Scala analysis: xen16-burt-drones-11
Scale 11 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: 81/64 407.820003 Pythagorean major third 5: 9/7 435.084095 septimal major third, BP third 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: 10/9 182.4037 minor whole tone 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 35/32 155.1396 septimal neutral second 5: 64/63 27.2641 septimal comma, Archytas' comma 6: 63/50 400.1085 quasi-equal major third 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: 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 : 21.5 203.9 252.7 407.8 435.1 835.2 870.2 947.3 996.1 1178.5 1200.0 21.5 : 182.4 231.2 386.3 413.6 813.7 848.7 925.8 974.6 1157.0 1178.5 1200.0 203.9 : 48.8 203.9 231.2 631.3 666.3 743.4 792.2 974.6 996.1 1017.6 1200.0 252.7 : 155.1 182.4 582.5 617.5 694.6 743.4 925.8 947.3 968.8 1151.2 1200.0 407.8 : 27.3 427.4 462.3 539.5 588.3 770.7 792.2 813.7 996.1 1044.9 1200.0 435.1 : 400.1 435.1 512.2 561.0 743.4 764.9 786.4 968.8 1017.6 1172.7 1200.0 835.2 : 35.0 112.1 160.9 343.3 364.8 386.3 568.7 617.5 772.6 799.9 1200.0 870.2 : 77.2 125.9 308.3 329.8 351.3 533.7 582.5 737.7 764.9 1165.0 1200.0 947.3 : 48.8 231.2 252.7 274.2 456.6 505.4 660.5 687.8 1087.9 1122.8 1200.0 996.1 : 182.4 203.9 225.4 407.8 456.6 611.7 639.0 1039.1 1074.1 1151.2 1200.0 1178.5: 21.5 43.0 225.4 274.2 429.3 456.6 856.7 891.7 968.8 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: 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 : 113.88282 cents, oct.: 1252.71097 cents Scale is not proper Step pattern alph. order: ABCDEFGHCBA Step pattern size order : AGDFBHCEDGA 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 : 0.144197 Specific harmonicity : 0.082749 Fundamental : 1/6350400, -22.5984 octaves, 0.0000 Hz. Guide tone : 90720, 16.4691 octaves, 23734671.284 Hz. Exponens Consonantiae : 5.761083E+11, 39.06755 octaves Euler's gradus suavitatis : 58 Sum of Mann's harmonic distance : 620.5, average 56.40909 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 : 32.76924, average 2.97902 Vogel's harmonic complexity : 42.72727 Wille's k value : 4018612 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: -6 .. 5 -0.27273 27 1 3: -4 .. 4 1.27273 34 3 5: -2 .. 1 -0.18182 6 3 7: -2 .. 1 -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 2 0 4 0 1 0 2 0 N SD: 23.2467 c. M:-37.5347 c. 14: 0 2 1 2 0 5 0 1 1 2 0 N SD: 19.5389 c. M:-32.4814 c. 17: 0 3 1 2 0 6 0 1 1 3 0 N SD: 18.7435 c. M: 29.6726 c. 18: 0 3 1 2 1 6 0 1 1 3 0 N SD: 17.6025 c. M:-31.5826 c. 19: 0 3 1 2 1 6 1 1 1 3 0 N SD: 15.4388 c. M: 28.8726 c. 22: 0 4 1 2 1 7 1 1 1 4 0 N SD: 16.8140 c. M: 26.0018 c. 23: 0 4 1 3 0 8 1 1 1 4 0 N SD: 12.7623 c. M:-21.5063 c. 29: 1 4 1 4 1 9 1 2 1 5 0 N SD: 11.3322 c. M:-21.5063 c. 30: 1 4 1 4 1 10 1 2 