Scala analysis: qujus16
scale 16 1568 2,2,1,1 4.109804 0.193741 impropriety 0.044238
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 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: 35/24 653.184619 septimal semi-diminished 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: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 21/20 84.4672 minor semitone 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: 49/48 35.6968 slendro diesis, septimal 1/6-tone 8: 21/20 84.4672 minor semitone 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: 1 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 4 21/20 84.467 cents minor semitone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 2 160/147 146.707 cents 2: 1 343/320 120.164 cents 2: 1 35/32 155.140 cents septimal neutral second 2: 2 10/9 182.404 cents minor whole tone 2: 1 28/25 196.198 cents middle second 2: 2 9/8 203.910 cents major whole tone 2: 5 8/7 231.174 cents septimal whole tone 3: 5 7/6 266.871 cents septimal minor third 3: 1 25/21 301.847 cents BP second, quasi-equal minor third 3: 4 6/5 315.641 cents minor third 3: 2 60/49 350.617 cents smaller approximation to neutral third 4: 2 49/40 351.338 cents larger approximation to neutral third 4: 1 56/45 378.602 cents septimal narrow major third 4: 4 5/4 386.314 cents major third 4: 1 63/50 400.108 cents quasi-equal major third 4: 1 80/63 413.578 cents wide major third 4: 1 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: 5 4/3 498.045 cents perfect fourth 5: 1 200/147 533.021 cents 5: 2 48/35 546.815 cents septimal semi-augmented fourth 6: 6 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 6 10/7 617.488 cents Euler's tritone 7: 2 35/24 653.185 cents septimal semi-diminished fifth 7: 1 147/100 666.979 cents 7: 5 3/2 701.955 cents perfect fifth 7: 4 32/21 729.219 cents wide fifth 8: 2 49/32 737.652 cents 8: 1 14/9 764.916 cents septimal minor sixth 8: 1 63/40 786.422 cents narrow minor sixth 8: 1 100/63 799.892 cents quasi-equal minor sixth 8: 4 8/5 813.686 cents minor sixth 8: 1 45/28 821.398 cents septimale wide minor sixth 8: 2 80/49 848.662 cents smaller approximation to neutral sixth 9: 2 49/30 849.383 cents larger approximation to neutral sixth 9: 4 5/3 884.359 cents major sixth, BP sixth 9: 1 42/25 898.153 cents quasi-equal major sixth 9: 5 12/7 933.129 cents septimal major sixth 10: 5 7/4 968.826 cents harmonic seventh 10: 2 16/9 996.090 cents Pythagorean minor seventh 10: 1 25/14 1003.802 cents middle minor seventh 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 10: 1 64/35 1044.860 cents septimal neutral seventh 10: 1 640/343 1079.836 cents 11: 2 147/80 1053.293 cents 11: 2 28/15 1080.557 cents grave major seventh 11: 2 15/8 1088.269 cents classic major seventh 11: 4 40/21 1115.533 cents acute major seventh 11: 1 48/25 1129.328 cents classic diminished octave 11: 1 96/49 1164.303 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.09091 = 56/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 70.7 155.1 266.9 386.3 470.8 617.5 653.2 737.7 884.4 968.8 1088.3 1200.0 70.7 : 84.5 196.2 315.6 400.1 546.8 582.5 667.0 813.7 898.2 1017.6 1129.3 1200.0 155.1 : 111.7 231.2 315.6 462.3 498.0 582.5 729.2 813.7 933.1 1044.9 1115.5 1200.0 266.9 : 119.4 203.9 350.6 386.3 470.8 617.5 702.0 821.4 933.1 1003.8 1088.3 1200.0 386.3 : 84.5 231.2 266.9 351.3 498.0 582.5 702.0 813.7 884.4 968.8 1080.6 1200.0 470.8 : 146.7 182.4 266.9 413.6 498.0 617.5 729.2 799.9 884.4 996.1 1115.5 1200.0 617.5 : 35.7 120.2 266.9 351.3 470.8 582.5 653.2 737.7 849.4 968.8 1053.3 1200.0 653.2 : 84.5 231.2 315.6 435.1 546.8 617.5 702.0 813.7 933.1 1017.6 1164.3 1200.0 737.7 : 146.7 231.2 350.6 462.3 533.0 617.5 729.2 848.7 933.1 1079.8 1115.5 1200.0 884.4 : 84.5 203.9 315.6 386.3 470.8 582.5 702.0 786.4 933.1 968.8 1053.3 1200.0 968.8 : 119.4 231.2 301.8 386.3 498.0 617.5 702.0 848.7 884.4 968.8 1115.5 1200.0 1088.3: 111.7 182.4 266.9 378.6 498.0 582.5 729.2 764.9 849.4 996.1 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 .. 