Scala analysis: xen12-chalmers-tritriadic-mt-15-11-5
Tritriadic M->T scale built from 15:11:5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 242/225 126.098455 2: 4/3 498.044999 perfect fourth 3: 15/11 536.950772 undecimal augmented fourth 4: 22/15 663.049228 undecimal diminished fifth 5: 20/11 1034.995772 large minor seventh 6: 88/45 1161.094227 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 45/44 38.9058 1/5-tone 1: 242/225 126.0985 2: 150/121 371.9465 3: 45/44 38.9058 1/5-tone 4: 242/225 126.0985 5: 150/121 371.9465 6: 242/225 126.0985 7: 45/44 38.9058 1/5-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 45/44 38.906 cents 1/5-tone 1: 3 242/225 126.098 cents 1: 2 150/121 371.947 cents 2: 3 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 1 3375/2662 410.852 cents 2: 3 4/3 498.045 cents perfect fourth 3: 1 1331/1125 291.103 cents 3: 5 15/11 536.951 cents undecimal augmented fourth 3: 1 968/675 624.143 cents 4: 1 675/484 575.857 cents 4: 5 22/15 663.049 cents undecimal diminished fifth 4: 1 2250/1331 908.897 cents 5: 3 3/2 701.955 cents perfect fifth 5: 1 5324/3375 789.148 cents 5: 3 20/11 1034.996 cents large minor seventh 6: 2 121/75 828.053 cents 6: 3 225/121 1073.902 cents two (undecimal augmented fourth) 6: 2 88/45 1161.094 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 : 126.1 498.0 537.0 663.0 1035.0 1161.1 1200.0 126.1 : 371.9 410.9 537.0 908.9 1035.0 1073.9 1200.0 498.0 : 38.9 165.0 537.0 663.0 702.0 828.1 1200.0 537.0 : 126.1 498.0 624.1 663.0 789.1 1161.1 1200.0 663.0 : 371.9 498.0 537.0 663.0 1035.0 1073.9 1200.0 1035.0: 126.1 165.0 291.1 663.0 702.0 828.1 1200.0 1161.1: 38.9 165.0 537.0 575.9 702.0 1073.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.9058 .. 371.9465 cents 40/33, 333.0408 cents 45/44, 38.9058 cents 2: 165.0042 .. 498.0450 cents 40/33, 333.0408 cents 1331/1500,-206.9423 cents 3: 291.1027 .. 624.1435 cents 40/33, 333.0408 cents 1331/1500,-206.9423 cents 4: 575.8565 .. 908.8973 cents 40/33, 333.0408 cents 455625/468512,-48.2869 cents 5: 701.9550 .. 1034.9958 cents 40/33, 333.0408 cents 1331/1500,-206.9423 cents 6: 828.0535 .. 1161.0942 cents 40/33, 333.0408 cents 1331/1500,-206.9423 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 45/44, 38.9058 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 150/121, 371.9465 cents Average / Smallest step : 4.406250 Largest / Average step : 2.169688 Largest / Smallest step : 9.560189 Median interval of one step : 242/225, 126.0985 cents, amount: 3 Most common interval of one step : 242/225, 126.0985 cents, amount: 3 Least squares average step : 185.19130 cents, oct.: 1296.33909 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : MLSMLMS Scale is a Constant Structure, by a margin of 38.90577 cents Scale diversity : 1.409353 Lumma stability : 0.064843 Lumma impropriety factor : 0.595307 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 : 45/44, 38.9058 cents Most common intervals : 15/11, 536.9508 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 498.045 663.049 cents Most common triad is 0.0 536.951 663.049 cents, amount: 3 Number of recognisable fifths : 3, average 701.9550 cents Scale contains two identical disjunct "tetrachords" of 3 notes Scale contains a complete diamond : 11 15 