Scala analysis: tertiadie3
Third Tertiadie 262144/253125 128/125 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: 1125/1024 162.851143 double augmented prime 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: 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: 16875/16384 51.1199 double augmentation diesis, Negri comma 3: 16/15 111.7313 minor diatonic semitone 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: 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: 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: 8 5/4 386.314 cents major third 4: 4 32/25 427.373 cents classic diminished fourth 5: 1 84375/65536 437.434 cents 5: 2 675/512 478.492 cents wide augmented third 5: 6 4/3 498.045 cents perfect fourth 5: 3 512/375 539.104 cents double diminished fifth 6: 2 5625/4096 549.165 cents double augmented third 6: 4 45/32 590.224 cents diatonic tritone 6: 4 64/45 609.776 cents 2nd tritone 6: 2 8192/5625 650.835 cents double diminished sixth 7: 3 375/256 660.896 cents double augmented fourth 7: 6 3/2 701.955 cents perfect fifth 7: 2 1024/675 721.508 cents narrow diminished sixth 7: 1 131072/84375 762.566 cents 8: 4 25/16 772.627 cents classic augmented fifth 8: 8 8/5 813.686 cents minor sixth 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: 3.09091 = 34/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 111.7 162.9 274.6 386.3 498.0 590.2 702.0 813.7 925.4 976.5 1088.3 1200.0 111.7 : 51.1 162.9 274.6 386.3 478.5 590.2 702.0 813.7 864.8 976.5 1088.3 1200.0 162.9 : 111.7 223.5 335.2 427.4 539.1 650.8 762.6 813.7 925.4 1037.1 1148.9 1200.0 274.6 : 111.7 223.5 315.6 427.4 539.1 650.8 702.0 813.7 925.4 1037.1 1088.3 1200.0 386.3 : 111.7 203.9 315.6 427.4 539.1 590.2 702.0 813.7 925.4 976.5 1088.3 1200.0 498.0 : 92.2 203.9 315.6 427.4 478.5 590.2 702.0 813.7 864.8 976.5 1088.3 1200.0 590.2 : 111.7 223.5 335.2 386.3 498.0 609.8 721.5 772.6 884.4 996.1 1107.8 1200.0 702.0 : 111.7 223.5 274.6 386.3 498.0 609.8 660.9 772.6 884.4 996.1 1088.3 1200.0 813.7 : 111.7 162.9 274.6 386.3 498.0 549.2 660.9 772.6 884.4 976.5 1088.3 1200.0 925.4 : 51.1 162.9 274.6 386.3 437.4 549.2 660.9 772.6 864.8 976.5 1088.3 1200.0 976.5 : 111.7 223.5 335.2 386.3 498.0 609.8 721.5 813.7 925.4 1037.1 1148.9 1200.0 1088.3: 111.7 223.5 274.6 386.3 498.0 609.8 702.0 813.7 925.4 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: 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: 386.3137 .. 427.3726 cents 128/125, 41.0589 cents 16875/16384, 51.1199 cents 5: 437.4336 .. 539.1039 cents 33554432/31640625, 101.6703 cents 2109375/2097152, 10.0610 cents 6: 549.1649 .. 650.8351 cents 33554432/31640625, 101.6703 cents 2109375/2097152, 10.0610 cents 7: 660.8961 .. 762.5664 cents 33554432/31640625, 101.6703 cents 2109375/2097152, 10.0610 cents 8: 772.6274 .. 813.6863 cents 128/125, 41.0589 cents 2109375/2097152, 10.0610 cents 9: 864.8061 .. 