546.8154 cents 256/245, 76.0345 cents 1029/1024, 8.4327 cents 6: 582.5122 .. 617.4878 cents 50/49, 34.9756 cents 49/48, 35.6968 cents 7: 653.1846 .. 729.2191 cents 256/245, 76.0345 cents 49/48, 35.6968 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 : 98.09924 cents, amount: 0 Most common interval of one step : 21/20, 84.4672 cents, amount: 4 Least squares average step : 97.35016 cents, oct.: 1168.20186 cents Scale is not proper Step pattern alph. order: ABCDBEFBEBDC Step pattern size order : BCDECFACFCED Scale is a Constant Structure, by a margin of 0.72120 cents Scale diversity : 1.521751 Lumma stability : 0.193741 Lumma impropriety factor : 0.044238 Rothenberg efficiency : 0.285997 redundancy: 0.714003 Efficiency x scale size : 3.431962 Number of different interval sizes : 56 = 5.09091 / class Number of one step interval sizes : 6 Highest interval variety : 7 Mean interval variety : 5.09091 = 56/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 2401/2400, 0.7212 cents Most common intervals : 7/5, 582.5122 cents & inv., amount: 6 Number of recognisable fifths : 5, 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 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 5 and 6 combined -- Rational properties -- Prime limit : 7 Odd number limit : 343 (O: 343 U: 343) Highest odd numerator or denominator: 49 Scale harmonicity : 0.018185 Average absolute harmonicity : 0.147076 Specific harmonicity : 0.123256 Fundamental : 1/672, -9.3923 octaves, 0.3893 Hz. Guide tone : 7350, 12.8435 octaves, 1922947.905 Hz. Exponens Consonantiae : 4.939200E+06, 22.23585 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 188.5, average 15.70833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.60782, average 1.05065 Sum of Tenney's harmonic distance : 24.24617, average 2.02051 Vogel's harmonic complexity : 19.16667 Wille's k value : 514 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 243.67908, average 3.12409 Lattice compactness (without 2's) : 127.61975, average 1.63615 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -2.16667 30 1 3: -1 .. 1 -0.16667 6 5: 0 .. 2 0.66667 8 4 7: -1 .. 2 0.50000 8 7 Average exponent except 2's : 12 / 12 = 1.00000 Average absolute exponent except 2's: 22 / 12 = 1.83333 Scale is weakly epimorphic with val: <12 17 26 32| Scale is JI-epimorphic with val: <12 19 28 34| = patent Scale is weakly epimorphic with val: <12 20 29 35|
FIT/MODE
12: 0 1 1 1 1 2 0 1 1 1 1 2 N B D3 SD: 64.0075 c. M: 88.2687 c. 13: 1 1 1 1 1 2 0 1 2 1 1 1 N D3 SD: 23.6839 c. M:-46.5587 c. 15: 1 1 1 2 1 2 0 1 2 1 2 1 N D3 SD: 16.3324 c. M:-31.7313 c. 18: 1 1 2 2 1 2 1 1 2 1 2 2 P D3 S SD: 16.4354 c. M: 35.4926 c. 21: 1 2 2 2 1 3 0 2 2 2 2 2 N SD: 14.9625 c. M: 27.2159 c. 22: 1 2 2 2 2 2 1 2 2 2 2 2 SP B ME SD: 13.1841 c. M:-25.9846 c. 23: 1 2 2 2 2 3 1 1 3 2 2 2 N SD: 13.3792 c. M:-25.0763 c. 24: 1 2 2 3 1 3 1 2 3 1 3 2 P T3 SD: 14.6136 c. M: 20.7809 c. 26: 1 2 3 2 2 3 1 2 3 2 2 3 P B D3 SD: 14.3860 c. M: 26.7303 c. 29: 2 2 2 3 2 4 1 2 3 2 3 3 N SD: 12.4512 c. M: 18.5950 c. 30: 2 2 3 3 2 3 1 2 4 2 3 3 N SD: 11.2243 c. M: 17.6518 c. 31: 2 2 3 3 2 4 1 2 4 2 3 3 N SD: 3.9827 c. M:-6.7469 c. 68: 4 5 6 7 5 8 2 5 8 5 7 6 N SD: 3.0025 