Scala analysis: classr
Marvel projection to the 5-limit of class
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 135/128 92.178716 major chroma, major limma 2: 1125/1024 162.851143 double augmented prime 3: 6/5 315.641287 minor third 4: 5/4 386.313714 major third 5: 675/512 478.492430 wide augmented third 6: 45/32 590.223716 diatonic tritone 7: 3/2 701.955001 perfect fifth 8: 25/16 772.627428 classic augmented fifth 9: 27/16 905.865003 Pythagorean major sixth 10: 225/128 976.537429 augmented sixth 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: 135/128 92.1787 major chroma, major limma 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 2048/1875 152.7901 double diminished third 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 135/128 92.1787 major chroma, major limma 6: 16/15 111.7313 minor diatonic semitone 7: 16/15 111.7313 minor diatonic semitone 8: 25/24 70.6724 classic chromatic semitone, minor chroma 9: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 10: 25/24 70.6724 classic chromatic semitone, minor chroma 11: 16/15 111.7313 minor diatonic semitone 12: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 135/128 92.179 cents major chroma, major limma 1: 4 16/15 111.731 cents minor diatonic semitone 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 1 2048/1875 152.790 cents double diminished third 2: 2 1125/1024 162.851 cents double augmented prime 2: 2 10/9 182.404 cents minor whole tone 2: 4 9/8 203.910 cents major whole tone 2: 4 256/225 223.463 cents Neapolitan diminished third 3: 3 75/64 274.582 cents classic augmented second 3: 3 32/27 294.135 cents Pythagorean minor third 3: 6 6/5 315.641 cents minor third 4: 8 5/4 386.314 cents major third 4: 4 32/25 427.373 cents classic diminished fourth 5: 2 125/96 456.986 cents classic augmented third 5: 1 675/512 478.492 cents wide augmented third 5: 5 4/3 498.045 cents perfect fourth 5: 2 27/20 519.551 cents acute fourth 5: 2 512/375 539.104 cents double diminished fifth 6: 6 45/32 590.224 cents diatonic tritone 6: 6 64/45 609.776 cents 2nd tritone 7: 2 375/256 660.896 cents double augmented fourth 7: 2 40/27 680.449 cents grave fifth 7: 5 3/2 701.955 cents perfect fifth 7: 1 1024/675 721.508 cents narrow diminished sixth 7: 2 192/125 743.014 cents classic diminished sixth 8: 4 25/16 772.627 cents classic augmented fifth 8: 8 8/5 813.686 cents minor sixth 9: 6 5/3 884.359 cents major sixth, BP sixth 9: 3 27/16 905.865 cents Pythagorean major sixth 9: 3 128/75 925.418 cents diminished seventh 10: 4 225/128 976.537 cents augmented sixth 10: 4 16/9 996.090 cents Pythagorean minor seventh 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 10: 2 2048/1125 1037.149 cents double diminished octave 11: 1 1875/1024 1047.210 cents double augmented sixth 11: 1 50/27 1066.762 cents grave major seventh 11: 4 15/8 1088.269 cents classic major seventh 11: 2 256/135 1107.821 cents octave - major chroma 11: 4 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 