Scala analysis: tertiadie2
Second 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: 5625/4096 549.164857 double augmented third 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: 16875/16384 51.1199 double augmentation diesis, Negri comma 7: 2048/1875 152.7901 double diminished third 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: 3 16875/16384 51.120 cents double augmentation diesis, Negri comma 1: 8 16/15 111.731 cents minor diatonic semitone 1: 1 2048/1875 152.790 cents double diminished third 2: 5 1125/1024 162.851 cents double augmented prime 2: 1 9/8 203.910 cents major whole tone 2: 5 256/225 223.463 cents Neapolitan diminished third 2: 1 32768/28125 264.521 cents 3: 7 75/64 274.582 cents classic augmented second 3: 2 6/5 315.641 cents minor third 3: 2 4096/3375 335.194 cents double diminished fourth 3: 1 524288/421875 376.253 cents 4: 8 5/4 386.314 cents major third 4: 4 32/25 427.373 cents classic diminished fourth 5: 2 84375/65536 437.434 cents 5: 1 675/512 478.492 cents wide augmented third 5: 5 4/3 498.045 cents perfect fourth 5: 4 512/375 539.104 cents double diminished fifth 6: 3 5625/4096 549.165 cents double augmented third 6: 3 45/32 590.224 cents diatonic tritone 6: 3 64/45 609.776 cents 2nd tritone 6: 3 8192/5625 650.835 cents double diminished sixth 7: 4 375/256 660.896 cents double augmented fourth 7: 5 3/2 701.955 cents perfect fifth 7: 1 1024/675 721.508 cents narrow diminished sixth 7: 2 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: 1 421875/262144 823.747 cents 9: 2 3375/2048 864.806 cents double augmented fifth 9: 2 5/3 884.359 cents major sixth, BP sixth 9: 7 128/75 925.418 cents diminished seventh 10: 1 28125/16384 935.479 cents 10: 5 225/128 976.537 cents augmented sixth 10: 1 16/9 996.090 cents Pythagorean minor seventh 10: 5 2048/1125 1037.149 cents double diminished octave 11: 1 1875/1024 1047.210 cents double augmented sixth 11: 8 15/8 1088.269 cents classic major seventh 11: 3 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 : 111.7 162.9 274.6 386.3 498.0 549.2 702.0 813.7 925.4 976.5 1088.3 1200.0 111.7 : 51.1 162.9 274.6 386.3 437.4 590.2 702.0 813.7 864.8 976.5 1088.3 1200.0 162.9 : 111.7 223.5 335.2 386.3 539.1 650.8 762.6 813.7 925.4 1037.1 1148.9 1200.0 274.6 : 111.7 223.5 274.6 427.4 539.1 650.8 702.0 813.7 925.4 1037.1 1088.3 1200.0 386.3 : 111.7 162.9 315.6 427.4 539.1 590.2 702.0 813.7 925.4 976.5 1088.3 1200.0 498.0 : 51.1 203.9 315.6 427.4 478.5 590.2 702.0 813.7 864.8 976.5 1088.3 1200.0 549.2 : 152.8 264.5 376.3 427.4 539.1 650.8 762.6 813.7 925.4 1037.1 1148.9 1200.0 702.0 : 111.7 223.5 274.6 386.3 498.0 609.8 660.9 772.6 884.4 996.1 1047.2 1200.0 813.7 : 111.7 162.9 274.6 386.3 498.0 549.2 660.9 772.6 884.4 935.5 1088.3 1200.0 925.4 : 51.1 162.9 274.6 386.3 437.4 549.2 660.9 772.6 823.7 976.5 1088.3 1200.0 976.5 : 111.7 223.5 335.2 386.3 498.0 609.8 721.5 772.6 925.4 1037.1 1148.9 1200.0 1088.3: 111.7 223.5 274.6 386.3 498.0 609.8 660.9 813.7 925.4 1037.1 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.1199 .. 152.7901 cents 33554432/31640625, 101.6703 cents 16875/16384, 51.1199 cents 2: 162.8511 .. 264.5214 cents 33554432/31640625, 101.6703 cents 2109375/2097152, 10.0610 cents 3: 274.5824 .. 376.2527 cents 33554432/31640625, 101.6703 cents 2109375/2097152, 10.0610 cents 4: 386.3137 .. 427.3726 cents 128/125, 41.0589 cents 2109375/2097152, 10.0610 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: 823.7473 .. 925.4176 cents 33554432/31640625, 101.6703 cents 2109375/2097152, 10.0610 cents 10: 935.4786 .. 