Scala analysis: tertiadia4
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: 6/5 315.641287 minor third 4: 10125/8192 366.761145 double augmented second 5: 675/512 478.492430 wide augmented third 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: 16/15 111.7313 minor diatonic semitone 3: 135/128 92.1787 major chroma, major limma 4: 16875/16384 51.1199 double augmentation diesis, Negri comma 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: 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: 1 2278125/2097152 143.299 cents 2: 3 1125/1024 162.851 cents double augmented prime 2: 1 9/8 203.910 cents major whole tone 2: 7 256/225 223.463 cents Neapolitan diminished third 3: 2 151875/131072 255.030 cents 3: 4 75/64 274.582 cents classic augmented second 3: 1 6/5 315.641 cents minor third 3: 5 4096/3375 335.194 cents double diminished fourth 4: 3 10125/8192 366.761 cents double augmented second 4: 5 5/4 386.314 cents major third 4: 1 32/25 427.373 cents classic diminished fourth 4: 3 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: 3 50625/32768 753.075 cents 8: 1 25/16 772.627 cents classic augmented fifth 8: 5 8/5 813.686 cents minor sixth 8: 3 16384/10125 833.239 cents double diminished seventh 9: 5 3375/2048 864.806 cents double augmented fifth 9: 1 5/3 884.359 cents major sixth, BP sixth 9: 4 128/75 925.418 cents diminished seventh 9: 2 262144/151875 944.970 cents 10: 7 225/128 976.537 cents augmented sixth 10: 1 16/9 996.090 cents Pythagorean minor seventh 10: 3 2048/1125 1037.149 cents double diminished octave 10: 1 4194304/2278125 1056.701 cents 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: 3.63636 = 40/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 111.7 223.5 315.6 366.8 478.5 590.2 702.0 813.7 925.4 976.5 1088.3 1200.0 111.7 : 111.7 203.9 255.0 366.8 478.5 590.2 702.0 813.7 864.8 976.5 1088.3 1200.0 223.5 : 92.2 143.3 255.0 366.8 478.5 590.2 702.0 753.1 864.8 976.5 1088.3 1200.0 315.6 : 51.1 162.9 274.6 386.3 498.0 609.8 660.9 772.6 884.4 996.1 1107.8 1200.0 366.8 : 111.7 223.5 335.2 446.9 558.7 609.8 721.5 833.2 945.0 1056.7 1148.9 1200.0 478.5 : 111.7 223.5 335.2 446.9 498.0 609.8 721.5 833.2 945.0 1037.1 1088.3 1200.0 590.2 : 111.7 223.5 335.2 386.3 498.0 609.8 721.5 833.2 925.4 976.5 1088.3 1200.0 702.0 : 111.7 223.5 274.6 386.3 498.0 609.8 721.5 813.7 864.8 976.5 1088.3 1200.0 813.7 : 111.7 162.9 274.6 386.3 498.0 609.8 702.0 753.1 864.8 976.5 1088.3 1200.0 925.4 : 51.1 162.9 274.6 386.3 498.0 590.2 641.3 753.1 864.8 976.5 1088.3 1200.0 976.5 : 111.7 223.5 335.2 446.9 539.1 590.2 702.0 813.7 925.4 1037.1 1148.9 1200.0 1088.3: 111.7 223.5 335.2 427.4 478.5 590.2 702.0 813.7 925.4 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: 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 .. 