Scala analysis: xen12-chalmers-tritriadic-mt-27-25-15
Tritriadic M->T scale built from 27:25:15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 250/243 49.166137 maximal diesis, Porcupine comma 2: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 3: 10/9 182.403712 minor whole tone 4: 6/5 315.641287 minor third 5: 1250/729 933.524850 6: 50/27 1066.762425 grave major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 1: 250/243 49.1661 maximal diesis, Porcupine comma 2: 6561/6250 84.0714 ripple 3: 250/243 49.1661 maximal diesis, Porcupine comma 4: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 5: 3125/2187 617.8836 6: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 7: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 250/243 49.166 cents maximal diesis, Porcupine comma 1: 1 6561/6250 84.071 cents ripple 1: 3 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 1 3125/2187 617.884 cents 2: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 2 10/9 182.404 cents minor whole tone 2: 1 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 2: 2 125/81 751.121 cents 3: 1 10/9 182.404 cents minor whole tone 3: 2 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 3: 1 6/5 315.641 cents minor third 3: 1 31250/19683 800.287 cents 3: 2 5/3 884.359 cents major sixth, BP sixth 4: 2 6/5 315.641 cents minor third 4: 1 19683/15625 399.713 cents 4: 1 5/3 884.359 cents major sixth, BP sixth 4: 2 1250/729 933.525 cents 4: 1 9/5 1017.596 cents just minor seventh, BP seventh 5: 2 162/125 448.879 cents 5: 1 1250/729 933.525 cents 5: 2 9/5 1017.596 cents just minor seventh, BP seventh 5: 2 50/27 1066.762 cents grave major seventh 6: 1 4374/3125 582.116 cents 6: 3 50/27 1066.762 cents grave major seventh 6: 1 12500/6561 1115.929 cents 6: 2 243/125 1150.834 cents octave - maximal diesis Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 49.2 133.2 182.4 315.6 933.5 1066.8 1200.0 49.2 : 84.1 133.2 266.5 884.4 1017.6 1150.8 1200.0 133.2 : 49.2 182.4 800.3 933.5 1066.8 1115.9 1200.0 182.4 : 133.2 751.1 884.4 1017.6 1066.8 1150.8 1200.0 315.6 : 617.9 751.1 884.4 933.5 1017.6 1066.8 1200.0 933.5 : 133.2 266.5 315.6 399.7 448.9 582.1 1200.0 1066.8: 133.2 182.4 266.5 315.6 448.9 1066.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 49.1661 .. 617.8836 cents 25/18, 568.7174 cents 250/243, 49.1661 cents 2: 133.2376 .. 751.1211 cents 3125/2187, 617.8836 cents 59049/78125,-484.6460 cents 3: 182.4037 .. 884.3587 cents 3/2, 701.9550 cents 18/25,-568.7174 cents 4: 315.6413 .. 1017.5963 cents 3/2, 701.9550 cents 18/25,-568.7174 cents 5: 448.8789 .. 1066.7624 cents 3125/2187, 617.8836 cents 18/25,-568.7174 cents 6: 582.1164 .. 1150.8339 cents 25/18, 568.7174 cents 59049/78125,-484.6460 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 250/243, 49.1661 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 3125/2187, 617.8836 cents Average / Smallest step : 3.486720 Largest / Average step : 3.604321 Largest / Smallest step : 12.567259 Median interval of one step : 27/25, 133.2376 cents, amount: 3 Most common interval of one step : 27/25, 133.2376 cents, amount: 3 Least squares average step : 154.24012 cents, oct.: 1079.68082 cents Scale is not proper Step pattern alph. order: ABACDCC Step pattern size order : ABACDCC Scale is not a Constant Structure Scale diversity : 1.415405 Lumma stability : 0.081944 Lumma impropriety factor : 0.777937 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 : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 1594323/1562500, 34.9053 cents Most common intervals : 27/25, 133.2376 cents & inv., amount: 5 Most common triad is 0.0 133.238 1066.762 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 25 27 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 5 Odd number limit : 19683 (O: 19683 U: 19683) Highest odd numerator or denominator: 729 Scale harmonicity : 0.015773 Average absolute