Scala analysis: tertiadia3
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: 16/15 111.731285 minor diatonic semitone 2: 256/225 223.462571 Neapolitan diminished third 3: 4096/3375 335.193856 double diminished fourth 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: 8/5 813.686286 minor sixth 9: 128/75 925.417571 diminished seventh 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: 16/15 111.7313 minor diatonic semitone 2: 16/15 111.7313 minor diatonic semitone 3: 16/15 111.7313 minor diatonic semitone 4: 16875/16384 51.1199 double augmentation diesis, Negri comma 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: 16/15 111.7313 minor diatonic semitone 9: 16/15 111.7313 minor diatonic semitone 10: 16875/16384 51.1199 double augmentation diesis, Negri comma 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: 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: 1 2278125/2097152 143.299 cents 2: 3 1125/1024 162.851 cents double augmented prime 2: 1 9/8 203.910 cents major whole tone 2: 7 256/225 223.463 cents Neapolitan diminished third 3: 2 151875/131072 255.030 cents 3: 4 75/64 274.582 cents classic augmented second 3: 1 6/5 315.641 cents minor third 3: 5 4096/3375 335.194 cents double diminished fourth 4: 3 10125/8192 366.761 cents double augmented second 4: 5 5/4 386.314 cents major third 4: 1 32/25 427.373 cents classic diminished fourth 4: 3 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: 3 50625/32768 753.075 cents 8: 1 25/16 772.627 cents classic augmented fifth 8: 5 8/5 813.686 cents minor sixth 8: 3 16384/10125 833.239 cents double diminished seventh 9: 5 3375/2048 864.806 cents double augmented fifth 9: 1 5/3 884.359 cents major sixth, BP sixth 9: 4 128/75 925.418 cents diminished seventh 9: 2 262144/151875 944.970 cents 10: 7 225/128 976.537 cents augmented sixth 10: 1 16/9 996.090 cents Pythagorean minor seventh 10: 3 2048/1125 1037.149 cents double diminished octave 10: 1 4194304/2278125 1056.701 cents 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: 3.63636 = 40/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 111.7 223.5 335.2 386.3 478.5 590.2 702.0 813.7 925.4 976.5 1088.3 1200.0 111.7 : 111.7 223.5 274.6 366.8 478.5 590.2 702.0 813.7 864.8 976.5 1088.3 1200.0 223.5 : 111.7 162.9 255.0 366.8 478.5 590.2 702.0 753.1 864.8 976.5 1088.3 1200.0 335.2 : 51.1 143.3 255.0 366.8 478.5 590.2 641.3 753.1 864.8 976.5 1088.3 1200.0 386.3 : 92.2 203.9 315.6 427.4 539.1 590.2 702.0 813.7 925.4 1037.1 1148.9 1200.0 478.5 : 111.7 223.5 335.2 446.9 498.0 609.8 721.5 833.2 945.0 1056.7 1107.8 1200.0 590.2 : 111.7 223.5 335.2 386.3 498.0 609.8 721.5 833.2 945.0 996.1 1088.3 1200.0 702.0 : 111.7 223.5 274.6 386.3 498.0 609.8 721.5 833.2 884.4 976.5 1088.3 1200.0 813.7 : 111.7 162.9 274.6 386.3 498.0 609.8 721.5 772.6 864.8 976.5 1088.3 1200.0 925.4 : 51.1 162.9 274.6 386.3 498.0 609.8 660.9 753.1 864.8 976.5 1088.3 1200.0 976.5 : 111.7 223.5 335.2 446.9 558.7 609.8 702.0 813.7 925.4 1037.1 1148.9 1200.0 1088.3: 111.7 223.5 335.2 446.9 498.0 590.2 702.0 813.7 925.4 1037.1 1088.3 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: 143.2986 .. 