Scala analysis: tertiadie4
Fourth 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: 2048/1875 152.790144 double diminished third 2: 32768/28125 264.521429 3: 6/5 315.641287 minor third 4: 32/25 427.372572 classic diminished fourth 5: 512/375 539.103858 double diminished fifth 6: 8192/5625 650.835143 double diminished sixth 7: 3/2 701.955001 perfect fifth 8: 8/5 813.686286 minor sixth 9: 128/75 925.417571 diminished seventh 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: 2048/1875 152.7901 double diminished third 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: 16/15 111.7313 minor diatonic semitone 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: 6 1125/1024 162.851 cents double augmented prime 2: 4 256/225 223.463 cents Neapolitan diminished third 2: 2 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: 4 5625/4096 549.165 cents double augmented third 6: 2 45/32 590.224 cents diatonic tritone 6: 2 64/45 609.776 cents 2nd tritone 6: 4 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: 2 28125/16384 935.479 cents 10: 4 225/128 976.537 cents augmented sixth 10: 6 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: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 152.8 264.5 315.6 427.4 539.1 650.8 702.0 813.7 925.4 1037.1 1088.3 1200.0 152.8 : 111.7 162.9 274.6 386.3 498.0 549.2 660.9 772.6 884.4 935.5 1047.2 1200.0 264.5 : 51.1 162.9 274.6 386.3 437.4 549.2 660.9 772.6 823.7 935.5 1088.3 1200.0 315.6 : 111.7 223.5 335.2 386.3 498.0 609.8 721.5 772.6 884.4 1037.1 1148.9 1200.0 427.4 : 111.7 223.5 274.6 386.3 498.0 609.8 660.9 772.6 925.4 1037.1 1088.3 1200.0 539.1 : 111.7 162.9 274.6 386.3 498.0 549.2 660.9 813.7 925.4 976.5 1088.3 1200.0 650.8 : 51.1 162.9 274.6 386.3 437.4 549.2 702.0 813.7 864.8 976.5 1088.3 1200.0 702.0 : 111.7 223.5 335.2 386.3 498.0 650.8 762.6 813.7 925.4 1037.1 1148.9 1200.0 813.7 : 111.7 223.5 274.6 386.3 539.1 650.8 702.0 813.7 925.4 1037.1 1088.3 1200.0 925.4 : 111.7 162.9 274.6 427.4 539.1 590.2 702.0 813.7 925.4 976.5 1088.3 1200.0 1037.1: 51.1 162.9 315.6 427.4 478.5 590.2 702.0 813.7 864.8 976.5 1088.3 1200.0 1088.3: 111.7 264.5 376.3 427.4 539.1 650.8 762.6 813.7 925.4 1037.1 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 : 102.20485 cents, oct.: 1226.45825 cents Scale is strictly proper Step pattern alph. order: ABCBBBCBBBCB Step pattern size order : LMSMMMSMMMSM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 10.06100 cents Scale diversity : 1.353778 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.169041 Rothenberg efficiency : 0.395893 redundancy: 0.604107 Efficiency x scale size : 4.750722 Number of different interval sizes : 36 = 3.27273 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 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 Formal octave complements present : 1 = 8.3333% Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 6-7 -- Rational properties -- Prime limit : 5 Odd number limit : 