Scala analysis: abacbadabc-marvtrans
Transversal of marvel tempering of 7-limit scale with mean variety four
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: 256/225 223.462571 Neapolitan diminished third 3: 4096/3375 335.193856 double diminished fourth 4: 4/3 498.044999 perfect fourth 5: 64/45 609.776284 2nd tritone 6: 1024/675 721.507570 narrow diminished sixth 7: 8/5 813.686286 minor sixth 8: 128/75 925.417571 diminished seventh 9: 2048/1125 1037.148857 double diminished octave 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 1125/1024 162.8511 double augmented prime 1: 16/15 111.7313 minor diatonic semitone 2: 16/15 111.7313 minor diatonic semitone 3: 16/15 111.7313 minor diatonic semitone 4: 1125/1024 162.8511 double augmented prime 5: 16/15 111.7313 minor diatonic semitone 6: 16/15 111.7313 minor diatonic semitone 7: 135/128 92.1787 major chroma, major limma 8: 16/15 111.7313 minor diatonic semitone 9: 16/15 111.7313 minor diatonic semitone 10: 1125/1024 162.8511 double augmented prime
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 135/128 92.179 cents major chroma, major limma 1: 7 16/15 111.731 cents minor diatonic semitone 1: 2 1125/1024 162.851 cents double augmented prime 2: 2 9/8 203.910 cents major whole tone 2: 4 256/225 223.463 cents Neapolitan diminished third 2: 4 75/64 274.582 cents classic augmented second 3: 3 6/5 315.641 cents minor third 3: 1 4096/3375 335.194 cents double diminished fourth 3: 6 5/4 386.314 cents major third 4: 2 32/25 427.373 cents classic diminished fourth 4: 2 675/512 478.492 cents wide augmented third 4: 6 4/3 498.045 cents perfect fourth 5: 1 512/375 539.104 cents double diminished fifth 5: 4 45/32 590.224 cents diatonic tritone 5: 4 64/45 609.776 cents 2nd tritone 5: 1 375/256 660.896 cents double augmented fourth 6: 6 3/2 701.955 cents perfect fifth 6: 2 1024/675 721.508 cents narrow diminished sixth 6: 2 25/16 772.627 cents classic augmented fifth 7: 6 8/5 813.686 cents minor sixth 7: 1 3375/2048 864.806 cents double augmented fifth 7: 3 5/3 884.359 cents major sixth, BP sixth 8: 4 128/75 925.418 cents diminished seventh 8: 4 225/128 976.537 cents augmented sixth 8: 2 16/9 996.090 cents Pythagorean minor seventh 9: 2 2048/1125 1037.149 cents double diminished octave 9: 7 15/8 1088.269 cents classic major seventh 9: 1 256/135 1107.821 cents octave - major chroma Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.11111 = 28/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 111.7 223.5 335.2 498.0 609.8 721.5 813.7 925.4 1037.1 1200.0 111.7 : 111.7 223.5 386.3 498.0 609.8 702.0 813.7 925.4 1088.3 1200.0 223.5 : 111.7 274.6 386.3 498.0 590.2 702.0 813.7 976.5 1088.3 1200.0 335.2 : 162.9 274.6 386.3 478.5 590.2 702.0 864.8 976.5 1088.3 1200.0 498.0 : 111.7 223.5 315.6 427.4 539.1 702.0 813.7 925.4 1037.1 1200.0 609.8 : 111.7 203.9 315.6 427.4 590.2 702.0 813.7 925.4 1088.3 1200.0 721.5 : 92.2 203.9 315.6 478.5 590.2 702.0 813.7 976.5 1088.3 1200.0 813.7 : 111.7 223.5 386.3 498.0 609.8 721.5 884.4 996.1 1107.8 1200.0 925.4 : 111.7 274.6 386.3 498.0 609.8 772.6 884.4 996.1 1088.3 1200.0 1037.1: 162.9 274.6 386.3 498.0 660.9 772.6 884.4 976.5 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 162.8511 cents 25/24, 70.6724 cents 135/128, 92.1787 cents 2: 203.9100 .. 274.5824 cents 25/24, 70.6724 cents 128/125, 41.0589 cents 3: 315.6413 .. 