Scala analysis: qujus17
scale 17 1568 2,2,1,1 4.109804 0.135448 impropriety 0.044238
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 35/32 155.139620 septimal neutral second 3: 7/6 266.870906 septimal minor third 4: 5/4 386.313714 major third 5: 21/16 470.780907 narrow fourth 6: 10/7 617.487807 Euler's tritone 7: 3/2 701.955001 perfect fifth 8: 49/32 737.651813 9: 5/3 884.358713 major sixth, BP sixth 10: 7/4 968.825906 harmonic seventh 11: 15/8 1088.268715 classic major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 15/14 119.4428 major diatonic semitone 2: 49/48 35.6968 slendro diesis, septimal 1/6-tone 3: 16/15 111.7313 minor diatonic semitone 4: 15/14 119.4428 major diatonic semitone 5: 21/20 84.4672 minor semitone 6: 160/147 146.7069 7: 21/20 84.4672 minor semitone 8: 49/48 35.6968 slendro diesis, septimal 1/6-tone 9: 160/147 146.7069 10: 21/20 84.4672 minor semitone 11: 15/14 119.4428 major diatonic semitone 12: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 3 21/20 84.467 cents minor semitone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 3 15/14 119.443 cents major diatonic semitone 1: 2 160/147 146.707 cents 2: 1 343/320 120.164 cents 2: 1 49/45 147.428 cents BP minor semitone 2: 1 35/32 155.140 cents septimal neutral second 2: 1 10/9 182.404 cents minor whole tone 2: 2 9/8 203.910 cents major whole tone 2: 6 8/7 231.174 cents septimal whole tone 3: 6 7/6 266.871 cents septimal minor third 3: 3 6/5 315.641 cents minor third 3: 3 60/49 350.617 cents smaller approximation to neutral third 4: 3 49/40 351.338 cents larger approximation to neutral third 4: 1 56/45 378.602 cents septimal narrow major third 4: 3 5/4 386.314 cents major third 4: 1 80/63 413.578 cents wide major third 4: 2 9/7 435.084 cents septimal major third, BP third 4: 2 64/49 462.348 cents 2 septatones or septatonic major third 5: 4 21/16 470.781 cents narrow fourth 5: 6 4/3 498.045 cents perfect fourth 5: 1 48/35 546.815 cents septimal semi-augmented fourth 5: 1 480/343 581.791 cents 6: 6 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 6 10/7 617.488 cents Euler's tritone 7: 1 343/240 618.209 cents 7: 1 35/24 653.185 cents septimal semi-diminished fifth 7: 6 3/2 701.955 cents perfect fifth 7: 4 32/21 729.219 cents wide fifth 8: 2 49/32 737.652 cents 8: 2 14/9 764.916 cents septimal minor sixth 8: 1 63/40 786.422 cents narrow minor sixth 8: 3 8/5 813.686 cents minor sixth 8: 1 45/28 821.398 cents septimale wide minor sixth 8: 3 80/49 848.662 cents smaller approximation to neutral sixth 9: 3 49/30 849.383 cents larger approximation to neutral sixth 9: 3 5/3 884.359 cents major sixth, BP sixth 9: 6 12/7 933.129 cents septimal major sixth 10: 6 7/4 968.826 cents harmonic seventh 10: 2 16/9 996.090 cents Pythagorean minor seventh 10: 1 9/5 1017.596 cents just minor seventh, BP seventh 10: 1 64/35 1044.860 cents septimal neutral seventh 10: 1 90/49 1052.572 cents 10: 1 640/343 1079.836 cents 11: 2 147/80 1053.293 cents 11: 3 28/15 1080.557 cents grave major seventh 11: 2 15/8 1088.269 cents classic major seventh 11: 3 40/21 1115.533 cents acute major seventh 11: 2 96/49 1164.303 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.54545 = 50/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 119.4 155.1 266.9 