Scala analysis: tertiadia2
Tertiadia 2048/2025 262144/253125 scale
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: 9/8 203.910002 major whole tone 3: 6/5 315.641287 minor third 4: 32/25 427.372572 classic diminished fourth 5: 675/512 478.492430 wide augmented third 6: 45/32 590.223716 diatonic tritone 7: 3/2 701.955001 perfect fifth 8: 8/5 813.686286 minor sixth 9: 128/75 925.417571 diminished seventh 10: 2048/1125 1037.148857 double diminished octave 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: 16/15 111.7313 minor diatonic semitone 3: 16/15 111.7313 minor diatonic semitone 4: 16/15 111.7313 minor diatonic semitone 5: 16875/16384 51.1199 double augmentation diesis, Negri comma 6: 16/15 111.7313 minor diatonic semitone 7: 16/15 111.7313 minor diatonic semitone 8: 16/15 111.7313 minor diatonic semitone 9: 16/15 111.7313 minor diatonic semitone 10: 16/15 111.7313 minor diatonic semitone 11: 16875/16384 51.1199 double augmentation diesis, Negri comma 12: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 16875/16384 51.120 cents double augmentation diesis, Negri comma 1: 1 135/128 92.179 cents major chroma, major limma 1: 9 16/15 111.731 cents minor diatonic semitone 2: 4 1125/1024 162.851 cents double augmented prime 2: 2 9/8 203.910 cents major whole tone 2: 6 256/225 223.463 cents Neapolitan diminished third 3: 1 151875/131072 255.030 cents 3: 5 75/64 274.582 cents classic augmented second 3: 2 6/5 315.641 cents minor third 3: 4 4096/3375 335.194 cents double diminished fourth 4: 2 10125/8192 366.761 cents double augmented second 4: 6 5/4 386.314 cents major third 4: 2 32/25 427.373 cents classic diminished fourth 4: 2 65536/50625 446.925 cents two (Neapolitan diminished third) 5: 4 675/512 478.492 cents wide augmented third 5: 6 4/3 498.045 cents perfect fourth 5: 1 512/375 539.104 cents double diminished fifth 5: 1 1048576/759375 558.656 cents 6: 6 45/32 590.224 cents diatonic tritone 6: 6 64/45 609.776 cents 2nd tritone 7: 1 759375/524288 641.344 cents 7: 1 375/256 660.896 cents double augmented fourth 7: 6 3/2 701.955 cents perfect fifth 7: 4 1024/675 721.508 cents narrow diminished sixth 8: 2 50625/32768 753.075 cents 8: 2 25/16 772.627 cents classic augmented fifth 8: 6 8/5 813.686 cents minor sixth 8: 2 16384/10125 833.239 cents double diminished seventh 9: 4 3375/2048 864.806 cents double augmented fifth 9: 2 5/3 884.359 cents major sixth, BP sixth 9: 5 128/75 925.418 cents diminished seventh 9: 1 262144/151875 944.970 cents 10: 6 225/128 976.537 cents augmented sixth 10: 2 16/9 996.090 cents Pythagorean minor seventh 10: 4 2048/1125 1037.149 cents double diminished octave 11: 9 15/8 1088.269 cents classic major seventh 11: 1 256/135 1107.821 cents octave - major chroma 11: 2 32768/16875 1148.880 cents octave - double augmentation diesis Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.45455 = 38/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 92.2 203.9 315.6 427.4 478.5 590.2 702.0 813.7 925.4 1037.1 1088.3 1200.0 92.2 : 111.7 223.5 335.2 386.3 498.0 609.8 721.5 833.2 945.0 996.1 1107.8 1200.0 203.9 : 111.7 223.5 274.6 386.3 498.0 609.8 721.5 833.2 884.4 996.1 1088.3 1200.0 315.6 : 111.7 162.9 274.6 386.3 498.0 609.8 721.5 772.6 884.4 976.5 1088.3 1200.0 427.4 : 51.1 162.9 274.6 386.3 498.0 609.8 660.9 772.6 864.8 976.5 1088.3 1200.0 478.5 : 111.7 223.5 335.2 446.9 558.7 609.8 721.5 813.7 925.4 1037.1 1148.9 1200.0 590.2 : 111.7 223.5 335.2 446.9 498.0 609.8 702.0 813.7 925.4 1037.1 1088.3 1200.0 702.0 : 111.7 223.5 335.2 386.3 498.0 590.2 702.0 813.7 925.4 976.5 1088.3 1200.0 813.7 : 111.7 223.5 274.6 386.3 478.5 590.2 702.0 813.7 864.8 976.5 1088.3 1200.0 925.4 : 111.7 162.9 274.6 366.8 478.5 590.2 702.0 753.1 864.8 976.5 1088.3 1200.0 1037.1: 51.1 162.9 255.0 366.8 478.5 590.2 641.3 753.1 864.8 976.5 1088.3 1200.0 1088.3: 111.7 203.9 315.6 427.4 539.1 590.2 702.0 813.7 925.4 1037.1 1148.