Scala analysis: fractal-01-this-track
Sevish: This Track, One With the Fractal
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major sixth 6: 15/8 1088.268715 classic major seventh 7: 33/16 1253.272943 undecimal comma, al-Farabi's 1/4-tone +1 octave 8: 9/4 1403.910002 major ninth 9: 81/32 1607.820003 Pythagorean major third +1 octave 10: 21/8 1670.780907 narrow fourth +1 octave 11: 3/1 1901.955001 perfect 12th 12: 27/8 2105.865003 Pythagorean major sixth +1 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 9/8 203.9100 major whole tone 2: 16/15 111.7313 minor diatonic semitone 3: 10/9 182.4037 minor whole tone 4: 9/8 203.9100 major whole tone 5: 9/8 203.9100 major whole tone 6: 10/9 182.4037 minor whole tone 7: 11/10 165.0042 Ptolemy's second, 4/5-tone 8: 12/11 150.6371 undecimal neutral second, 3/4-tone 9: 9/8 203.9100 major whole tone 10: 28/27 62.9609 Archytas' 1/3-tone 11: 8/7 231.1741 septimal whole tone 12: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 2 10/9 182.404 cents minor whole tone 1: 5 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 2 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 2 5/4 386.314 cents major third 2: 2 81/64 407.820 cents Pythagorean major third 2: 1 9/7 435.084 cents septimal major third, BP third 3: 1 14/11 417.508 cents undecimal diminished fourth or major third 3: 5 4/3 498.045 cents perfect fourth 3: 2 27/20 519.551 cents acute fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 2 45/32 590.224 cents diatonic tritone 3: 1 81/56 638.994 cents 4: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 7 3/2 701.955 cents perfect fifth 4: 1 54/35 750.725 cents septimal semi-augmented fifth 4: 1 99/64 755.228 cents 4: 1 25/16 772.627 cents classic augmented fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 2 8/5 813.686 cents minor sixth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 5 27/16 905.865 cents Pythagorean major sixth 5: 1 12/7 933.129 cents septimal major sixth 5: 1 55/32 937.632 cents 6: 1 7/4 968.826 cents harmonic seventh 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 81/44 1056.502 cents 2nd undecimal neutral seventh 6: 2 15/8 1088.269 cents classic major seventh 6: 2 243/128 1109.775 cents Pythagorean major seventh 6: 1 27/14 1137.039 cents septimal major seventh 7: 1 108/55 1168.233 cents 7: 1 63/32 1172.736 cents octave - septimal comma 7: 5 2/1 1200.000 cents octave 7: 1 81/40 1221.506 cents syntonic comma, Didymus comma +1 octave 7: 1 33/16 1253.273 cents undecimal comma, al-Farabi's 1/4-tone +1 octave 7: 2 135/64 1292.179 cents major chroma, major limma +1 octave 7: 1 243/112 1340.949 cents Archytas' 2/3-tone +1 octave 8: 1 54/25 1333.238 cents large limma, BP small semitone, Zarlino semitone +1 octave 8: 1 24/11 1350.637 cents undecimal neutral second, 3/4-tone +1 octave 8: 1 35/16 1355.140 cents septimal neutral second +1 octave 8: 7 9/4 1403.910 cents major ninth 8: 1 297/128 1457.183 cents 8: 1 135/56 1523.353 cents septimal wide minor third +1 octave 9: 1 7/3 1466.871 cents minimal tenth, BP tenth 9: 2 12/5 1515.641 cents minor 10th 9: 1 27/11 1554.547 cents neutral third, Zalzal wosta of al-Farabi +1 octave 9: 2 5/2 1586.314 cents major 10th 9: 5 81/32 1607.820 cents Pythagorean major third +1 