciable fifths : 1, 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 : 7 = 63.6364% -- Rational properties -- Prime limit : 7 Odd number limit : 6561 (O: 6561 U: 6561) Highest odd numerator or denominator: 81 Scale harmonicity : 0.012137 Average absolute harmonicity : 0.143302 Specific harmonicity : 0.082749 Fundamental : 1/45360, -15.4691 octaves, 0.0058 Hz. Guide tone : 12700800, 23.5984 octaves, 3322853979.775 Hz. Exponens Consonantiae : 5.761083E+11, 39.06755 octaves Euler's gradus suavitatis : 58 Sum of Mann's harmonic distance : 705.5, average 64.13636 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 : 33.97336, average 3.08849 Vogel's harmonic complexity : 28.36364 Wille's k value : 22963 Wilson's harmonic complexity : 60 Rectangular lattice diameter : 14 Triangular lattice diameter : 8 Lattice compactness : 378.52962, average 5.73530 Lattice compactness (without 2's) : 266.73689, average 4.04147 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 7 1.36364 31 1 3: -4 .. 4 -1.27273 34 3 5: -1 .. 2 0.18182 6 3 7: -1 .. 2 0.27273 5 4 Average exponent except 2's :-9 / 11 =-0.81818 Average absolute exponent except 2's: 45 / 11 = 4.09091
FIT/MODE
11: 0 2 0 1 0 4 0 2 0 2 0 N SD: 23.2467 c. M: 37.5347 c. 14: 0 2 1 1 0 5 0 2 1 2 0 N SD: 19.5389 c. M:-32.4814 c. 17: 0 3 1 1 0 6 0 2 1 3 0 N SD: 18.7435 c. M: 29.6726 c. 18: 0 3 1 1 0 6 1 2 1 3 0 N SD: 17.6025 c. M: 31.5826 c. 19: 0 3 1 1 1 6 1 2 1 3 0 N SD: 15.4388 c. M:-28.8726 c. 21: 0 4 0 2 0 7 1 3 0 4 0 N SD: 20.2330 c. M:-24.6614 c. 23: 0 4 1 1 1 8 0 3 1 4 0 N SD: 12.7623 c. M:-21.5063 c. 29: 0 5 1 2 1 9 1 4 1 4 1 N SD: 11.3322 c. M: 21.5063 c. 32: 1 4 2 2 1 10 1 4 2 4 1 N SD: 12.2478 c. M:-16.4100 c. 33: 1 5 1 2 1 11 1 4 1 5 1 N SD: 9.1776 c. M:-14.8573 c. 36: 1 5 2 2 1 12 1 4 2 5 1 N SD: 8.4289 c. M: 13.9863 c. 39: 1 6 1 3 1 13 1 5 1 6 1 N SD: 7.9426 c. M:-11.4746 c. 41: 1 6 2 2 1 14 1 5 2 6 1 N SD: 7.5005 c. M: 13.5879 c. 42: 1 6 2 3 1 14 1 5 2 6 1 N SD: 6.6558 c. M:-13.0253 c. 43: 1 6 2 3 1 14 1 6 2 6 1 N SD: 6.8065 c. M: 11.4275 c. 46: 1 7 2 3 1 15 1 6 2 7 1 N SD: 6.5408 c. M: 9.5713 c. 47: 1 7 2 3 1 16 1 6 2 7 1 N SD: 3.1138 c. M: 7.3606 c. 70: 1 11 3 4 2 24 1 9 3 11 1 N SD: 4.0443 c. M:-6.5127 c. 72: 1 11 3 5 2 24 2 9 3 11 1 N SD: 3.9511 c. M:-7.8200 c. 76: 1 12 3 5 2 25 2 10 3 12 1 N SD: 3.4566 c. M: 7.0212 c. 77: 1 12 3 5 2 26 2 10 3 12 1 N SD: 3.7094 c. M: 6.3659 c. 89: 2 13 4 5 3 30 2 11 4 13 