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.1199 .. 111.7313 cents 262144/253125, 60.6114 cents 16875/16384, 51.1199 cents 2: 162.8511 .. 223.4626 cents 262144/253125, 60.6114 cents 16875/16384, 51.1199 cents 3: 255.0299 .. 335.1939 cents 536870912/512578125, 80.1640 cents 34171875/33554432, 31.5673 cents 4: 366.7611 .. 446.9251 cents 536870912/512578125, 80.1640 cents 34171875/33554432, 31.5673 cents 5: 478.4924 .. 558.6564 cents 536870912/512578125, 80.1640 cents 34171875/33554432, 31.5673 cents 6: 590.2237 .. 609.7763 cents 2048/2025, 19.5526 cents 34171875/33554432, 31.5673 cents 7: 641.3436 .. 721.5076 cents 536870912/512578125, 80.1640 cents 34171875/33554432, 31.5673 cents 8: 753.0749 .. 833.2389 cents 536870912/512578125, 80.1640 cents 34171875/33554432, 31.5673 cents 9: 864.8061 .. 944.9701 cents 536870912/512578125, 80.1640 cents 34171875/33554432, 31.5673 cents 10: 976.5374 .. 1037.1489 cents 262144/253125, 60.6114 cents 34171875/33554432, 31.5673 cents 11: 1088.2687 .. 1148.8801 cents 262144/253125, 60.6114 cents 16875/16384, 51.1199 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 16875/16384, 51.1199 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 16/15, 111.7313 cents Average / Smallest step : 1.956187 Largest / Average step : 1.117313 Largest / Smallest step : 2.185673 Median interval of one step : 16/15, 111.7313 cents, amount: 9 Most common interval of one step : 16/15, 111.7313 cents, amount: 9 Least squares average step : 100.89938 cents, oct.: 1210.79253 cents Scale is strictly proper Step pattern alph. order: ABBBCBBBBBCB Step pattern size order : MLLLSLLLLLSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 31.56729 cents Scale diversity : 1.424570 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.380848 Rothenberg efficiency : 0.409689 redundancy: 0.590311 Efficiency x scale size : 4.916270 Number of different interval sizes : 38 = 3.45455 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.45455 = 38/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 2048/2025, 19.5526 cents Most common intervals : 16/15, 111.7313 cents & inv., amount: 9 Most common triad is 0.0 111.731 1088.269 cents, amount: 6 Number of recognisable fifths : 6, average 701.9550 cents Formal octave complements present : 1 = 8.3333% -- Rational properties -- Prime limit : 5 Odd number limit : 759375 (O: 759375 U: 759375) Highest odd numerator or denominator: 1125 Scale harmonicity : 0.015306 Average absolute harmonicity : 0.162516 Specific harmonicity : 0.099100 Fundamental : 1/576000, -19.1357 octaves, 0.0005 Hz. Guide tone : 1382400, 20.3987 octaves, 361671181.472 Hz. Exponens Consonantiae : 7.962624E+11, 39.53445 octaves Euler's gradus suavitatis : 51 Sum of Mann's harmonic distance : 2516.0, average 209.66667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 16.94240, average 1.41187 Sum of Tenney's harmonic distance : 34.27720, average 2.85643 Vogel's harmonic complexity : 30.83333 Wille's k value : 379687 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 10 Triangular lattice diameter : 10 Lattice compactness : 555.35461, average 7.11993 Lattice compactness (without 2's) : 197.72503, average 2.53494 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -9 .. 11 0.00000 56 1 3: -2 .. 3 0.83333 16 2 5: -3 .. 2 -0.33333 14 9 Average exponent except 2's : 6 / 12 = 0.50000 Average absolute exponent except 2's: 30 / 12 = 2.50000 Scale is JI-epimorphic with val: <12 19 28| = patent
