Scala analysis: xen10-chalmers-tritriadic-19-27-21
Tritriadic scale built from 19:27:21
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/19 173.267891 2: 441/361 346.535782 3: 9/7 435.084095 septimal major third, BP third 4: 27/19 608.351986 5: 567/361 781.619878 6: 38/21 1026.732109 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 21/19 173.2679 1: 21/19 173.2679 2: 21/19 173.2679 3: 361/343 88.5483 4: 21/19 173.2679 5: 21/19 173.2679 6: 13718/11907 245.1122 7: 21/19 173.2679
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 361/343 88.548 cents 1: 5 21/19 173.268 cents 1: 1 13718/11907 245.112 cents 2: 2 57/49 261.816 cents 2: 3 441/361 346.536 cents 2: 2 722/567 418.380 cents 3: 3 9/7 435.084 cents septimal major third, BP third 3: 1 9261/6859 519.804 cents 3: 3 38/27 591.648 cents 4: 3 27/19 608.352 cents 4: 1 13718/9261 680.196 cents 4: 3 14/9 764.916 cents septimal minor sixth 5: 2 567/361 781.620 cents 5: 3 722/441 853.464 cents 5: 2 98/57 938.184 cents 6: 1 11907/6859 954.888 cents 6: 5 38/21 1026.732 cents 6: 1 686/361 1111.452 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 173.3 346.5 435.1 608.4 781.6 1026.7 1200.0 173.3 : 173.3 261.8 435.1 608.4 853.5 1026.7 1200.0 346.5 : 88.5 261.8 435.1 680.2 853.5 1026.7 1200.0 435.1 : 173.3 346.5 591.6 764.9 938.2 1111.5 1200.0 608.4 : 173.3 418.4 591.6 764.9 938.2 1026.7 1200.0 781.6 : 245.1 418.4 591.6 764.9 853.5 1026.7 1200.0 1026.7: 173.3 346.5 519.8 608.4 781.6 954.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.5483 .. 245.1122 cents 266/243, 156.5639 cents 361/343, 88.5483 cents 2: 261.8162 .. 418.3801 cents 266/243, 156.5639 cents 729/722, 16.7040 cents 3: 435.0841 .. 591.6480 cents 266/243, 156.5639 cents 729/722, 16.7040 cents 4: 608.3520 .. 764.9159 cents 266/243, 156.5639 cents 729/722, 16.7040 cents 5: 781.6199 .. 938.1838 cents 266/243, 156.5639 cents 729/722, 16.7040 cents 6: 954.8878 .. 1111.4517 cents 266/243, 156.5639 cents 729/722, 16.7040 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 361/343, 88.5483 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 13718/11907, 245.1122 cents Average / Smallest step : 1.935989 Largest / Average step : 1.429821 Largest / Smallest step : 2.768119 Median interval of one step : 21/19, 173.2679 cents, amount: 5 Most common interval of one step : 21/19, 173.2679 cents, amount: 5 Least squares average step : 164.81066 cents, oct.: 1153.67459 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: AABAACA Step pattern size order : MMSMMLM Scale is a Constant Structure, by a margin of 16.70397 cents Scale diversity : 1.418525 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.217180 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 : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 729/722, 16.7040 cents Most common intervals : 21/19, 173.2679 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 435.084 1026.732 cents Most common triad is 0.0 173.268 1026.732 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 19 21 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 19 Odd number limit : 11907 (O: 11907 U: 11907) Highest odd numerator or denominator: 567 Scale harmonicity : 0.006779 Average absolute harmonicity : 0.164524 Specific harmonicity : 0.037483 Fundamental : 1/7581, -12.8882 octaves, 0.0345 Hz. Guide tone : 150822, 17.2025 octaves, 39458891.010 Hz. Exponens Consonantiae : 1.143382E+09, 30.09066 octaves Euler's gradus suavitatis : 84 Sum of Mann's harmonic distance : 947.0, average 135.28571 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.42807, average 1.48972 Sum of Tenney's harmonic distance : 20.82650, average 2.97521 Vogel's harmonic complexity : 41.42857 Wille's k value : 5953 Wilson's harmonic complexity : 93 Rectangular lattice diameter : 11 Triangular lattice diameter : 7 Lattice compactness : 83.91950, average 2.99712 Lattice compactness (without 2's) : 81.18697, average 2.89953 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.28571 2 1 3: -1 .. 