Scala analysis: tertiadie1
First 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: 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: 64/45 609.776284 2nd tritone 7: 375/256 660.896142 double augmented fourth 8: 25/16 772.627428 classic augmented fifth 9: 5/3 884.358713 major sixth, BP sixth 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: 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: 16/15 111.7313 minor diatonic semitone 7: 16875/16384 51.1199 double augmentation diesis, Negri comma 8: 16/15 111.7313 minor diatonic semitone 9: 16/15 111.7313 minor diatonic semitone 10: 2048/1875 152.7901 double diminished third 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: 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 : 111.7 223.5 274.6 386.3 498.0 609.8 660.9 772.6 884.4 1037.1 1088.3 1200.0 111.7 : 111.7 162.9 274.6 386.3 498.0 549.2 660.9 772.6 925.4 976.5 1088.3 1200.0 223.5 : 51.1 162.9 274.6 386.3 437.4 549.2 660.9 813.7 864.8 976.5 1088.3 1200.0 274.6 : 111.7 223.5 335.2 386.3 498.0 609.8 762.6 813.7 925.4 1037.1 1148.9 1200.0 386.3 : 111.7 223.5 274.6 386.3 498.0 650.8 702.0 813.7 925.4 1037.1 1088.3 1200.0 498.0 : 111.7 162.9 274.6 386.3 539.1 590.2 702.0 813.7 925.4 976.5 1088.3 1200.0 609.8 : 51.1 162.9 274.6 427.4 478.5 590.2 702.0 813.7 864.8 976.5 1088.3 1200.0 660.9 : 111.7 223.5 376.3 427.4 539.1 650.8 762.6 813.7 925.4 1037.1 1148.9 1200.0 772.6 : 111.7 264.5 315.6 427.4 539.1 650.8 702.0 813.7 925.4 1037.1 1088.3 1200.0 884.4 : 152.8 203.9 315.6 427.4 539.1 590.2 702.0 813.7 925.4 976.5 1088.3 1200.0 1037.1: 51.1 162.9 274.6 386.3 437.4 549.2 660.9 772.6 823.7 935.5 1047.2 1200.0 1088.3: 111.7 223.5 335.2 386.3 498.0 609.8 721.5 772.6 884.4 996.1 1148.9 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 : 99.36232 cents, oct.: 1192.34781 cents Scale is strictly proper Step pattern alph. order: AABAAABAACBA Step pattern size order : MMSMMMSMMLSM 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 15 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 25.0000% -- Rational properties -- Prime limit : 5 Odd number limit : 421875 (O: 421875 U: 421875) Highest odd numerator or denominator: 1125 Scale harmonicity : 0.015291 Average absolute harmonicity : 0.155451 Specific harmonicity : 0.095718 Fundamental : 1/288000, -18.1357 octaves, 0.0009 Hz. Guide tone : 768000, 19.5507 octaves, 200928434.151 Hz. Exponens Consonantiae : 2.211840E+11, 37.68646 octaves Euler's gradus suavitatis : 50 Sum of Mann's harmonic distance : 2327.5, average 193.95833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 17.13082, average 1.42757 Sum of Tenney's harmonic distance : 34.16459, average 2.84705 Vogel's harmonic complexity : 29.50000 Wille's k value : 210937 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 9 Triangular lattice diameter : 9 Lattice compactness : 546.37074, average 7.00475 Lattice compactness (without 2's) : 195.01847, average 2.50024 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -8 .. 11 0.75000 55 1 3: -2 .. 1 -0.50000 12 1 5: -3 .. 3 0.25000 17 10 Average exponent except 2's :-3 / 12 =-0.25000 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: 21.7209 c. M:-39.1039 c. Twelve-tone Chromatic (1/11-comma) 15: 1 2 0 2 1 2 0 2 1 2 1 1 N D3 SD: 22.5880 c. M: 34.5824 c. 16: 2 1 1 1 2 1 1 1 2 2 1 1 N D3 SD: 21.4728 c. M:-38.2687 c. 18: 1 2 1 2 1 2 1 1 2 2 1 2 P D3 SD: 25.2463 c. M: 45.0646 c. 19: 1 2 1 2 2 1 1 2 2 2 1 2 P D3 SD: 25.5133 c. M: 48.5734 c. 20: 2 2 1 1 2 2 1 2 2 2 1 2 P D3 SD: 15.1761 c. M: 26.3137 c. 21: 2 2 1 2 2 2 1 2 2 2 1 2 SP B ME SD: 16.5876 c. M:-29.9270 c. 22: 2 2 1 2 2 2 1 2 2 3 1 2 P D3 SD: 6.2520 c. M: 11.6314 c. 31: 3 3 1 3 3 3 1 3 3 4 1 3 P SD: 5.4662 c. M:-9.5786 c. 43: 4 4 2 4 4 4 2 4 4 5 2 4 SP SD: 5.2195 c. M:-8.8713 c. 53: 5 5 2 5 5 5 2 5 5 7 2 5 P SD: 2.4653 c. M:-4.3606 c. 65: 6 6 3 6 6 6 3 6 6 8 3 6 SP SD: 2.0201 c. M:-3.7192 c. 87: 8 8 4 8 8 8 4 8 8 11 4 8 SP SD: 1.7028 c. M: 2.8797 c. 96: 9 9 4 9 9 9 4 9 9 12 4 9 SP SD: 1.6971 