Scala analysis: xen09-chalmers-tritriadic-11-14-20
Tritriadic scale built from 11:14:20
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 140/121 252.503736 3: 14/11 417.507964 undecimal diminished fourth or major third 4: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 5: 200/121 869.991543 6: 20/11 1034.995772 large minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 11/10 165.0042 Ptolemy's second, 4/5-tone 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 1400/1331 87.4995 3: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 1000/847 287.4794 6: 11/10 165.0042 Ptolemy's second, 4/5-tone 7: 11/10 165.0042 Ptolemy's second, 4/5-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 1400/1331 87.500 cents 1: 5 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 1000/847 287.479 cents 2: 2 140/121 252.504 cents 2: 3 121/100 330.008 cents two (Ptolemy's second, 4/5-tone) 2: 2 100/77 452.484 cents 3: 3 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 1331/1000 495.013 cents 3: 3 10/7 617.488 cents Euler's tritone 4: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 1 2000/1331 704.987 cents 4: 3 11/7 782.492 cents undecimal augmented fifth 5: 2 77/50 747.516 cents 5: 3 200/121 869.992 cents 5: 2 121/70 947.496 cents 6: 1 847/500 912.521 cents 6: 5 20/11 1034.996 cents large minor seventh 6: 1 1331/700 1112.500 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 : 165.0 252.5 417.5 582.5 870.0 1035.0 1200.0 165.0 : 87.5 252.5 417.5 705.0 870.0 1035.0 1200.0 252.5 : 165.0 330.0 617.5 782.5 947.5 1112.5 1200.0 417.5 : 165.0 452.5 617.5 782.5 947.5 1035.0 1200.0 582.5 : 287.5 452.5 617.5 782.5 870.0 1035.0 1200.0 870.0 : 165.0 330.0 495.0 582.5 747.5 912.5 1200.0 1035.0: 165.0 330.0 417.5 582.5 747.5 1035.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 87.4995 .. 287.4794 cents 55/49, 199.9798 cents 1400/1331, 87.4995 cents 2: 252.5037 .. 452.4836 cents 55/49, 199.9798 cents 49/50,-34.9756 cents 3: 417.5080 .. 617.4878 cents 55/49, 199.9798 cents 49/50,-34.9756 cents 4: 582.5122 .. 782.4920 cents 55/49, 199.9798 cents 49/50,-34.9756 cents 5: 747.5164 .. 947.4963 cents 55/49, 199.9798 cents 49/50,-34.9756 cents 6: 912.5206 .. 1112.5005 cents 55/49, 199.9798 cents 49/50,-34.9756 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 1400/1331, 87.4995 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 1000/847, 287.4794 cents Average / Smallest step : 1.959195 Largest / Average step : 1.676963 Largest / Smallest step : 3.285497 Median interval of one step : 11/10, 165.0042 cents, amount: 5 Most common interval of one step : 11/10, 165.0042 cents, amount: 5 Least squares average step : 165.80369 cents, oct.: 1160.62584 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABAACAA Step pattern size order : MSMMLMM Scale is a Constant Structure, by a margin of 34.97561 cents Scale diversity : 1.444532 Lumma stability : 0.145833 Lumma impropriety factor : 0.145732 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 : 50/49, 34.9756 cents Most common intervals : 11/10, 165.0042 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 417.508 1034.996 cents Most common triad is 0.0 165.004 1034.996 cents, amount: 3 Number of recognisable fifths : 1, average 704.9873 cents Scale contains a complete diamond : 5 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 : 0.011360 Average absolute harmonicity : 0.172559 Specific harmonicity : 0.060822 Fundamental : 1/1210, -10.2408 octaves, 