386.3137 cents 25/24, 70.6724 cents 128/125, 41.0589 cents 4: 427.3726 .. 498.0450 cents 25/24, 70.6724 cents 128/125, 41.0589 cents 5: 539.1039 .. 660.8961 cents 140625/131072, 121.7923 cents 128/125, 41.0589 cents 6: 701.9550 .. 772.6274 cents 25/24, 70.6724 cents 128/125, 41.0589 cents 7: 813.6863 .. 884.3587 cents 25/24, 70.6724 cents 128/125, 41.0589 cents 8: 925.4176 .. 996.0900 cents 25/24, 70.6724 cents 128/125, 41.0589 cents 9: 1037.1489 .. 1107.8213 cents 25/24, 70.6724 cents 128/125, 41.0589 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 135/128, 92.1787 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 1125/1024, 162.8511 cents Average / Smallest step : 1.301819 Largest / Average step : 1.357093 Largest / Smallest step : 1.766689 Median interval of one step : 16/15, 111.7313 cents, amount: 7 Most common interval of one step : 16/15, 111.7313 cents, amount: 7 Least squares average step : 117.83852 cents, oct.: 1178.38517 cents Scale is strictly proper Step pattern alph. order: AAABAACAAB Step pattern size order : MMMLMMSMML Scale is a Constant Structure, by a margin of 41.05886 cents Scale diversity : 1.379823 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.427357 Rothenberg efficiency : 0.447857 redundancy: 0.552143 Efficiency x scale size : 4.478571 Number of different interval sizes : 28 = 3.11111 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.11111 = 28/9 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2048/2025, 19.5526 cents Most common intervals : 16/15, 111.7313 cents & inv., amount: 7 Most common triad is 0.0 111.731 1088.269 cents, amount: 4 Number of recognisable fifths : 6, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 10.0000% Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 Scale is n-1 differentially coherent in interval classes 6 and 7 combined Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 6-7 -- Rational properties -- Prime limit : 5 Odd number limit : 3375 (O: 3375 U: 3375) Highest odd numerator or denominator: 3375 Scale harmonicity : 0.025510 Average absolute harmonicity : 0.162248 Specific harmonicity : 0.130556 Fundamental : 1/3375, -11.7207 octaves, 0.0775 Hz. Guide tone : 4096, 12.0000 octaves, 1071618.315 Hz. Exponens Consonantiae : 1.382400E+07, 23.72067 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 6595.0, average 659.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 17.64137, average 1.76414 Sum of Tenney's harmonic distance : 36.90729, average 3.69073 Vogel's harmonic complexity : 18.40000 Wille's k value : 1687 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 297.21933, average 5.40399 Lattice compactness (without 2's) : 110.50231, average 2.00913 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 12 6.40000 64 1 3: -3 .. 0 -1.50000 15 1 5: -3 .. 0 -1.50000 15 8 Average exponent except 2's :-30 / 10 =-3.00000 Average absolute exponent except 2's: 30 / 10 = 3.00000 Scale is JI-epimorphic with val: <10 16 23| = patent Scale is weakly epimorphic with val: <10 17 24|
