Scala analysis: qujus18
scale 18 1960 2,2,1,1 4.109804 0.135448 improriety 0.044238
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 8/7 231.174094 septimal whole tone 3: 7/6 266.870906 septimal minor third 4: 49/40 351.338099 larger approximation to neutral third 5: 4/3 498.044999 perfect fourth 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 3/2 701.955001 perfect fifth 8: 8/5 813.686286 minor sixth 9: 49/30 849.383098 larger approximation to neutral sixth 10: 7/4 968.825906 harmonic seventh 11: 28/15 1080.557192 grave major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 15/14 119.4428 major diatonic semitone 1: 21/20 84.4672 minor semitone 2: 160/147 146.7069 3: 49/48 35.6968 slendro diesis, septimal 1/6-tone 4: 21/20 84.4672 minor semitone 5: 160/147 146.7069 6: 21/20 84.4672 minor semitone 7: 15/14 119.4428 major diatonic semitone 8: 16/15 111.7313 minor diatonic semitone 9: 49/48 35.6968 slendro diesis, septimal 1/6-tone 10: 15/14 119.4428 major diatonic semitone 11: 16/15 111.7313 minor diatonic semitone 12: 15/14 119.4428 major 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 : 84.5 231.2 266.9 351.3 498.0 582.5 702.0 813.7 849.4 968.8 1080.6 1200.0 84.5 : 146.7 182.4 266.9 413.6 498.0 617.5 729.2 764.9 884.4 996.1 1115.5 1200.0 231.2 : 35.7 120.2 266.9 351.3 470.8 582.5 618.2 737.7 849.4 968.8 1053.3 1200.0 266.9 : 84.5 231.2 315.6 435.1 546.8 582.5 702.0 813.7 933.1 1017.6 1164.3 1200.0 351.3 : 146.7 231.2 350.6 462.3 498.0 617.5 729.2 848.7 933.1 1079.8 1115.5 1200.0 498.0 : 84.5 203.9 315.6 351.3 470.8 582.5 702.0 786.4 933.1 968.8 1053.3 1200.0 582.5 : 119.4 231.2 266.9 386.3 498.0 617.5 702.0 848.7 884.4 968.8 1115.5 1200.0 702.0 : 111.7 147.4 266.9 378.6 498.0 582.5 729.2 764.9 849.4 996.1 1080.6 1200.0 813.7 : 35.7 155.1 266.9 386.3 470.8 617.5 653.2 737.7 884.4 968.8 1088.3 1200.0 849.4 : 119.4 231.2 350.6 435.1 581.8 617.5 702.0 848.7 933.1 1052.6 1164.3 1200.0 968.8 : 111.7 231.2 315.6 462.3 498.0 582.5 729.2 813.7 933.1 1044.9 1080.6 1200.0 1080.6: 119.4 203.9 350.6 386.3 470.8 617.5 702.0 821.4 933.1 968.8 1088.3 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 : 98.12322 cents, oct.: 1177.47858 cents Scale is not proper Step pattern alph. order: ABCABADECDED Step pattern size order : BEABEBDCADCD 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 Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 6 Length of longest subharmonic part : 2 at degree 10 Formal octave complements present : 5 = 41.6667% 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 -- 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 : 0.170111 Specific harmonicity : 0.121829 Fundamental : 1/840, -9.7142 octaves, 0.3115 Hz. Guide tone : 1176, 10.1997 octaves, 307671.665 Hz. Exponens Consonantiae : 9.878400E+05, 19.91392 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 165.5, average 13.79167 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.91231, average 0.90936 Sum of Tenney's harmonic distance : 21.82916, average 1.81910 Vogel's harmonic complexity : 19.75000 Wille's k value : 514 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 234.39224, average 3.00503 Lattice compactness (without 2's) : 126.72901, average 1.62473 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.08333 21 1 3: -1 .. 