Scala analysis: xen12-chalmers-tritriadic-mt-9-11-15
Tritriadic M->T scale built from 9:11:15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 55/54 31.766654 telepathma 2: 11/9 347.407941 undecimal neutral third 3: 15/11 536.950772 undecimal augmented fourth 4: 121/81 694.815881 two (undecimal neutral third) 5: 18/11 852.592059 undecimal neutral sixth 6: 5/3 884.358713 major sixth, BP sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 55/54 31.7667 telepathma 2: 6/5 315.6413 minor third 3: 135/121 189.5428 4: 1331/1215 157.8651 5: 1458/1331 157.7762 6: 55/54 31.7667 telepathma 7: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 55/54 31.767 cents telepathma 1: 1 1458/1331 157.776 cents 1: 1 1331/1215 157.865 cents 1: 1 135/121 189.543 cents 1: 2 6/5 315.641 cents minor third 2: 1 135/121 189.543 cents 2: 1 6/5 315.641 cents minor third 2: 4 11/9 347.408 cents undecimal neutral third 2: 1 162/121 505.184 cents 3: 1 11/9 347.408 cents undecimal neutral third 3: 1 605/486 379.175 cents 3: 2 162/121 505.184 cents 3: 1 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: 1 22/15 663.049 cents undecimal diminished fifth 4: 2 121/81 694.816 cents two (undecimal neutral third) 4: 1 972/605 820.825 cents 4: 1 18/11 852.592 cents undecimal neutral sixth 5: 1 121/81 694.816 cents two (undecimal neutral third) 5: 4 18/11 852.592 cents undecimal neutral sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 242/135 1010.457 cents 6: 2 5/3 884.359 cents major sixth, BP sixth 6: 1 242/135 1010.457 cents 6: 1 2430/1331 1042.135 cents 6: 1 1331/729 1042.224 cents 6: 2 108/55 1168.233 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 31.8 347.4 537.0 694.8 852.6 884.4 1200.0 31.8 : 315.6 505.2 663.0 820.8 852.6 1168.2 1200.0 347.4 : 189.5 347.4 505.2 537.0 852.6 884.4 1200.0 537.0 : 157.9 315.6 347.4 663.0 694.8 1010.5 1200.0 694.8 : 157.8 189.5 505.2 537.0 852.6 1042.1 1200.0 852.6 : 31.8 347.4 379.2 694.8 884.4 1042.2 1200.0 884.4 : 315.6 347.4 663.0 852.6 1010.5 1168.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.7667 .. 315.6413 cents 324/275, 283.8746 cents 55/54, 31.7667 cents 2: 189.5428 .. 505.1841 cents 6/5, 315.6413 cents 225/242,-126.0985 cents 3: 347.4079 .. 663.0492 cents 6/5, 315.6413 cents 1331/1458,-157.7762 cents 4: 536.9508 .. 852.5921 cents 6/5, 315.6413 cents 225/242,-126.0985 cents 5: 694.8159 .. 1010.4572 cents 6/5, 315.6413 cents 1331/1458,-157.7762 cents 6: 884.3587 .. 1168.2333 cents 324/275, 283.8746 cents 225/242,-126.0985 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 55/54, 31.7667 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 5.396494 Largest / Average step : 1.841241 Largest / Smallest step : 9.936246 Median interval of one step : 1331/1215, 157.8651 cents, amount: 1 Least squares average step : 164.89865 cents, oct.: 1154.29055 cents Scale is not proper Step pattern alph. order: ABCDEAB Step pattern size order : AEDCBAE Scale is not a Constant Structure Scale diversity : 1.271469 Lumma stability : 0.052944 Lumma impropriety factor : 0.578206 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 : 4.66667 = 14/3 Median interval variety : 4.5 Lowest interval variety : 4 Smallest interval difference : 1771561/1771470, 0.0889 cents Most common intervals : 11/9, 347.4079 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 536.951 852.592 cents Most common triad is 0.0 347.408 852.592 cents, amount: 3 Number of recognisable fifths : 3, average 694.8159 cents Scale contains a complete diamond : 9 11 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 11 Odd number limit : 1331 (O: 1331 U: 1331) Highest odd numerator or denominator: 121 Scale harmonicity : 0.012667 Average absolute harmonicity : 0.183050 Specific harmonicity : 0.069779 Fundamental : 1/1782, -10.7993 octaves, 0.1468 Hz. Guide tone : 10890, 13.4107 octaves, 2849102.406 Hz. Exponens Consonantiae : 1.940598E+07, 24.21000 octaves Euler's gradus suavitatis : 49 Sum of Mann's harmonic distance : 198.5, average 28.35714 Mersenne's string divisions : 498047160 Sum of van Prooijen's expressibility: 7.78099, average 1.11157 Sum of Tenney's harmonic distance : 15.45093, average 2.20728 Vogel's harmonic complexity : 26.42857 Wille's k value : 907 Wilson's harmonic complexity : 56 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 86.40093, average 3.08575 Lattice compactness (without 2's) : 81.66078, average 2.91646 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 0.14286 3 1 3: -4 .. 