Scala analysis: xen16-burt-drones-02
Scale 2 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: 14/9 764.915905 septimal minor sixth 7: 128/81 792.179997 Pythagorean minor sixth 8: 81/50 835.192576 acute minor sixth 9: 81/49 870.168191 two (septimal major third, BP third) 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: 98/81 329.8318 7: 64/63 27.2641 septimal comma, Archytas' comma 8: 6561/6400 43.0126 Mathieu superdiesis 9: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 10: 7840/6561 308.3255 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 : 21.5 203.9 252.7 407.8 435.1 764.9 792.2 835.2 870.2 1178.5 1200.0 21.5 : 182.4 231.2 386.3 413.6 743.4 770.7 813.7 848.7 1157.0 1178.5 1200.0 203.9 : 48.8 203.9 231.2 561.0 588.3 631.3 666.3 974.6 996.1 1017.6 1200.0 252.7 : 155.1 182.4 512.2 539.5 582.5 617.5 925.8 947.3 968.8 1151.2 1200.0 407.8 : 27.3 357.1 384.4 427.4 462.3 770.7 792.2 813.7 996.1 1044.9 1200.0 435.1 : 329.8 357.1 400.1 435.1 743.4 764.9 786.4 968.8 1017.6 1172.7 1200.0 764.9 : 27.3 70.3 105.3 413.6 435.1 456.6 639.0 687.8 842.9 870.2 1200.0 792.2 : 43.0 78.0 386.3 407.8 429.3 611.7 660.5 815.6 842.9 1172.7 1200.0 835.2 : 35.0 343.3 364.8 386.3 568.7 617.5 772.6 799.9 1129.7 1157.0 1200.0 870.2 : 308.3 329.8 351.3 533.7 582.5 737.7 764.9 1094.7 1122.0 1165.0 1200.0 1178.5: 21.5 43.0 225.4 274.2 429.3 456.6 786.4 813.7 856.7 891.7 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 : 107.95813 cents, oct.: 1187.53945 cents Scale is not proper Step pattern alph. order: ABCDEFEGHIA Step pattern size order : AGEFBIBDCHA 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 : 0.141976 Specific harmonicity : 0.084378 Fundamental : 1/6350400, -22.5984 octaves, 0.0000 Hz. Guide tone : 362880, 18.4691 octaves, 94938685.136 Hz. Exponens Consonantiae : 2.304433E+12, 41.06755 octaves Euler's gradus suavitatis : 60 Sum of Mann's harmonic distance : 613.5, average 55.77273 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 : 32.67233, average 2.97021 Vogel's harmonic complexity : 42.45455 Wille's k value : 4018612 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 -0.09091 29 1 3: -4 .. 4 1.27273 34 3 5: -2 .. 1 -0.27273 5 3 7: -2 .. 1 -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 2 0 2 0 3 0 1 0 3 0 N SD: 22.0887 c. M:-37.5347 c. 14: 0 2 1 2 0 4 0 1 0 4 0 N SD: 18.0845 c. M: 32.4814 c. 17: 0 3 1 2 0 5 0 1 0 5 0 N SD: 17.3274 c. M:-29.6726 c. 23: 0 4 1 3 0 7 0 1 1 6 0 N SD: 13.8377 c. M:-21.5063 c. 29: 0 5 1 4 0 8 1 1 1 7 1 N SD: 13.0498 c. M: 21.5063 c. 30: 1 4 1 4 1 8 1 1 1 7 1 N SD: 10.2271 c. M:-18.4937 c. 32: 1 4 2 4 1 8 1 1 1 8 1 N SD: 11.7890 c. M: 16.4100 c. 33: 1 5 1 4 1 9 1 1 1 8 1 N SD: 8.4323 c. M:-14.8573 c. 36: 1 5 2 4 1 10 1 1 1 9 1 N SD: 7.5967 c. M:-13.9863 c. 39: 1 6 1 5 1 11 1 1 1 10 1 N SD: 7.3821 