1 4 1 N SD: 10.6228 c. M:-18.4937 c. 33: 1 5 1 4 1 11 1 2 1 5 1 N SD: 9.1776 c. M:-14.8573 c. 35: 1 5 1 5 1 11 1 3 1 5 1 N SD: 10.0117 c. M: 13.0253 c. 41: 1 6 2 5 1 14 1 2 2 6 1 N SD: 7.5005 c. M:-13.5879 c. 42: 1 6 2 5 1 14 1 3 2 6 1 N SD: 6.6558 c. M: 13.0253 c. 43: 1 6 2 6 1 14 1 3 2 6 1 N SD: 6.8065 c. M:-11.4275 c. 46: 1 7 2 6 1 15 1 3 2 7 1 N SD: 6.5408 c. M:-9.5713 c. 47: 1 7 2 6 1 16 1 3 2 7 1 N SD: 3.1138 c. M:-7.3606 c. 70: 1 11 3 9 1 24 2 4 3 11 1 N SD: 4.0443 c. M: 6.5127 c. 72: 1 11 3 9 2 24 2 5 3 11 1 N SD: 3.9511 c. M: 7.8200 c. 76: 1 12 3 10 2 25 2 5 3 12 1 N SD: 3.4566 c. M:-7.0212 c. 77: 1 12 3 10 2 26 2 5 3 12 1 N SD: 3.7094 c. M:-6.3659 c. 89: 2 13 4 11 2 30 3 5 4 13 2 N SD: 3.7332 c. M:-6.2363 c. 92: 2 14 3 12 2 31 3 6 3 14 2 N SD: 4.0761 c. M: 4.8543 c. 94: 2 14 4 12 2 31 3 6 4 14 2 N SD: 2.7252 c. M: 5.4053 c. 95: 2 14 4 12 2 32 3 6 4 14 2 N SD: 2.7554 c. M: 5.6104 c. 99: 2 15 4 13 2 33 3 6 4 15 2 N SD: 2.3206 c. M:-4.3012 c. 105: 2 16 4 14 2 35 3 7 4 16 2 N SD: 1.6604 c. M:-3.6086 c. 124: 2 19 5 16 3 41 4 8 5 19 2 N SD: 1.4696 c. M: 2.9345 c. 148: 3 22 6 19 4 49 4 10 6 22 3 N SD: 1.9659 c. M:-2.8180 c. 152: 3 23 6 20 3 51 4 10 6 23 3 N SD: 1.5671 c. M:-2.7063 c. 165: 3 25 7 21 4 55 5 10 7 25 3 N SD: 1.2489 c. M:-2.5591 c. 171: 3 26 7 22 4 57 5 11 7 26 3 N SD: 0.3559 c. M: 0.8025 c. 389: 7 59 16 50 9 130 11 25 16 59 7 N SD: 0.3642 c. M:-0.7971 c. 441: 8 67 18 57 10 147 13 28 18 67 8 N SD: 0.3102 c. M:-0.5801 c. 447: 8 68 18 58 10 149 13 29 18 68 8 N SD: 0.2256 c. M: 0.3695 c. 612: 11 93 25 79 14 204 18 39 25 93 11 N SD: 0.1848 c. M:-0.4200 c. 618: 11 94 25 80 14 206 18 40 25 94 11 N SD: 0.1710 c. M: 0.2653 c. 783: 14 119 32 101 18 261 23 50 32 119 14 N SD: 0.1525 c. M:-0.3299 c. 789: 14 120 32 102 18 263 23 51 32 120 14 N SD: 0.1774 c. M: 0.2154 c. 836: 15 127 34 108 19 279 24 54 34 127 15 N SD: 0.1394 c. M: 0.3117 c. 888: 16 135 36 115 20 296 26 57 36 135 16 N SD: 0.1237 c. M:-0.2881 c. 1059: 19 161 43 137 24 353 31 68 43 161 19 N SD: 0.0554 c. M:-0.1120 c. 1230: 22 187 50 159 28 410 36 79 50 187 22 N SD: 0.0384 c. M:-0.0757 c. 1895: 34 288 77 245 43 632 55 122 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: 66.6188 cents 3 x x x x 4 x 5 x x x 6 S SD: 21.5134 cents 4 x x x 5 x 6 x 7 x x 8 S SD: 34.1662 cents 5 x x 6 x x 8 x x 9 x 10 S SD: 17.4806 cents 6 x x 7 x 8 x 10 x 11 x 12 S SD: 16.9762 cents 7 x x 8 x 9:11 x 12 x x 14 SD: 11.7324 cents 8 x 9 x 10 x 13 x 14 x x 16 SD: 6.1758 cents 9 x 10 x 11:12 x 15 x 16 x 18 S SD: 15.1635 cents 10 x 11:12 x 13:16 x 17:18 x 20 SD: 12.4467 cents 11 x 12:13:14 x 18 x 19:20 x 22 SD: 11.1428 cents 12 x x 14:15 x 19:20:21 x x 24 SD: 8.9732 cents 13 x x 15:16:17:21 x 22:23 x 26 SD: 9.7430 cents 14 x x 16 x 18 x 23:24:25 x 28 SD: 4.8255 cents 15:16:17 x 19 x 24:25:26:27 