Scala analysis: cv13
Thirteenth 12/5 scale <12 19 28 34| epimorphic
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 28/25 196.198479 middle second 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: 16/15 111.7313 minor diatonic semitone 2: 21/20 84.4672 minor semitone 3: 15/14 119.4428 major diatonic 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: 2 21/20 84.467 cents minor semitone 1: 4 16/15 111.731 cents minor diatonic semitone 1: 4 15/14 119.443 cents major diatonic semitone 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: 1 125/112 190.115 cents classic augmented semitone 2: 2 28/25 196.198 cents middle second 2: 2 9/8 203.910 cents major whole tone 2: 4 8/7 231.174 cents septimal whole tone 3: 4 7/6 266.871 cents septimal minor third 3: 1 75/64 274.582 cents classic augmented second 3: 1 25/21 301.847 cents BP second, quasi-equal minor third 3: 4 6/5 315.641 cents minor third 3: 1 128/105 342.905 cents septimal neutral third 3: 1 60/49 350.617 cents smaller approximation to neutral third 4: 2 56/45 378.602 cents septimal narrow major third 4: 6 5/4 386.314 cents major third 4: 2 32/25 427.373 cents classic diminished fourth 4: 2 9/7 435.084 cents septimal major third, BP third 5: 1 98/75 463.069 cents 5: 2 21/16 470.781 cents narrow fourth 5: 5 4/3 498.045 cents perfect fourth 5: 2 75/56 505.757 cents marvelous fourth 5: 2 48/35 546.815 cents septimal semi-augmented fourth 6: 5 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 1 45/32 590.224 cents diatonic tritone 6: 1 64/45 609.776 cents 2nd tritone 6: 5 10/7 617.488 cents Euler's tritone 7: 2 35/24 653.185 cents septimal semi-diminished fifth 7: 2 112/75 694.243 cents marvelous fifth 7: 5 3/2 701.955 cents perfect fifth 7: 2 32/21 729.219 cents wide fifth 7: 1 75/49 736.931 cents BP fifth 8: 2 14/9 764.916 cents septimal minor sixth 8: 2 25/16 772.627 cents classic augmented fifth 8: 6 8/5 813.686 cents minor sixth 8: 2 45/28 821.398 cents septimale wide minor sixth 9: 1 49/30 849.383 cents larger approximation to neutral sixth 9: 1 105/64 857.095 cents septimal 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: 1 128/75 925.418 cents diminished seventh 9: 4 12/7 933.129 cents septimal major sixth 10: 4 7/4 968.826 cents harmonic seventh 10: 2 16/9 996.090 cents Pythagorean minor seventh 10: 2 25/14 1003.802 cents middle minor seventh 10: 1 224/125 1009.885 cents 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 11: 4 28/15 1080.557 cents grave major seventh 11: 4 15/8 1088.269 cents classic major seventh 11: 2 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: 5.27273 = 58/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 111.7 196.2 315.6 386.3 498.0 582.5 702.0 813.7 933.1 968.8 1080.6 1200.0 111.7 : 84.5 203.9 274.6 386.3 470.8 590.2 702.0 821.4 857.1 968.8 1088.3 1200.0 196.2 : 119.4 190.1 301.8 386.3 505.8 617.5 736.9 772.6 884.4 1003.8 1115.5 1200.0 315.6 : 70.7 182.4 266.9 386.3 498.0 617.5 653.2 764.9 884.4 996.1 1080.6 1200.0 386.3 : 111.7 196.2 315.6 427.4 546.8 582.5 694.2 813.7 925.4 1009.9 1129.3 1200.0 498.0 : 84.5 203.9 315.6 435.1 470.8 582.5 702.0 813.7 898.2 1017.6 1088.3 1200.0 582.5 : 119.4 231.2 350.6 386.3 498.0 617.5 729.2 813.7 933.1 1003.8 1115.5 1200.0 702.0 : 111.7 231.2 266.9 378.6 498.0 609.8 694.2 813.7 884.4 996.1 1080.6 1200.0 813.7 : 119.4 155.1 266.9 386.3 498.0 582.5 702.0 772.6 884.4 968.8 1088.3 1200.0 933.1 : 35.7 147.4 266.9 378.6 463.1 582.5 653.2 764.9 849.4 968.8 1080.6 1200.0 968.8 : 111.7 231.2 342.9 427.4 546.8 617.5 729.2 813.7 933.1 1044.9 1164.3 1200.0 1080.6: 119.4 231.2 315.6 435.1 505.8 617.5 702.0 821.4 933.1 1052.6 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 119.4428 cents 360/343, 83.7460 cents 49/48, 35.6968 cents 2: 147.4281 .. 