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.2194 c. M: 37.1489 c. Twelve-tone Chromatic (1/11-comma) 15: 1 2 1 1 1 1 2 1 2 1 1 1 N D3 SD: 22.0958 c. M:-36.0900 c. 18: 1 2 2 1 1 2 2 1 2 2 0 2 N T3 SD: 19.4430 c. M:-31.3783 c. 19: 1 2 2 2 0 2 2 2 1 2 1 2 P D3 SD: 21.9714 c. M: 41.2070 c. 20: 1 2 2 2 1 2 1 2 2 2 1 2 P B D3 SD: 22.1877 c. M: 41.9550 c. 21: 1 2 2 2 1 2 2 2 2 2 1 2 P D3 SD: 21.1967 c. M: 35.0359 c. 22: 2 2 2 2 1 2 2 2 2 2 1 2 SP B ME SD: 9.2994 c. M:-16.9122 c. 31: 2 3 3 3 1 3 3 3 3 3 1 3 P SD: 8.0331 c. M: 14.7594 c. 39: 3 4 3 4 2 3 4 3 4 4 1 4 P SD: 8.4865 c. M:-13.8153 c. 40: 3 4 4 3 2 4 3 4 4 4 1 4 P SD: 8.2221 c. M:-14.3587 c. 41: 3 4 4 4 1 4 4 4 4 3 2 4 P SD: 7.4916 c. M: 12.7586 c. 43: 3 4 4 4 2 4 4 4 4 4 2 4 SP SD: 5.8423 c. M: 8.7679 c. 53: 4 5 5 5 2 5 5 5 5 5 2 5 SP SD: 2.1478 c. M:-4.3606 c. 65: 5 6 6 6 3 6 6 6 6 6 3 6 SP SD: 1.6706 c. M: 3.3027 c. 118: 9 11 11 11 5 11 11 11 11 11 5 11 SP SD: 0.3493 c. M: 0.6533 c. 376: 29 35 35 35 16 35 35 35 35 35 16 35 SP SD: 0.2250 c. M:-0.3745 c. 494: 38 46 46 46 21 46 46 46 46 46 21 46 SP SD: 0.0989 c. M:-0.1578 c. 612: 47 57 57 57 26 57 57 57 57 57 26 57 SP SD: 0.0520 c. M:-0.1060 c. 1171: 90 109 109 109 50 109 109 109 109 109 50 109 SP SD: 0.0449 c. M: 0.0865 c. 1289: 99 120 120 120 55 120 120 120 120 120 55 120 SP SD: 0.0368 c. M: 0.0658 c. 1783: 137 166 166 166 76 166 166 166 166 166 76 166 SP SD: 0.0149 c. M:-0.0269 c. 1901: 146 177 177 177 81 177 177 177 177 177 81 177 SP SD: 0.0120 c. M: 0.0185 c. 2395: 184 223 223 223 102 223 223 223 223 223 102 223 SP SD: 0.0109 c. M:-0.0178 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: 15.1589 cents 4 x x x 5 x x 6 x 7 x x 8 S SD: 14.9376 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 4.2037 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 11.2988 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 7.6307 cents 8 x 9 x 10 x 11:12:13:14 x 15:16 S SD: 9.5232 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 11.0665 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 5.5827 cents 11 x 12:13:14 x 15:17:18:19:20:21:22 SD: 10.9846 cents 12:13 x 14:15:16:17:18:19:20:22:23:24 S SD: 9.2593 cents 13:14:15:16 x 17:18:20:21:22:24 x 26 S SD: 9.5206 cents 14:15:16:17:18 x 20:21:22:24:25:26:28 S SD: 6.5102 cents 15:16:17:18:19:20:21:23:24:26:27:28:30 SD: 5.2215 cents 17:18:19:20:22 x 24:26:27:29:31:32:34 SD: 5.0658 cents 18:19:20:22:23:24:25:27:29:31:33:34:36 SD: 4.5873 cents 20:21:23:24 x 26:28:30:32:34:36:38:40 SD: 5.0700 cents 22:23:25:26:28:29:31:33:35:38:40:41:44 SD: 3.7147 cents 24:25:27:29:31:32:34:36:38:41:44:45:48 SD: 3.6123 cents 25:26:28:30:32:33:35:38:40:43:46:47:50 SD: 3.5196 cents 30:32:34:36:38:40:42:45:48:51:55:56:60 SD: 3.3025 cents 32:34:36:38:41:42:45:48:51:55:58:60:64 SD: 2.3668 cents 40:42:45:48:51:53:56:60:64:68:73:75:80 SD: 1.4557 cents 50:53:56:60:64:66:70:75:80:85:91:94:100 SD: 1.3606 cents 54:57:61:65:69:71:76:81:86:92:98:101:108 SD: 1.2761 cents 71:75:80:85:91:94:100:107:114:121:129:133:142 SD: 1.2367 cents 72:76:81:86:92:95:101:108:115:123:131:135:144 SD: 0.8691 cents 96:101:108:115:123:127:135:144:154:164:175:180:192 SD: 0.8104 cents 104:110:117:125:133:137:146:156:166:177:189:195:208 SD: 0.8103 cents 106:112:119:127:136:140:149:159:170:181:193:199:212 SD: 0.7444 cents 110:116:124:132:141:145:155:165:176:188:200:206:220 SD: 0.5630 cents 128:135:144:154:164:169:180:192:205:218:233:240:256 SD: 0.5621 cents 150:158:169:180:192:198:211:225:240:256:273:281:300 SD: 0.3629 cents 160:169:180:192:205:211:225:240:256:273:291:300:320 SD: 0.2942 cents 200:211:225:240:256:264:281:300:320:341:364:375:400 SD: 0.2676 cents 280:295:315:336:358:369:394:420:448:478:510:525:560 SD: 0.2615 cents 290:306:326:348:371:382:408:435:464:495:528:544:580 SD: 0.2173 cents 310:327:349:372:397:409:436:465:496:529:564:581:620 SD: 0.2008 cents 330:348:371:396:422:435:464:495:528:563:601:619:660 SD: 0.1974 cents 386:407:434:463:494:509:543:579:618:659:703:724:772 SD: 0.1845 cents 400:422:450:480:512:527:563:600:640:683:728:750:800 SD: 0.1825 cents 424:447:477:509:543:559:596:636:678:724:772:795:848 SD: 0.1717 cents 440:464:495:528:563:580:619:660:704:751:801:825:880 SD: 0.0833 cents 600:633:675:720:768:791:844:900:960:1024:1092:1125:1200 SD: 0.0700 cents