Scala analysis: qujus10
scale 10 840 2,2,1,1 4.109804 0.207795 strictly proper
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: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 10/7 617.487807 Euler's tritone 7: 3/2 701.955001 perfect fifth 8: 8/5 813.686286 minor sixth 9: 5/3 884.358713 major sixth, BP sixth 10: 7/4 968.825906 harmonic seventh 11: 40/21 1115.532807 acute major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 21/20 84.4672 minor 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: 15/14 119.4428 major diatonic semitone 5: 16/15 111.7313 minor diatonic semitone 6: 15/14 119.4428 major diatonic semitone 7: 21/20 84.4672 minor semitone 8: 16/15 111.7313 minor diatonic semitone 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 21/20 84.4672 minor semitone 11: 160/147 146.7069 12: 21/20 84.4672 minor 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: 2 35/32 155.140 cents septimal neutral second 2: 1 441/400 168.934 cents two (minor semitone) 2: 2 10/9 182.404 cents minor whole tone 2: 1 28/25 196.198 cents middle second 2: 1 9/8 203.910 cents major whole tone 2: 5 8/7 231.174 cents septimal whole tone 3: 4 7/6 266.871 cents septimal minor third 3: 2 25/21 301.847 cents BP second, quasi-equal minor third 3: 5 6/5 315.641 cents minor third 3: 1 60/49 350.617 cents smaller approximation to neutral third 4: 2 49/40 351.338 cents larger approximation to neutral third 4: 4 5/4 386.314 cents major third 4: 1 63/50 400.108 cents quasi-equal 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 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: 1 49/32 737.652 cents 8: 1 14/9 764.916 cents septimal minor sixth 8: 1 25/16 772.627 cents classic augmented fifth 8: 2 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: 2 80/49 848.662 cents smaller approximation to neutral sixth 9: 1 49/30 849.383 cents larger approximation to neutral sixth 9: 5 5/3 884.359 cents major sixth, BP sixth 9: 2 42/25 898.153 cents quasi-equal major sixth 9: 4 12/7 933.129 cents septimal major sixth 10: 5 7/4 968.826 cents harmonic seventh 10: 1 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: 1 800/441 1031.066 cents 10: 2 64/35 1044.860 cents septimal neutral seventh 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 : 84.5 231.2 266.9 386.3 498.0 617.5 702.0 813.7 884.4 968.8 1115.5 1200.0 84.5 : 146.7 182.4 301.8 413.6 533.0 617.5 729.2 799.9 884.4 1031.1 1115.5 1200.0 231.2 : 35.7 155.1 266.9 386.3 470.8 582.5 653.2 737.7 884.4 968.8 1053.3 1200.0 266.9 : 119.4 231.2 350.6 435.1 546.8 617.5 702.0 848.7 933.1 1017.6 1164.3 1200.0 386.3 : 111.7 231.2 315.6 427.4 498.0 582.5 729.2 813.7 898.2 1044.9 1080.6 1200.0 498.0 : 119.4 203.9 315.6 386.3 470.8 617.5 702.0 786.4 933.1 968.8 1088.3 1200.0 617.5 : 84.5 196.2 266.9 351.3 498.0 582.5 667.0 813.7 849.4 968.8 1080.6 1200.0 702.0 : 111.7 182.4 266.9 413.6 498.0 582.5 729.2 764.9 884.4 996.1 1115.5 1200.0 813.7 : 70.7 155.1 301.8 386.3 470.8 617.5 653.2 772.6 884.4 1003.8 1088.3 1200.0 884.4 : 84.5 231.2 315.6 400.1 546.8 582.5 702.0 813.7 933.1 1017.6 1129.3 1200.0 968.8 : 146.7 231.2 315.6 462.3 498.0 617.5 729.2 848.7 933.1 1044.9 1115.5 1200.0 1115.5: 84.5 168.9 315.6 351.3 470.8 582.5 702.0 786.4 898.2 968.8 1053.3 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: 155.1396 .. 