octave 9: 1 297/112 1688.357 cents 10: 1 21/8 1670.781 cents narrow fourth +1 octave 10: 2 8/3 1698.045 cents perfect 11th 10: 2 27/10 1719.551 cents acute fourth +1 octave 10: 1 11/4 1751.318 cents undecimal semi-augmented fourth +1 octave 10: 1 243/88 1758.457 cents 10: 2 45/16 1790.224 cents diatonic tritone +1 octave 10: 2 729/256 1811.730 cents Pythagorean tritone +1 octave 10: 1 81/28 1838.994 cents 11: 1 189/64 1874.691 cents 11: 5 3/1 1901.955 cents perfect 12th 11: 2 243/80 1923.461 cents acute fifth +1 octave 11: 1 135/44 1940.861 cents 11: 1 99/32 1955.228 cents 11: 1 405/128 1994.134 cents wide augmented fifth +1 octave 11: 1 729/224 2042.904 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.90909 = 76/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 203.9 315.6 498.0 702.0 905.9 1088.3 1253.3 1403.9 1607.8 1670.8 1902.0 2105.9 203.9 : 111.7 294.1 498.0 702.0 884.4 1049.4 1200.0 1403.9 1466.9 1698.0 1902.0 2105.9 315.6 : 182.4 386.3 590.2 772.6 937.6 1088.3 1292.2 1355.1 1586.3 1790.2 1994.1 2105.9 498.0 : 203.9 407.8 590.2 755.2 905.9 1109.8 1172.7 1403.9 1607.8 1811.7 1923.5 2105.9 702.0 : 203.9 386.3 551.3 702.0 905.9 968.8 1200.0 1403.9 1607.8 1719.6 1902.0 2105.9 905.9 : 182.4 347.4 498.0 702.0 764.9 996.1 1200.0 1403.9 1515.6 1698.0 1902.0 2105.9 1088.3: 165.0 315.6 519.6 582.5 813.7 1017.6 1221.5 1333.2 1515.6 1719.6 1923.5 2105.9 1253.3: 150.6 354.5 417.5 648.7 852.6 1056.5 1168.2 1350.6 1554.5 1758.5 1940.9 2105.9 1403.9: 203.9 266.9 498.0 702.0 905.9 1017.6 1200.0 1403.9 1607.8 1790.2 1955.2 2105.9 1607.8: 63.0 294.1 498.0 702.0 813.7 996.1 1200.0 1403.9 1586.3 1751.3 1902.0 2105.9 1670.8: 231.2 435.1 639.0 750.7 933.1 1137.0 1340.9 1523.4 1688.4 1839.0 2042.9 2105.9 1902.0: 203.9 407.8 519.6 702.0 905.9 1109.8 1292.2 1457.2 1607.8 1811.7 1874.7 2105.9 2105.9
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 231.1741 cents 54/49, 168.2132 cents 28/27, 62.9609 cents 2: 266.8709 .. 435.0841 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 3: 417.5080 .. 638.9941 cents 891/784, 221.4861 cents 98/99,-17.5761 cents 4: 582.5122 .. 772.6274 cents 125/112, 190.1152 cents 392/405,-56.4819 cents 5: 764.9159 .. 937.6317 cents 495/448, 172.7158 cents 224/225,-7.7115 cents 6: 968.8259 .. 1137.0391 cents 54/49, 168.2132 cents 56/55, 31.1943 cents 7: 1168.2333 .. 1340.9491 cents 495/448, 172.7158 cents 56/55, 31.1943 cents 8: 1333.2376 .. 1523.3528 cents 125/112, 190.1152 cents 224/225,-7.7115 cents 9: 1466.8709 .. 1688.3570 cents 891/784, 221.4861 cents 392/405,-56.4819 cents 10: 1670.7809 .. 1838.9941 cents 54/49, 168.2132 cents 98/99,-17.5761 cents 11: 1874.6909 .. 2042.9041 cents 54/49, 168.2132 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 175.4888 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.787265 Largest / Average step : 1.317316 Largest / Smallest step : 3.671709 Median interval of one step : 193.15686 cents, amount: 0 Most common interval of one step : 9/8, 203.9100 cents, amount: 5 Least squares average step : 174.72361 cents, oct.: 2096.68338 cents Scale is not proper Step pattern alph. order: ABCAACDEAFGA Step pattern size order : FBEFFEDCFAGF Scale is a Constant Structure, by a margin of 7.71152 cents Scale diversity : 0.184587 Lumma stability : 0.123324 Lumma impropriety factor : 0.077659 Rothenberg efficiency : 0.254813 redundancy: 0.745187 Efficiency x scale size : 3.057756 Number of different interval sizes : 76 = 6.90909 / class Number of one step interval sizes : 7 Highest interval variety : 8 Mean interval variety : 6.90909 = 76/11 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 385/384, 4.5026 cents Most common intervals : 3/2, 701.9550 cents & inv., amount: 7 Most common triad is 0.0 701.955 1403.910 cents, amount: 6 Number of recognisable fifths : 7, average 701.9550 cents Number of recognisable fourths : 5, average 498.0450 cents Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 4 at degree 4 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 7 = 58.3333% 2/1 octave complements present : 2 = 16.6667% Scale is differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 729 (O: 729 U: 55) Highest odd numerator or denominator: 81 Scale harmonicity : 0.016234 Average absolute harmonicity : 0.136799 Specific harmonicity : 0.169246 Fundamental : 1/480, -8.9069 octaves, 0.5451 Hz. Guide tone : 124740, 16.9286 octaves, 32635173.016 Hz. Exponens Consonantiae : 5.987520E+07, 25.83546 octaves Euler's gradus suavitatis : 42 Sum of Mann's harmonic distance : 174.5, average 14.54167 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.82686, average 1.06890 Sum of Tenney's harmonic distance : 22.63591, average 1.88633 Vogel's harmonic complexity : 17.16667 Wille's k value : 607 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 9 Triangular lattice diameter : 5 Lattice compactness : 252.42019, average 3.23616 Lattice compactness (without 2's) : 141.52356, average 1.81440 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -2.08333 31 3: -1 .. 4 1.58333 21 8 5: -1 .. 1 0.00000 2 2 7: 0 .. 1 0.08333 1 1 11: 0 .. 1 0.08333 1 1 Average exponent except 2's : 21 / 12 = 1.75000 Average absolute exponent except 2's: 25 / 12 = 2.08333 Scale is JI-epimorphic with val: <7 11 16 20 24|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 34.4331 c. M:-84.1066 c. Twelve-tone Chromatic (1/11-comma) 13: 1 1 1 1 2 1 1 1 1 0 2 1 N D3 SD: 41.3976 c. M:-66.0727 c. 15: 1 1 2 1 1 2 1 1 1 1 2 1 P D3 SD: 43.6865 c. M: 63.5190 c. 18: 2 1 1 2 2 1 2 1 2 0 2 2 N SD: 27.7388 c. M:-35.3362 c. 20: 2 1 2 2 2 1 2 1 2 1 2 2 P D3 SD: 24.9344 c. M:-41.7742 c. 21: 2 1 2 2 2 2 1 2 2 1 2 2 P D3 SD: 18.5750 c. M: 49.9215 c. 27: 3 1 2 3 3 2 2 2 3 0 3 3 N SD: 21.7169 c. M: 32.8859 c. 29: 3 1 3 3 2 3 2 2 3 1 3 3 N SD: 18.1388 c. M: 34.4726 c. 30: 3 2 2 3 3 3 2 2 3 1 3 3 N SD: 15.7723 c. M:-35.3362 c. 31: 3 2 2 3 3 3 2 3 3 1 3 3 P SD: 20.0503 c. M: 30.5126 c. 33: 3 2 3 3 3 3 3 2 3 1 4 3 N SD: 11.0493 c. M:-23.0089 c. 38: 4 2 3 4 3 4 3 2 4 1 4 4 N SD: 15.5272 c. M:-21.3296 c. 39: 4 2 3 4 4 3 3 3 4 1 4 4 N SD: 9.1596 c. M:-12.0762 c. 42: 4 2 4 4 4 4 3 3 4 1 5 4 N SD: 7.9375 c. M: 16.1727 c. 54: 5 3 5 5 5 5 4 4 5 2 6 5 N SD: 6.3958 c. M: 8.9225 c. 60: 6 3 5 6 6 5 5 4 6 2 6 6 N SD: 6.5922 c. M:-13.9111 c. 72: 7 4 6 7 7 6 6 5 7 2 8 7 N SD: 3.0292 c. M:-6.0881 c. 93: 9 5 8 9 9 8 7 7 9 3 10 9 N SD: 2.7280 c. M: 7.8689 c. 114: 11 6 10 11 11 10 9 8 11 3 13 11 N SD: 2.6463 c. M: 8.2559 c. 126: 12 7 11 12 12 11 10 9 12 4 14 12 N SD: 2.3057 c. M: 3.3514 c. 135: 13 7 12 13 13 