c. M:-5.8489 c. 72: 4 5 7 7 5 9 2 5 9 5 7 7 N SD: 3.2641 c. M: 5.1396 c. 84: 5 6 8 8 6 10 3 6 10 6 8 8 N SD: 2.8031 c. M:-5.2053 c. 99: 6 7 9 10 7 12 3 7 12 7 10 9 N SD: 1.5752 c. M:-2.6404 c. 130: 8 9 12 13 9 16 4 9 16 9 13 12 N SD: 1.4884 c. M:-3.1737 c. 140: 8 10 13 14 10 17 4 10 17 10 14 13 N SD: 1.0461 c. M: 2.1010 c. 171: 10 12 16 17 12 21 5 12 21 12 17 16 N SD: 0.4828 c. M: 0.8097 c. 270: 16 19 25 27 19 33 8 19 33 19 27 25 N SD: 0.3107 c. M:-0.6202 c. 410: 24 29 38 41 29 50 12 29 50 29 41 38 N SD: 0.3409 c. M: 0.5294 c. 441: 26 31 41 44 31 54 13 31 54 31 44 41 N SD: 0.1321 c. M: 0.2368 c. 966: 57 68 90 96 68 118 29 68 118 68 96 90 N SD: 0.1395 c. M:-0.2364 c. 1106: 65 78 103 110 78 135 33 78 135 78 110 103 N SD: 0.0859 c. M: 0.1480 c. 1137: 67 80 106 113 80 139 34 80 139 80 113 106 N SD: 0.0822 c. M:-0.1476 c. 1277: 75 90 119 127 90 156 38 90 156 90 127 119 N SD: 0.0880 c. M: 0.1947 c. 1308: 77 92 122 130 92 160 39 92 160 92 130 122 N SD: 0.0869 c. M: 0.1953 c. 1376: 81 97 128 137 97 168 41 97 168 97 137 128 N SD: 0.0780 c. M:-0.1493 c. 1407: 83 99 131 140 99 172 42 99 172 99 140 131 N SD: 0.0700 c. M:-0.1203 c. 1547: 91 109 144 154 109 189 46 109 189 109 154 144 N SD: 0.0440 c. M: 0.0842 c. 1578: 93 111 147 157 111 193 47 111 193 111 157 147 N SD: 0.0371 c. M: 0.0585 c. 2019: 119 142 188 201 142 247 60 142 247 142 201 188 N SD: 0.0348 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 x 3 x x x 4 S SD: 17.8484 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 x 6 x 7 x 8 S SD: 8.9242 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 x 9:10 x 11:12 S SD: 9.9041 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 x 12:13:14:15:16 S SD: 12.4702 cents 9 x 10 x 11:12 x 13:14:15:16:17:18 S SD: 7.7973 cents 10 x 11:12 x 13:14 x 15:17:18:19:20 SD: 10.7310 cents 11 x 12:13:14 x x 16:17:18:19:21:22 SD: 7.2542 cents 12 x 13:14:15:16:17 x 18:20:21:23:24 SD: 6.2847 cents 13 x 14:15:16:17 x 19:20:22:23:24:26 SD: 6.0868 cents 14 x 15:16 x 18:20 x 21:23:25:26:28 SD: 9.4381 cents 15:16 x 18:19:20:21:22:23:25:26:28:30 SD: 7.6025 cents 16:17:18:19:20:21:23 x 25:27:28:30:32 SD: 7.2128 cents 17:18:19:20:21:22:24:25:26:28:30:32:34 S SD: 5.7345 cents 18:19:20:21:23:24 x 26:28:30:32:34:36 SD: 6.6710 cents 19:20:21:22:24:25:27:28:29:32:33:36:38 SD: 4.1220 cents 20:21:22:23:25:26 x 29:31:33:35:38:40 SD: 4.5939 cents 23:24:25:27:29:30:33:34:35:38:40:43:46 SD: 3.4120 cents 24:25:26:28:30:32:34:35:37:40:42:45:48 SD: 3.0793 cents 25:26:27:29:31:33:36 x 38:42:44:47:50 SD: 3.5659 cents 27:28:30:32:34:35 x 39:41:45:47:51:54 SD: 4.8980 cents 28:29:31:33:35:37:40:41:43:47:49:53:56 SD: 3.2116 cents 31:32:34:36:39:41:44:45:47:52:54:58:62 SD: 3.0270 cents 32:33:35:37:40:42:46:47:49:53:56:60:64 SD: 2.5411 cents 41:43:45:48:51:54:59:60:63:68:72:77:82 SD: 2.1521 cents 44:46:48:51:55:58:63:64:67:73:77:83:88 SD: 1.9430 cents 48:50:53:56:60:63:69:70:74:80:84:90:96 SD: 1.9065 cents 51:53:56:60:64:67:73:74:78:85:89:96:102 SD: 1.8312 cents 52:54:57:61:65:68:74:76:80:87:91:98:104 SD: 1.7098 cents 54:56:59:63:68:71:77:79:83:90:95:101:108 SD: 1.7083 cents 55:57:60:64:69:72:79:80:84:92:96:103:110 SD: 1.6068 cents 64:67:70:75:80:84:91:93:98:107:112:120:128 SD: 1.3635 cents 68:71:74:79:85:89:97:99:104:113:119:128:136 SD: 1.3465 cents 72:75:79:84:90:95:103:105:110:120:126:135:144 SD: 0.9675 cents 96:100:105:112:120:126:137:140:147:160:168:180:192 SD: 0.1504 cents 384:400:420:448:480:504:549:560:588:640:672:720:768 SD: 0.1127 cents 480:500:525:560:600:630:686:700:735:800:840:900:960 SD: 0.0601 cents 576:600:630:672:720:756:823:840:882:960:1008:1080:1152 SD: 0.0250 cents