x 30 SD: 12.1557 cents 16:17:18:19:20:21:26 x 28 x x 32 SD: 13.2296 cents 17:18:19:20 x 22 x 28:29:30 x 34 SD: 11.0360 cents 18:19:20:21 x 23:29:30:31:32 x 36 SD: 8.8242 cents 19:20:21:22:24 x 31 x 33:34 x 38 SD: 9.5462 cents 20:21 x 23:25:26:32:33:35:36 x 40 SD: 8.8229 cents 21:22 x 24 x 27:34:35:36:37:41:42 SD: 7.8572 cents 22:23:25 x 28 x 36 x 38:39:43:44 SD: 8.0373 cents 23:24:26:27:29:30:37:38:40:41:45:46 SD: 6.1884 cents 24:25:27:28:30:31:39:40:41:43:47:48 SD: 5.8834 cents 25:26:28:29 x 32 x 41:43:44:49:50 SD: 6.1196 cents 26:27:29:30:33 x 42:43:45:46:51:52 SD: 4.9373 cents 28:29 x 32:35:36:45:46:48:50:55:56 SD: 5.5903 cents 29:30:33:34 x 37:47:48:50:52:57:58 SD: 5.2776 cents 30:31:34:35:38:39:49:50:52:53:59:60 SD: 4.6162 cents 31:32:35:36:39:40:50:51:54:55:61:62 SD: 3.7566 cents 32:33:36:37 x 41:52:53:55:57:63:64 SD: 3.5003 cents 33:34:37:38:42 x 53:55:57:59:65:66 SD: 4.0703 cents 34:35:38:39:43:44:55:56:59:60:67:68 SD: 3.6177 cents 36:37:41:42 x 46:58:60:62:64:71:72 SD: 4.2161 cents 37:38:42:43:47:48:60:61:64:66:73:74 SD: 3.2158 cents 38:39:43:44:48:49:62:63:66:68:75:76 SD: 2.9742 cents 40:41:45:46:51 x 65:66:69:71:79:80 SD: 2.8056 cents 42:43:47:49:53:54:68:69:73:75:83:84 SD: 2.8041 cents 45:46:51:52:57:58:73:74:78:80:89:90 SD: 2.1883 cents 49:50:55:57:62:63:79:81:85:87:97:98 SD: 1.8366 cents 55:56:62:64:70:71:89:91:95:98:109:110 SD: 1.8133 cents 56:57:63:65:71:72:91:93:97:100:111:112 SD: 1.6336 cents 63:64:71:73:80:81:102:104:109:112:124:126 SD: 1.0342 cents 71:72:80:82:90:91:115:117:123:126:140:142 SD: 1.0228 cents 81:82:91:94:103:104:131:134:140:144:160:162 SD: 0.9672 cents 87:88:98:101:110:112:141:144:150:155:172:174 SD: 0.8493 cents 95:96:107:110:120:122:154:157:164:169:188:190 SD: 0.6399 cents 144:146:162:167:182:185:233:238:249:256:284:288 SD: 0.5768 cents 147:149:165:170:186:189:238:243:254:261:290:294 SD: 0.5086 cents 153:155:172:177:194:197:248:253:264:272:302:306 SD: 0.5037 cents 158:160:178:183:200:203:256:261:273:281:312:316 SD: 0.3254 cents 234:237:263:271:296:301:379:387:404:416:462:468 SD: 0.3120 cents 242:245:272:280:306:311:392:400:418:430:478:484 SD: 0.2553 cents 248:251:279:287:314:319:402:410:429:441:490:496 SD: 0.2063 cents 305:309:343:353:386:392:494:504:527:542:602:610 SD: 0.2063 cents 392:397:441:454:496:504:635:648:678:697:774:784 SD: 0.1981 cents 395:400:444:457:500:508:640:653:683:702:780:790 SD: 0.1771 cents 400:405:450:463:506:514:648:661:691:711:790:800 SD: 0.1636 cents 406:411:457:470:514:522:658:671:702:722:802:812 SD: 0.1634 cents 479:485:539:554:606:616:776:792:828:852:946:958 SD: 0.1470 cents 482:488:542:558:610:620:781:797:833:857:952:964 SD: 0.1410 cents 490:496:551:567:620:630:794:810:847:871:968:980 SD: 0.1036 cents 553:560:622:640:700:711:896:914:956:983:1092:1106 SD: 0.0888 cents