1 -0.16667 6 2 5: -1 .. 0 -0.50000 6 1 7: -1 .. 2 0.66667 10 8 Average exponent except 2's : 0 / 12 = 0.00000 Average absolute exponent except 2's: 22 / 12 = 1.83333 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 1 1 1 1 1 SP B ME I SD: 27.5247 c. M:-50.6169 c. Twelve-tone Chromatic (1/11-comma) 14: 1 2 0 1 2 1 1 1 1 1 2 1 N D3 SD: 21.0827 c. M: 42.2577 c. 15: 1 2 0 1 2 1 2 1 0 2 1 2 N D3 SD: 24.6793 c. M: 49.3831 c. 16: 1 2 1 1 2 1 1 2 0 2 1 2 N D3 SD: 20.8936 c. M:-33.1291 c. 17: 1 2 1 1 2 1 2 1 1 2 1 2 P M ME SD: 16.8301 c. M: 37.2157 c. Schism-12 20: 1 3 0 2 2 2 2 2 0 2 2 2 N SD: 16.5563 c. M: 26.8709 c. 21: 1 3 1 1 3 1 2 2 1 2 2 2 N D3 SD: 13.2654 c. M: 27.3243 c. 22: 2 2 1 2 2 2 2 2 1 2 2 2 SP B ME SD: 15.7777 c. M:-30.4801 c. Jubilee-12 24: 2 3 0 2 3 2 2 2 1 2 3 2 N SD: 13.2781 c. M:-19.4428 c. 26: 2 3 1 2 3 2 2 3 0 3 2 3 N SD: 12.8289 c. M: 19.0187 c. 27: 2 3 1 2 3 2 3 2 1 3 2 3 P D3 SD: 8.1260 c. M: 13.8905 c. 31: 2 4 1 2 4 2 3 3 1 3 3 3 N SD: 3.5502 c. M: 7.0478 c. 41: 3 5 1 3 5 3 4 4 1 4 4 4 N SD: 2.7279 c. M:-5.8259 c. 68: 5 8 2 5 8 5 7 6 2 7 6 7 N SD: 2.6510 c. M: 4.0866 c. 72: 5 9 2 5 9 5 7 7 2 7 7 7 N SD: 1.7732 c. M:-2.9804 c. 99: 7 12 3 7 12 7 10 9 3 10 9 10 N SD: 0.9538 c. M: 1.7693 c. 130: 9 16 4 9 16 9 13 12 4 13 12 13 N SD: 0.7521 c. M: 1.3903 c. 140: 10 17 4 10 17 10 14 13 4 14 13 14 N SD: 0.7133 c. M:-1.2471 c. 171: 12 21 5 12 21 12 17 16 5 17 16 17 N SD: 0.2801 c. M: 0.4609 c. 270: 19 33 8 19 33 19 27 25 8 27 25 27 N SD: 0.2898 c. M: 0.5572 c. 441: 31 54 13 31 54 31 44 41 13 44 41 44 N SD: 0.2018 c. M: 0.4035 c. 612: 43 75 18 43 75 43 61 57 18 61 57 61 N SD: 0.1954 c. M: 0.3635 c. 836: 59 102 25 59 102 59 83 78 25 83 78 83 N SD: 0.2101 c. M:-0.3777 c. 894: 63 109 27 63 109 63 89 83 27 89 83 89 N SD: 0.2088 c. M:-0.3398 c. 935: 66 114 28 66 114 66 93 87 28 93 87 93 N SD: 0.1632 c. M:-0.3197 c. 966: 68 118 29 68 118 68 96 90 29 96 90 96 N SD: 0.1511 c. M:-0.3063 c. 1007: 71 123 30 71 123 71 100 94 30 100 94 100 N SD: 0.1615 c. M:-0.2770 c. 1065: 75 130 32 75 130 75 106 99 32 106 99 106 N SD: 0.1331 c. M:-0.2112 c. 1106: 78 135 33 78 135 78 110 103 33 110 103 110 N SD: 0.1062 c. M:-0.1990 c. 1205: 85 147 36 85 147 85 120 112 36 120 112 120 N SD: 0.1143 c. M:-0.1972 c. 1236: 87 151 37 87 151 87 123 115 37 123 115 123 N SD: 0.0806 c. M:-0.1315 c. 1277: 90 156 38 90 156 90 127 119 38 127 119 127 N SD: 0.0738 c. M:-0.1106 c. 1376: 97 168 41 97 168 97 137 128 41 137 128 137 N SD: 0.0688 c. M:-0.1258 c. 1407: 99 172 42 99 172 99 140 131 42 140 131 140 N SD: 0.0470 c. M:-0.0839 