Scala analysis: qujus13
scale 13 420 2,2,1,1 4.109804 0.194943 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: 6/5 315.641287 minor third 4: 5/4 386.313714 major 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: 12/7 933.129094 septimal major 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: 21/20 84.4672 minor semitone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 16/15 111.7313 minor diatonic semitone 6: 21/20 84.4672 minor semitone 7: 15/14 119.4428 major diatonic semitone 8: 16/15 111.7313 minor diatonic semitone 9: 15/14 119.4428 major diatonic semitone 10: 49/48 35.6968 slendro diesis, septimal 1/6-tone 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: 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: 3 21/20 84.467 cents minor semitone 1: 3 16/15 111.731 cents minor diatonic semitone 1: 3 15/14 119.443 cents major diatonic semitone 1: 1 160/147 146.707 cents 2: 1 49/45 147.428 cents BP minor semitone 2: 2 35/32 155.140 cents septimal neutral second 2: 1 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 80/63 413.578 cents wide major third 4: 1 32/25 427.373 cents classic diminished fourth 4: 2 9/7 435.084 cents septimal major third, BP third 4: 1 64/49 462.348 cents 2 septatones or septatonic major third 5: 3 21/16 470.781 cents narrow fourth 5: 6 4/3 498.045 cents perfect fourth 5: 1 75/56 505.757 cents marvelous fourth 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: 1 112/75 694.243 cents marvelous fifth 7: 6 3/2 701.955 cents perfect fifth 7: 3 32/21 729.219 cents wide fifth 8: 1 49/32 737.652 cents 8: 2 14/9 764.916 cents septimal minor sixth 8: 1 25/16 772.627 cents classic augmented fifth 8: 1 63/40 786.422 cents narrow 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: 1 9/5 1017.596 cents just minor seventh, BP seventh 10: 2 64/35 1044.860 cents septimal neutral seventh 10: 1 90/49 1052.572 cents 11: 1 147/80 1053.293 cents 11: 3 28/15 1080.557 cents grave major seventh 11: 3 15/8 1088.269 cents classic major seventh 11: 3 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 : 84.5 231.2 315.6 386.3 498.0 582.5 702.0 813.7 933.1 968.8 1080.6 1200.0 84.5 : 146.7 231.2 301.8 413.6 498.0 617.5 729.2 848.7 884.4 996.1 1115.5 1200.0 231.2 : 84.5 155.1 266.9 351.3 470.8 582.5 702.0 737.7 849.4 968.8 1053.3 1200.0 315.6 : 70.7 182.4 266.9 386.3 498.0 617.5 653.2 764.9 884.4 968.8 1115.5 1200.0 386.3 : 111.7 196.2 315.6 427.4 546.8 582.5 694.2 813.7 898.2 1044.9 1129.3 1200.0 498.0 : 84.5 203.9 315.6 435.1 470.8 582.5 702.0 786.4 933.1 1017.6 1088.3 1200.0 582.5 : 119.4 231.2 350.6 386.3 498.0 617.5 702.0 848.7 933.1 1003.8 1115.5 1200.0 702.0 : 111.7 231.2 266.9 378.6 498.0 582.5 729.2 813.7 884.4 996.1 1080.6 1200.0 813.7 : 119.4 155.1 266.9 386.3 470.8 617.5 702.0 772.6 884.4 968.8 1088.3 1200.0 933.1 : 35.7 147.4 266.9 351.3 498.0 582.5 653.2 764.9 849.4 968.8 1080.6 1200.0 968.8 : 111.7 231.2 315.6 462.3 546.8 617.5 729.2 813.7 933.1 1044.9 1164.3 1200.0 1080.6: 119.4 203.9 350.6 435.1 505.8 617.5 702.0 821.4 933.1 1052.6 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: 147.4281 .. 