harmonicity : 0.189302 Specific harmonicity : 0.087559 Fundamental : 1/18225, -14.1536 octaves, 0.0144 Hz. Guide tone : 33750, 15.0426 octaves, 8829862.829 Hz. Exponens Consonantiae : 6.150938E+08, 29.19623 octaves Euler's gradus suavitatis : 44 Sum of Mann's harmonic distance : 1317.0, average 188.14286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.76427, average 1.39490 Sum of Tenney's harmonic distance : 20.43522, average 2.91932 Vogel's harmonic complexity : 28.71429 Wille's k value : 9841 Wilson's harmonic complexity : 57 Rectangular lattice diameter : 15 Triangular lattice diameter : 9 Lattice compactness : 127.45435, average 4.55194 Lattice compactness (without 2's) : 125.03021, average 4.46536 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.85714 6 1 3: -6 .. 3 -1.71429 20 5: -2 .. 4 1.00000 13 6 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 33 / 7 = 4.71429
FIT/MODE
7: 0 1 0 1 3 1 1 N SD: 41.4553 c. M: 76.3820 c. 8: 0 1 0 1 4 1 1 N SD: 27.7690 c. M: 49.1661 c. 13: 1 0 1 1 7 2 1 N SD: 31.2247 c. M:-43.1416 c. 15: 1 1 0 2 8 1 2 N SD: 22.6937 c. M:-30.8339 c. 17: 1 1 1 1 9 2 2 N SD: 20.0259 c. M: 33.2883 c. 18: 1 1 1 2 9 2 2 N SD: 11.5199 c. M:-17.6920 c. 19: 1 1 1 2 10 2 2 N SD: 8.7280 c. M:-13.9918 c. 26: 1 2 1 3 13 3 3 N SD: 5.7693 c. M: 10.4479 c. 27: 1 2 1 3 14 3 3 N SD: 3.0301 c. M: 4.7217 c. 45: 2 3 2 5 23 5 5 N SD: 2.7926 c. M:-4.3587 c. 72: 3 5 3 8 37 8 8 N SD: 0.6171 c. M:-1.0254 c. 99: 4 7 4 11 51 11 11 N SD: 0.3968 c. M: 0.6813 c. 171: 7 12 7 19 88 19 19 N SD: 0.1080 c. M: 0.1915 c. 441: 18 31 18 49 227 49 49 N SD: 0.1184 c. M: 0.1915 c. 612: 25 43 25 68 315 68 68 N SD: 0.1076 c. M: 0.1915 c. 730: 30 51 30 81 376 81 81 N SD: 0.1014 c. M:-0.1738 c. 829: 34 58 34 92 427 92 92 N SD: 0.0703 c. M:-0.1302 c. 901: 37 63 37 100 464 100 100 N SD: 0.0683 c. M:-0.1124 c. 1000: 41 70 41 111 515 111 111 N SD: 0.0402 c. M:-0.0751 c. 1171: 48 82 48 130 603 130 130 N SD: 0.0196 c. M:-0.0362 c. 1342: 55 94 55 149 691 149 149 N SD: 0.0079 c. M:-0.0142 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 115.7849 cents 3 x x x 4:5 x 6 S SD: 62.9713 cents 4 x x x 5:7 x 8 SD: 26.3328 cents 5 x x x 6 x 9:10 S SD: 16.3887 cents 6 x x x 7:10:11:12 SD: 17.8511 cents 7 x x 8 x 12:13:14 S SD: 12.2554 cents 8 x x 9:10:14:15:16 SD: 16.9302 cents 9 x x 10:11:15:17:18 SD: 13.5672 cents 10 x x 11:12:17:19:20 SD: 9.9978 cents 11 x 12 x 13:19:20:22 SD: 9.3189 cents 12 x 13 x 14:21:22:24 S SD: 12.5792 cents 13 x 14 x 16:22:24:26 SD: 9.9817 cents 14 x 15:16:17:24:26:28 SD: 9.1487 cents 15 x 16:17:18:26:28:30 SD: 7.7801 cents 16 x 17:18:19:27:30:32 SD: 8.8485 cents 17 x 18:19:20:29:31:34 SD: 9.4941 cents 18 x 19:20:22:31:33:36 SD: 9.0378 cents 19:20 x 21:23:33:35:38 SD: 8.2678 cents 20:21 x 22:24:34:37:40 SD: 7.0187 cents 21:22:23 x 25:36:39:42 SD: 7.0461 cents 22:23:24 x 26:38:41:44 SD: 7.5550 cents 24:25:26:27:29:41:44:48 SD: 5.4229 cents 25:26:27:28:30:43:46:50 SD: 3.7623 cents 34:35:37:38:41:58:63:68 SD: 2.9591 cents 35:36:38:39:42:60:65:70 SD: 1.6448 cents 64:66:69:71:77:110:119:128 SD: 1.5626 cents 73:75:79:81:88:125:135:146 SD: 1.4074 cents 74:76:80:82:89:127:137:148 SD: 1.0275 cents 99:102:107:110:119:170:183:198 SD: 0.8175 cents 100:103:108:111:120:171:185:200 SD: 0.8131 cents 101:104:109:112:121:173:187:202 SD: 0.7462 cents 134:138:145:149:161:230:248:268 SD: 0.7105 cents 135:139:146:150:162:231:250:270 SD: 0.6475 cents 136:140:147:151:163:233:252:272 SD: 0.5015 cents 200:206:216:222:240:343:370:400 SD: 0.4548 cents 210:216:227:233:252:360:389:420 SD: 0.4289 cents 214:220:231:238:257:367:396:428 SD: 0.4207 cents 215:221:232:239:258:369:398:430 SD: 0.4089 cents 235:242:254:261:282:403:435:470 SD: 0.3415 cents 250:257:270:278:300:429:463:500 SD: 0.3369 cents 314:323:339:349:377:538:581:628 SD: 0.3310 cents 315:324:340:350:378:540:583:630 SD: 0.2180 cents 350:360:378:389:420:600:648:700 SD: 0.1208 cents