c. M:-11.4746 c. 41: 1 6 2 5 1 11 1 2 1 10 1 N SD: 6.8883 c. M:-13.5879 c. 44: 1 6 2 6 1 12 1 2 1 11 1 N SD: 6.0760 c. M: 13.0009 c. 46: 1 7 2 6 1 12 1 2 1 12 1 N SD: 7.0240 c. M:-9.5713 c. 47: 1 7 2 6 1 13 1 2 1 12 1 N SD: 3.0322 c. M:-7.3606 c. 70: 1 11 3 9 1 20 1 3 2 18 1 N SD: 4.3920 c. M: 6.5127 c. 71: 1 11 3 9 2 19 2 2 2 19 1 N SD: 4.3513 c. M: 8.1964 c. 76: 1 12 3 10 2 20 2 3 2 20 1 N SD: 4.1144 c. M: 7.0212 c. 77: 1 12 3 10 2 21 2 3 2 20 1 N SD: 3.6566 c. M:-6.3659 c. 88: 2 13 4 11 2 24 2 3 3 22 2 N SD: 3.4699 c. M:-6.4105 c. 89: 2 13 4 11 2 25 2 3 3 22 2 N SD: 3.8433 c. M:-6.2363 c. 90: 2 13 4 12 2 24 2 4 2 23 2 N SD: 4.4053 c. M:-5.5133 c. 91: 1 14 4 12 2 25 2 3 3 23 2 N SD: 3.7688 c. M: 8.3195 c. 94: 2 14 4 12 2 26 2 3 3 24 2 N SD: 2.6315 c. M: 5.4053 c. 99: 2 15 4 13 2 27 2 4 3 25 2 N SD: 2.5454 c. M:-4.3012 c. 105: 2 16 4 14 2 29 2 4 3 27 2 N SD: 1.8869 c. M:-3.6086 c. 118: 2 18 5 15 3 32 3 4 4 30 2 N SD: 1.8685 c. M:-4.4081 c. 124: 2 19 5 16 3 34 3 4 4 32 2 N SD: 1.4826 c. M: 2.9345 c. 152: 3 23 6 20 3 42 3 6 4 39 3 N SD: 1.7391 c. M:-2.7063 c. 157: 3 24 6 20 4 43 4 5 5 40 3 N SD: 1.6921 c. M:-2.7245 c. 165: 3 25 7 21 4 45 4 6 5 42 3 N SD: 1.1886 c. M:-2.5591 c. 171: 3 26 7 22 4 47 4 6 5 44 3 N SD: 0.4127 c. M: 0.8025 c. 389: 7 59 16 50 9 107 9 14 11 100 7 N SD: 0.3917 c. M:-0.7971 c. 441: 8 67 18 57 10 121 10 16 13 113 8 N SD: 0.3142 c. M:-0.5801 c. 447: 8 68 18 58 10 123 10 16 13 115 8 N SD: 0.2185 c. M: 0.3695 c. 612: 11 93 25 79 14 168 14 22 18 157 11 N SD: 0.1789 c. M:-0.4200 c. 618: 11 94 25 80 14 170 14 22 18 159 11 N SD: 0.1588 c. M: 0.2653 c. 783: 14 119 32 101 18 215 18 28 23 201 14 N SD: 0.1550 c. M:-0.3299 c. 789: 14 120 32 102 18 217 18 28 23 203 14 N SD: 0.1778 c. M:-0.2154 c. 836: 15 127 34 108 19 230 19 30 24 215 15 N SD: 0.1526 c. M: 0.3117 c. 888: 16 135 36 115 20 244 20 32 26 228 16 N SD: 0.1455 c. M:-0.2881 c. 1059: 19 161 43 137 24 291 24 38 31 272 19 N SD: 0.0639 c. M:-0.1120 c. 1230: 22 187 50 159 28 338 28 44 36 316 22 N SD: 0.0402 c. M:-0.0757 c. 1895: 34 288 77 245 43 521 43 68 55 487 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 x 5 x 6 S SD: 21.5134 cents 4 x x x 5 x 6 x x 7 x 8 S SD: 29.7489 cents 5 x x 6 x x x x 8 x x 10 S SD: 22.1776 cents 6 x x 7 x 8:9 x x 10 x 12 S SD: 18.2547 cents 7 x x 8 x 9 x 11 x 12 x 14 SD: 13.4469 cents 8 x 9 x 10 x 12 x 13 x x 16 SD: 13.3492 cents 9 x 10 x 11:12:14 x x 15 x 18 S SD: 15.1635 cents 10 x 11:12 x 13 x x 16:17 x 20 SD: 15.5062 cents 11 x 12:13:14 x 17 x 18 x x 22 SD: 11.4215 cents 12 x x 14:15 x x 19 x 20 x 24 SD: 5.9217 cents 13 x x 15:16:17:20 x 21 x x 26 SD: 10.0184 cents 14 x x 16 x 18 x 22 x 23 x 28 SD: 5.1819 cents 15:16:17 x 19 x 23 x 24:25 x 30 SD: 13.9900 cents 16:17:18:19:20:21:25 x 26 x x 32 SD: 12.9894 cents 17:18:19:20 x 22:26:27 x 28 x 34 SD: 11.2178 