231.1741 cents 360/343, 83.7460 cents 2401/2400, 0.7212 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 .. 1052.5719 cents 360/343, 83.7460 cents 49/48, 35.6968 cents 11: 1053.2931 .. 1164.3032 cents 2560/2401, 111.0101 cents 2401/2400, 0.7212 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: 3 Least squares average step : 99.72310 cents, oct.: 1196.67725 cents Scale is strictly proper Step pattern alph. order: ABACDAEDEFDE Step pattern size order : CFCBDCEDEADE Scale is a Constant Structure, by a margin of 0.72120 cents Scale diversity : 1.509250 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.194943 Rothenberg efficiency : 0.289671 redundancy: 0.710329 Efficiency x scale size : 3.476046 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 Number of recognisable fifths : 7, average 700.8534 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 6 Length of longest subharmonic part : 2 at degree 7 Formal octave complements present : 7 = 58.3333% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 7 Odd number limit : 147 (O: 147 U: 147) Highest odd numerator or denominator: 21 Scale harmonicity : 0.022881 Average absolute harmonicity : 0.182410 Specific harmonicity : 0.134764 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 : 94.5, average 7.87500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.92986, average 0.74415 Sum of Tenney's harmonic distance : 18.44877, average 1.53740 Vogel's harmonic complexity : 17.58333 Wille's k value : 367 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 222.34506, average 2.85058 Lattice compactness (without 2's) : 121.12503, average 1.55289 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.58333 21 1 3: -1 .. 1 0.16667 6 2 5: -1 .. 1 -0.33333 6 3 7: -1 .. 1 0.16667 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 27 37| Scale is weakly epimorphic with val: <12 20 29 35| Scale is weakly epimorphic with val: <12 20 31 33|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 19.5645 c. M: 33.1291 c. Twelve-tone Chromatic (1/11-comma) 15: 1 2 1 1 1 1 2 1 2 0 2 1 N D3 SD: 18.2693 c. M:-39.4428 c. 19: 1 3 1 1 2 1 2 2 2 0 2 2 N SD: 13.0264 c. M:-21.4575 c. 22: 2 2 2 1 2 2 2 2 2 1 2 2 SP B ME SD: 11.7925 c. M:-24.6237 c. Pajara-12 26: 2 3 2 1 3 2 2 3 2 1 2 3 P SD: 11.7454 c. M: 19.0187 c. 27: 2 3 2 2 2 2 3 2 3 1 2 3 P D3 SD: 8.9352 c. M: 13.8905 c. 31: 2 4 2 2 3 2 3 3 3 1 3 3 P SD: 3.8051 c. M: 7.0478 c. 41: 3 5 3 2 4 3 4 4 4 1 4 4 P SD: 3.6819 c. M:-6.3099 c. 53: 4 6 4 3 5 4 5 5 5 2 5 5 SP SD: 3.9631 c. M:-6.2353 c. 68: 5 8 5 4 6 5 7 6 7 2 6 7 P SD: 2.6470 c. M: 4.0866 c. 72: 5 9 5 4 7 5 7 7 7 2 7 7 P SD: 1.9471 c. M: 2.9804 c. 99: 7 12 7 6 9 7 10 9 10 3 9 10 P SD: 1.0315 c. M: 1.7693 c. 130: 9 16 9 8 12 9 13 12 13 4 12 13 P SD: 0.9817 c. M: 1.7951 c. 140: 10 17 10 8 13 10 14 13 14 4 13 14 P SD: 0.8192 c. M:-1.5016 c. 171: 12 21 12 10 16 12 17 16 17 5 16 17 P SD: 0.2590 c. M:-0.4049 c. 270: 19 33 19 16 25 19 27 25 27 8 25 27 P SD: 