231.1741 cents 256/245, 76.0345 cents 1029/1024, 8.4327 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 .. 1044.8604 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 11: 1053.2931 .. 1164.3032 cents 2560/2401, 111.0101 cents 1029/1024, 8.4327 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 : 99.73747 cents, oct.: 1196.84969 cents Scale is strictly proper Step pattern alph. order: ABCDEDAEFABA Step pattern size order : CFAEDECDBCFC Scale is a Constant Structure, by a margin of 0.72120 cents Scale diversity : 1.524843 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.207795 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 Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 4 Formal octave complements present : 9 = 75.0000% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 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 : 441 (O: 441 U: 441) Highest odd numerator or denominator: 21 Scale harmonicity : 0.022881 Average absolute harmonicity : 0.183265 Specific harmonicity : 0.127932 Fundamental : 1/420, -8.7142 octaves, 0.6229 Hz. Guide tone : 840, 9.7142 octaves, 219765.475 Hz. Exponens Consonantiae : 3.528000E+05, 18.42849 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 101.5, average 8.45833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.07598, average 0.75633 Sum of Tenney's harmonic distance : 18.44877, average 1.53740 Vogel's harmonic complexity : 17.75000 Wille's k value : 367 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 230.48394, average 2.95492 Lattice compactness (without 2's) : 124.58913, average 1.59730 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.41667 21 1 3: -1 .. 1 -0.16667 6 2 5: -1 .. 1 0.16667 6 3 7: -1 .. 1 0.00000 6 6 Average exponent except 2's : 0 / 12 = 0.00000 Average absolute exponent except 2's: 18 / 12 = 1.50000 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: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 19.2710 c. M:-33.1291 c. Twelve-tone Chromatic (1/11-comma) 15: 1 2 0 2 1 2 1 1 1 1 2 1 N D3 SD: 14.3452 c. M: 26.8709 c. 19: 1 3 0 2 2 2 1 2 1 1 3 1 N SD: 14.2685 c. M:-21.4575 c. 22: 1 3 1 2 2 2 2 2 1 2 2 2 P D3 SD: 14.3088 c. M: 29.9217 c. 25: 2 3 1 2 2 3 2 2 1 2 3 2 P SD: 12.8682 c. M:-21.1291 c. 26: 2 3 1 2 3 2 2 3 1 2 3 2 P B D3 SD: 10.6271 c. M: 17.4878 c. 27: 2 3 1 3 2 3 2 2 2 2 3 2 P D3 SD: 8.0863 c. M: 13.6863 c. 31: 2 4 1 3 3 3 2 3 2 2 4 2 P SD: 4.2075 c. M:-7.0478 c. 41: 3 5 1 4 4 4 3 4 2 3 5 3 P SD: 3.7439 c. M: 6.3099 c. 53: 4 6 2 5 5 5 4 5 3 4 6 4 SP SD: 3.9454 c. M: 6.1671 c. 58: 4 7 2 6 5 6 4 5 4 4 7 4 P SD: 3.7742 c. M: 6.7897 c. 68: 5 8 2 7 6 7 5 6 4 5 8 5 P SD: 2.6073 c. M:-3.9274 c. 72: 5 9 2 7 7 7 5 7 4 5 9 5 P SD: 1.8045 c. M: 2.9804 c. 99: 7 12 3 10 9 10 7 9 6 7 12 7 P SD: 0.9029 c. M:-1.5651 c. 140: 10 17 4 14 13 14 10 13 8 10 17 10 P SD: 0.8802 c. M: 1.5016 c. 171: 12 21 5 17 16 17 12 16 10 12 21 12 P SD: 0.2662 c. M:-0.4049 c. 270: 19 33 8 27 25 27 19 25 16 19 33 19 P SD: 0.2110 c. M:-0.3530 