386.3 470.8 617.5 702.0 737.7 884.4 968.8 1088.3 1200.0 119.4 : 35.7 147.4 266.9 351.3 498.0 582.5 618.2 764.9 849.4 968.8 1080.6 1200.0 155.1 : 111.7 231.2 315.6 462.3 546.8 582.5 729.2 813.7 933.1 1044.9 1164.3 1200.0 266.9 : 119.4 203.9 350.6 435.1 470.8 617.5 702.0 821.4 933.1 1052.6 1088.3 1200.0 386.3 : 84.5 231.2 315.6 351.3 498.0 582.5 702.0 813.7 933.1 968.8 1080.6 1200.0 470.8 : 146.7 231.2 266.9 413.6 498.0 617.5 729.2 848.7 884.4 996.1 1115.5 1200.0 617.5 : 84.5 120.2 266.9 351.3 470.8 582.5 702.0 737.7 849.4 968.8 1053.3 1200.0 702.0 : 35.7 182.4 266.9 386.3 498.0 617.5 653.2 764.9 884.4 968.8 1115.5 1200.0 737.7 : 146.7 231.2 350.6 462.3 581.8 617.5 729.2 848.7 933.1 1079.8 1164.3 1200.0 884.4 : 84.5 203.9 315.6 435.1 470.8 582.5 702.0 786.4 933.1 1017.6 1053.3 1200.0 968.8 : 119.4 231.2 350.6 386.3 498.0 617.5 702.0 848.7 933.1 968.8 1115.5 1200.0 1088.3: 111.7 231.2 266.9 378.6 498.0 582.5 729.2 813.7 849.4 996.1 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 146.7069 cents 2560/2401, 111.0101 cents 49/48, 35.6968 cents 2: 120.1640 .. 231.1741 cents 2560/2401, 111.0101 cents 50421/51200,-26.5429 cents 3: 266.8709 .. 350.6169 cents 360/343, 83.7460 cents 49/48, 35.6968 cents 4: 351.3381 .. 462.3482 cents 2560/2401, 111.0101 cents 2401/2400, 0.7212 cents 5: 470.7809 .. 581.7910 cents 2560/2401, 111.0101 cents 1029/1024, 8.4327 cents 6: 582.5122 .. 617.4878 cents 50/49, 34.9756 cents 2401/2400, 0.7212 cents 7: 618.2090 .. 729.2191 cents 2560/2401, 111.0101 cents 2401/2400, 0.7212 cents 8: 737.6518 .. 848.6619 cents 2560/2401, 111.0101 cents 1029/1024, 8.4327 cents 9: 849.3831 .. 933.1291 cents 360/343, 83.7460 cents 2401/2400, 0.7212 cents 10: 968.8259 .. 1079.8360 cents 2560/2401, 111.0101 cents 49/48, 35.6968 cents 11: 1053.2931 .. 1164.3032 cents 2560/2401, 111.0101 cents 50421/51200,-26.5429 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 49/48, 35.6968 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 160/147, 146.7069 cents Average / Smallest step : 2.801371 Largest / Average step : 1.467069 Largest / Smallest step : 4.109804 Median interval of one step : 16/15, 111.7313 cents, amount: 2 Least squares average step : 97.95041 cents, oct.: 1175.40487 cents Scale is not proper Step pattern alph. order: ABCADEDBEDAC Step pattern size order : DACDBEBAEBDC Scale is a Constant Structure, by a margin of 0.72120 cents Scale diversity : 1.445613 Lumma stability : 0.135448 Lumma impropriety factor : 0.044238 Rothenberg efficiency : 0.310149 redundancy: 0.689851 Efficiency x scale size : 3.721789 Number of different interval sizes : 50 = 4.54545 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 4.54545 = 50/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 2401/2400, 0.7212 cents Number of recognisable fifths : 6, average 701.9550 cents Length of longest harmonic part : 2 at degree 10 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 1 = 8.3333% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 7 Odd number limit : 343 (O: 343 U: 343) Highest odd numerator or denominator: 49 Scale harmonicity : 0.020580 Average absolute harmonicity : 0.165657 Specific harmonicity : 0.123123 Fundamental : 1/672, -9.3923 octaves, 0.3893 Hz. Guide tone : 1470, 10.5216 octaves, 384589.581 Hz. Exponens