Scala analysis: tertiadia5
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: 75/64 274.582429 classic augmented second 4: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 45/32 590.223716 diatonic tritone 7: 3/2 701.955001 perfect fifth 8: 8/5 813.686286 minor sixth 9: 3375/2048 864.806144 double augmented fifth 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: 16875/16384 51.1199 double augmentation diesis, Negri comma 4: 16/15 111.7313 minor diatonic semitone 5: 16/15 111.7313 minor diatonic semitone 6: 135/128 92.1787 major chroma, major limma 7: 16/15 111.7313 minor diatonic semitone 8: 16/15 111.7313 minor diatonic semitone 9: 16875/16384 51.1199 double augmentation diesis, Negri comma 10: 16/15 111.7313 minor diatonic semitone 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: 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: 6 75/64 274.582 cents classic augmented second 3: 3 6/5 315.641 cents minor third 3: 3 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: 3 3375/2048 864.806 cents double augmented fifth 9: 3 5/3 884.359 cents major sixth, BP sixth 9: 6 128/75 925.418 cents diminished seventh 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: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 111.7 223.5 274.6 386.3 498.0 590.2 702.0 813.7 864.8 976.5 1088.3 1200.0 111.7 : 111.7 162.9 274.6 386.3 478.5 590.2 702.0 753.1 864.8 976.5 1088.3 1200.0 223.5 : 51.1 162.9 274.6 366.8 478.5 590.2 641.3 753.1 864.8 976.5 1088.3 1200.0 274.6 : 111.7 223.5 315.6 427.4 539.1 590.2 702.0 813.7 925.4 1037.1 1148.9 1200.0 386.3 : 111.7 203.9 315.6 427.4 478.5 590.2 702.0 813.7 925.4 1037.1 1088.3 1200.0 498.0 : 92.2 203.9 315.6 366.8 478.5 590.2 702.0 813.7 925.4 976.5 1088.3 1200.0 590.2 : 111.7 223.5 274.6 386.3 498.0 609.8 721.5 833.2 884.4 996.1 1107.8 1200.0 702.0 : 111.7 162.9 274.6 386.3 498.0 609.8 721.5 772.6 884.4 996.1 1088.3 1200.0 813.7 : 51.1 162.9 274.6 386.3 498.0 609.8 660.9 772.6 884.4 976.5 1088.3 1200.0 864.8 : 111.7 223.5 335.2 446.9 558.7 609.8 721.5 833.2 925.4 1037.1 1148.9 1200.0 976.5 : 111.7 223.5 335.2 446.9 498.0 609.8 721.5 813.7 925.4 1037.1 1088.3 1200.0 1088.3: 111.7 223.5 335.2 386.3 498.0 609.8 702.0 813.7 925.4 976.5 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: 162.8511 .. 223.4626 cents 262144/253125, 60.6114 cents 16875/16384, 51.1199 cents 3: 274.5824 .. 335.1939 cents 262144/253125, 60.6114 cents 16875/16384, 51.1199 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 .. 925.4176 cents 262144/253125, 60.6114 cents 34171875/33554432, 31.5673 cents 10: 976.5374 .. 