c. 441: 31 54 13 44 41 44 31 41 26 31 54 31 P SD: 0.1166 c. M: 0.2042 c. 966: 68 118 29 96 90 96 68 90 57 68 118 68 SP SD: 0.0966 c. M:-0.2098 c. 1065: 75 130 32 106 99 106 75 99 63 75 130 75 SP SD: 0.1228 c. M:-0.1882 c. 1106: 78 135 33 110 103 110 78 103 65 78 135 78 SP SD: 0.0901 c. M:-0.1621 c. 1137: 80 139 34 113 106 113 80 106 67 80 139 80 SP SD: 0.0729 c. M:-0.1476 c. 1236: 87 151 37 123 115 123 87 115 73 87 151 87 SP SD: 0.0744 c. M:-0.1194 c. 1277: 90 156 38 127 119 127 90 119 75 90 156 90 SP SD: 0.0716 c. M:-0.1060 c. 1376: 97 168 41 137 128 137 97 128 81 97 168 97 SP SD: 0.0710 c. M:-0.1258 c. 1407: 99 172 42 140 131 140 99 131 83 99 172 99 SP SD: 0.0447 c. M:-0.0801 c. 1578: 111 193 47 157 147 157 111 147 93 111 193 111 SP SD: 0.0381 c. M: 0.0565 c. 1848: 130 226 55 184 172 184 130 172 109 130 226 130 SP SD: 0.0363 c. M:-0.0569 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: 0.0000 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 8 x 9 x 10 S SD: 15.4666 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 11.0283 cents 7 x 8 x 9 x 10 x 11 x 12:13:14 S SD: 11.5591 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 8.8786 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 9.6800 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 11.6078 cents 11:12 x 13:14:15:16:17 x 18:19:21:22 SD: 11.2005 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 5.4411 cents 13:14:15 x 16:17:19:20:21:22:23:25:26 SD: 8.6879 cents 14:15:16 x 18:19:20:21:22:23:25:27:28 SD: 8.0393 cents 15:16:17:18:19:20:21:23:24:25:26:29:30 SD: 7.2013 cents 16:17:18:19:20:21:23:24:26:27:28:30:32 SD: 5.8262 cents 18:19 x 21:23:24:26:27:29:30:32:34:36 SD: 4.9743 cents 19:20 x 22:24:25:27:29:30:32:33:36:38 SD: 5.0963 cents 20:21:23 x 25:27:29:30:32:33:35:38:40 SD: 3.5961 cents 24:25:27:28:30:32:34:36:38:40:42:46:48 SD: 3.3213 cents 25:26 x 29:31:33:36:38:40:42:44:48:50 SD: 4.1291 cents 26:27:30 x 33:35:37:39:42:43:46:50:52 SD: 4.7618 cents 27:28:31:32:34:36:39:41:43:45:47:51:54 SD: 4.2565 cents 28:29:32:33:35:37:40:42:45:47:49:53:56 SD: 3.1640 cents 32:34 x 37:40:43:46:48:51:53:56:61:64 SD: 3.0482 cents 35:37:40:41:44:47:50:53:56:58:61:67:70 SD: 2.5400 cents 36:38:41:42:45:48:51:54:58:60:63:69:72 SD: 2.0233 cents 40:42:46:47:50:53:57:60:64:67:70:76:80 SD: 1.8599 cents 42:44:48:49:53:56:60:63:67:70:74:80:84 SD: 1.7660 cents 48:50:55:56:60:64:69:72:77:80:84:91:96 SD: 1.6943 cents 56:59:64:65:70:75:80:84:90:93:98:107:112 SD: 1.4421 cents 60:63:69:70:75:80:86:90:96:100:105:114:120 SD: 1.0812 cents 72:76:82:84:90:96:103:108:115:120:126:137:144 SD: 0.9782 cents 84:88:96:98:105:112:120:126:134:140:147:160:168 SD: 0.5405 cents 120:126:137:140:150:160:171:180:192:200:210:229:240 SD: 0.4755 cents 156:164:178:182:195:208:223:234:250:260:273:297:312 SD: 0.3889 cents 168:176:192:196:210:224:240:252:269:280:294:320:336 SD: 0.3446 cents 180:189:206:210:225:240:257:270:288:300:315:343:360 SD: 0.2239 cents 240:252:274:280:300:320:343:360:384:400:420:457:480 SD: 0.1681 cents 336:353:384:392:420:448:480:504:538:560:588:640:672 SD: 0.1349 cents 420:441:480:490:525:560:600:630:672:700:735:800:840 SD: 0.0000 cents