Scala analysis: xen09-chalmers-tritriadic-11-13-15
Tritriadic scale built from 11:13:15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 13/11 289.209719 tridecimal minor third 2: 15/11 536.950772 undecimal augmented fourth 3: 22/15 663.049228 undecimal diminished fifth 4: 195/121 826.160492 5: 26/15 952.258947 tridecimal semi-augmented sixth 6: 225/121 1073.901545 two (undecimal augmented fourth) 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 242/225 126.0985 1: 13/11 289.2097 tridecimal minor third 2: 15/13 247.7411 tridecimal 5/4-tone 3: 242/225 126.0985 4: 2925/2662 163.1113 5: 242/225 126.0985 6: 3375/3146 121.6426 7: 242/225 126.0985
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 3375/3146 121.643 cents 1: 3 242/225 126.098 cents 1: 1 2925/2662 163.111 cents 1: 1 15/13 247.741 cents tridecimal 5/4-tone 1: 1 13/11 289.210 cents tridecimal minor third 2: 2 15/13 247.741 cents tridecimal 5/4-tone 2: 2 13/11 289.210 cents tridecimal minor third 2: 1 242/195 373.840 cents 2: 1 286/225 415.308 cents 2: 1 15/11 536.951 cents undecimal augmented fourth 3: 1 242/195 373.840 cents 3: 1 3375/2662 410.852 cents 3: 1 286/225 415.308 cents 3: 2 15/11 536.951 cents undecimal augmented fourth 3: 2 22/15 663.049 cents undecimal diminished fifth 4: 2 15/11 536.951 cents undecimal augmented fourth 4: 2 22/15 663.049 cents undecimal diminished fifth 4: 1 225/143 784.692 cents 4: 1 5324/3375 789.148 cents 4: 1 195/121 826.160 cents 5: 1 22/15 663.049 cents undecimal diminished fifth 5: 1 225/143 784.692 cents 5: 1 195/121 826.160 cents 5: 2 22/13 910.790 cents tridecimal major sixth 5: 2 26/15 952.259 cents tridecimal semi-augmented sixth 6: 1 22/13 910.790 cents tridecimal major sixth 6: 1 26/15 952.259 cents tridecimal semi-augmented sixth 6: 1 5324/2925 1036.889 cents 6: 3 225/121 1073.902 cents two (undecimal augmented fourth) 6: 1 6292/3375 1078.357 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 289.2 537.0 663.0 826.2 952.3 1073.9 1200.0 289.2 : 247.7 373.8 537.0 663.0 784.7 910.8 1200.0 537.0 : 126.1 289.2 415.3 537.0 663.0 952.3 1200.0 663.0 : 163.1 289.2 410.9 537.0 826.2 1073.9 1200.0 826.2 : 126.1 247.7 373.8 663.0 910.8 1036.9 1200.0 952.3 : 121.6 247.7 537.0 784.7 910.8 1073.9 1200.0 1073.9: 126.1 415.3 663.0 789.1 952.3 1078.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 121.6426 .. 289.2097 cents 3718/3375, 167.5671 cents 3375/3146, 121.6426 cents 2: 247.7411 .. 536.9508 cents 13/11, 289.2097 cents 165/169,-41.4687 cents 3: 373.8395 .. 663.0492 cents 13/11, 289.2097 cents 2662/2925,-163.1113 cents 4: 536.9508 .. 826.1605 cents 13/11, 289.2097 cents 225/242,-126.0985 cents 5: 663.0492 .. 952.2589 cents 13/11, 289.2097 cents 2662/2925,-163.1113 cents 6: 910.7903 .. 1078.3574 cents 3718/3375, 167.5671 cents 165/169,-41.4687 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 3375/3146, 121.6426 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 13/11, 289.2097 cents Average / Smallest step : 1.409281 Largest / Average step : 1.687057 Largest / Smallest step : 2.377537 Median interval of one step : 242/225, 126.0985 cents, amount: 3 Most common interval of one step : 242/225, 126.0985 cents, amount: 3 Least squares average step : 187.58289 cents, oct.: 