Scala analysis: tertiadia6
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: 64/45 609.776284 2nd tritone 7: 1024/675 721.507570 narrow diminished sixth 8: 16384/10125 833.238855 double diminished seventh 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: 16/15 111.7313 minor diatonic semitone 7: 16/15 111.7313 minor diatonic semitone 8: 16/15 111.7313 minor diatonic semitone 9: 34171875/33554432 31.5673 Ampersand's 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: 1 34171875/33554432 31.567 cents Ampersand's comma 1: 1 16875/16384 51.120 cents double augmentation diesis, Negri comma 1: 10 16/15 111.731 cents minor diatonic semitone 2: 2 2278125/2097152 143.299 cents 2: 2 1125/1024 162.851 cents double augmented prime 2: 8 256/225 223.463 cents Neapolitan diminished third 3: 3 151875/131072 255.030 cents 3: 3 75/64 274.582 cents classic augmented second 3: 6 4096/3375 335.194 cents double diminished fourth 4: 4 10125/8192 366.761 cents double augmented second 4: 4 5/4 386.314 cents major third 4: 4 65536/50625 446.925 cents two (Neapolitan diminished third) 5: 5 675/512 478.492 cents wide augmented third 5: 5 4/3 498.045 cents perfect fourth 5: 2 1048576/759375 558.656 cents 6: 6 45/32 590.224 cents diatonic tritone 6: 6 64/45 609.776 cents 2nd tritone 7: 2 759375/524288 641.344 cents 7: 5 3/2 701.955 cents perfect fifth 7: 5 1024/675 721.508 cents narrow diminished sixth 8: 4 50625/32768 753.075 cents 8: 4 8/5 813.686 cents minor sixth 8: 4 16384/10125 833.239 cents double diminished seventh 9: 6 3375/2048 864.806 cents double augmented fifth 9: 3 128/75 925.418 cents diminished seventh 9: 3 262144/151875 944.970 cents 10: 8 225/128 976.537 cents augmented sixth 10: 2 2048/1125 1037.149 cents double diminished octave 10: 2 4194304/2278125 1056.701 cents 11: 10 15/8 1088.269 cents classic major seventh 11: 1 32768/16875 1148.880 cents octave - double augmentation diesis 11: 1 67108864/34171875 1168.433 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.90909 = 32/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 111.7 223.5 274.6 386.3 498.0 609.8 721.5 833.2 864.8 976.5 1088.3 1200.0 111.7 : 111.7 162.9 274.6 386.3 498.0 609.8 721.5 753.1 864.8 976.5 1088.3 1200.0 223.5 : 51.1 162.9 274.6 386.3 498.0 609.8 641.3 753.1 864.8 976.5 1088.3 1200.0 274.6 : 111.7 223.5 335.2 446.9 558.7 590.2 702.0 813.7 925.4 1037.1 1148.9 1200.0 386.3 : 111.7 223.5 335.2 446.9 478.5 590.2 702.0 813.7 925.4 1037.1 1088.3 1200.0 498.0 : 111.7 223.5 335.2 366.8 478.5 590.2 702.0 813.7 925.4 976.5 1088.3 1200.0 609.8 : 111.7 223.5 255.0 366.8 478.5 590.2 702.0 813.7 864.8 976.5 1088.3 1200.0 721.5 : 111.7 143.3 255.0 366.8 478.5 590.2 702.0 753.1 864.8 976.5 1088.3 1200.0 833.2 : 31.6 143.3 255.0 366.8 478.5 590.2 641.3 753.1 864.8 976.5 1088.3 1200.0 864.8 : 111.7 223.5 335.2 446.9 558.7 609.8 721.5 833.2 945.0 1056.7 1168.4 1200.0 976.5 : 111.7 223.5 335.2 446.9 498.0 609.8 721.5 833.2 945.0 1056.7 1088.3 1200.0 1088.3: 111.7 223.5 335.2 386.3 498.0 609.8 721.5 833.2 945.0 976.5 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.5673 .. 111.7313 cents 536870912/512578125, 80.1640 cents 34171875/33554432, 31.5673 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 .. 