223.4626 cents 536870912/512578125, 80.1640 cents 34171875/33554432, 31.5673 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 .. 1056.7014 cents 536870912/512578125, 80.1640 cents 34171875/33554432, 31.5673 cents 11: 1088.2687 .. 1148.8801 cents 262144/253125, 60.6114 cents 34171875/33554432, 31.5673 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 : 99.89471 cents, oct.: 1198.73651 cents Scale is strictly proper Step pattern alph. order: AAABCAAAABAA Step pattern size order : LLLSMLLLLSLL Scale is a Constant Structure, by a margin of 31.56729 cents Scale diversity : 1.449081 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.348261 Rothenberg efficiency : 0.393353 redundancy: 0.606647 Efficiency x scale size : 4.720238 Number of different interval sizes : 40 = 3.63636 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.63636 = 40/11 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: 7 Number of recognisable fifths : 6, average 701.9550 cents Scale contains a complete diamond : 1 15 225 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 58.3333% -- Rational properties -- Prime limit : 5 Odd number limit : 2278125 (O: 2278125 U: 2278125) Highest odd numerator or denominator: 3375 Scale harmonicity : 0.014493 Average absolute harmonicity : 0.158246 Specific harmonicity : 0.089373 Fundamental : 1/1728000, -20.7207 octaves, 0.0002 Hz. Guide tone : 2764800, 21.3987 octaves, 723342362.944 Hz. Exponens Consonantiae : 4.777574E+12, 42.11942 octaves Euler's gradus suavitatis : 54 Sum of Mann's harmonic distance : 4928.0, average 410.66667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 18.81746, average 1.56812 Sum of Tenney's harmonic distance : 37.48132, average 3.12344 Vogel's harmonic complexity : 33.33333 Wille's k value : 1139062 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 11 Triangular lattice diameter : 11 Lattice compactness : 605.68688, average 7.76522 Lattice compactness (without 2's) : 217.54216, average 2.78900 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -9 .. 12 0.66667 62 1 3: -3 .. 3 0.16667 16 1 5: -3 .. 2 -0.16667 16 10 Average exponent except 2's : 0 / 12 = 0.00000 Average absolute exponent except 2's: 32 / 12 = 2.66667 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: 18.7027 c. M: 35.1939 c. Twelve-tone Chromatic (1/11-comma) 15: 1 2 1 1 1 1 2 1 2 0 2 1 N D3 SD: 21.6093 c. M:-34.5824 c. 16: 1 2 1 1 1 2 1 2 1 1 1 2 P B D3 SD: 23.4397 c. M: 38.2687 c. 18: 2 1 2 1 1 2 2 1 2 1 1 2 P B D3 SD: 17.5477 c. M:-31.3783 c. 21: 2 2 2 1 1 2 2 2 2 1 2 2 P D3 SD: 11.8861 c. M: 21.3496 c. 22: 2 2 2 1 2 2 2 2 2 1 2 2 SP B ME SD: 6.3047 c. M:-12.4167 c. Pajara-12 32: 3 3 3 1 3 3 3 3 3 1 3 3 SP B DE SD: 7.6437 c. M:-12.0824 c. Pajaro-12 43: 4 4 4 2 3 4 4 4 4 2 4 4 SP SD: 3.0434 c. M: 4.4873 c. 53: 5 5 5 2 4 5 5 5 5 2 5 5 SP SD: 2.3311 c. M:-4.4288 c. 65: 6 6 6 3 5 6 6 6 6 3 6 6 SP SD: 1.5708 c. M: 2.8862 c. 75: 7 7 7 3 6 7 7 7 7 3 7 7 SP SD: 1.5372 c. M:-2.5824 c. 118: 11 11 11 5 9 11 11 11 11 5 11 11 SP SD: 0.2690 c. M: 0.5263 c. 301: 28 28 28 13 23 28 28 28 28 13 28 28 SP SD: 0.2738 c. M: 0.5006 c. 376: 35 35 35 16 29 35 35 35 35 16 35 35 SP SD: 0.1272 c. M:-0.2310 c. 494: 46 46 46 21 38 46 46 