3.63636 = 40/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 92.2 162.9 315.6 386.3 478.5 590.2 702.0 772.6 905.9 976.5 1088.3 1200.0 92.2 : 70.7 223.5 294.1 386.3 498.0 609.8 680.4 813.7 884.4 996.1 1107.8 1200.0 162.9 : 152.8 223.5 315.6 427.4 539.1 609.8 743.0 813.7 925.4 1037.1 1129.3 1200.0 315.6 : 70.7 162.9 274.6 386.3 457.0 590.2 660.9 772.6 884.4 976.5 1047.2 1200.0 386.3 : 92.2 203.9 315.6 386.3 519.6 590.2 702.0 813.7 905.9 976.5 1129.3 1200.0 478.5 : 111.7 223.5 294.1 427.4 498.0 609.8 721.5 813.7 884.4 1037.1 1107.8 1200.0 590.2 : 111.7 182.4 315.6 386.3 498.0 609.8 702.0 772.6 925.4 996.1 1088.3 1200.0 702.0 : 70.7 203.9 274.6 386.3 498.0 590.2 660.9 813.7 884.4 976.5 1088.3 1200.0 772.6 : 133.2 203.9 315.6 427.4 519.6 590.2 743.0 813.7 905.9 1017.6 1129.3 1200.0 905.9 : 70.7 182.4 294.1 386.3 457.0 609.8 680.4 772.6 884.4 996.1 1066.8 1200.0 976.5 : 111.7 223.5 315.6 386.3 539.1 609.8 702.0 813.7 925.4 996.1 1129.3 1200.0 1088.3: 111.7 203.9 274.6 427.4 498.0 590.2 702.0 813.7 884.4 1017.6 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 152.7901 cents 16384/15625, 82.1177 cents 25/24, 70.6724 cents 2: 162.8511 .. 223.4626 cents 262144/253125, 60.6114 cents 2109375/2097152, 10.0610 cents 3: 274.5824 .. 315.6413 cents 128/125, 41.0589 cents 16875/16384, 51.1199 cents 4: 386.3137 .. 427.3726 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 5: 456.9861 .. 539.1039 cents 16384/15625, 82.1177 cents 3125/3072, 29.6136 cents 6: 590.2237 .. 609.7763 cents 2048/2025, 19.5526 cents 16875/16384, 51.1199 cents 7: 660.8961 .. 743.0139 cents 16384/15625, 82.1177 cents 16875/16384, 51.1199 cents 8: 772.6274 .. 813.6863 cents 128/125, 41.0589 cents 3125/3072, 29.6136 cents 9: 884.3587 .. 925.4176 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 10: 976.5374 .. 1037.1489 cents 262144/253125, 60.6114 cents 16875/16384, 51.1199 cents 11: 1047.2099 .. 1129.3276 cents 16384/15625, 82.1177 cents 2109375/2097152, 10.0610 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 2048/1875, 152.7901 cents Average / Smallest step : 1.414979 Largest / Average step : 1.527901 Largest / Smallest step : 2.161948 Median interval of one step : 101.95500 cents, amount: 0 Least squares average step : 98.81182 cents, oct.: 1185.74185 cents Scale is strictly proper Step pattern alph. order: ABCBADDBEBDD Step pattern size order : BAEABCCADACC Scale is a Constant Structure, by a margin of 10.06100 cents Scale diversity : 1.376837 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.472099 Rothenberg efficiency : 0.362608 redundancy: 0.637392 Efficiency x scale size : 4.351299 Number of different interval sizes : 40 = 3.63636 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 3.63636 = 40/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 2109375/2097152, 10.0610 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 8 Most common triad is 0.0 386.314 813.686 cents, amount: 4 Number of recognisable fifths : 5, average 