1313.08025 cents Scale is not proper Step pattern alph. order: ABCDCEC Step pattern size order : EDBCBAB Scale is not a Constant Structure Scale diversity : 1.309080 Lumma stability : 0.202738 Lumma impropriety factor : 0.446049 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 5.00000 = 5 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 761332/759375, 4.4559 cents Most common intervals : 15/11, 536.9508 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 289.210 536.951 cents Most common triad is 0.0 536.951 663.049 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 11 15 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 13 Odd number limit : 3375 (O: 3375 U: 3375) Highest odd numerator or denominator: 225 Scale harmonicity : 0.009533 Average absolute harmonicity : 0.165867 Specific harmonicity : 0.049538 Fundamental : 1/1815, -10.8258 octaves, 0.1441 Hz. Guide tone : 64350, 15.9737 octaves, 16835605.127 Hz. Exponens Consonantiae : 1.167953E+08, 26.79941 octaves Euler's gradus suavitatis : 62 Sum of Mann's harmonic distance : 396.5, average 56.64286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.28443, average 1.32635 Sum of Tenney's harmonic distance : 18.59122, average 2.65589 Vogel's harmonic complexity : 30.42857 Wille's k value : 1687 Wilson's harmonic complexity : 70 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 70.71069, average 2.52538 Lattice compactness (without 2's) : 67.06225, average 2.39508 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.42857 3 1 3: -1 .. 2 0.28571 6 5: -1 .. 2 0.28571 6 11: -2 .. 1 -0.71429 7 3 13: 0 .. 1 0.42857 3 3 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 22 / 7 = 3.14286 Scale is weakly epimorphic with val: <7 10 15 22 27| Scale is weakly epimorphic with val: <7 10 15 23 24| Scale is weakly epimorphic with val: <7 10 15 24 28| Scale is weakly epimorphic with val: <7 10 15 26 29| Scale is weakly epimorphic with val: <7 10 16 22 24| Scale is weakly epimorphic with val: <7 10 16 23 28| Scale is weakly epimorphic with val: <7 10 16 24 25| Scale is weakly epimorphic with val: <7 10 16 25 29| Scale is weakly epimorphic with val: <7 10 17 22 28| Scale is weakly epimorphic with val: <7 10 17 23 25| Scale is weakly epimorphic with val: <7 10 17 24 29| Scale is weakly epimorphic with val: <7 10 17 25 26| Scale is weakly epimorphic with val: <7 10 18 22 25| Scale is weakly epimorphic with val: <7 10 18 23 29| Scale is weakly epimorphic with val: <7 10 18 24 26| Scale is weakly epimorphic with val: <7 10 18 26 27| Scale is weakly epimorphic with val: <7 11 15 22 24| Scale is weakly epimorphic with val: <7 11 15 23 28| Scale is weakly epimorphic with val: <7 11 15 24 25| Scale is weakly epimorphic with val: <7 11 15 25 29| Scale is weakly epimorphic with val: <7 11 16 22 28| Scale is weakly epimorphic with val: <7 11 16 23 25| Scale is weakly epimorphic with val: <7 11 16 24 29| Scale is weakly epimorphic with val: <7 11 16 25 26| Scale is weakly epimorphic with val: <7 11 17 22 25| Scale is weakly epimorphic with val: <7 11 17 23 29| Scale is weakly epimorphic with val: <7 11 17 24 26| Scale is weakly epimorphic with val: <7 11 17 26 27| Scale is weakly epimorphic with val: <7 11 18 23 26| Scale is weakly epimorphic