12 10 10 13 4 15 13 N SD: 2.3205 c. M: 5.3529 c. 153: 15 8 13 15 15 13 12 11 15 4 17 15 N SD: 2.2996 c. M: 5.3583 c. 165: 16 9 14 16 16 14 13 12 16 5 18 16 N SD: 1.6229 c. M:-3.4292 c. 195: 19 10 17 19 19 17 15 14 19 6 21 19 N SD: 1.5879 c. M:-3.1118 c. 207: 20 11 18 20 20 18 16 15 20 6 23 20 N SD: 0.9391 c. M: 2.3661 c. 267: 26 14 23 26 26 23 21 19 26 8 29 26 N SD: 0.8662 c. M:-1.2917 c. 321: 31 17 28 31 31 28 25 23 31 10 35 31 N SD: 0.7666 c. M:-2.1025 c. 381: 37 20 33 37 37 33 30 27 37 11 42 37 N SD: 0.7579 c. M: 1.5651 c. 393: 38 21 34 38 38 34 31 28 38 12 43 38 N SD: 0.4469 c. M:-1.0509 c. 435: 42 23 38 42 42 38 34 31 42 13 48 42 N SD: 0.5981 c. M:-0.9718 c. 474: 46 25 41 46 46 41 37 34 46 14 52 46 N SD: 0.3409 c. M: 0.4566 c. 600: 58 32 52 58 58 52 47 43 58 18 66 58 N SD: 0.2580 c. M:-0.3431 c. 867: 84 46 75 84 84 75 68 62 84 26 95 84 N SD: 0.1275 c. M:-0.3092 c. 1074: 104 57 93 104 104 93 84 77 104 32 118 104 N SD: 0.1168 c. M: 0.3421 c. 1302: 126 69 113 126 126 113 102 93 126 39 143 126 N SD: 0.1406 c. M:-0.2468 c. 1341: 130 71 116 130 130 116 105 96 130 40 147 130 N SD: 0.1596 c. M:-0.2380 c. 1374: 133 73 119 133 133 119 108 98 133 41 151 133 N SD: 0.1483 c. M:-0.4371 c. 1467: 142 78 127 142 142 127 115 105 142 44 161 142 N SD: 0.0937 c. M: 0.1667 c. 1941: 188 103 168 188 188 168 152 139 188 58 213 188 N SD: 0.0694 c. M: 0.1693 c. 2169: 210 115 188 210 210 188 170 155 210 65 238 210 N SD: 0.0711 c. M:-0.1488 c. 2376: 230 126 206 230 230 206 186 170 230 71 261 230 N SD: 0.0673 c. M:-0.1161 c.
FIT/HARMONIC
1 x x x x x x 2 x x x 3 x S SD: 26.6365 cents 2 x x x 3 x x 4 x 5 x 6:7 S SD: 17.0465 cents 3 x x 4 x 5 x 6:7 x 8:9:10 S SD: 13.1479 cents 4 x 5 x 6:7 x 8:9:10:11:12:14 S SD: 16.7441 cents 5 x 6:7 x 8:9:10:11 x 13:15:17 SD: 17.7136 cents 6 x 7:8:9:10:11:12:14:15:16:18:20 S SD: 10.2953 cents 7:8 x 9:11:12:13:14:16:18 x 21:24 SD: 13.1451 cents 8:9:10:11:12:14:15:17:18:20:21:24:27 SD: 10.1825 cents 9:10:11:12:14:15:17:19:20:23:24:27:30 SD: 8.1777 cents 10:11:12:13:15:17:19:21:23:25:26:30:34 SD: 7.1904 cents 12 x 14:16:18:20:23:25:27:30:32:36:41 SD: 7.1863 cents 14:16:17:19:21:24:26:29:32:35:37:42:47 SD: 5.6542 cents 15:17:18:20:23:25:28:31:34:38:39:45:51 SD: 4.3687 cents 16:18:19:21:24:27:30:33:36:41:42:48:54 SD: 3.2524 cents 24:27:29:32:36:41:45:50:54:61:63:72:81 SD: 2.5659 cents 30:34:36:40:45:51:56:62:68:76:79:90:101 SD: 2.0613 cents 32:36:38:43:48:54:60:66:72:81:84:96:108 SD: 1.8822 cents 40:45:48:53:60:68:75:83:90:101:105:120:135 SD: 1.6849 cents 48:54:58:64:72:81:90:99:108:122:126:144:162 SD: 1.1610 cents 64:72:77:85:96:108:120:132:144:162:168:192:216 SD: 0.6780 cents 80:90:96:107:120:135:150:165:180:203:210:240:270 SD: 0.5738 cents 96:108:115:128:144:162:180:198:216:243:252:288:324 SD: 0.2507 cents 160:180:192:213:240:270:300:330:360:405:420:480:540 SD: 0.2256 cents 224:252:269:299:336:378:420:462:504:567:588:672:756 SD: 0.1934 cents 240:270:288:320:360:405:450:495:540:608:630:720:810 SD: 0.1187 cents 320:360:384:427:480:540:600:660:720:810:840:960:1080 SD: 0.1127 cents 336:378:403:448:504:567:630:693:756:851:882:1008:1134 SD: 0.1110 cents 384:432:461:512:576:648:720:792:864:972:1008:1152:1296 SD: 0.0626 cents 480:540:576:640:720:810:900:990:1080:1215:1260:1440:1620 S SD: 0.0000 cents