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 22.5948 c. M:-42.8511 c. 12: 1 1 1 2 1 1 1 1 1 2 P D3 SD: 21.6843 c. M: 37.1489 c. Raga Gambhir Basant 15: 1 2 1 2 2 1 1 2 1 2 P D3 SD: 20.3567 c. M:-34.5824 c. 17: 2 1 2 2 2 1 2 1 2 2 P D3 SD: 19.6811 c. M:-33.3725 c. 18: 2 1 2 2 2 2 1 2 2 2 SP B ME S SD: 18.3355 c. M: 31.3783 c. 21: 2 2 2 3 2 2 1 2 2 3 P SD: 12.4458 c. M:-21.3496 c. 22: 2 2 2 3 2 2 2 2 2 3 SP D3 SD: 6.5003 c. M: 12.4167 c. Standard Pentachordal Minor 43: 4 4 4 6 4 4 3 4 4 6 SP SD: 3.3608 c. M: 4.5907 c. 53: 5 5 5 7 5 5 4 5 5 7 SP SD: 2.6710 c. M:-4.4288 c. 65: 6 6 6 9 6 6 5 6 6 9 SP SD: 1.8436 c. M: 3.3027 c. 75: 7 7 7 10 7 7 6 7 7 10 SP SD: 1.7542 c. M:-2.8511 c. 118: 11 11 11 16 11 11 9 11 11 16 SP SD: 0.2798 c. M:-0.5263 c. 376: 35 35 35 51 35 35 29 35 35 51 SP SD: 0.1329 c. M: 0.2310 c. 494: 46 46 46 67 46 46 38 46 46 67 SP SD: 0.0599 c. M:-0.0981 c. 612: 57 57 57 83 57 57 47 57 57 83 SP SD: 0.0618 c. M:-0.1060 c. 1106: 103 103 103 150 103 103 85 103 103 150 SP SD: 0.0537 c. M:-0.1025 c. 1171: 109 109 109 159 109 109 90 109 109 159 SP SD: 0.0568 c. M: 0.0956 c. 1289: 120 120 120 175 120 120 99 120 120 175 SP SD: 0.0351 c. M: 0.0658 c. 1407: 131 131 131 191 131 131 108 131 131 191 SP SD: 0.0305 c. M: 0.0486 c. 1783: 166 166 166 242 166 166 137 166 166 242 SP SD: 0.0170 c. M: 0.0284 c. 1901: 177 177 177 258 177 177 146 177 177 258 SP SD: 0.0070 c. M: 0.0105 c. 2395: 223 223 223 325 223 223 184 223 223 325 SP SD: 0.0069 c. M:-0.0119 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 9.7763 cents 3 x x x 4 x x x 5 x 6 S SD: 13.6863 cents 4 x x 5 x x 6 x 7 x 8 S SD: 17.4639 cents 5 x x 6 x 7 x 8 x 9:10 S SD: 7.7664 cents 6 x 7 x 8 x 9 x 10:11:12 S SD: 10.6740 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 11.3474 cents 8 x 9:10:11 x 12:13:14:15:16 S SD: 13.3661 cents 9 x 10:11:12:13:14 x 15:16:18 S SD: 11.0478 cents 10:11 x 12:13:14:15:16:17:18:20 S SD: 9.0917 cents 11:12 x 13:15:16:17:18:19:20:22 SD: 10.9081 cents 12:13:14:15:16:17:18:19:20:22:24 S SD: 8.8373 cents 13:14:15:16:17:18:20:21:22:24:26 S SD: 8.0020 cents 14:15:16:17:19:20:21:22:24:25:28 SD: 6.0375 cents 15:16:17:18:20:21:23:24:26:27:30 SD: 5.1152 cents 23:25:26:28:31:33:35:37:39:42:46 SD: 4.5515 cents 24:26:27:29:32:34:36:38:41:44:48 SD: 4.5486 cents 27:29:31:33:36:38:41:43:46:49:54 SD: 3.1198 cents 28:30:32:34:37:40:42:45:48:51:56 SD: 3.0372 cents 33:35:38:40:44:47:50:53:56:60:66 SD: 2.6251 cents 42:45:48:51:56:60:64:67:72:76:84 SD: 2.0817 cents 43:46:49:52:57:61:65:69:73:78:86 SD: 1.9426 cents 45:48:51:55:60:64:68:72:77:82:90 SD: 1.6252 cents 57:61:65:69:76:81:86:91:97:104:114 SD: 1.4608 cents 60:64:68:73:80:85:91:96:102:109:120 SD: 1.3022 cents 72:77:82:87:96:102:109:115:123:131:144 SD: 1.2333 cents 75:80:85:91:100:107:114:120:128:137:150 SD: 1.1026 cents 78:83:89:95:104:111:118:125:133:142:156 SD: 1.0676 cents 85:91:97:103:113:121:129:136:145:155:170 SD: 1.0600 cents 88:94:100:107:117:125:134:141:150:160:176 SD: 1.0365 cents 89:95:101:108:119:127:135:142:152:162:178 SD: 1.0187 cents 93:99:106:113:124:132:141:149:159:169:186 SD: 0.7947 cents 102:109:116:124:136:145:155:163:174:186:204 SD: 0.6503 cents 123:131:140:149:164:175:187:197:210:224:246 SD: 0.6013 cents 150:160:171:182:200:213:228:240:256:273:300 SD: 0.5523 cents 168:179:191:204:224:239:255:269:287:306:336 SD: 0.3588 cents 211:225:240:256:281:300:320:338:360:384:422 SD: 0.3203 cents 225:240:256:273:300:320:341:360:384:410:450 SD: 0.2428 cents 300:320:341:364:400:427:455:480:512:546:600 SD: 0.2286 cents 313:334:356:380:417:445:475:501:534:570:626 SD: 0.2255 cents 327:349:372:397:436:465:496:523:558:595:654 SD: 0.1658 cents 435:464:495:528:580:619:660:696:742:792:870 SD: 0.1399 cents 450:480:512:546:600:640:683:720:768:819:900 SD: 0.1035 cents