2 N SD: 3.7332 c. M: 6.2363 c. 90: 2 13 4 6 2 30 2 12 4 13 2 N SD: 3.9843 c. M: 5.5133 c. 91: 2 13 4 6 3 30 2 12 4 13 2 N SD: 3.7126 c. M:-6.1078 c. 94: 2 14 4 6 3 31 2 12 4 14 2 N SD: 2.7252 c. M:-5.4053 c. 95: 2 14 4 6 3 32 2 12 4 14 2 N SD: 2.7554 c. M:-5.6104 c. 96: 2 14 4 6 3 32 2 13 4 14 2 N SD: 3.3813 c. M: 4.8318 c. 99: 2 15 4 6 3 33 2 13 4 15 2 N SD: 2.3206 c. M: 4.3012 c. 105: 2 16 4 7 3 35 2 14 4 16 2 N SD: 1.6604 c. M: 3.6086 c. 124: 2 19 5 8 4 41 3 16 5 19 2 N SD: 1.4696 c. M:-2.9345 c. 148: 3 22 6 10 4 49 4 19 6 22 3 N SD: 1.9659 c. M:-2.8180 c. 152: 3 23 6 10 4 51 3 20 6 23 3 N SD: 1.5671 c. M: 2.7063 c. 165: 3 25 7 10 5 55 4 21 7 25 3 N SD: 1.2489 c. M: 2.5591 c. 171: 3 26 7 11 5 57 4 22 7 26 3 N SD: 0.3559 c. M:-0.8025 c. 389: 7 59 16 25 11 130 9 50 16 59 7 N SD: 0.3642 c. M: 0.7971 c. 441: 8 67 18 28 13 147 10 57 18 67 8 N SD: 0.3102 c. M: 0.5801 c. 447: 8 68 18 29 13 149 10 58 18 68 8 N SD: 0.2256 c. M:-0.3695 c. 612: 11 93 25 39 18 204 14 79 25 93 11 N SD: 0.1848 c. M: 0.4200 c. 618: 11 94 25 40 18 206 14 80 25 94 11 N SD: 0.1710 c. M:-0.2653 c. 783: 14 119 32 50 23 261 18 101 32 119 14 N SD: 0.1525 c. M: 0.3299 c. 789: 14 120 32 51 23 263 18 102 32 120 14 N SD: 0.1774 c. M:-0.2154 c. 836: 15 127 34 54 24 279 19 108 34 127 15 N SD: 0.1394 c. M:-0.3117 c. 888: 16 135 36 57 26 296 20 115 36 135 16 N SD: 0.1237 c. M: 0.2881 c. 1059: 19 161 43 68 31 353 24 137 43 161 19 N SD: 0.0554 c. M: 0.1120 c. 1230: 22 187 50 79 36 410 28 159 50 187 22 N SD: 0.0384 c. M: 0.0757 c. 1895: 34 288 77 122 55 632 43 245 77 288 34 N SD: 0.0370 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: 49.1215 cents 4 x x x x 5:6 x 7 x x 8 S SD: 17.4806 cents 5 x x x 6 x x 8 x 9 x 10 S SD: 8.3905 cents 6 x x 7 x x 9 x 10:11 x 12 SD: 20.9452 cents 7 x x 8 x 9 x 11:12 x x 14 SD: 15.0951 cents 8 x 9 x x 10:12:13:14 x x 16 S SD: 14.1682 cents 9 x 10 x x 11:14 x x 16 x 18 SD: 5.5327 cents 10 x 11 x 12 x x 16:17:18 x 20 S SD: 9.8072 cents 11 x 12:13 x 14:17 x 19:20 x 22 SD: 13.2418 cents 12 x x 14 x 15 x 19:21 x x 24 SD: 6.7463 cents 13 x x 15 x 16:20:21:22:23 x 26 SD: 8.1721 cents 14 x x 16:17 x x 22:24:25 x 28 SD: 4.8787 cents 15:16:17 x 18:19:23:24:26:27 x 30 SD: 12.1968 cents 16:17:18 x 19:20:25 x 28 x x 32 SD: 13.5472 cents 17:18:19:20 x 21:26:27:29:30 x 34 SD: 10.2838 cents 18:19:20:21 x 22:28 x 31:32 x 36 SD: 9.8448 cents 19:20:21:22:23 x x 30:33:34 x 38 SD: 9.4139 cents 