421875 (O: 421875 U: 421875) Highest odd numerator or denominator: 28125 Scale harmonicity : 0.015528 Average absolute harmonicity : 0.149157 Specific harmonicity : 0.088167 Fundamental : 1/225000, -17.7796 octaves, 0.0012 Hz. Guide tone : 491520, 18.9069 octaves, 128594197.857 Hz. Exponens Consonantiae : 1.105920E+11, 36.68646 octaves Euler's gradus suavitatis : 49 Sum of Mann's harmonic distance : 41504.0, average 3458.66667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 23.42155, average 1.95180 Sum of Tenney's harmonic distance : 47.98107, average 3.99842 Vogel's harmonic complexity : 28.50000 Wille's k value : 210937 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 9 Triangular lattice diameter : 9 Lattice compactness : 585.38686, average 7.50496 Lattice compactness (without 2's) : 208.91852, average 2.67844 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 15 6.00000 80 1 3: -2 .. 1 -0.50000 12 1 5: -5 .. 1 -2.00000 26 10 Average exponent except 2's :-30 / 12 =-2.50000 Average absolute exponent except 2's: 38 / 12 = 3.16667 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: 34.6553 c. M: 64.5214 c. Twelve-tone Chromatic (1/11-comma) 13: 2 1 1 1 1 1 1 1 1 1 1 1 P M ME SD: 25.7002 c. M:-53.5895 c. 14: 2 1 1 1 1 2 0 2 1 1 1 1 P D3 SD: 22.6997 c. M:-43.4566 c. 15: 2 1 1 1 2 1 1 1 2 1 1 1 P B ME SD: 19.7895 c. M:-34.5824 c. Inflated-12 17: 2 2 0 2 2 1 1 2 1 2 0 2 N SD: 20.4105 c. M:-33.3725 c. 18: 2 2 1 1 2 2 1 1 2 2 0 2 N T3 SD: 18.9339 c. M:-31.3783 c. 20: 2 2 1 2 2 2 0 2 2 2 1 2 P D3 SD: 22.2931 c. M: 41.9550 c. 21: 2 2 1 2 2 2 1 2 2 2 1 2 SP B ME SD: 22.7057 c. M: 38.5044 c. 22: 3 2 1 2 2 2 1 2 2 2 1 2 P D3 SD: 6.6918 c. M:-11.6314 c. 31: 4 3 1 3 3 3 1 3 3 3 1 3 P SD: 4.7268 c. M:-8.0124 c. 53: 7 5 2 5 5 5 2 5 5 5 2 5 P SD: 3.8398 c. M:-7.1767 c. 65: 8 6 3 6 6 6 3 6 6 6 3 6 SP SD: 3.2745 c. M: 6.0599 c. 86: 11 8 4 8 8 8 3 8 8 8 4 8 P SD: 3.9273 c. M:-5.2889 c. 87: 11 8 4 8 8 8 4 8 8 8 4 8 SP SD: 1.5966 c. M: 2.6661 c. 96: 12 9 4 9 9 9 4 9 9 9 4 9 SP SD: 1.7501 c. M: 3.1413 c. 118: 15 11 5 11 11 11 5 11 11 11 5 11 SP SD: 0.1881 c. M: 0.3870 c. 494: 63 46 21 46 46 46 21 46 46 46 21 46 SP SD: 0.1475 c. M:-0.2559 c. 612: 78 57 26 57 57 57 26 57 57 57 26 57 SP SD: 0.0991 c. M:-0.1845 c. 730: 93 68 31 68 68 68 31 68 68 68 31 68 SP SD: 0.0754 c. M:-0.1361 c. 848: 108 79 36 79 79 79 36 79 79 79 36 79 SP SD: 0.0685 c. M:-0.1153 c. 1171: 149 109 50 109 109 109 50 109 109 109 50 109 SP SD: 0.0705 c. M: 0.1320 c. 1289: 164 120 55 120 120 120 55 120 120 120 55 120 SP SD: 0.0713 c. M: 0.1304 c. 1311: 167 122 56 122 122 122 56 122 122 122 56 122 SP SD: 0.0704 c. M:-0.1482 c. 1407: 179 131 60 131 131 131 60 131 131 131 60 131 SP SD: 0.0747 c. M: 0.1291 c. 1429: 182 133 61 133 133 133 61 133 133 133 61 133 SP SD: 0.0497 c. M:-0.1040 c. 1547: 197 144 66 144 144 144 66 144 144 144 66 144 SP SD: 0.0327 c. M:-0.0665 c. 1665: 212 155 71 155 155 155 71 155 155 155 71 155 SP SD: 0.0196 c. M:-0.0344 