1148.8801 cents 262144/253125, 60.6114 cents 34171875/33554432, 31.5673 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 : 99.68414 cents, oct.: 1196.20972 cents Scale is strictly proper Step pattern alph. order: AABCAAAAACAA Step pattern size order : LLMSLLLLLSLL Scale is a Constant Structure, by a margin of 31.56729 cents Scale diversity : 1.449081 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.348261 Rothenberg efficiency : 0.393353 redundancy: 0.606647 Efficiency x scale size : 4.720238 Number of different interval sizes : 40 = 3.63636 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.63636 = 40/11 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: 7 Number of recognisable fifths : 6, 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% -- Rational properties -- Prime limit : 5 Odd number limit : 2278125 (O: 2278125 U: 2278125) Highest odd numerator or denominator: 10125 Scale harmonicity : 0.014493 Average absolute harmonicity : 0.156421 Specific harmonicity : 0.088934 Fundamental : 1/1843200, -20.8138 octaves, 0.0001 Hz. Guide tone : 2592000, 21.3056 octaves, 678133465.260 Hz. Exponens Consonantiae : 4.777574E+12, 42.11942 octaves Euler's gradus suavitatis : 54 Sum of Mann's harmonic distance : 10352.0, average 862.66667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 19.29458, average 1.60788 Sum of Tenney's harmonic distance : 38.43556, average 3.20296 Vogel's harmonic complexity : 31.16667 Wille's k value : 1139062 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 11 Triangular lattice diameter : 11 Lattice compactness : 610.65282, average 7.82888 Lattice compactness (without 2's) : 218.71373, average 2.80402 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -13 .. 8 -1.16667 62 1 3: -2 .. 4 0.83333 18 1 5: -2 .. 3 0.16667 16 10 Average exponent except 2's : 12 / 12 = 1.00000 Average absolute exponent except 2's: 34 / 12 = 2.83333 Scale is JI-epimorphic with val: <12 19 28| = patent
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.5316 c. M:-33.2389 c. Twelve-tone Chromatic (1/11-comma) 16: 1 2 1 1 1 2 1 2 1 1 1 2 P B D3 SD: 21.4844 c. M: 38.2687 c. 19: 2 2 1 1 2 1 2 2 2 1 1 2 N D3 SD: 19.0619 c. M:-33.9889 c. 20: 2 2 1 1 2 2 2 2 1 1 2 2 P B D3 I SD: 15.0997 c. M:-26.3137 c. 21: 2 2 1 1 2 2 2 2 2 1 2 2 P D3 SD: 15.5893 c. M: 29.9270 c. 22: 2 2 2 1 2 2 2 2 2 1 2 2 SP B ME SD: 7.9375 c. M:-15.0570 c. Pajara-12 38: 4 3 3 2 3 4 3 4 3 2 3 4 P SD: 8.6762 c. M: 14.5845 c. 41: 4 4 3 2 3 4 4 4 4 1 4 4 P SD: 8.1656 c. M:-13.7267 c. 42: 4 4 3 2 4 4 4 4 3 2 4 4 SP B SD: 7.8216 c. M:-14.8851 c. 43: 4 4 3 2 4 4 4 4 4 2 4 4 SP SD: 3.9016 c. M: 8.6645 c. 53: 5 5 4 2 5 5 5 5 5 2 5 5 SP SD: 2.3386 c. M: 4.4970 c. 65: 6 6 5 3 6 6 6 6 6 3 6 6 SP SD: 1.5465 c. M:-2.4696 c. 118: 11 11 9 5 11 11 11 11 11 5 11 11 SP SD: 0.3263 c. M: 0.6595 c. 301: 28 28 23 13 28 28 28 28 28 13 28 28 SP SD: 0.3060 c. M: 0.6911 c. 376: 35 35 29 16 35 35 35 35 35 16 35 35 SP SD: 0.1668 c. M:-0.3162 c. 494: 46 46 38 21 46 46 46 46 46 21 46 46 SP SD: 0.0642 c. M:-0.1482 c. 612: 57 57 47 26 57 57 57 57 57 26 57 57 SP SD: 0.0528 c. M: 0.0945 c. 1106: 103 103 85 47 103 103 103 103 103 47 103 103 SP SD: 0.0463 c. M:-0.0911 c. 1289: 120 120 99 55 120 120 120 120 120 55 120 120 SP SD: 0.0293 c. M: 0.0491 c. 1407: 131 131 108 60 131 131 131 131 131 60 