1168.4327 cents 536870912/512578125, 80.1640 cents 34171875/33554432, 31.5673 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 34171875/33554432, 31.5673 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 16/15, 111.7313 cents Average / Smallest step : 3.167836 Largest / Average step : 1.117313 Largest / Smallest step : 3.539464 Median interval of one step : 16/15, 111.7313 cents, amount: 10 Most common interval of one step : 16/15, 111.7313 cents, amount: 10 Least squares average step : 99.55783 cents, oct.: 1194.69398 cents Scale is strictly proper Scale is 3-distributional even Step pattern alph. order: AABAAAAACAAA Step pattern size order : LLMLLLLLSLLL Scale is a Constant Structure, by a margin of 31.56729 cents Scale diversity : 1.329620 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.315673 Rothenberg efficiency : 0.514153 redundancy: 0.485847 Efficiency x scale size : 6.169841 Number of different interval sizes : 32 = 2.90909 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 2.90909 = 32/11 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: 10 Most common triad is 0.0 111.731 1088.269 cents, amount: 8 Number of recognisable fifths : 5, 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 : 5 = 41.6667% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 8-9 -- Rational properties -- Prime limit : 5 Odd number limit : 34171875 (O: 34171875 U: 34171875) Highest odd numerator or denominator: 10125 Scale harmonicity : 0.012185 Average absolute harmonicity : 0.146267 Specific harmonicity : 0.076855 Fundamental : 1/20736000, -24.3056 octaves, 0.0000 Hz. Guide tone : 55296000, 25.7207 octaves, 14466847258.884 Hz. Exponens Consonantiae : 1.146618E+15, 50.02631 octaves Euler's gradus suavitatis : 64 Sum of Mann's harmonic distance : 17393.0, average 1449.41667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 22.12389, average 1.84366 Sum of Tenney's harmonic distance : 44.40010, average 3.70001 Vogel's harmonic complexity : 37.83333 Wille's k value : 17085937 Wilson's harmonic complexity : 51 Rectangular lattice diameter : 13 Triangular lattice diameter : 13 Lattice compactness : 710.23888, average 9.10563 Lattice compactness (without 2's) : 250.21345, average 3.20786 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -11 .. 14 1.33333 74 1 3: -4 .. 3 -0.50000 20 1 5: -3 .. 3 0.00000 18 10 Average exponent except 2's :-6 / 12 =-0.50000 Average absolute exponent except 2's: 38 / 12 = 3.16667 Scale is weakly epimorphic with val: <12 17 29| Scale is weakly epimorphic with val: <12 19 27| Scale is JI-epimorphic with val: <12 19 28| = patent Scale is weakly epimorphic with val: <12 19 31| Scale is weakly epimorphic with val: <12 21 25| Scale is weakly epimorphic with val: <12 21 29|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 20.6458 c. M:-35.1939 c. Twelve-tone Chromatic (1/11-comma) 15: 1 2 0 2 1 2 1 1 1 1 2 1 N D3 SD: 23.3113 c. M: 34.5824 c. 17: 1 2 1 1 2 1 2 2 0 2 1 2 N D3 SD: 23.8125 c. M: 45.0704 c. 18: 2 1 1 2 1 2 2 1 1 2 1 2 P B D3 SD: 19.6056 c. M: 33.2389 c. 19: 2 2 0 2 2 2 1 2 1 1 2 2 N SD: 19.2188 c. M:-29.1690 c. 20: 2 1 1 2 2 2 2 2 0 2 2 2 N T3 SD: 20.9605 c. M: 43.4626 c. 21: 2 2 1 2 2 2 2 2 0 2 2 2 P D3 SD: 13.1638 c. M:-23.9040 c. 22: 2 2 1 2 2 2 2 2 1 2 2 2 SP B ME SD: 7.5471 c. M: 15.0570 c. Jubilee-12 32: 3 3 1 3 3 3 3 3 1 3 3 3 SP B DE SD: 7.3087 c. M: 12.0824 c. 43: 4 4 2 4 4 4 4 4 1 4 4 4 SP D3 SD: 2.9957 c. M:-4.4873 c. 53: 5 5 2 5 5 5 5 5 1 5 5 5 SP D3 SD: 2.6370 c. M:-4.4970 c. 65: 6 6 3 6 6 6 6 6 2 6 6 6 SP D3 SD: 1.6785 c. M:-2.8862 c. 75: 7 7 3 7 7 7 7 7 2 7 7 7 SP D3 SD: 1.4300 c. M: 2.5824 c. 118: 11 11 5 11 11 11 11 11 3 11 11 11 SP D3 SD: 0.3275 c. M:-0.6595 c. 258: 24 24 11 24 24 24 24 24 7 24 24 24 SP D3 SD: 0.3488 c. M: 0.6807 c. 301: 28 28 13 28 28 28 28 28 8 28 28 28 SP D3 SD: 0.2487 c. M:-0.5006 c. 376: 35 35 16 35 35 35 35 35 10 35 35 35 SP D3 SD: 0.1418 c. M: 0.2601 c. 494: 46 46 21 46 46 46 46 46 13 46 46 46 SP D3 SD: 0.0486 c. M: 0.0885 c. 