46 46 21 46 46 SP SD: 0.0524 c. M:-0.0885 c. 1106: 103 103 103 47 85 103 103 103 103 47 103 103 SP SD: 0.0448 c. M:-0.0797 c. 1289: 120 120 120 55 99 120 120 120 120 55 120 120 SP SD: 0.0295 c. M: 0.0503 c. 1407: 131 131 131 60 108 131 131 131 131 60 131 131 SP SD: 0.0268 c. M: 0.0444 c. 1783: 166 166 166 76 137 166 166 166 166 76 166 166 SP SD: 0.0156 c. M: 0.0284 c. 1901: 177 177 177 81 146 177 177 177 177 81 177 177 SP SD: 0.0063 c. M: 0.0099 c. 2395: 223 223 223 102 184 223 223 223 223 102 223 223 SP SD: 0.0059 c. M:-0.0104 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 x 7 x 8 S SD: 1.9279 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 9.2252 cents 6 x 7 x x 8 x 9 x 10 x 11:12 S SD: 12.3222 cents 7 x 8 x x 9:10 x 11:12 x 13:14 S SD: 9.0284 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 6.4661 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 10.5290 cents 10:11 x 12 x 13:14:15:16:17:18:19:20 S SD: 7.8274 cents 11:12 x 13:14 x 15:17:18:19 x 21:22 SD: 12.6826 cents 12:13:14 x 15:16:17:18:19:20:21:23:24 SD: 7.4257 cents 13:14:15:16 x 17:18:20:21:22:23:24:26 S SD: 6.8196 cents 14:15:16:17 x 18:20:21:22:24:25:26:28 S SD: 6.2969 cents 15:16:17:18:19:20:21:23:24 x 26:28:30 SD: 5.3725 cents 17:18:19 x 21:22:24:26:27:29:30:32:34 SD: 5.7512 cents 20:21:23:24:25:26:28:30:32:34:35:38:40 SD: 4.3684 cents 24:26:27:29:30:32:34:36:38:41:42:45:48 SD: 3.8157 cents 27:29:31:33:34:36:38:41:43:46:47:51:54 SD: 3.7828 cents 28:30:32:34:35:37:39:42:45:48:49:53:56 SD: 2.4412 cents 32:34:36:39:40:42:45:48:51:55:56:60:64 SD: 2.3502 cents 42:45:48:51:53:55:59:63:67:72:74:79:84 SD: 2.1415 cents 44:47:50:53:55:58:62:66:70:75:77:83:88 SD: 1.7931 cents 56:60:64:68:70:74:79:84:90:96:98:105:112 SD: 1.5468 cents 57:61:65:69:71:75:80:86:91:97:100:107:114 SD: 1.4040 cents 71:76:81:86:89:94:100:107:114:121:125:133:142 SD: 1.3785 cents 72:77:82:87:90:95:101:108:115:123:127:135:144 SD: 1.0152 cents 88:94:100:107:110:116:124:132:141:150:155:165:176 SD: 0.6257 cents 116:124:132:141:145:153:163:174:186:198:204:218:232 SD: 0.6122 cents 132:141:150:160:165:174:186:198:211:225:232:248:264 SD: 0.5723 cents 136:145:155:165:170:179:191:204:218:232:239:255:272 SD: 0.4848 cents 160:171:182:194:200:211:225:240:256:273:281:300:320 SD: 0.3436 cents 224:239:255:272:280:295:315:336:358:382:394:420:448 SD: 0.2893 cents 268:286:305:325:335:353:377:402:429:457:471:503:536 SD: 0.2804 cents 296:316:337:359:370:390:416:444:474:505:520:555:592 SD: 0.2687 cents 313:334:356:380:391:413:440:470:501:534:550:587:626 SD: 0.2605 cents 320:341:364:388:400:422:450:480:512:546:563:600:640 SD: 0.2422 cents 327:349:372:397:409:431:460:491:523:558:575:613:654 SD: 0.2229 cents 364:388:414:442:455:480:512:546:582:621:640:683:728 SD: 0.2148 cents 376:401:428:456:470:496:529:564:602:642:661:705:752 SD: 0.2033 cents 384:410:437:466:480:506:540:576:614:655:675:720:768 SD: 0.2027 cents 392:418:446:476:490:517:551:588:627:669:689:735:784 SD: 0.1342 cents 524:559:596:636:655:691:737:786:838:894:921:983:1048 SD: 0.1315 cents 552:589:628:670:690:728:776:828:883:942:970:1035:1104 SD: 0.1055 cents 600:640:683:728:750:791:844:900:960:1024:1055:1125:1200 SD: 0.0993 cents