with val: <7 11 18 25 27| Scale is weakly epimorphic with val: <7 12 15 22 28| Scale is weakly epimorphic with val: <7 12 15 23 25| Scale is weakly epimorphic with val: <7 12 15 24 29| Scale is weakly epimorphic with val: <7 12 15 25 26| Scale is weakly epimorphic with val: <7 12 16 22 25| Scale is weakly epimorphic with val: <7 12 16 23 29| Scale is weakly epimorphic with val: <7 12 16 24 26| Scale is weakly epimorphic with val: <7 12 16 26 27| Scale is weakly epimorphic with val: <7 12 17 23 26| Scale is weakly epimorphic with val: <7 12 17 25 27| Scale is weakly epimorphic with val: <7 12 18 22 26| Scale is weakly epimorphic with val: <7 12 18 24 27| Scale is weakly epimorphic with val: <7 12 18 26 28|
FIT/MODE
7: 2 1 1 1 1 0 1 N T3 SD: 42.6678 c. M:-76.3125 c. 9: 2 2 1 1 1 1 1 N D3 S SD: 15.2562 c. M: 26.1605 c. 16: 4 3 2 2 2 1 2 N SD: 14.5987 c. M: 23.9015 c. 20: 5 4 2 3 2 2 2 N SD: 7.7798 c. M:-13.8395 c. 29: 7 6 3 4 3 3 3 N SD: 1.0878 c. M:-1.9605 c. 125: 30 26 13 17 13 13 13 N SD: 1.0530 c. M: 1.8589 c. 141: 34 29 15 19 15 14 15 N SD: 0.8404 c. M: 1.5611 c. 170: 41 35 18 23 18 17 18 N SD: 0.5301 c. M: 0.9604 c. 199: 48 41 21 27 21 20 21 N SD: 0.3254 c. M: 0.5347 c. 228: 55 47 24 31 24 23 24 N SD: 0.2082 c. M:-0.3726 c. 257: 62 53 27 35 27 26 27 N SD: 0.1868 c. M:-0.2987 c. 485: 117 100 51 66 51 49 51 N SD: 0.1858 c. M:-0.3184 c. 494: 119 102 52 67 52 50 52 N SD: 0.1483 c. M: 0.2496 c. 523: 126 108 55 71 55 53 55 N SD: 0.0877 c. M: 0.1567 c. 552: 133 114 58 75 58 56 58 N SD: 0.0523 c. M: 0.0850 c. 780: 188 161 82 106 82 79 82 N SD: 0.0327 c. M: 0.0554 c. 809: 195 167 85 110 85 82 85 N SD: 0.0254 c. M:-0.0447 c. 1332: 321 275 140 181 140 135 140 N SD: 0.0200 c. M: 0.0344 c. 1361: 328 281 143 185 143 138 143 N SD: 0.0105 c. M: 0.0179 c. 2141: 516 442 225 291 225 217 225 N SD: 0.0058 c. M: 0.0108 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x 4 S SD: 19.4529 cents 3 x 4 x 5 x x 6 S SD: 23.3350 cents 4:5 x 6 x 7 x 8 S SD: 26.4779 cents 5:6:7 x 8 x 9:10 S SD: 15.6210 cents 6:7:8:9:10 x 11:12 S SD: 14.4487 cents 7:8 x 10:11:12:13:14 S SD: 14.6455 cents 8:9:11:12:13:14:15:16 SD: 14.0578 cents 10:12:14:15:16:17:19:20 SD: 11.9223 cents 11:13:15:16:18:19:20:22 SD: 7.0790 cents 15:18:20:22:24:26:28:30 S SD: 7.0163 cents 16:19:22:23:26:28:30:32 SD: 6.6577 cents 17:20:23:25:27:29:32:34 SD: 6.5734 cents 19:22:26:28:31:33:35:38 SD: 6.5341 cents 20:24:27:29:32:35:37:40 SD: 6.2296 cents 21:25:29:31:34:36:39:42 SD: 4.9435 cents 22:26:30:32:35:38:41:44 SD: 3.9305 cents 28:33:38:41:45:49:52:56 SD: 2.8602 cents 33:39:45:48:53:57:61:66 SD: 2.8002 cents 34:40:46:50:55:59:63:68 SD: 2.6825 cents 38:45:52:56:61:66:71:76 SD: 2.2326 cents 44:52:60:65:71:76:82:88 SD: 2.0803 cents 49:58:67:72:79:85:91:98 SD: 0.9795 cents 77:91:105:113:124:133:143:154 SD: 0.9504 cents 93:110:127:136:150:161:173:186 SD: 0.9165 cents 105:124:143:154:169:182:195:210 SD: 0.5737 cents 116:137:158:170:187:201:216:232 SD: 0.5237 cents 154:182:210:226:248:267:286:308 SD: 0.3959 cents 165:195:225:242:266:286:307:330 SD: 0.1692 cents 270:319:368:396:435:468:502:540 SD: 0.1610 cents 319:377:435:468:514:553:593:638 SD: 0.1163 cents 435:514:593:638:701:754:809:870 SD: 0.0951 cents 484:572:660:710:780:839:900:968 SD: 0.0504 cents