c. 1547: 109 189 46 109 189 109 154 144 46 154 144 154 N SD: 0.0385 c. M:-0.0835 c. 1578: 111 193 47 111 193 111 157 147 47 157 147 157 N SD: 0.0369 c. M: 0.0565 c. 1718: 121 210 51 121 210 121 171 160 51 171 160 171 N SD: 0.0303 c. M:-0.0506 c. 1848: 130 226 55 130 226 130 184 172 55 184 172 184 N SD: 0.0309 c. M: 0.0516 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: 11.6585 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.7439 cents 5 x x x 6 x 7 x 8 x 9 x 10 S SD: 12.0877 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 7.8109 cents 7 x 8 x x 9:10 x 11 x 12:13:14 S SD: 12.3826 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 6.9345 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 11.1590 cents 10 x 11 x 12:13:14:15:16 x 18:19:20 S SD: 11.5957 cents 11:12 x 13 x 15 x 17 x 18:19:21:22 SD: 13.1686 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 7.6577 cents 13:14:15 x 16:17:18:20:21 x 23:24:26 SD: 8.1716 cents 14:15:16 x 17:19:20:21:22:23:25:26:28 SD: 7.0376 cents 15:16:17 x 18:20:21:23:24:25:26:28:30 SD: 6.5386 cents 16:17:18:19:20:21:22:24 x 26:28:30:32 S SD: 6.5427 cents 17:18:19:20:21:23:24:26:27:28:30:32:34 SD: 5.8289 cents 18:19 x 21:22:24:25:27:29 x 32:34:36 SD: 3.9948 cents 19:20 x 22:23:25:27:29:30:31:33:35:38 SD: 5.7054 cents 20:21:23 x 25:27:28:30:32:33:35:37:40 SD: 4.4090 cents 21:22:24:25:26:28:29:32 x 34:37:39:42 SD: 5.2467 cents 22:23:25:26:27:29:31:33:35:36:39:41:44 SD: 3.5302 cents 25:26 x 29:31:33:35:38:40:41:44:47:50 SD: 4.0085 cents 26:27:30 x 32:35:36:39:42 x 46:49:52 SD: 4.7475 cents 27:28:31:32:33:36:38:41:43:44:47:50:54 SD: 3.8860 cents 28:29:32:33:34:37:39:42:45:46:49:52:56 SD: 3.3967 cents 30:32:34:35:37:40:42:45:48:49:53:56:60 SD: 3.0735 cents 32:34 x 37:39:43:45:48:51:52:56:60:64 SD: 3.1017 cents 35:37:40:41:43:47:49:53:56:57:61:65:70 SD: 2.3394 cents 36:38:41:42:44:48:50:54:58:59:63:67:72 SD: 1.9188 cents 40:42:46:47:49:53:56:60:64:65:70:75:80 SD: 1.9074 cents 48:50:55:56:59:64:67:72:77:78:84:90:96 SD: 1.7279 cents 54:57:62:63:66:72:76:81:86:88:95:101:108 SD: 1.7110 cents 55:58:63:64:67:73:77:83:88:90:96:103:110 SD: 1.7052 cents 58:61:66:68:71:77:81:87:93:95:102:108:116 SD: 1.5370 cents 60:63:69:70:74:80:84:90:96:98:105:112:120 SD: 1.3284 cents 72:76:82:84:88:96:101:108:115:118:126:134:144 SD: 1.2281 cents 76:80:87:89:93:101:106:114:122:124:133:142:152 SD: 1.1366 cents 80:84:91:93:98:107:112:120:128:131:140:149:160 SD: 1.0805 cents 84:88:96:98:103:112:118:126:134:137:147:157:168 SD: 0.7937 cents 98:103:112:114:120:131:137:147:157:160:172:183:196 SD: 0.7724 cents 112:118:128:131:137:149:157:168:179:183:196:209:224 SD: 0.7668 cents 120:126:137:140:147:160:168:180:192:196:210:224:240 SD: 0.1504 cents 420:441:480:490:515:560:588:630:672:686:735:784:840 SD: 0.1401 cents 480:504:549:560:588:640:672:720:768:784:840:896:960 SD: 0.1127 cents 600:630:686:700:735:800:840:900:960:980:1050:1120:1200 SD: 0.0601 cents