1037.1489 cents 262144/253125, 60.6114 cents 16875/16384, 51.1199 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 : 98.92613 cents, oct.: 1187.11360 cents Scale is strictly proper Step pattern alph. order: AABAACAABAAA Step pattern size order : LLSLLMLLSLLL Scale is a Constant Structure, by a margin of 31.56729 cents Scale diversity : 1.401467 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.413436 Rothenberg efficiency : 0.415278 redundancy: 0.584722 Efficiency x scale size : 4.983333 Number of different interval sizes : 36 = 3.27273 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 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 Scale contains two identical disjunct hexachords Scale contains a complete diamond : 1 3 15 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 9 = 75.0000% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties -- Prime limit : 5 Odd number limit : 759375 (O: 759375 U: 759375) Highest odd numerator or denominator: 3375 Scale harmonicity : 0.015544 Average absolute harmonicity : 0.173535 Specific harmonicity : 0.104682 Fundamental : 1/460800, -18.8138 octaves, 0.0006 Hz. Guide tone : 864000, 19.7207 octaves, 226044488.420 Hz. Exponens Consonantiae : 3.981312E+11, 38.53445 octaves Euler's gradus suavitatis : 50 Sum of Mann's harmonic distance : 3282.0, average 273.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 16.46528, average 1.37211 Sum of Tenney's harmonic distance : 32.41987, average 2.70166 Vogel's harmonic complexity : 29.58333 Wille's k value : 379687 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 10 Triangular lattice diameter : 10 Lattice compactness : 510.09510, average 6.53968 Lattice compactness (without 2's) : 188.25566, average 2.41353 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -11 .. 8 -1.41667 53 1 3: -2 .. 3 0.50000 14 2 5: -2 .. 3 0.50000 14 9 Average exponent except 2's : 12 / 12 = 1.00000 Average absolute exponent except 2's: 28 / 12 = 2.33333 Scale is JI-epimorphic with val: <12 19 28| = patent Scale is weakly epimorphic with val: <12 20 29|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 17.6511 c. M:-35.1939 c. Twelve-tone Chromatic (1/11-comma) 21: 2 2 1 2 2 1 2 2 1 2 2 2 P D3 SD: 11.1926 c. M: 18.7951 c. 22: 2 2 1 2 2 2 2 2 1 2 2 2 SP B ME SD: 5.5808 c. M:-9.7763 c. Jubilee-12 43: 4 4 2 4 4 3 4 4 2 4 4 4 SP SD: 3.0669 c. M:-4.4873 c. 53: 5 5 2 5 5 4 5 5 2 5 5 5 SP SD: 2.1619 c. M: 4.4288 c. 65: 6 6 3 6 6 5 6 6 3 6 6 6 SP SD: 1.5141 c. M:-2.8862 c. 75: 7 7 3 7 7 6 7 7 3 7 7 7 SP SD: 1.5882 c. M: 2.5824 c. 96: 9 9 4 9 9 7 9 9 4 9 9 9 SP SD: 1.5620 c. M: 2.7237 c. 118: 11 11 5 11 11 9 11 11 5 11 11 11 SP SD: 0.2343 c. M: 0.3994 c. 376: 35 35 16 35 35 29 35 35 16 35 35 35 SP SD: 0.1193 c. M:-0.2018 c. 494: 46 46 21 46 46 38 46 46 21 46 46 46 SP SD: 0.0542 c. M: 0.0885 c. 612: 57 57 26 57 57 47 57 57 26 57 57 57 SP SD: 0.0503 c. M: 0.1003 c. 1106: 103 103 47 103 103 85 103 103 47 103 103 103 SP SD: 0.0458 c. M: 0.0797 c. 1171: 109 109 50 109 109 90 109 109 50 109 109 109 SP SD: 0.0458 c. M:-0.0956 c. 1289: 120 120 55 120 120 99 120 120 55 120 120 120 SP SD: 0.0293 c. M:-0.0503 c. 1407: 131 131 60 131 131 108 131 131 60 131 131 131 SP SD: 0.0276 c. M:-0.0444 c. 1783: 166 166 76 166 166 137 166 166 76 166 166 166 SP SD: 0.0137 c. M:-0.0284 c. 1901: 177 177 81 177 177 146 177 177 81 177 177 177 SP SD: 0.0064 c. M:-0.0099 c. 2395: 223 223 102 223 223 184 223 223 102 223 223 223 SP SD: 0.0062 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: 