cents 18:19:20:21 x 23:28 x 29:30 x 36 SD: 9.8970 cents 19:20:21:22:24 x x 30:31 x x 38 SD: 10.7231 cents 20:21 x 23:25:26:31 x 32:33 x 40 SD: 9.2014 cents 21:22 x 24 x 27 x 33:34:35:41:42 SD: 8.5256 cents 22:23:25 x 28 x 34:35:36 x 43:44 SD: 8.2646 cents 23:24:26:27:29:30:36 x 37:38:45:46 SD: 6.7910 cents 24:25:27:28:30:31:37:38:39:40:47:48 SD: 5.6413 cents 25:26:28:29 x 32:39 x x 41:49:50 SD: 6.4759 cents 26:27:29:30:33 x 40:41:42:43:51:52 SD: 5.2361 cents 27:28:30:31:34:35:42:43:44:45:53:54 SD: 5.1803 cents 28:29 x 32:35:36 x 44:45:46:55:56 SD: 6.0432 cents 29:30:33:34 x 37:45:46:47:48:57:58 SD: 5.1058 cents 30:31:34:35:38:39:47 x 49:50:59:60 SD: 5.0873 cents 31:32:35:36:39:40:48:49:50:51:61:62 SD: 3.6101 cents 32:33:36:37 x 41:50:51:52:53:63:64 SD: 3.7368 cents 33:34:37:38:42 x 51:52:53:55:65:66 SD: 4.1361 cents 34:35:38:39:43:44:53:54:55:56:67:68 SD: 3.4763 cents 36:37:41:42 x 46:56:57:58:60:71:72 SD: 4.1840 cents 37:38:42:43:47:48:58 x 60:61:73:74 SD: 3.7320 cents 38:39:43:44:48:49:59:60:62:63:75:76 SD: 2.7012 cents 40:41:45:46:51 x 62:63:65:66:79:80 SD: 2.8978 cents 42:43:47:49:53:54:65:66:68:69:83:84 SD: 2.8318 cents 43:44:48:50:54:55:67:68:70:71:85:86 SD: 2.7808 cents 45:46:51:52:57:58:70:71:73:74:89:90 SD: 2.1558 cents 49:50:55:57:62:63:76:77:79:81:97:98 SD: 1.9979 cents 50:51:56:58:63:64:78:79:81:83:99:100 SD: 1.9366 cents 56:57:63:65:71:72:87:88:91:93:111:112 SD: 1.6962 cents 57:58:64:66:72:73:89:90:92:94:113:114 SD: 1.5347 cents 63:64:71:73:80:81:98:100:102:104:124:126 SD: 1.2390 cents 71:72:80:82:90:91:110:112:115:117:140:142 SD: 1.1474 cents 79:80:89:91:100:102:123:125:128:131:156:158 SD: 1.1427 cents 81:82:91:94:103:104:126:128:131:134:160:162 SD: 0.9672 cents 87:88:98:101:110:112:135:137:141:144:172:174 SD: 0.9547 cents 90:91:101:104:114:116:140:142:146:149:178:180 SD: 0.7837 cents 95:96:107:110:120:122:148:150:154:157:188:190 SD: 0.6600 cents 144:146:162:167:182:185:224:228:233:238:284:288 SD: 0.6497 cents 147:149:165:170:186:189:229:232:238:243:290:294 SD: 0.5560 cents 153:155:172:177:194:197:238:242:248:253:302:306 SD: 0.4523 cents 158:160:178:183:200:203:246:250:256:261:312:316 SD: 0.4008 cents 230:233:259:266:291:296:358:363:373:380:454:460 SD: 0.3997 cents 231:234:260:267:292:297:359:365:374:382:456:462 SD: 0.3525 cents 234:237:263:271:296:301:364:370:379:387:462:468 SD: 0.2762 cents 241:244:271:279:305:310:375:381:390:398:476:482 SD: 0.2738 cents 248:251:279:287:314:319:386:392:402:410:490:496 SD: 0.1831 cents 400:405:450:463:506:514:622:632:648:661:790:800 SD: 0.1526 cents 407:412:458:471:515:523:633:643:659:673:804:814 SD: 0.1515 cents 479:485:539:554:606:616:745:757:776:792:946:958 SD: 0.1234 cents 553:560:622:640:700:711:860:874:896:914:1092:1106 SD: 0.0930 cents 560:567:630:648:709:720:871:885:907:926:1106:1120 SD: 0.0882 cents