1037.1489 cents 33554432/31640625, 101.6703 cents 2109375/2097152, 10.0610 cents 11: 1047.2099 .. 1148.8801 cents 33554432/31640625, 101.6703 cents 2109375/2097152, 10.0610 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 : 2048/1875, 152.7901 cents Average / Smallest step : 1.956187 Largest / Average step : 1.527901 Largest / Smallest step : 2.988861 Median interval of one step : 16/15, 111.7313 cents, amount: 8 Most common interval of one step : 16/15, 111.7313 cents, amount: 8 Least squares average step : 99.19987 cents, oct.: 1190.39840 cents Scale is strictly proper Step pattern alph. order: ABAAABCAABAA Step pattern size order : MSMMMSLMMSMM Scale is a Constant Structure, by a margin of 10.06100 cents Scale diversity : 1.380592 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.169041 Rothenberg efficiency : 0.387296 redundancy: 0.612704 Efficiency x scale size : 4.647547 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 : 2109375/2097152, 10.0610 cents Number of recognisable fifths : 5, 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% -- Rational properties -- Prime limit : 5 Odd number limit : 421875 (O: 421875 U: 421875) Highest odd numerator or denominator: 5625 Scale harmonicity : 0.015291 Average absolute harmonicity : 0.171248 Specific harmonicity : 0.095286 Fundamental : 1/307200, -18.2288 octaves, 0.0009 Hz. Guide tone : 720000, 19.4576 octaves, 188370407.017 Hz. Exponens Consonantiae : 2.211840E+11, 37.68646 octaves Euler's gradus suavitatis : 50 Sum of Mann's harmonic distance : 6328.0, average 527.33333 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 17.60795, average 1.46733 Sum of Tenney's harmonic distance : 35.06768, average 2.92231 Vogel's harmonic complexity : 28.25000 Wille's k value : 210937 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 9 Triangular lattice diameter : 9 Lattice compactness : 553.23687, average 7.09278 Lattice compactness (without 2's) : 194.91411, average 2.49890 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -12 .. 7 -2.00000 58 1 3: -1 .. 2 0.50000 12 2 5: -2 .. 4 0.75000 17 9 Average exponent except 2's : 15 / 12 = 1.25000 Average absolute exponent except 2's: 29 / 12 = 2.41667 Scale is weakly epimorphic with val: <12 17 28| Scale is JI-epimorphic with val: <12 19 28| = patent 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: 23.2099 c. M:-50.8351 c. Twelve-tone Chromatic (1/11-comma) 13: 1 1 1 1 1 1 2 1 1 1 1 1 P M ME SD: 22.3966 c. M:-38.8472 c. 15: 1 1 1 2 1 1 2 1 2 0 2 1 N SD: 22.0426 c. M: 34.5824 c. 17: 2 0 2 1 2 1 2 2 1 1 1 2 N SD: 20.3332 c. M: 33.3725 c. 18: 2 0 2 2 1 1 3 1 2 1 1 2 N SD: 20.5647 c. M: 31.3783 c. 19: 2 1 1 2 2 1 2 2 2 0 2 2 N SD: 17.1567 c. M: 29.1690 c. 20: 2 1 2 1 2 1 3 2 1 1 2 2 N SD: 18.5213 c. M:-26.3137 c. 21: 2 1 2 2 2 1 2 2 2 1 2 2 SP B ME SD: 12.1050 c. M:-22.2637 c. Twelve-tone Chromatic 22: 2 1 2 2 2 1 3 2 2 1 2 2 P D3 SD: 4.1368 c. M:-7.1359 c. 43: 4 2 4 4 4 2 5 4 4 2 4 4 SP SD: 4.2529 c. M:-8.9747 c. 53: 5 2 5 5 5 2 7 5 5 2 5 5 P SD: 2.6768 c. M: 5.7686 c. 65: 6 3 6 6 6 3 8 6 6 3 6 6 SP SD: 2.1111 c. M:-4.6813 c. 74: 7 3 7 7 7 3 9 7 7 3 7 7 SP SD: 2.6868 c. M:-4.6577 c. 75: 7 3 7 7 7 3 10 7 7 3 7 7 P SD: 2.3743 c. M: 5.1649 c. 87: 8 4 8 8 8 4 11 8 8 4 8 8 SP SD: 1.6570 c. M:-2.7729 c. 96: 9 4 9 9 9 4 12 9 9 4 9 9 SP SD: 1.1245 c. M: 1.9550 c. 118: 11 5 11 11 11 5 15 11 11 5 11 11 SP SD: 0.1564 c. M: 0.2662 c. 376: 35 16 35 35 35 16 48 35 35 16 35 35 SP SD: 0.1264 c. M: 0.2287 c. 494: 46 21 46 46 46 21 63 46 46 21 46 46 SP SD: 0.0813 c. M: 0.1770 c. 612: 57 26 57 57 57 26 78 57 57 26 57 57 SP SD: 0.0663 c. M: 0.1452 c. 730: 68 31 68 68 68 