231.1741 cents 360/343, 83.7460 cents 686/675, 27.9853 cents 3: 266.8709 .. 350.6169 cents 360/343, 83.7460 cents 49/48, 35.6968 cents 4: 378.6022 .. 435.0841 cents 405/392, 56.4819 cents 686/675, 27.9853 cents 5: 463.0694 .. 546.8154 cents 360/343, 83.7460 cents 686/675, 27.9853 cents 6: 582.5122 .. 617.4878 cents 50/49, 34.9756 cents 49/48, 35.6968 cents 7: 653.1846 .. 736.9306 cents 360/343, 83.7460 cents 49/48, 35.6968 cents 8: 764.9159 .. 821.3978 cents 405/392, 56.4819 cents 686/675, 27.9853 cents 9: 849.3831 .. 933.1291 cents 360/343, 83.7460 cents 686/675, 27.9853 cents 10: 968.8259 .. 1052.5719 cents 360/343, 83.7460 cents 49/48, 35.6968 cents 11: 1080.5572 .. 1164.3032 cents 360/343, 83.7460 cents 686/675, 27.9853 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 : 15/14, 119.4428 cents Average / Smallest step : 2.801371 Largest / Average step : 1.194428 Largest / Smallest step : 3.346036 Median interval of one step : 16/15, 111.7313 cents, amount: 4 Least squares average step : 99.65743 cents, oct.: 1195.88918 cents Scale is strictly proper Step pattern alph. order: ABCDABCACEAC Step pattern size order : DCEBDCEDEADE Scale is a Constant Structure, by a margin of 27.98529 cents Scale diversity : 1.519771 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.318411 Rothenberg efficiency : 0.279642 redundancy: 0.720358 Efficiency x scale size : 3.355700 Number of different interval sizes : 58 = 5.27273 / class Number of one step interval sizes : 5 Highest interval variety : 7 Mean interval variety : 5.27273 = 58/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 3136/3125, 6.0832 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 6 Number of recognisable fifths : 7, average 699.7517 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 6 Length of longest subharmonic part : 2 at degree 7 Formal octave complements present : 5 = 41.6667% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 83.7460 cents: 7 -- Rational properties -- Prime limit : 7 Odd number limit : 125 (O: 125 U: 125) Highest odd numerator or denominator: 25 Scale harmonicity : 0.019568 Average absolute harmonicity : 0.181934 Specific harmonicity : 0.135839 Fundamental : 1/2100, -11.0362 octaves, 0.1246 Hz. Guide tone : 1680, 10.7142 octaves, 439530.950 Hz. Exponens Consonantiae : 3.528000E+06, 21.75042 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 108.5, average 9.04167 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.33657, average 0.77805 Sum of Tenney's harmonic distance : 19.30264, average 1.60855 Vogel's harmonic complexity : 22.25000 Wille's k value : 1837 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 223.86875, average 2.87011 Lattice compactness (without 2's) : 125.48153, average 1.60874 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.00000 22 1 3: -1 .. 1 0.00000 6 2 5: -2 .. 1 -0.50000 8 4 7: -1 .. 1 0.25000 5 5 Average exponent except 2's :-3 / 12 =-0.25000 Average absolute exponent except 2's: 19 / 12 = 1.58333 Scale is JI-epimorphic with val: <12 19 28 34| = patent