701.9550 cents Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 8-9 -- Rational properties -- Prime limit : 5 Odd number limit : 1875 (O: 1875 U: 1875) Highest odd numerator or denominator: 1125 Scale harmonicity : 0.022422 Average absolute harmonicity : 0.160469 Specific harmonicity : 0.133491 Fundamental : 1/5120, -12.3219 octaves, 0.0511 Hz. Guide tone : 6750, 12.7207 octaves, 1765972.566 Hz. Exponens Consonantiae : 3.456000E+07, 25.04260 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 2082.0, average 173.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 17.89664, average 1.49139 Sum of Tenney's harmonic distance : 34.62938, average 2.88578 Vogel's harmonic complexity : 20.33333 Wille's k value : 2812 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 385.30851, average 4.93985 Lattice compactness (without 2's) : 166.10670, average 2.12957 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -10 .. 1 -4.16667 54 1 3: 0 .. 3 1.50000 18 2 5: -1 .. 3 1.00000 14 9 Average exponent except 2's : 30 / 12 = 2.50000 Average absolute exponent except 2's: 32 / 12 = 2.66667 Scale is weakly epimorphic with val: <12 17 28| Scale is weakly epimorphic with val: <12 19 25| Scale is JI-epimorphic with val: <12 19 28| = patent Scale is weakly epimorphic with val: <12 21 28|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.0437 c. M:-37.1489 c. Twelve-tone Chromatic (1/11-comma) 15: 1 1 2 1 1 1 2 1 1 1 2 1 P B ME SD: 18.9357 c. M:-31.7313 c. Augene-12 16: 1 1 2 1 1 2 1 1 2 1 1 2 P B ME S SD: 19.3221 c. M: 38.2687 c. 19: 1 1 3 1 1 2 2 1 2 1 2 2 N D3 SD: 22.0460 c. M: 36.5354 c. 20: 2 1 2 1 2 2 2 1 2 1 2 2 P B D3 SD: 15.4360 c. M:-27.8213 c. 22: 2 1 3 1 2 2 2 1 3 1 2 2 P B D3 SD: 10.4754 c. M:-21.4077 c. 25: 2 1 4 1 2 2 3 1 3 1 3 2 N SD: 12.5831 c. M:-20.3587 c. 27: 2 2 3 2 2 2 3 1 3 2 2 3 P D3 SD: 12.3697 c. M: 21.6020 c. 28: 2 2 3 2 2 3 2 2 3 2 2 3 SP B ME S SD: 9.8879 c. M: 16.8401 c. Demolished-12 31: 2 2 4 2 2 3 3 2 3 2 3 3 P D3 SD: 9.0040 c. M: 15.5424 c. 34: 3 2 4 2 3 3 3 2 4 2 3 3 SP B D3 SD: 9.4020 c. M:-15.6252 c. 36: 3 2 4 3 2 4 3 2 4 2 4 3 SP T3 SD: 9.3627 c. M: 15.6413 c. 37: 3 2 5 2 3 3 4 2 4 2 4 3 P SD: 7.1208 c. M:-14.4340 c. 42: 3 3 5 3 3 4 4 2 5 2 4 4 SP SD: 7.6880 c. M:-13.6863 c. 43: 3 3 5 3 3 4 4 3 4 3 4 4 SP D3 SD: 6.3319 c. M: 12.8417 c. 44: 3 3 6 2 4 4 4 2 5 3 4 4 P SD: 7.7148 c. M:-12.4167 c. 45: 3 3 6 2 4 4 4 3 5 3 4 4 P SD: 6.8471 c. M: 12.9804 c. 49: 4 3 6 3 4 4 5 3 5 3 5 4 SP SD: 7.4605 c. M:-13.7721 c. 50: 4 3 6 3 4 5 4 3 6 3 4 5 SP B SD: 5.5987 c. M:-9.7763 c. 53: 4 3 7 3 4 5 5 3 6 3 5 5 P SD: 2.1559 c. M: 4.3606 c. 65: 5 4 8 4 5 6 6 4 7 4 6 6 SP SD: 1.6478 c. M:-3.3027 c. 118: 9 7 15 7 9 11 11 7 13 7 11 11 SP SD: 0.3951 c. M: 0.7803 c. 323: 25 19 41 19 25 30 30 19 36 19 30 30 SP SD: 0.4626 c. M:-0.7645 c. 376: 29 22 48 22 29 35 35 22 42 22 35 35 SP SD: 0.2495 c. M:-0.5180 c. 441: 34 26 56 26 34 41 41 26 49 26 41 41 SP SD: 0.2534 c. M:-0.4191 c. 494: 38 29 63 29 38 46 46 29 55 29 46 46 