Consonantiae : 9.878400E+05, 19.91392 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 151.5, average 12.62500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.31902, average 0.94325 Sum of Tenney's harmonic distance : 21.64411, average 1.80368 Vogel's harmonic complexity : 18.50000 Wille's k value : 514 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 239.22190, average 3.06695 Lattice compactness (without 2's) : 125.96826, average 1.61498 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -1.83333 26 1 3: -1 .. 1 0.16667 6 1 5: 0 .. 1 0.50000 6 3 7: -1 .. 2 0.33333 8 7 Average exponent except 2's : 12 / 12 = 1.00000 Average absolute exponent except 2's: 20 / 12 = 1.66667 Scale is weakly epimorphic with val: <12 17 26 32| Scale is weakly epimorphic with val: <12 17 26 35| Scale is JI-epimorphic with val: <12 19 28 34| = patent Scale is weakly epimorphic with val: <12 19 28 37| Scale is weakly epimorphic with val: <12 20 29 35|
FIT/MODE
12: 1 1 1 1 1 1 1 0 2 1 1 1 N T3 SD: 25.1835 c. M:-44.8604 c. 13: 1 1 1 1 1 2 1 0 2 1 1 1 N D3 SD: 26.2720 c. M:-46.5587 c. 15: 1 1 1 2 1 2 1 0 2 1 2 1 N D3 SD: 20.0447 c. M: 39.4428 c. 16: 2 0 2 1 1 2 1 1 2 1 2 1 N D3 SD: 21.2806 c. M:-36.7313 c. 18: 2 0 2 2 1 2 2 0 2 2 1 2 P B D3 SD: 18.1046 c. M:-31.3783 c. 19: 2 0 2 2 1 3 1 1 2 1 2 2 N SD: 16.5604 c. M: 28.8238 c. 21: 2 1 2 2 1 3 1 1 2 2 2 2 N D3 SD: 13.5031 c. M: 27.2159 c. 22: 2 1 2 2 2 2 2 1 2 2 2 2 SP B ME SD: 12.8518 c. M:-25.9846 c. 23: 2 1 2 2 2 3 1 1 3 1 3 2 N SD: 13.9727 c. M: 29.6955 c. 24: 2 1 2 3 1 3 2 1 3 1 3 2 P T3 SD: 14.4541 c. M: 20.7809 c. 26: 2 1 3 2 2 3 2 1 3 2 2 3 P B D3 SD: 14.8948 c. M: 27.1351 c. 29: 3 1 2 3 2 4 2 1 3 2 3 3 N SD: 11.7603 c. M: 18.5950 c. 30: 3 1 3 3 2 3 3 0 4 2 3 3 N SD: 11.4634 c. M:-18.0450 c. 31: 3 1 3 3 2 4 2 1 4 2 3 3 N SD: 3.6381 c. M: 6.2648 c. 68: 7 2 6 7 5 8 5 2 8 5 7 6 N SD: 3.4185 c. M:-5.8489 c. 72: 7 2 7 7 5 9 5 2 9 5 7 7 N SD: 3.0713 c. M: 5.1396 c. 84: 8 3 8 8 6 10 6 3 10 6 8 8 N SD: 3.0065 c. M:-5.2053 c. 90: 9 3 8 9 6 11 7 2 11 7 9 8 N SD: 3.6980 c. M:-5.0646 c. 91: 9 3 8 9 7 11 6 3 11 6 9 9 N SD: 3.5744 c. M: 6.9500 c. 94: 9 3 9 9 7 11 7 3 11 7 9 9 N SD: 2.7953 c. M: 4.7218 c. 99: 10 3 9 10 7 12 7 3 12 7 10 9 N SD: 1.5272 c. M:-2.6404 c. 130: 13 4 12 13 9 16 9 4 16 9 13 12 N SD: 1.0065 c. M:-1.7951 c. 140: 14 4 13 14 10 17 10 4 17 10 14 13 N SD: 0.7505 c. M: 1.5016 c. 171: 17 5 16 17 12 21 12 5 21 12 17 16 N SD: 0.4383 c. M: 0.8097 c. 270: 27 8 25 27 19 33 19 8 33 19 27 25 N SD: 0.3324 c. M:-0.6202 c. 301: 30 9 28 30 21 37 21 9 37 21 30 28 N SD: 0.3257 c. M:-0.6911 c. 410: 41 12 38 41 29 50 29 12 50 29 41 38 N SD: 0.3541 c. M:-0.5572 c. 441: 44 13 41 44 31 54 31 13 54 31 44 41 N SD: 0.1519 c. M:-0.2851 c. 836: 83 25 78 83 59 102 59 25 102 59 83 78 N SD: 0.1655 c. M: 0.3041 c. 935: 93 28 87 93 66 114 66 28 114 66 93 87 N SD: 0.1477 c. M:-0.3161 c. 966: 96 29 90 96 68 118 68 29 118 68 96 90 N SD: 0.1309 c. M:-0.2364 c. 1106: 110 33 103 110 78 135 78 33 135 78 110 103 N SD: 0.0797 c. M:-0.1420 c. 1277: 127 38 119 127 90 156 90 38 156 90 127 119 N SD: 0.0688 c. M: 0.1033 c. 1407: 140 42 131 140 99 172 99 42 172 99 140 131 N SD: 0.0529 c. M:-0.0881 c. 1547: 154 46 144 154 109 189 109 46 189 109 154 144 N SD: 0.0369 c. M: 0.0665 c. 1578: 157 47 147 157 