2 -1.00000 13 5: 0 .. 1 0.42857 3 1 11: -1 .. 2 0.28571 6 5 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 23| Scale is weakly epimorphic with val: <7 10 16 25| Scale is weakly epimorphic with val: <7 10 18 22| Scale is weakly epimorphic with val: <7 11 15 23| Scale is weakly epimorphic with val: <7 11 16 25| Scale is weakly epimorphic with val: <7 12 15 23| Scale is weakly epimorphic with val: <7 12 16 25| Scale is weakly epimorphic with val: <7 12 18 22|
FIT/MODE
7: 0 2 1 1 1 0 2 N T3 SD: 18.4692 c. M: 31.7667 c. 14: 0 4 2 2 2 0 4 N T3 SD: 18.4692 c. M: 31.7667 c. 20: 1 5 3 3 2 1 5 N SD: 16.9133 c. M:-28.2333 c. 24: 1 6 4 3 3 1 6 N SD: 10.6079 c. M:-18.2333 c. 27: 1 7 4 4 3 1 7 N SD: 9.2012 c. M:-16.2952 c. 31: 1 8 5 4 4 1 8 N SD: 4.0422 c. M:-6.9430 c. 38: 1 10 6 5 5 1 10 N SD: 0.1058 c. M: 0.1877 c. 601: 16 158 95 79 79 16 158 N SD: 0.1103 c. M:-0.1801 c. 639: 17 168 101 84 84 17 168 N SD: 0.0977 c. M:-0.1582 c. 677: 18 178 107 89 89 18 178 N SD: 0.0865 c. M:-0.1388 c. 715: 19 188 113 94 94 19 188 N SD: 0.0766 c. M:-0.1215 c. 753: 20 198 119 99 99 20 198 N SD: 0.0678 c. M:-0.1059 c. 791: 21 208 125 104 104 21 208 N SD: 0.0598 c. M:-0.0918 c. 829: 22 218 131 109 109 22 218 N SD: 0.0526 c. M:-0.0818 c. 867: 23 228 137 114 114 23 228 N SD: 0.0462 c. M:-0.0734 c. 905: 24 238 143 119 119 24 238 N SD: 0.0404 c. M:-0.0658 c. 943: 25 248 149 124 124 25 248 N SD: 0.0351 c. M:-0.0588 c. 981: 26 258 155 129 129 26 258 N SD: 0.0305 c. M:-0.0523 c. 1019: 27 268 161 134 134 27 268 N SD: 0.0263 c. M:-0.0463 c. 1057: 28 278 167 139 139 28 278 N SD: 0.0228 c. M:-0.0407 c. 1095: 29 288 173 144 144 29 288 N SD: 0.0199 c. M:-0.0355 c. 1133: 30 298 179 149 149 30 298 N SD: 0.0176 c. M:-0.0307 c. 1171: 31 308 185 154 154 31 308 N SD: 0.0161 c. M:-0.0262 c. 1209: 32 318 191 159 159 32 318 N SD: 0.0154 c. M: 0.0268 c. 1247: 33 328 197 164 164 33 328 N SD: 0.0154 c. M: 0.0284 c. 2380: 63 626 376 313 313 63 626 N SD: 0.0156 c. M: 0.0260 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 3.5696 cents 3 x x 4 x x 5:6 S SD: 12.9686 cents 4 x 5 x 6 x 7:8 S SD: 23.3176 cents 5 x 6:7 x 8 x 10 S SD: 16.9533 cents 6 x 7:8:9 x 10:12 S SD: 17.9453 cents 7 x 9 x 10:11:12:14 SD: 28.9547 cents 8 x 10:11:12:13 x 16 SD: 8.7558 cents 9:10:11:12:13 x 15:18 SD: 27.6848 cents 10:11:12:14:15:16:17:20 SD: 21.9355 cents 11:12:13:15:16:18 x 22 SD: 23.3604 cents 12:13:15:16:18 x 20:24 SD: 20.0595 cents 13:14:16:18:19:21:22:26 SD: 16.1570 cents 14:15:17:19:21:23 x 28 SD: 14.8890 cents 15:16:18:20:22 x 25:30 SD: 16.6051 cents 16:17:20:22:24:26:27:32 SD: 12.5647 cents 17:18:21:23:25:28 x 34 SD: 12.8054 cents 18:19:22:25:27:29:30:36 SD: 10.6988 cents 19:20:23:26:28:31:32:38 SD: 9.5549 cents 20:21:24:27:30:33 x 40 SD: 10.9881 cents 21:22:26:29:31:34:35:42 SD: 9.1660 cents 22:23:27:30:33:36:37:44 SD: 6.9832 cents 23:24:28:31:34 x 38:46 SD: 8.7701 cents 24:25:29:33:36:39:40:48 SD: 6.8632 cents 26:27:32:35:39 x 43:52 SD: 7.4559 cents 27:28:33:37:40:44:45:54 SD: 5.1571 cents 28:29:34:38:42:46:47:56 SD: 5.1218 cents 30:31:37:41:45:49:50:60 SD: 4.3951 cents 33:34:40:45:49:54:55:66 SD: 3.8119 cents 36:37:44:49:54:59:60:72 SD: 2.5309 cents 41:42:50:56:61:67:68:82 SD: 2.2488 cents 44:45:54:60:66:72:73:88 SD: 2.0952 cents 49:50:60:67:73:80:82:98 SD: 1.6275 cents 55:56:67:75:82:90:92:110 SD: 1.3104 cents 63:64:77:86:94:103:105:126 SD: 0.7843 cents 99:101:121:135:148:162:165:198 SD: 0.4487 cents 162:165:198:221:242:265:270:324 SD: 0.1325 cents 531:541:649:724:793:869:885:1062 SD: 0.1106 cents 594:605:726:810:887:972:990:1188 SD: 0.0929 cents