SP SD: 0.1056 c. M:-0.2079 c. 612: 47 36 78 36 47 57 57 36 68 36 57 57 SP SD: 0.0515 c. M: 0.1060 c. 1171: 90 69 149 69 90 109 109 69 130 69 109 109 SP SD: 0.0463 c. M:-0.0865 c. 1289: 99 76 164 76 99 120 120 76 143 76 120 120 SP SD: 0.0367 c. M:-0.0658 c. 1783: 137 105 227 105 137 166 166 105 198 105 166 166 SP SD: 0.0164 c. M:-0.0269 c. 1901: 146 112 242 112 146 177 177 112 211 112 177 177 SP SD: 0.0129 c. M: 0.0260 c. 2395: 184 141 305 141 184 223 223 141 266 141 223 223 SP SD: 0.0115 c. M:-0.0223 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: 9.6886 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 1.9279 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 11.7152 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 11.4710 cents 7 x 8 x x 9:10 x 11:12 x 13:14 S SD: 13.1014 cents 8 x 9 x 10 x 11:12 x x 14:15:16 S SD: 8.1553 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 7.8518 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.8660 cents 11 x 12:13:14 x 15 x 17 x 19:21:22 SD: 10.3933 cents 12 x 13:14:15:16:17:18:19:20:21:23:24 SD: 7.0472 cents 13 x 14 x 16:17:18 x 20:22:23:24:26 S SD: 7.3899 cents 14:15 x 17 x 18:20:21:22:24:25:26:28 SD: 7.5161 cents 15:16 x 18:19:20:21 x 23:25:26:28:30 SD: 5.9376 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 5.0994 cents 19:20:21:23:24:25:27:29:30:32:33:36:38 SD: 4.5827 cents 20:21:22:24:25:26:28:30:31:34:35:38:40 SD: 3.3900 cents 32:34:35:38:40:42:45:48:50:54:56:60:64 SD: 2.1575 cents 40:42:44:48:50:53:56:60:63:68:70:75:80 SD: 2.0620 cents 41:43:45:49:51:54:58:62:64:69:72:77:82 SD: 1.9716 cents 50:53:55:60:63:66:70:75:78:84:88:94:100 SD: 1.7235 cents 54:57:59:65:68:71:76:81:84:91:95:101:108 SD: 1.6542 cents 59:62:65:71:74:78:83:89:92:100:104:111:118 SD: 1.5978 cents 60:63:66:72:75:79:84:90:94:101:105:113:120 SD: 1.4105 cents 69:73:76:83:86:91:97:104:108:116:121:129:138 SD: 1.3319 cents 71:75:78:85:89:94:100:107:111:120:125:133:142 SD: 1.1562 cents 84:89:92:101:105:111:118:126:131:142:148:158:168 SD: 1.1465 cents 88:93:97:106:110:116:124:132:138:149:155:165:176 SD: 1.1355 cents 89:94:98:107:111:117:125:134:139:150:156:167:178 SD: 1.0181 cents 91:96:100:109:114:120:128:137:142:154:160:171:182 SD: 0.8716 cents 110:116:121:132:138:145:155:165:172:186:193:206:220 SD: 0.7684 cents 112:118:123:134:140:148:158:168:175:189:197:210:224 SD: 0.7357 cents 128:135:141:154:160:169:180:192:200:216:225:240:256 SD: 0.5779 cents 144:152:158:173:180:190:203:216:225:243:253:270:288 SD: 0.4712 cents 160:169:176:192:200:211:225:240:250:270:281:300:320 SD: 0.3100 cents 224:236:246:269:280:295:315:336:350:378:394:420:448 SD: 0.2638 cents 276:291:303:331:345:364:388:414:431:466:485:518:552 SD: 0.2459 cents 345:364:379:414:431:455:485:518:539:582:606:647:690 SD: 0.2206 cents 352:371:387:422:440:464:495:528:550:594:619:660:704 SD: 0.2071 cents 364:384:400:437:455:480:512:546:569:614:640:683:728 SD: 0.1709 cents 384:405:422:461:480:506:540:576:600:648:675:720:768 SD: 0.1040 cents