Scala analysis: xen09-chalmers-tritriadic-11-16-20
Tritriadic scale built from 11:16:20
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: 160/121 483.677829 3: 16/11 648.682058 undecimal semi-diminished fifth 4: 8/5 813.686286 minor sixth 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: 1600/1331 318.6736 3: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 125/121 56.3053 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: 1 125/121 56.305 cents 1: 5 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 1600/1331 318.674 cents 2: 2 25/22 221.309 cents undecimal acute whole tone 2: 3 121/100 330.008 cents two (Ptolemy's second, 4/5-tone) 2: 2 160/121 483.678 cents 3: 3 5/4 386.314 cents major third 3: 1 1331/1000 495.013 cents 3: 3 16/11 648.682 cents undecimal semi-diminished fifth 4: 3 11/8 551.318 cents undecimal semi-augmented fourth 4: 1 2000/1331 704.987 cents 4: 3 8/5 813.686 cents minor sixth 5: 2 121/80 716.322 cents 5: 3 200/121 869.992 cents 5: 2 44/25 978.691 cents undecimal grave minor seventh 6: 1 1331/800 881.326 cents 6: 5 20/11 1034.996 cents large minor seventh 6: 1 242/125 1143.695 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 : 165.0 483.7 648.7 813.7 870.0 1035.0 1200.0 165.0 : 318.7 483.7 648.7 705.0 870.0 1035.0 1200.0 483.7 : 165.0 330.0 386.3 551.3 716.3 881.3 1200.0 648.7 : 165.0 221.3 386.3 551.3 716.3 1035.0 1200.0 813.7 : 56.3 221.3 386.3 551.3 870.0 1035.0 1200.0 870.0 : 165.0 330.0 495.0 813.7 978.7 1143.7 1200.0 1035.0: 165.0 330.0 648.7 813.7 978.7 1035.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 56.3053 .. 318.6736 cents 64/55, 262.3683 cents 125/121, 56.3053 cents 2: 221.3095 .. 483.6778 cents 64/55, 262.3683 cents 121/128,-97.3641 cents 3: 386.3137 .. 648.6821 cents 64/55, 262.3683 cents 121/128,-97.3641 cents 4: 551.3179 .. 813.6863 cents 64/55, 262.3683 cents 121/128,-97.3641 cents 5: 716.3222 .. 978.6905 cents 64/55, 262.3683 cents 121/128,-97.3641 cents 6: 881.3264 .. 1143.6947 cents 64/55, 262.3683 cents 121/128,-97.3641 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 125/121, 56.3053 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 1600/1331, 318.6736 cents Average / Smallest step : 3.044628 Largest / Average step : 1.858929 Largest / Smallest step : 5.659749 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 : 180.66488 cents, oct.: 1264.65418 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABAACAA Step pattern size order : MLMMSMM Scale is a Constant Structure, by a margin of 11.33486 cents Scale diversity : 1.386836 Lumma stability : 0.093842 Lumma impropriety factor : 0.405684 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 : 161051/160000, 11.3349 cents Most common intervals : 11/10, 165.0042 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 648.682 1034.996 cents Most common triad is 0.0 165.004 1034.996 cents, amount: 3 Number of recognisable fifths : 3, average 712.5439 cents Number of appreciable 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% Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 -- Rational properties -- Prime limit : 11 Odd number limit : 1331 (O: 1331 U: 1331) Highest odd numerator or denominator: 121 Scale harmonicity : 0.012540 Average absolute harmonicity : 0.181183 Specific harmonicity : 0.069341 Fundamental : 1/1210, -10.2408 octaves, 0.2162 Hz. Guide tone : 8800, 13.1033 octaves, 2302304.975 Hz. Exponens Consonantiae : 1.064800E+07, 23.34408 octaves Euler's gradus