111 193 111 47 193 111 157 147 N SD: 0.0380 c. M: 0.0585 c. 1718: 171 51 160 171 121 210 121 51 210 121 171 160 N SD: 0.0421 c. M: 0.0756 c. 1848: 184 55 172 184 130 226 130 55 226 130 184 172 N SD: 0.0346 c. M:-0.0569 c. 2019: 201 60 188 201 142 247 142 60 247 142 201 188 N SD: 0.0321 c. M: 0.0589 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 9.0880 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 0.0000 cents 5 x x 6 x x 7 x x 8:9 x 10 S SD: 20.9523 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 7.9180 cents 7 x x 8 x 9:10 x 11 x 12:13:14 S SD: 11.1647 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 11.6446 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.8694 cents 10 x 11:12 x 13:14:15 x 17:18:19:20 SD: 9.9711 cents 11 x 12:13:14 x 16 x 17:18:19:21:22 SD: 8.0242 cents 12 x 13:14:15:16:17:18 x 20:21:23:24 SD: 5.1726 cents 13:14 x 15:16:17:19 x 20:22:23:24:26 SD: 6.7886 cents 14:15 x 16 x 18:20:21 x 23:25:26:28 SD: 7.5904 cents 15:16 x 18:19:20:21 x 23:25:26:28:30 SD: 7.2594 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 6.0836 cents 17:18:19:20:21:22:24 x 26:28:30:32:34 S SD: 5.8532 cents 19:20:21:22:24:25:27 x 29:32:33:36:38 SD: 4.7485 cents 21 x 23:25:26:28:30 x 32:35:37:39:42 SD: 5.2249 cents 22 x 24:26:28:29:31:33:34:37:39:41:44 SD: 5.1619 cents 23 x 25:27:29:30:33 x 35:38:40:43:46 SD: 3.3396 cents 24 x 26:28:30:32:34:36:37:40:42:45:48 SD: 3.3593 cents 25:27 x 29:31:33:36 x 38:42:44:47:50 SD: 3.5235 cents 26:28 x 30:33:34:37:39:40:43:46:49:52 SD: 3.9722 cents 27:29:30:32:34:35:39 x 41:45:47:51:54 SD: 4.9402 cents 28:30:31:33:35:37:40:42:43:47:49:53:56 SD: 3.0473 cents 29:31:32:34:36:38:41 x 44:48:51:54:58 SD: 3.4138 cents 30:32:33:35:38:39:43:45:46:50:53:56:60 SD: 3.0329 cents 31:33:34:36:39:41:44 x 47:52:54:58:62 SD: 3.0617 cents 32:34:35:37:40:42:46:48:49:53:56:60:64 SD: 2.1813 cents 35 x 38:41:44:46:50:53:54:58:61:66:70 SD: 2.8771 cents 36 x 39:42:45:47:51:54:55:60:63:68:72 SD: 2.4853 cents 37:40 x 43:46:49:53:56:57:62:65:69:74 SD: 3.1588 cents 38:41:42:44:48:50:54:57:58:63:67:71:76 SD: 3.1144 cents 39:42:43:46:49:51:56:59:60:65:68:73:78 SD: 2.8371 cents 40:43:44:47:50:53:57:60:61:67:70:75:80 SD: 2.1970 cents 42:45:46:49:53:55:60:63:64:70:74:79:84 SD: 1.9171 cents 44:47:48:51:55:58:63:66:67:73:77:83:88 SD: 1.8846 cents 52:56:57:61:65:68:74:78:80:87:91:98:104 SD: 1.7804 cents 54:58:59:63:68:71:77:81:83:90:95:101:108 SD: 1.5565 cents 56:60:61:65:70:74:80:84:86:93:98:105:112 SD: 1.5140 cents 60:64:66:70:75:79:86:90:92:100:105:113:120 SD: 1.4057 cents 64:69:70:75:80:84:91:96:98:107:112:120:128 SD: 1.3722 cents 68:73:74:79:85:89:97:102:104:113:119:128:136 SD: 1.3111 cents 72:77:79:84:90:95:103:108:110:120:126:135:144 SD: 1.0038 cents 84:90:92:98:105:110:120:126:129:140:147:158:168 SD: 0.7289 cents 96:103:105:112:120:126:137:144:147:160:168:180:192 SD: 0.2504 cents 224:240:245:261:280:294:320:336:343:373:392:420:448 SD: 0.2248 cents 320:343:350:373:400:420:457:480:490:533:560:600:640 SD: 0.1743 cents 352:377:385:411:440:462:503:528:539:587:616:660:704 SD: 0.1584 cents 448:480:490:523:560:588:640:672:686:747:784:840:896 SD: 0.1123 cents 480:514:525:560:600:630:686:720:735:800:840:900:960 SD: 0.1002 cents 576:617:630:672:720:756:823:864:882:960:1008:1080:1152 SD: 0.0417 cents