4 1.57143 13 7: -1 .. 2 0.28571 6 1 19: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 8 / 7 = 1.14286 Average absolute exponent except 2's: 26 / 7 = 3.71429 Scale is weakly epimorphic with val: <7 10 18 32| Scale is weakly epimorphic with val: <7 10 19 31| Scale is weakly epimorphic with val: <7 10 21 29| Scale is weakly epimorphic with val: <7 10 22 28| Scale is weakly epimorphic with val: <7 11 18 30| Scale is JI-epimorphic with val: <7 11 19 29| Scale is weakly epimorphic with val: <7 11 20 28| Scale is weakly epimorphic with val: <7 11 21 27| Scale is weakly epimorphic with val: <7 12 18 28| Scale is weakly epimorphic with val: <7 12 19 27| Scale is weakly epimorphic with val: <7 12 20 33| Scale is JI-epimorphic with val: <7 12 21 32| Scale is weakly epimorphic with val: <7 12 22 31|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 50.6837 c. M:-79.2016 c. Lebeng 8: 1 1 1 1 1 2 1 P M ME S SD: 25.4683 c. M: 46.5358 c. 13: 2 2 1 2 2 2 2 SP M ME S SD: 27.5605 c. M:-49.1494 c. Oukranian 14: 2 2 1 2 2 3 2 P T3 SD: 5.8105 c. M: 10.1913 c. 41: 6 6 3 6 6 8 6 SP T3 SD: 4.8147 c. M:-8.6240 c. 49: 7 7 4 7 7 10 7 SP T3 SD: 3.2189 c. M:-5.7322 c. 55: 8 8 4 8 8 11 8 SP T3 SD: 2.1605 c. M:-3.8347 c. 63: 9 9 5 9 9 13 9 SP T3 SD: 2.1107 c. M: 3.6786 c. 69: 10 10 5 10 10 14 10 SP T3 SD: 0.7255 c. M:-1.2903 c. 132: 19 19 10 19 19 27 19 SP T3 SD: 0.7537 c. M:-1.2795 c. 146: 21 21 11 21 21 30 21 SP T3 SD: 0.7164 c. M: 1.3303 c. 152: 22 22 11 22 22 31 22 SP T3 SD: 0.5364 c. M: 0.8736 c. 201: 29 29 15 29 29 41 29 SP T3 SD: 0.4199 c. M:-0.7368 c. 215: 31 31 16 31 31 44 31 SP T3 SD: 0.2619 c. M: 0.4893 c. 284: 41 41 21 41 41 58 41 SP T3 SD: 0.0714 c. M:-0.1272 c. 651: 94 94 48 94 94 133 94 SP T3 SD: 0.0376 c. M: 0.0611 c. 935: 135 135 69 135 135 191 135 SP T3 SD: 0.0089 c. M: 0.0156 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: 39.8324 cents 3 x x 4 x 5 x 6 S SD: 40.1654 cents 4 x 5 x x 6:7:8 S SD: 26.5541 cents 5 x 6 x 7:8:9:10 S SD: 10.4573 cents 6 x 7:8 x 9:11:12 SD: 26.2063 cents 7:8 x 9:10:11:13:14 SD: 12.3149 cents 8:9:10 x 11:13:14:16 SD: 18.7063 cents 9:10:11:12:13:14:16:18 S SD: 11.1256 cents 10:11:12:13:14:16:18:20 S SD: 8.0409 cents 12:13:15 x 17:19:22:24 SD: 9.8898 cents 14:15:17:18:20:22:25:28 SD: 8.5898 cents 17:19:21:22:24:27:31:34 SD: 5.6253 cents 21:23:26:27:30:33:38:42 SD: 4.2181 cents 27:30:33:35:38:42:49:54 SD: 4.2117 cents 28:31:34:36:40:44:51:56 SD: 2.5953 cents 45:50:55:58:64:71:81:90 SD: 2.2570 cents 46:51:56:59:65:72:83:92 SD: 2.2053 cents 49:54:60:63:70:77:89:98 SD: 1.8551 cents 59:65:72:76:84:93:107:118 SD: 1.4921 cents 67:74:82:86:95:105:121:134 SD: 1.1166 cents 95:105:116:122:135:149:172:190 SD: 0.4869 cents 189:209:231:243:269:297:342:378 SD: 0.4435 cents 199:220:243:256:283:313:360:398 SD: 0.4403 cents 200:221:244:257:284:314:362:400 SD: 0.4197 cents 221:244:270:284:314:347:400:442 SD: 0.3138 cents 256:283:313:329:364:402:463:512 SD: 0.3131 cents 266:294:325:342:378:418:481:532 SD: 0.2156 cents 294:325:359:378:418:462:532:588 SD: 0.2090 cents 361:399:441:464:513:567:653:722 SD: 0.1180 cents