6.5175 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: 7.3700 cents 7 x 8 x 9 x 10 x 11 x 12:13:14 S SD: 11.3508 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 6.3058 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 10.3389 cents 10:11 x 12 x 13:14:15:16 x 18:19:20 S SD: 10.3733 cents 11:12 x 13:14:15 x 17 x 18:19:21:22 SD: 10.4989 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 5.1115 cents 13:14:15 x 16:17:18:20:21 x 23:24:26 SD: 8.0478 cents 14:15:16 x 18:19:20:21:22:23:25:26:28 SD: 7.1578 cents 15:16:17:18:19:20:21:23:24:25:26:28:30 SD: 5.7711 cents 16:17:18:19:20:21:23:24 x 26:28:30:32 SD: 5.5997 cents 17:18:19:20:21:23:24:26:27:28:30:32:34 SD: 5.0379 cents 19:20 x 22:24:25:27:29:30:31:33:36:38 SD: 6.1872 cents 20:21:23 x 25:27:28:30:32:33:35:38:40 SD: 4.2615 cents 24:26:27:28:30:32:34:36:38:40:42:45:48 S SD: 3.8151 cents 26:28:30 x 33:35:37:39:42:43:46:49:52 SD: 4.7914 cents 27:29:31:32:34:36:38:41:43:44:47:51:54 SD: 3.9764 cents 28:30:32:33:35:37:39:42:45:46:49:53:56 SD: 2.8244 cents 30:32:34:35:38:40:42:45:48:49:53:56:60 SD: 2.7178 cents 36:38:41:42:45:48:51:54:58:59:63:68:72 SD: 2.6504 cents 40:43:46:47:50:53:56:60:64:66:70:75:80 SD: 2.3368 cents 42:45:48:49:53:56:59:63:67:69:74:79:84 SD: 1.9591 cents 45:48:51:53:56:60:63:68:72:74:79:84:90 SD: 1.8291 cents 56:60:64:66:70:75:79:84:90:92:98:105:112 SD: 1.7746 cents 57:61:65:67:71:76:80:86:91:94:100:107:114 SD: 1.3361 cents 72:77:82:84:90:96:101:108:115:119:127:135:144 SD: 1.0907 cents 87:93:99:102:109:116:122:131:139:143:153:163:174 SD: 0.9381 cents 88:94:100:103:110:117:124:132:141:145:155:165:176 SD: 0.6965 cents 116:124:132:136:145:155:163:174:186:191:204:218:232 SD: 0.6599 cents 123:131:140:144:154:164:173:185:197:203:216:231:246 SD: 0.6495 cents 136:145:155:159:170:181:191:204:218:224:239:255:272 SD: 0.6028 cents 140:149:159:164:175:187:197:210:224:231:246:263:280 SD: 0.6006 cents 145:155:165:170:181:193:204:218:232:239:255:272:290 SD: 0.5715 cents 150:160:171:176:188:200:211:225:240:247:264:281:300 SD: 0.5676 cents 152:162:173:178:190:203:214:228:243:250:267:285:304 SD: 0.4636 cents 168:179:191:197:210:224:236:252:269:277:295:315:336 SD: 0.3323 cents 240:256:273:281:300:320:338:360:384:396:422:450:480 SD: 0.3120 cents 256:273:291:300:320:341:360:384:410:422:450:480:512 SD: 0.2466 cents 312:333:355:366:390:416:439:468:499:514:548:585:624 SD: 0.2341 cents 327:349:372:383:409:436:460:491:523:539:575:613:654 SD: 0.2286 cents 360:384:410:422:450:480:506:540:576:593:633:675:720 SD: 0.1806 cents 372:397:423:436:465:496:523:558:595:613:654:698:744 SD: 0.1670 cents 408:435:464:478:510:544:574:612:653:672:717:765:816 SD: 0.1537 cents 480:512:546:563:600:640:675:720:768:791:844:900:960 SD: 0.1397 cents 495:528:563:580:619:660:696:743:792:816:870:928:990 SD: 0.1384 cents 552:589:628:647:690:736:776:828:883:910:970:1035:1104 SD: 0.1072 cents 588:627:669:689:735:784:827:882:941:969:1034:1103:1176 SD: 0.1059 cents 600:640:683:703:750:800:844:900:960:989:1055:1125:1200 SD: 0.1020 cents