suavitatis : 49 Sum of Mann's harmonic distance : 348.5, average 49.78571 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.98872, average 1.14125 Sum of Tenney's harmonic distance : 17.20314, average 2.45759 Vogel's harmonic complexity : 24.00000 Wille's k value : 665 Wilson's harmonic complexity : 48 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 91.04741, average 3.25169 Lattice compactness (without 2's) : 51.84729, average 1.85169 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 5 2.42857 19 1 5: -1 .. 2 0.28571 6 1 11: -2 .. 1 -0.71429 7 5 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 16 26| Scale is JI-epimorphic with val: <7 17 25| Scale is weakly epimorphic with val: <7 18 24|
FIT/MODE
7: 1 2 1 1 0 1 1 N T3 SD: 25.1973 c. M:-43.4566 c. 13: 2 3 2 2 0 2 2 N T3 SD: 21.0304 c. M: 39.2223 c. 15: 2 4 2 2 1 2 2 N T3 SD: 7.8054 c. M: 13.6863 c. 22: 3 6 3 3 1 3 3 N T3 SD: 4.1076 c. M:-7.2313 c. 37: 5 10 5 5 2 5 5 N T3 SD: 3.0384 c. M:-5.6841 c. 59: 8 16 8 8 3 8 8 N T3 SD: 2.8311 c. M:-4.5847 c. 65: 9 17 9 9 3 9 9 N T3 SD: 2.0615 c. M: 3.6778 c. 72: 10 19 10 10 3 10 10 N T3 SD: 1.9756 c. M: 3.3249 c. 87: 12 23 12 12 4 12 12 N T3 SD: 0.6095 c. M: 1.0260 c. 109: 15 29 15 15 5 15 15 N T3 SD: 0.5803 c. M:-0.9926 c. 124: 17 33 17 17 6 17 17 N T3 SD: 0.5564 c. M:-0.9762 c. 196: 27 52 27 27 9 27 27 N T3 SD: 0.3770 c. M: 0.6038 c. 211: 29 56 29 29 10 29 29 N T3 SD: 0.2372 c. M: 0.4161 c. 298: 41 79 41 41 14 41 41 N T3 SD: 0.2572 c. M: 0.4564 c. 320: 44 85 44 44 15 44 44 N T3 SD: 0.0447 c. M:-0.0722 c. 851: 117 226 117 117 40 117 117 N T3 SD: 0.0320 c. M: 0.0553 c. 1171: 161 311 161 161 55 161 161 N T3 SD: 0.0186 c. M:-0.0341 c. 1491: 205 396 205 205 70 205 205 N T3 SD: 0.0166 c. M:-0.0286 c. 1811: 249 481 249 249 85 249 249 N T3 SD: 0.0189 c. M:-0.0328 c. 1898: 261 504 261 261 89 261 261 N T3 SD: 0.0124 c. M: 0.0232 c. 2218: 305 589 305 305 104 305 305 N T3 SD: 0.0121 c. M:-0.0198 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: 26.6365 cents 3 x 4 x x 5 x 6 S SD: 6.7727 cents 4 x 5:6 x x 7:8 S SD: 32.3035 cents 5:6 x 7:8 x 9:10 S SD: 33.0894 cents 6:7:8:9 x 10:11:12 S SD: 19.6031 cents 7:8:9:10:11:12:13:14 H SD: 16.9149 cents 8:9:11:12:13 x 15:16 SD: 18.6230 cents 9:10:12:13:14:15:16:18 S SD: 9.8492 cents 11:12:15:16 x 18:20:22 S SD: 9.6424 cents 12:13:16:17:19:20:22:24 SD: 8.7287 cents 13:14:17:19:21 x 24:26 SD: 8.7558 cents 15:17:20:22:24:25:27:30 SD: 8.5632 cents 16:18:21:23:26 x 29:32 SD: 8.8918 cents 17:19:22:25:27:28:31:34 SD: 7.4762 cents 18:20:24:26:29:30:33:36 SD: 4.9715 cents 20:22:26:29:32:33:36:40 SD: 4.9681 cents 22:24:29:32:35:36:40:44 SD: 3.6022 cents 28:31:37:41:45:46:51:56 SD: 2.9986 cents 31:34:41:45:50:51:56:62 SD: 2.9381 cents 37:41:49:54:59:61:67:74 SD: 2.5000 cents 38:42:50:55:61:63:69:76 SD: 2.3898 cents 40:44:53:58:64:66:73:80 SD: 1.3768 cents 72:79:95:105:115:119:131:144 SD: 1.1436 cents 81:89:107:118:130:134:147:162 SD: 1.0587 cents 90:99:119:131:144:149:164:180 SD: 0.6998 cents 121:133:160:176:194:200:220:242 SD: 0.5433 cents 130:143:172:189:208:215:236:260 SD: 0.4470 cents 170:187:225:247:272:281:309:340 SD: 0.3626 cents 220:242:291:320:352:364:400:440 SD: 0.2590 cents 242:266:320:352:387:400:440:484 SD: 0.2256 cents 363:399:480:528:581:600:660:726 SD: 0.2045 cents 400:440:529:582:640:661:727:800 SD: 0.1387 cents 440:484:582:640:704:727:800:880 SD: 0.1207 cents 490:539:648:713:784:810:891:980 SD: 0.1042 cents 550:605:727:800:880:909:1000:1100 SD: 0.0960 cents