0.2652 c. M: 0.5572 c. 441: 31 54 31 26 41 31 44 41 44 13 41 44 P SD: 0.1389 c. M: 0.2851 c. 612: 43 75 43 36 57 43 61 57 61 18 57 61 P SD: 0.1297 c. M:-0.2042 c. 935: 66 114 66 55 87 66 93 87 93 28 87 93 SP SD: 0.1173 c. M:-0.2387 c. 966: 68 118 68 57 90 68 96 90 96 29 90 96 SP SD: 0.1108 c. M: 0.2098 c. 1065: 75 130 75 63 99 75 106 99 106 32 99 106 SP SD: 0.1223 c. M:-0.1882 c. 1106: 78 135 78 65 103 78 110 103 110 33 103 110 SP SD: 0.0817 c. M:-0.1621 c. 1236: 87 151 87 73 115 87 123 115 123 37 115 123 SP SD: 0.0748 c. M: 0.1194 c. 1277: 90 156 90 75 119 90 127 119 127 38 119 127 SP SD: 0.0709 c. M:-0.1060 c. 1376: 97 168 97 81 128 97 137 128 137 41 128 137 SP SD: 0.0618 c. M:-0.1258 c. 1407: 99 172 99 83 131 99 140 131 140 42 131 140 SP SD: 0.0453 c. M: 0.0801 c. 1547: 109 189 109 91 144 109 154 144 154 46 144 154 SP SD: 0.0406 c. M:-0.0835 c. 1578: 111 193 111 93 147 111 157 147 157 47 147 157 SP SD: 0.0374 c. M: 0.0565 c. 1718: 121 210 121 101 160 121 171 160 171 51 160 171 SP SD: 0.0394 c. M:-0.0747 c. 1848: 130 226 130 109 172 130 184 172 184 55 172 184 SP SD: 0.0349 c. M: 0.0569 c. 2019: 142 247 142 119 188 142 201 188 201 60 188 201 SP SD: 0.0320 c. M: 0.0690 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: 16.2568 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: 9.7541 cents 6 x 7 x x 8 x 9 x 10 x 11:12 S SD: 11.3357 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.7451 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 6.2454 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 12.2904 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 9.9131 cents 11:12 x 13:14:15 x 17:18:19 x 21:22 SD: 12.8778 cents 12:13:14 x 15:16:17:18:19 x 21:22:24 SD: 7.6962 cents 13:14:15 x 16:17:18:20:21:22:23:24:26 S SD: 8.0447 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.6642 cents 15:16:17:18:19:20:21:23:24 x 26:28:30 SD: 5.1437 cents 19:20:22:23:24:25:27:29:30 x 33:35:38 SD: 6.0375 cents 20:21:23:24:25:27:28:30:32:34:35:37:40 SD: 2.6743 cents 35:37:40:42:44:47:49:53:56:60:61:65:70 SD: 2.3344 cents 36:38:41:43:45:48:50:54:58:62:63:67:72 SD: 2.0559 cents 40:42:46:48:50:53:56:60:64:69:70:75:80 SD: 1.6873 cents 55:58:63:66:69:73:77:83:88:94:96:103:110 SD: 1.5852 cents 56:59:64:67:70:75:78:84:90:96:98:105:112 SD: 1.4861 cents 60:63:69:72:75:80:84:90:96:103:105:112:120 SD: 0.9209 cents 80:84:91:96:100:107:112:120:128:137:140:149:160 SD: 0.8881 cents 84:88:96:101:105:112:118:126:134:144:147:157:168 SD: 0.8048 cents 100:105:114:120:125:133:140:150:160:171:175:187:200 SD: 0.6764 cents 105:110:120:126:131:140:147:158:168:180:184:196:210 SD: 0.6561 cents 120:126:137:144:150:160:168:180:192:206:210:224:240 SD: 0.2504 cents 240:252:274:288:300:320:336:360:384:411:420:448:480 SD: 0.2126 cents 260:273:297:312:325:347:364:390:416:446:455:485:520 SD: 0.2059 cents 280:294:320:336:350:373:392:420:448:480:490:523:560 SD: 0.1583 cents 300:315:343:360:375:400:420:450:480:514:525:560:600 SD: 0.1002 cents 420:441:480:504:525:560:588:630:672:720:735:784:840 SD: 0.0000 cents