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 17.1566 c. M: 33.1291 c. Twelve-tone Chromatic (1/11-comma) 18: 2 1 2 1 2 1 2 1 2 1 1 2 P D3 SD: 20.1437 c. M:-35.2883 c. 19: 2 1 2 1 2 1 2 2 2 0 2 2 P D3 SD: 10.7225 c. M: 21.4575 c. 22: 2 2 2 1 2 2 2 2 2 1 2 2 SP B ME SD: 10.7388 c. M:-21.9833 c. Pajara-12 24: 2 2 2 2 2 2 2 2 3 0 3 2 P T3 SD: 13.2347 c. M:-19.4428 c. 27: 2 2 3 2 2 2 3 2 3 1 2 3 P D3 SD: 11.9703 c. M: 22.8424 c. 29: 3 2 3 1 3 2 3 3 3 0 3 3 P SD: 11.4264 c. M:-18.5950 c. 31: 3 2 3 2 3 2 3 3 3 1 3 3 SP D3 SD: 3.5269 c. M: 5.9639 c. Marvel-12 68: 6 5 7 4 6 5 7 6 7 2 6 7 SP SD: 2.9625 c. M: 5.8489 c. 72: 7 5 7 4 7 5 7 7 7 2 7 7 SP SD: 2.5553 c. M:-4.9354 c. Marvel-12 87: 8 6 9 5 8 6 9 8 9 2 8 9 SP SD: 2.6590 c. M:-4.8019 c. 94: 9 6 10 5 9 7 9 9 9 3 9 9 SP SD: 3.0710 c. M:-4.7218 c. 99: 9 7 10 6 9 7 10 9 10 3 9 10 SP SD: 1.4124 c. M: 2.6404 c. 130: 12 9 13 8 12 9 13 12 13 4 12 13 SP SD: 1.1521 c. M: 2.3523 c. 140: 13 10 14 8 13 10 14 13 14 4 13 14 SP SD: 0.7862 c. M:-1.5016 c. 171: 16 12 17 10 16 12 17 16 17 5 16 17 SP SD: 0.2833 c. M:-0.5494 c. 441: 41 31 44 26 41 31 44 41 44 13 41 44 SP SD: 0.1609 c. M: 0.2851 c. 612: 57 43 61 36 57 43 61 57 61 18 57 61 SP SD: 0.1134 c. M:-0.2042 c. 935: 87 66 93 55 87 66 93 87 93 28 87 93 SP SD: 0.0983 c. M:-0.1652 c. 1106: 103 78 110 65 103 78 110 103 110 33 103 110 SP SD: 0.0834 c. M:-0.1849 c. 1236: 115 87 123 73 115 87 123 115 123 37 115 123 SP SD: 0.0759 c. M: 0.1194 c. 1376: 128 97 137 81 128 97 137 128 137 41 128 137 SP SD: 0.0551 c. M: 0.1034 c. 1407: 131 99 140 83 131 99 140 131 140 42 131 140 SP SD: 0.0437 c. M: 0.0801 c. 1547: 144 109 154 91 144 109 154 144 154 46 144 154 SP SD: 0.0368 c. M:-0.0665 c. 1578: 147 111 157 93 147 111 157 147 157 47 147 157 SP SD: 0.0373 c. M:-0.0558 c. 2019: 188 142 201 119 188 142 201 188 201 60 188 201 SP SD: 0.0296 c. M: 0.0618 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 x 7 x 8 x 9 x 10 x 11:12 S SD: 12.6163 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.9513 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 5.3216 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 11.1372 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.0135 cents 11:12 x 13:14:15 x 17:18:19 x 21:22 SD: 11.4224 cents 12:13 x 14:15:16:17:18:19 x 21:22:24 SD: 6.9430 cents 13:14:15 x 16:17:18:20:21:22:23:24:26 S SD: 8.4140 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.6911 cents 15:16:17:18:19:20:21:23:24 x 26:28:30 SD: 4.6956 cents 19:20:21:23:24:25:27:29:30 x 33:35:38 SD: 6.3839 cents 20:21:22:24:25:27:28:30:32:34:35:37:40 SD: 4.2735 cents 24:26:27:29:30:32:34:36:38:41:42:45:48 SD: 3.5036 cents 25:27:28:30:31:33:35:38:40:43:44:47:50 SD: 3.5027 cents 28:30:31:34:35:37:39:42:45:48:49:52:56 SD: 3.0461 cents 32:34:36:38:40:43:45:48:51:55:56:60:64 SD: 2.3580 cents 40:43:45:48:50:53:56:60:64:69:70:75:80 SD: 1.9268 cents 45:48:50:54:56:60:63:68:72:77:79:84:90 SD: 1.7745 cents 48:51:54:58:60:64:67:72:77:82:84:90:96 SD: 1.6490 cents 59:63:66:71:74:79:83:89:94:101:103:110:118 SD: 1.5956 cents 60:64:67:72:75:80:84:90:96:103:105:112:120 SD: 0.4743 cents 160:171:179:192:200:213:224:240:256:274:280:299:320 SD: 0.4523 cents 165:176:185:198:206:220:231:248:264:283:289:308:330 SD: 0.4008 cents 180:192:202:216:225:240:252:270:288:309:315:336:360 SD: 0.3491 cents 200:213:224:240:250:267:280:300:320:343:350:373:400 SD: 0.3219 cents 225:240:252:270:281:300:315:338:360:386:394:420:450 SD: 0.2861 cents 240:256:269:288:300:320:336:360:384:411:420:448:480 SD: 0.1847 cents 300:320:336:360:375:400:420:450:480:514:525:560:600 SD: 0.0802 cents 360:384:403:432:450:480:504:540:576:617:630:672:720 SD: 0.0790 cents 540:576:605:648:675:720:756:810:864:926:945:1008:1080 SD: 0.0652 cents 600:640:672:720:750:800:840:900:960:1029:1050:1120:1200 SD: 0.0601 cents