925.4176 cents 262144/253125, 60.6114 cents 16875/16384, 51.1199 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 : 99.57887 cents, oct.: 1194.94646 cents Scale is strictly proper Step pattern alph. order: ABAAACAAABAA Step pattern size order : LSLLLMLLLSLL Scale is a Constant Structure, by a margin of 10.06100 cents Scale diversity : 1.365792 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.374336 Rothenberg efficiency : 0.439743 redundancy: 0.560257 Efficiency x scale size : 5.276912 Number of different interval sizes : 34 = 3.09091 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.09091 = 34/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 2109375/2097152, 10.0610 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 a complete diamond : 1 5 15 75 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% Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties -- Prime limit : 5 Odd number limit : 84375 (O: 84375 U: 84375) Highest odd numerator or denominator: 1125 Scale harmonicity : 0.017544 Average absolute harmonicity : 0.174287 Specific harmonicity : 0.110718 Fundamental : 1/76800, -16.2288 octaves, 0.0034 Hz. Guide tone : 144000, 17.1357 octaves, 37674081.403 Hz. Exponens Consonantiae : 1.105920E+10, 33.36453 octaves Euler's gradus suavitatis : 44 Sum of Mann's harmonic distance : 1506.0, average 125.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 15.51104, average 1.29259 Sum of Tenney's harmonic distance : 30.86356, average 2.57196 Vogel's harmonic complexity : 25.58333 Wille's k value : 42187 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 8 Triangular lattice diameter : 8 Lattice compactness : 482.66699, average 6.18804 Lattice compactness (without 2's) : 174.05798, average 2.23151 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -10 .. 7 -1.41667 51 1 3: -1 .. 2 0.50000 12 2 5: -2 .. 3 0.50000 14 9 Average exponent except 2's : 12 / 12 = 1.00000 Average absolute exponent except 2's: 26 / 12 = 2.16667 Scale is weakly epimorphic with val: <12 17 28| Scale is weakly epimorphic with val: <12 19 26| Scale is JI-epimorphic with val: <12 19 28| = patent Scale is weakly epimorphic with val: <12 20 25| Scale is weakly epimorphic with val: <12 20 31| 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: 18.2019 c. M:-37.1489 c. Twelve-tone Chromatic (1/11-comma) 21: 2 1 2 2 2 1 2 2 2 1 2 2 SP B ME SD: 11.6045 c. M: 18.7951 c. Twelve-tone Chromatic 22: 2 1 2 2 2 2 2 2 2 1 2 2 P D3 SD: 4.8919 c. M:-9.7763 c. 31: 3 1 3 3 3 2 3 3 3 1 3 3 P SD: 5.4239 c. M: 9.5786 c. 43: 4 2 4 4 4 3 4 4 4 2 4 4 SP SD: 3.5817 c. M:-4.5907 c. 53: 5 2 5 5 5 4 5 5 5 2 5 5 P SD: 2.1426 c. M: 4.3606 c. 65: 6 3 6 6 6 5 6 6 6 3 6 6 SP SD: 1.6295 c. M:-3.3027 c. 75: 7 3 7 7 7 6 7 7 7 3 7 7 P SD: 1.9176 c. M: 2.8511 c. 87: 8 4 8 8 8 7 8 8 8 4 8 8 SP SD: 1.7003 c. M:-2.8797 c. 96: 9 4 9 9 9 7 9 9 9 4 9 9 SP SD: 1.3508 c. M: 2.7237 c. 118: 11 5 11 11 11 9 11 11 11 5 11 11 SP SD: 0.1932 c. M: 0.3932 c. 376: 35 16 35 35 35 29 35 35 35 16 35 35 SP SD: 0.1225 c. M:-0.2018 c. 494: 46 21 46 46 46 38 46 46 46 21 46 46 SP SD: 0.0655 c. M: 0.0981 c. 612: 57 26 57 57 57 47 57 57 57 26 57 57 SP SD: 0.0520 c. M: 0.1060 c. 1171: 109 50 109 109 109 90 109 109 109 50 109 109 SP SD: 0.0432 c. M:-0.0865 c. 1289: 120 55 120 120 120 99 120 120 120 55 120 120 SP