131 131 SP SD: 0.0332 c. M: 0.0763 c. 1783: 166 166 137 76 166 166 166 166 166 76 166 166 SP SD: 0.0170 c. M:-0.0364 c. 1901: 177 177 146 81 177 177 177 177 177 81 177 177 SP SD: 0.0079 c. M: 0.0179 c. 2395: 223 223 184 102 223 223 223 223 223 102 223 223 SP SD: 0.0070 c. M:-0.0163 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: 15.1589 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: 8.3554 cents 6 x 7 x x 8 x 9 x 10 x 11:12 S SD: 12.3222 cents 7 x 8 x x 9:10 x 11:12 x 13:14 S SD: 9.0284 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 6.9126 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 10.6603 cents 10:11 x 12 x 13:14:15:16:17:18:19:20 S SD: 7.5792 cents 11:12 x 13:14 x 15:17:18:19 x 21:22 SD: 12.7730 cents 12:13:14 x 15:16:17:18:19:20:21:23:24 SD: 7.6355 cents 13:14:15 x 16:17:18:20:21:22:23:24:26 S SD: 6.4865 cents 14:15:16:17 x 18:20:21:22:24:25:26:28 S SD: 6.5660 cents 15:16:17:18:19:20:21:23:24 x 26:28:30 SD: 6.0229 cents 16:17:18:19:20:21:23:24:26:27:28:30:32 SD: 5.1429 cents 18:19:20 x 22:24:25:27:29:31:32:34:36 SD: 5.8703 cents 19:20:22:23 x 25:27:29:30:32:33:36:38 SD: 6.2547 cents 20:21:23:24:25:26:28:30:32:34:35:38:40 SD: 4.3684 cents 23:25:26:28 x 30:32:35:37:39:40:43:46 SD: 5.5271 cents 24:26:27:29:30:32:34:36:38:41:42:45:48 SD: 4.2206 cents 25:27:28:30:31:33:35:38:40:43:44:47:50 SD: 3.7593 cents 28:30:32:34:35:37:39:42:45:48:49:53:56 SD: 3.3946 cents 29:31:33:35:36:38:41:44:46:49:51:54:58 SD: 3.1491 cents 30:32:34:36:37:40:42:45:48:51:53:56:60 SD: 2.1768 cents 42:45:48:50:52:55:59:63:67:72:74:79:84 SD: 2.0232 cents 44:47:50:53:54:58:62:66:70:75:77:83:88 SD: 1.8367 cents 50:53:57:60:62:66:70:75:80:85:88:94:100 SD: 1.4362 cents 60:64:68:72:74:79:84:90:96:102:105:113:120 SD: 1.4148 cents 64:68:73:77:79:84:90:96:102:109:113:120:128 SD: 1.3620 cents 72:77:82:86:89:95:101:108:115:123:127:135:144 SD: 1.0397 cents 86:92:98:103:106:113:121:129:138:147:151:161:172 SD: 1.0012 cents 88:94:100:106:109:116:124:132:141:150:155:165:176 SD: 0.8444 cents 94:100:107:113:116:124:132:141:150:160:165:176:188 SD: 0.8343 cents 106:113:121:127:131:140:149:159:170:181:186:199:212 SD: 0.7569 cents 110:117:125:132:136:145:155:165:176:188:193:206:220 SD: 0.6577 cents 135:144:154:162:167:178:190:203:216:230:237:253:270 SD: 0.6323 cents 136:145:155:163:168:179:191:204:218:232:239:255:272 SD: 0.5198 cents 150:160:171:180:185:198:211:225:240:256:264:281:300 SD: 0.5062 cents 160:171:182:192:198:211:225:240:256:273:281:300:320 SD: 0.3636 cents 195:208:222:234:241:257:274:293:312:333:343:366:390 SD: 0.3493 cents 224:239:255:269:277:295:315:336:358:382:394:420:448 SD: 0.3079 cents 255:272:290:306:315:336:359:383:408:435:448:478:510 SD: 0.3011 cents 270:288:307:324:334:356:380:405:432:461:475:506:540 SD: 0.2491 cents 310:331:353:372:383:409:436:465:496:529:545:581:620 SD: 0.2347 cents 330:352:375:396:408:435:464:495:528:563:580:619:660 SD: 0.2038 cents 406:433:462:487:502:535:571:609:650:693:714:761:812 SD: 0.1659 cents 450:480:512:540:556:593:633:675:720:768:791:844:900 SD: 0.0998 cents