31 93 68 68 31 68 68 SP SD: 0.0666 c. M: 0.1238 c. 848: 79 36 79 79 79 36 108 79 79 36 79 79 SP SD: 0.0723 c. M: 0.1223 c. 1053: 98 45 98 98 98 45 134 98 98 45 98 98 SP SD: 0.0669 c. M:-0.1229 c. 1171: 109 50 109 109 109 50 149 109 109 50 109 109 SP SD: 0.0522 c. M:-0.1093 c. 1289: 120 55 120 120 120 55 164 120 120 55 120 120 SP SD: 0.0438 c. M:-0.0981 c. 1407: 131 60 131 131 131 60 179 131 131 60 131 131 SP SD: 0.0410 c. M:-0.0889 c. 1525: 142 65 142 142 142 65 194 142 142 65 142 142 SP SD: 0.0422 c. M:-0.0810 c. 1547: 144 66 144 144 144 66 197 144 144 66 144 144 SP SD: 0.0346 c. M:-0.0624 c. 1665: 155 71 155 155 155 71 212 155 155 71 155 155 SP SD: 0.0219 c. M:-0.0391 c. 1783: 166 76 166 166 166 76 227 166 166 76 166 166 SP SD: 0.0123 c. M:-0.0219 c. 1901: 177 81 177 177 177 81 242 177 177 81 177 177 SP SD: 0.0092 c. M:-0.0198 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: 13.3921 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: 14.4546 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 6.2129 cents 9 x 10 x 11:12 x x 14:15:16:17:18 S SD: 10.0824 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.3554 cents 11 x 12:13:14 x 15:17:18:19 x 21:22 SD: 9.3458 cents 12 x 13:14:15:16 x 18:19:20:21:23:24 SD: 6.4581 cents 13:14 x 15:16:17:18:20:21:22:23:24:26 S SD: 7.2176 cents 14:15 x 16:18 x 19:21:22:24:25:26:28 SD: 8.2413 cents 15:16 x 18:19:20:21:23:24 x 26:28:30 SD: 7.3624 cents 16:17:18:19:20:21:22:24:26:27:28:30:32 S SD: 5.3798 cents 17:18:19:20:21:23 x 26:27:29:30:32:34 SD: 5.4058 cents 18:19:20:21:23:24:25:27:29:31:32:34:36 SD: 4.9556 cents 20:21:22:23:25:27 x 30:32:34:35:38:40 SD: 4.9005 cents 23 x 25:27:29:31:32:35:37:39:40:43:46 SD: 4.6682 cents 24 x 26:28:30:32:33:36:38:41:42:45:48 SD: 2.9381 cents 25:27 x 29:31:33:34:38:40:43:44:47:50 SD: 4.3468 cents 27:29:30:32:34:36:37:41:43:46:47:51:54 SD: 3.7809 cents 28:30:31:33:35:37:38:42:45:48:49:53:56 SD: 3.1659 cents 30:32:33:35:38:40:41:45:48:51:53:56:60 SD: 2.4167 cents 40:43:44:47:50:53:55:60:64:68:70:75:80 SD: 1.7385 cents 48:51:53:56:60:64:66:72:77:82:84:90:96 SD: 1.3649 cents 70:75:77:82:88:93:96:105:112:119:123:131:140 SD: 1.3514 cents 72:77:79:84:90:96:99:108:115:123:127:135:144 SD: 0.9751 cents 88:94:97:103:110:117:121:132:141:150:155:165:176 SD: 0.8123 cents 104:111:114:122:130:139:143:156:166:177:183:195:208 SD: 0.7691 cents 112:119:123:131:140:149:154:168:179:191:197:210:224 SD: 0.7617 cents 120:128:132:141:150:160:165:180:192:205:211:225:240 SD: 0.4834 cents 152:162:167:178:190:203:209:228:243:259:267:285:304 SD: 0.4360 cents 180:192:198:211:225:240:247:270:288:307:316:338:360 SD: 0.3680 cents 192:205:211:225:240:256:264:288:307:328:338:360:384 SD: 0.3579 cents 222:237:244:260:278:296:305:333:355:379:390:416:444 SD: 0.3479 cents 240:256:264:281:300:320:330:360:384:410:422:450:480 SD: 0.3202 cents 252:269:277:295:315:336:346:378:403:430:443:473:504 SD: 0.2657 cents 273:291:300:320:341:364:375:410:437:466:480:512:546 SD: 0.2513 cents 327:349:359:383:409:436:449:491:523:558:575:613:654 SD: 0.2441 cents 343:366:377:402:429:457:471:515:549:585:603:643:686 SD: 0.2410 cents 344:367:378:403:430:459:472:516:550:587:605:645:688 SD: 0.2176 cents 348:371:382:408:435:464:478:522:557:594:612:653:696 SD: 0.2143 cents 372:397:409:436:465:496:511:558:595:635:654:698:744 SD: 0.1823 cents 408:435:448:478:510:544:560:612:653:696:717:765:816 SD: 0.1605 cents 495:528:544:580:619:660:680:743:792:845:870:928:990 SD: 0.1397 cents 528:563:580:619:660:704:725:792:845:901:928:990:1056 SD: 0.0932 cents 600:640:659:703:750:800:824:900:960:1024:1055:1125:1200 SD: 0.0637 cents