20:21 x 23:24:25:31:32:35:36 x 40 SD: 8.7269 cents 21:22 x 24:25:26 x 33:36:37:41:42 SD: 8.3884 cents 22:23:25 x x 27:34:35:38:39:43:44 SD: 7.1195 cents 23:24:26:27:28 x 36 x 40:41:45:46 SD: 7.0735 cents 24:25:27:28:29:30:37:38:41:43:47:48 SD: 5.8577 cents 25:26:28:29:30:31:39:40:43:44:49:50 SD: 5.4023 cents 26:27:29:30:31:32:40:41:45:46:51:52 SD: 5.3299 cents 27:28:30:31 x 33:42:43:47:48:53:54 SD: 5.5834 cents 28:29 x 32:34:35 x 44:48:50:55:56 SD: 6.0384 cents 29:30:33:34:35:36:45:46:50:52:57:58 SD: 4.7865 cents 30:31:34:35:36:37:47 x 52:53:59:60 SD: 4.6518 cents 31:32:35:36 x 38:48:49:54:55:61:62 SD: 4.0635 cents 33:34:37:38:40:41:51:52:57:59:65:66 SD: 3.4258 cents 36:37:41:42 x 44:56:57:62:64:71:72 SD: 4.1045 cents 37:38:42:43:45:46:58 x 64:66:73:74 SD: 3.6766 cents 38:39:43:44:46:47:59:60:66:68:75:76 SD: 2.6960 cents 43:44:48:50:52:53:67:68:74:76:85:86 SD: 2.5150 cents 47:48:53:54:57:58:73:74:81:84:93:94 SD: 2.1798 cents 51:52:57:59:62:63:79:81:88:91:101:102 SD: 2.1194 cents 52:53:59:60:63:64:81:82:90:92:103:104 SD: 2.0814 cents 55:56:62:64:67:68:86:87:95:98:109:110 SD: 1.9898 cents 56:57:63:65:68:69:87:88:97:100:111:112 SD: 1.7515 cents 57:58:64:66:69:70:89:90:99:101:113:114 SD: 1.7204 cents 58:59:65:67:70:72:90:92:100:103:115:116 SD: 1.7059 cents 62:63:70:72:75:77:96:98:107:110:122:124 SD: 1.6971 cents 63:64:71:73:76:78:98:100:109:112:124:126 SD: 1.2824 cents 71:72:80:82:86:88:110:112:123:126:140:142 SD: 1.1807 cents 72:73:81:83:87:89:112:114:124:128:142:144 SD: 0.9754 cents 77:78:87:89:93:95:120:122:133:137:152:154 SD: 0.9367 cents 81:82:91:94:98:100:126:128:140:144:160:162 SD: 0.5044 cents 153:155:172:177:185:189:238:242:264:272:302:306 SD: 0.3799 cents 166:168:187:192:201:205:258:262:287:295:328:332 SD: 0.3684 cents 229:232:258:265:277:283:356:362:396:407:452:458 SD: 0.3498 cents 234:237:263:271:283:289:364:370:404:416:462:468 SD: 0.3075 cents 243:246:273:281:294:300:378:384:420:432:480:486 SD: 0.2410 cents 247:250:278:286:299:305:384:390:427:439:488:494 SD: 0.2352 cents 248:251:279:287:300:306:386:392:429:441:490:496 SD: 0.2072 cents 319:323:359:369:386:394:496:504:551:567:630:638 SD: 0.1717 cents 400:405:450:463:484:494:622:632:691:711:790:800 SD: 0.1314 cents 401:406:451:464:485:495:624:634:693:713:792:802 SD: 0.1261 cents 553:560:622:640:669:683:860:874:956:983:1092:1106 SD: 0.1127 cents 567:574:638:656:686:700:882:896:980:1008:1120:1134 SD: 0.0458 cents