0.2162 Hz. Guide tone : 15400, 13.9106 octaves, 4029033.706 Hz. Exponens Consonantiae : 1.863400E+07, 24.15143 octaves Euler's gradus suavitatis : 53 Sum of Mann's harmonic distance : 337.0, average 48.14286 Mersenne's string divisions : 606015900 Sum of van Prooijen's expressibility: 8.13485, average 1.16212 Sum of Tenney's harmonic distance : 17.02916, average 2.43274 Vogel's harmonic complexity : 25.71429 Wille's k value : 665 Wilson's harmonic complexity : 55 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 73.35402, average 2.61979 Lattice compactness (without 2's) : 56.50032, average 2.01787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.14286 10 1 5: -1 .. 2 0.28571 6 7: 0 .. 1 0.42857 3 1 11: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is JI-epimorphic with val: <7 15 19 23| Scale is weakly epimorphic with val: <7 15 20 25| Scale is weakly epimorphic with val: <7 16 19 22| Scale is JI-epimorphic with val: <7 16 20 24| = patent Scale is weakly epimorphic with val: <7 16 21 26| Scale is weakly epimorphic with val: <7 17 18 26| Scale is weakly epimorphic with val: <7 17 20 23| Scale is JI-epimorphic with val: <7 17 21 25| Scale is weakly epimorphic with val: <7 18 20 22| Scale is weakly epimorphic with val: <7 18 21 24| Scale is JI-epimorphic with val: <7 18 22 26|
FIT/MODE
7: 1 0 1 1 2 1 1 N T3 SD: 49.3507 c. M: 81.0752 c. 8: 1 1 1 1 2 1 1 P M ME S SD: 26.6410 c. M:-47.4963 c. 14: 2 1 2 2 3 2 2 P T3 SD: 9.9813 c. M:-17.4878 c. 23: 3 2 3 3 6 3 3 N T3 SD: 9.0685 c. M:-16.9650 c. 29: 4 2 4 4 7 4 4 N T3 SD: 2.4930 c. M: 4.2279 c. 66: 9 5 9 9 16 9 9 N T3 SD: 1.5274 c. M:-2.7357 c. 80: 11 6 11 11 19 11 11 N T3 SD: 1.6314 c. M:-2.4963 c. 95: 13 7 13 13 23 13 13 N T3 SD: 0.9539 c. M:-1.5874 c. 109: 15 8 15 15 26 15 15 N T3 SD: 0.5685 c. M:-0.9740 c. 138: 19 10 19 19 33 19 19 N T3 SD: 0.2403 c. M: 0.4263 c. 342: 47 25 47 47 82 47 47 N T3 SD: 0.1011 c. M:-0.1839 c. 480: 66 35 66 66 115 66 66 N T3 SD: 0.0069 c. M: 0.0122 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: 59.7214 cents 3 x x 4 x 5 x 6 S SD: 27.2695 cents 4 x x 5:6 x 7:8 S SD: 35.0162 cents 5 x 6 x 7:8:9:10 S SD: 17.2735 cents 6 x 7:8 x 10:11:12 S SD: 16.8588 cents 7 x 8:9:10:12:13:14 S SD: 14.2603 cents 8:9 x 10:11:13:15:16 SD: 14.1087 cents 9:10 x 11:13:15:16:18 SD: 16.5531 cents 10:11:12:13:14:17:18:20 SD: 12.7801 cents 11:12:13:14:15:18:20:22 S SD: 8.9583 cents 12:13:14:15:17:20:22:24 SD: 7.4378 cents 15 x 17:19:21:25:27:30 SD: 7.1885 cents 18:20:21:23:25:30:33:36 SD: 4.8641 cents 26:29:30:33:36:43:47:52 SD: 4.7182 cents 28:31:32:36:39:46:51:56 SD: 4.7133 cents 29:32:34:37:41:48:53:58 SD: 4.3899 cents 30:33:35:38:42:50:55:60 SD: 3.7458 cents 32:35:37:41:45:53:58:64 SD: 2.6082 cents 38:42:44:48:53:63:69:76 SD: 2.5386 cents 40:44:46:51:56:66:73:80 SD: 1.8729 cents 58:64:67:74:81:96:105:116 SD: 1.6601 cents 69:76:80:88:97:114:125:138 SD: 1.5784 cents 70:77:81:89:98:116:127:140 SD: 0.8656 cents 110:121:127:140:154:182:200:220 SD: 0.5853 cents 158:174:183:201:221:261:287:316 SD: 0.5356 cents 172:189:199:219:241:284:313:344 SD: 0.4845 cents 190:209:220:242:266:314:345:380 SD: 0.4203 cents 198:218:229:252:277:327:360:396 SD: 0.3682 cents 210:231:243:267:294:347:382:420 SD: 0.2900 cents 242:266:280:308:339:400:440:484 SD: 0.2363 cents 363:399:420:462:508:600:660:726 SD: 0.2098 cents 400:440:463:509:560:661:727:800 SD: 0.1559 cents 440:484:509:560:616:727:800:880 SD: 0.1027 cents 510:561:590:649:714:843:927:1020 SD: 0.0880 cents