SD: 0.0334 c. M:-0.0658 c. 1407: 131 60 131 131 131 108 131 131 131 60 131 131 SP SD: 0.0332 c. M:-0.0486 c. 1665: 155 71 155 155 155 128 155 155 155 71 155 155 SP SD: 0.0247 c. M:-0.0466 c. 1783: 166 76 166 166 166 137 166 166 166 76 166 166 SP SD: 0.0117 c. M:-0.0204 c. 1901: 177 81 177 177 177 146 177 177 177 81 177 177 SP SD: 0.0076 c. M:-0.0105 c. 2395: 223 102 223 223 223 184 223 223 223 102 223 223 SP SD: 0.0075 c. M: 0.0119 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: 13.6863 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: 9.5145 cents 7 x x 8:9 x 10 x 11:12 x 13:14 S SD: 11.3508 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 7.8853 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 10.3389 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.6998 cents 11 x 12:13:14:15 x 17:18:19 x 21:22 SD: 10.2074 cents 12 x 13:14:15:16:17:18:19:20:21:23:24 SD: 5.9848 cents 13:14 x 15:16:17:18:20:21:22:23:24:26 S SD: 7.5085 cents 14:15 x 16:18:19:20:21:22:24:25:26:28 S SD: 8.1590 cents 15:16 x 18:19:20:21:23:24 x 26:28:30 SD: 6.6090 cents 16:17:18:19:20:21:23:24:26:27:28:30:32 SD: 6.2422 cents 17:18:19:20:21:23:24:26:27:29:30:32:34 SD: 4.9874 cents 20:21:22:23:25:27:28:30:32:34:35:38:40 SD: 4.5379 cents 23 x 25:27:29:31:32:35:37:39:40:43:46 SD: 4.5181 cents 24 x 26:28:30:32:34:36:38:41:42:45:48 SD: 3.1533 cents 25:27 x 29:31:33:35:38:40:43:44:47:50 SD: 4.1283 cents 27:29:30:32:34:36:38:41:43:46:47:51:54 SD: 3.7703 cents 28:30:31:33:35:37:39:42:45:48:49:53:56 SD: 3.0029 cents 30:32:33:35:38:40:42:45:48:51:53:56:60 SD: 2.4014 cents 40:43:44:47:50:53:56:60:64:68:70:75:80 SD: 1.8448 cents 48:51:53:56:60:64:68:72:77:82:84:90:96 SD: 1.7218 cents 57:61:63:67:71:76:80:86:91:97:100:107:114 SD: 1.6109 cents 59:63:65:69:74:79:83:89:94:101:104:111:118 SD: 1.5850 cents 60:64:66:70:75:80:84:90:96:102:105:113:120 SD: 1.4139 cents 64:68:70:75:80:85:90:96:102:109:113:120:128 SD: 1.3670 cents 71:76:78:83:89:95:100:107:114:121:125:133:142 SD: 1.2961 cents 72:77:79:84:90:96:101:108:115:123:127:135:144 SD: 1.0227 cents 88:94:97:103:110:117:124:132:141:150:155:165:176 SD: 0.8440 cents 103:110:113:121:129:137:145:155:165:176:181:193:206 SD: 0.8438 cents 104:111:114:122:130:139:146:156:166:177:183:195:208 SD: 0.7875 cents 120:128:132:141:150:160:169:180:192:205:211:225:240 SD: 0.4971 cents 152:162:167:178:190:203:214:228:243:259:267:285:304 SD: 0.4316 cents 180:192:198:211:225:240:253:270:288:307:316:338:360 SD: 0.3576 cents 192:205:211:225:240:256:270:288:307:328:338:360:384 SD: 0.3097 cents 252:269:277:295:315:336:354:378:403:430:443:473:504 SD: 0.3051 cents 256:273:281:300:320:341:360:384:410:437:450:480:512 SD: 0.2416 cents 344:367:378:403:430:459:484:516:550:587:605:645:688 SD: 0.1924 cents 372:397:409:436:465:496:523:558:595:635:654:698:744 SD: 0.1816 cents 408:435:448:478:510:544:574:612:653:696:717:765:816 SD: 0.1537 cents 495:528:544:580:619:660:696:743:792:845:870:928:990 SD: 0.1331 cents 588:627:646:689:735:784:827:882:941:1004:1034:1103:1176 SD: 0.1263 cents 600:640:659:703:750:800:844:900:960:1024:1055:1125:1200 SD: 0.0765 cents