1106: 103 103 47 103 103 103 103 103 29 103 103 103 SP D3 SD: 0.0429 c. M: 0.0797 c. 1289: 120 120 55 120 120 120 120 120 34 120 120 120 SP D3 SD: 0.0297 c. M:-0.0503 c. 1407: 131 131 60 131 131 131 131 131 37 131 131 131 SP D3 SD: 0.0251 c. M:-0.0444 c. 1783: 166 166 76 166 166 166 166 166 47 166 166 166 SP D3 SD: 0.0188 c. M: 0.0364 c. 1901: 177 177 81 177 177 177 177 177 50 177 177 177 SP D3 SD: 0.0060 c. M:-0.0099 c. 2395: 223 223 102 223 223 223 223 223 63 223 223 223 SP D3 SD: 0.0054 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: 9.7763 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: 5.2546 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 x 11:12 S SD: 8.0584 cents 7 x 8 x 9 x 10 x 11 x 12:13:14 S SD: 12.1483 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 7.6191 cents 9 x 10 x 11:12:13:14 x 15:16:17:18 S SD: 9.1166 cents 10:11 x 12 x 13:14:15:16 x 18:19:20 S SD: 11.2022 cents 11:12 x 13:14:15:16:17 x 18:19:21:22 SD: 9.3826 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.1103 cents 13:14:15 x 16:17:18:20:21 x 23:24:26 SD: 7.9444 cents 14:15:16 x 18:19:20:21 x 23:25:26:28 SD: 7.0176 cents 15:16:17:18:19:20:21:23:24:25:26:28:30 SD: 5.7473 cents 16:17:18:19:20:21:23:24:26 x 28:30:32 SD: 4.5767 cents 17:18:19:20:21:23:24:26 x 28:30:32:34 SD: 4.7032 cents 19:20 x 22:24:25:27:29:31 x 33:36:38 SD: 5.3757 cents 20:21:23 x 25:27:28:30:32:33:35:38:40 SD: 5.4892 cents 21:22:24:25:26:28:30:32:34:35:37:39:42 SD: 4.4434 cents 22:23:25:26:28:29:31:33 x 36:39:41:44 SD: 5.6820 cents 23:25:26:27:29:31:33:35:37:38:40:43:46 SD: 4.1873 cents 24:26:27:28:30:32:34:36:39:40:42:45:48 S SD: 3.8055 cents 26:28:30 x 33:35:37:39:42:43:46:49:52 SD: 4.5196 cents 27:29:31:32:34:36:38:41:44 x 47:51:54 SD: 3.9262 cents 28:30:32:33:35:37:40:42:45:46:49:53:56 SD: 3.1144 cents 29:31:33:34:36:39:41:44:47:48:51:54:58 SD: 2.1948 cents 30:32:34:35:38:40:43:46 x 49:53:56:60 SD: 3.5535 cents 31:33:35:36:39:41:44:47:50:51:54:58:62 SD: 2.7288 cents 36:38:41:42:45:48:51:55:58:59:63:68:72 SD: 2.5782 cents 40:43:46:47:50:53:57:61:65:66:70:75:80 SD: 2.4630 cents 41:44:47:48:51:55:58:62:66:68:72:77:82 SD: 2.3514 cents 42:45:48:49:53:56:60:64:68:69:74:79:84 SD: 2.1123 cents 45:48:51:53:56:60:64:68:73:74:79:84:90 SD: 1.4993 cents 57:61:65:67:71:76:81:86:92:94:100:107:114 SD: 1.2922 cents 71:76:81:83:89:95:101:108:115:117:125:133:142 SD: 1.0929 cents 81:86:92:95:101:108:115:123:131:133:142:152:162 SD: 1.0866 cents 87:93:99:102:109:116:124:132:141:143:153:163:174 SD: 0.7176 cents 116:124:132:136:145:155:165:176:188:191:204:218:232 SD: 0.6147 cents 123:131:140:144:154:164:175:187:199:203:216:231:246 SD: 0.5903 cents 145:155:165:170:181:193:206:220:235:239:255:272:290 SD: 0.5360 cents 151:161:172:177:189:201:215:229:244:249:265:283:302 SD: 0.5130 cents 152:162:173:178:190:203:216:231:246:250:267:285:304 SD: 0.5028 cents 165:176:188:193:206:220:235:250:267:272:290:309:330 SD: 0.5019 cents 168:179:191:197:210:224:239:255:272:277:295:315:336 SD: 0.2990 cents 239:255:272:280:299:319:340:363:387:394:420:448:478 SD: 0.2953 cents 255:272:290:299:319:340:363:387:413:420:448:478:510 SD: 0.2738 cents 256:273:291:300:320:341:364:388:414:422:450:480:512 SD: 0.2608 cents 267:285:304:313:334:356:380:405:432:440:469:501:534 SD: 0.2606 cents 296:316:337:347:370:395:421:449:479:488:520:555:592 SD: 0.2294 cents 327:349:372:383:409:436:465:496:529:539:575:613:654 SD: 0.1661 cents 408:435:464:478:510:544:580:619:660:672:717:765:816 SD: 0.1564 cents 464:495:528:544:580:619:660:704:751:765:816:870:928 SD: 0.1476 cents 495:528:563:580:619:660:704:751:801:816:870:928:990 SD: 0.0976 cents