c. M:-3.1413 c. 118: 11 11 5 11 11 11 5 11 11 15 5 11 SP SD: 0.2223 c. M:-0.3932 c. 376: 35 35 16 35 35 35 16 35 35 48 16 35 SP SD: 0.1745 c. M: 0.3162 c. 494: 46 46 21 46 46 46 21 46 46 63 21 46 SP SD: 0.0946 c. M: 0.1674 c. 612: 57 57 26 57 57 57 26 57 57 78 26 57 SP SD: 0.0621 c. M: 0.1118 c. 730: 68 68 31 68 68 68 31 68 68 93 31 68 SP SD: 0.0624 c. M:-0.1114 c. 1171: 109 109 50 109 109 109 50 109 109 149 50 109 SP SD: 0.0475 c. M: 0.0865 c. 1289: 120 120 55 120 120 120 55 120 120 164 55 120 SP SD: 0.0436 c. M:-0.0814 c. 1407: 131 131 60 131 131 131 60 131 131 179 60 131 SP SD: 0.0482 c. M:-0.0847 c. 1547: 144 144 66 144 144 144 66 144 144 197 66 144 SP SD: 0.0436 c. M: 0.0801 c. 1665: 155 155 71 155 155 155 71 155 155 212 71 155 SP SD: 0.0255 c. M: 0.0466 c. 1783: 166 166 76 166 166 166 76 166 166 227 76 166 SP SD: 0.0117 c. M: 0.0204 c. 1901: 177 177 81 177 177 177 81 177 177 242 81 177 SP SD: 0.0111 c. M:-0.0192 c. 2395: 223 223 102 223 223 223 102 223 223 305 102 223 SP SD: 0.0108 c. M: 0.0193 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: 20.5294 cents 3 x x x x 4 x x x 5 x x 6 S SD: 0.0000 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 19.9278 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 13.4124 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 7.2543 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.3488 cents 8 x 9 x 10:11 x 12 x 13 x 15:16 SD: 11.8039 cents 9 x 10 x 11:12 x 13:14:15:16:17:18 S SD: 8.3868 cents 10:11 x 12 x 13:14:15:16:17:18:19:20 S SD: 11.2443 cents 11:12 x 13:14:15 x 16:17:18:20:21:22 S SD: 8.1921 cents 12:13 x 14:15:16:17:18:19:20:22:23:24 S SD: 6.1888 cents 13:14:15 x 16:17:18:19:20:22:24 x 26 S SD: 8.3010 cents 14:15:16 x 18:19:20:21:22:23:25:26:28 SD: 7.7599 cents 15:16:17:18:19:20:21:22:23:25:27:28:30 SD: 5.5973 cents 16:17:18:19:20:21:23 x 25:27:29:30:32 SD: 4.5991 cents 18:19:20:21:23:24 x 26:28:30:33:34:36 SD: 6.0869 cents 19:20 x 22:24:25:27:28:30:32:35:36:38 SD: 5.2442 cents 20:21:23 x 25:27:28:29:31:33:36:38:40 SD: 5.7543 cents 21:22:24:25:26:28:30:31:33:35:38:39:42 SD: 4.3847 cents 23:25:26:27:29:31:33:34:36:38:42:43:46 SD: 4.2051 cents 24:26:27:28:30:32:34:35:38:40:44:45:48 SD: 3.6729 cents 26:28:30 x 33:35:37:38:41:43:47:49:52 SD: 4.5560 cents 27:29:31:32:34:36:38:40:42:45:49:51:54 SD: 3.6307 cents 28:30:32:33:35:37:40:41:44:47:51:53:56 SD: 2.6829 cents 36:38:41:42:45:48:51:53:56:60:66:68:72 SD: 2.4783 cents 41:44:47:48:51:55:58:60:64:68:75:77:82 SD: 2.2138 cents 43:46:49:50:54:57:61:63:67:72:78:81:86 SD: 2.0252 cents 45:48:51:53:56:60:64:66:70:75:82:84:90 SD: 1.4612 cents 57:61:65:67:71:76:81:83:89:95:104:107:114 SD: 1.2953 cents 64:68:73:75:80:85:91:94:100:107:117:120:128 SD: 1.2199 cents 71:76:81:83:89:95:101:104:111:118:129:133:142 SD: 1.1067 cents 75:80:85:88:94:100:107:110:117:125:137:141:150 SD: 1.0848 cents 80:85:91:94:100:107:114:117:125:133:146:150:160 SD: 1.0312 cents 87:93:99:102:109:116:124:127:136:145:158:163:174 SD: 0.8330 cents 93:99:106:109:116:124:132:136:145:155:169:174:186 SD: 0.8061 cents 105:112:119:123:131:140:149:154:164:175:191:197:210 SD: 0.7465 cents 116:124:132:136:145:155:165:170:181:193:211:218:232 SD: 0.6539 cents 123:131:140:144:154:164:175:180:192:205:224:231:246 SD: 0.4763 cents 151:161:172:177:189:201:215:221:236:252:275:283:302 SD: 0.4622 cents 168:179:191:197:210:224:239:246:263:280:306:315:336 SD: 0.3643 cents 228:243:259:267:285:304:324:334:356:380:415:428:456 SD: 0.3613 cents 239:255:272:280:299:319:340:350:373:398:435:448:478 SD: 0.3007 cents 240:256:273:281:300:320:341:352:375:400:437:450:480 SD: 0.2659 cents 256:273:291:300:320:341:364:375:400:427:466:480:512 SD: 0.2307 cents 297:317:338:348:371:396:422:435:464:495:541:557:594 SD: 0.2178 cents 327:349:372:383:409:436:465:479:511:545:595:613:654 SD: 0.1652 cents 407:434:463:477:509:543:579:596:636:678:741:763:814 SD: 0.1589 cents 464:495:528:544:580:619:660:680:725:773:845:870:928 SD: 0.1507 cents 495:528:563:580:619:660:704:725:773:825:901:928:990 SD: 0.1191 cents