c. 1783: 227 166 76 166 166 166 76 166 166 166 76 166 SP SD: 0.0133 c. M: 0.0234 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: 19.3553 cents 4 x x x 5 x x 6 x 7 x x 8 S SD: 14.9376 cents 5 x x 6 x 7 x x 8 x 9 x 10 S SD: 9.5217 cents 6 x 7 x x 8 x 9 x 10:11 x 12 S SD: 9.8972 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 8.5602 cents 8:9 x x 10:11 x 12:13:14 x 15:16 S SD: 10.4978 cents 9:10 x 11 x 12:13 x 14:15:16:17:18 S SD: 10.9361 cents 10:11 x 12:13:14 x 15:16:17:18:19:20 S SD: 6.0893 cents 11:12:13 x 14:15:16:17:18:19:20:21:22 S SD: 7.2242 cents 12:13:14 x 15:16:17:18:19:20:22:23:24 S SD: 8.8509 cents 13:14:15:16:17:18:19:20:21:22:24 x 26 S SD: 8.0299 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 6.6369 cents 16:17 x 19:20:22:23:24:26:27:29:30:32 SD: 7.1124 cents 17:19:20 x 22:23:25:26:27:29:31:32:34 SD: 5.8258 cents 18:20:21:22:23:25:26:27:29:31:33:34:36 SD: 5.0569 cents 20:22:23:24:26:27:29:30:32:34:36:38:40 SD: 4.3877 cents 22:24:26 x 28:30:32:33:35:38:40:41:44 SD: 3.3589 cents 24:26:28:29:31:33:35:36:38:41:44:45:48 SD: 2.9266 cents 30:33:35:36:38:41:44:45:48:51:55:56:60 SD: 2.4860 cents 35:38:41:42:45:48:51:53:56:60:64:66:70 SD: 2.3603 cents 40:44:47:48:51:55:58:60:64:68:73:75:80 SD: 2.1755 cents 42:46:49:50:54:57:61:63:67:72:76:79:84 SD: 2.0966 cents 44:48:51:53:56:60:64:66:70:75:80:83:88 SD: 1.7674 cents 50:55:58:60:64:68:73:75:80:85:91:94:100 SD: 1.5332 cents 54:59:63:65:69:74:79:81:86:92:98:101:108 SD: 1.3592 cents 55:60:64:66:70:75:80:83:88:94:100:103:110 SD: 1.2920 cents 65:71:76:78:83:89:95:98:104:111:118:122:130 SD: 1.2451 cents 68:74:79:82:87:93:99:102:109:116:124:128:136 SD: 1.2129 cents 72:79:84:86:92:98:105:108:115:123:131:135:144 SD: 1.1414 cents 74:81:86:89:95:101:108:111:118:126:135:139:148 SD: 1.0591 cents 79:86:92:95:101:108:115:119:126:135:144:148:158 SD: 1.0299 cents 85:93:99:102:109:116:124:128:136:145:155:159:170 SD: 0.8334 cents 90:98:105:108:115:123:131:135:144:154:164:169:180 SD: 0.7302 cents 96:105:112:115:123:131:140:144:154:164:175:180:192 SD: 0.6347 cents 110:120:128:132:141:150:160:165:176:188:200:206:220 SD: 0.5248 cents 140:153:163:168:179:191:204:210:224:239:255:263:280 SD: 0.3785 cents 200:218:233:240:256:273:291:300:320:341:364:375:400 SD: 0.3610 cents 224:245:261:269:287:306:326:336:358:382:408:420:448 SD: 0.3605 cents 225:246:262:270:288:307:328:338:360:384:410:422:450 SD: 0.3493 cents 230:251:268:276:294:314:335:345:368:393:419:431:460 SD: 0.3197 cents 250:273:291:300:320:341:364:375:400:427:455:469:500 SD: 0.2455 cents 290:317:338:348:371:396:422:435:464:495:528:544:580 SD: 0.2010 cents 350:382:408:420:448:478:510:525:560:597:637:656:700 SD: 0.1918 cents 400:437:466:480:512:546:583:600:640:683:728:750:800 SD: 0.1461 cents 490:535:571:588:627:669:714:735:784:836:892:919:980 SD: 0.1259 cents 550:601:641:660:704:751:801:825:880:939:1001:1031:1100 SD: 0.1051 cents 600:655:699:720:768:819:874:900:960:1024:1092:1125:1200 SD: 0.0991 cents