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 -- Rational properties -- Prime limit : 11 Odd number limit : 3375 (O: 3375 U: 3375) Highest odd numerator or denominator: 225 Scale harmonicity : 0.011800 Average absolute harmonicity : 0.196057 Specific harmonicity : 0.066451 Fundamental : 1/2475, -11.2732 octaves, 0.1057 Hz. Guide tone : 14520, 13.8258 octaves, 3798803.208 Hz. Exponens Consonantiae : 3.593700E+07, 25.09897 octaves Euler's gradus suavitatis : 52 Sum of Mann's harmonic distance : 352.0, average 50.28571 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.87609, average 1.12516 Sum of Tenney's harmonic distance : 16.79232, average 2.39890 Vogel's harmonic complexity : 28.00000 Wille's k value : 1687 Wilson's harmonic complexity : 57 Rectangular lattice diameter : 9 Triangular lattice diameter : 6 Lattice compactness : 76.40290, average 2.72868 Lattice compactness (without 2's) : 62.99576, average 2.24985 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 3 1.42857 10 1 3: -2 .. 1 -0.71429 7 1 5: -2 .. 1 -0.28571 6 11: -1 .. 2 0.28571 6 5 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 19 / 7 = 2.71429 Scale is weakly epimorphic with val: <7 10 15 26| Scale is weakly epimorphic with val: <7 10 18 22| Scale is weakly epimorphic with val: <7 11 15 25| Scale is weakly epimorphic with val: <7 11 16 26| Scale is JI-epimorphic with val: <7 12 15 24| Scale is JI-epimorphic with val: <7 12 16 25| Scale is JI-epimorphic with val: <7 12 17 26|
FIT/MODE
7: 1 2 0 1 2 1 0 N T3 SD: 26.4600 c. M:-45.3301 c. 9: 1 3 0 1 3 1 0 N T3 SD: 23.4231 c. M:-38.9058 c. 16: 2 5 0 2 5 2 0 N T3 SD: 21.7856 c. M:-38.9058 c. 18: 2 5 1 2 5 2 1 N T3 SD: 20.9028 c. M: 34.9958 c. 19: 2 6 0 2 6 2 1 N SD: 21.4927 c. M: 31.6876 c. 20: 2 6 1 2 6 2 1 N T3 SD: 12.2547 c. M: 21.0942 c. 22: 2 7 1 2 7 2 1 N T3 SD: 10.2210 c. M: 17.0075 c. 27: 3 8 1 3 8 3 1 N T3 SD: 7.1333 c. M: 12.7735 c. 29: 3 9 1 3 9 3 1 N T3 SD: 1.4331 c. M: 2.4735 c. 94: 10 29 3 10 29 10 3 N T3 SD: 0.8421 c. M:-1.5611 c. 123: 13 38 4 13 38 13 4 N T3 SD: 0.5030 c. M: 0.8494 c. 152: 16 47 5 16 47 16 5 N T3 SD: 0.4579 c. M: 0.7852 c. 219: 23 68 7 23 68 23 7 N T3 SD: 0.3849 c. M:-0.6207 c. 248: 26 77 8 26 77 26 8 N T3 SD: 0.2730 c. M:-0.4881 c. 277: 29 86 9 29 86 29 9 N T3 SD: 0.2681 c. M: 0.4667 c. 342: 36 106 11 36 106 36 11 N T3 SD: 0.1753 c. M:-0.3093 c. 371: 39 115 12 39 115 39 12 N T3 SD: 0.0513 c. M:-0.0918 c. 771: 81 239 25 81 239 81 25 N T3 SD: 0.0164 c. M: 0.0284 c. 1142: 120 354 37 120 354 120 37 N T3 SD: 0.0188 c. M:-0.0305 c. 1913: 201 593 62 201 593 201 62 N T3 SD: 0.0155 c. M:-0.0278 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: 19.4529 cents 3 x 4 x x 5 x 6 S SD: 50.2124 cents 4 x 5 x 6:7 x 8 S SD: 33.8895 cents 5 x x 7 x 9 x 10 SD: 16.2569 cents 6:7:8 x 9:11 x 12 SD: 29.3510 cents 7:8:9 x 10:13 x 14 SD: 27.1501 cents 8:9 x 11:12:15 x 16 SD: 20.6036 cents 9:10:12 x 13:16 x 18 SD: 14.6732 cents 10:11:13:14:15:18 x 20 SD: 14.2664 cents 11:12 x 15:16:20 x 22 S SD: 5.6870 cents 12:13:16 x 18:22:23:24 SD: 9.2571 cents 13:14:17:18:19:24:25:26 SD: 8.3418 cents 14:15 x 19:21:25:27:28 SD: 9.3956 cents 15:16:20 x 22:27:29:30 SD: 5.0018 cents 17:18 x 23:25:31:33:34 SD: 5.6102 cents 20:22 x 27:29:36:39:40 SD: 8.3913 cents 21:23:28:29:31:38:41:42 SD: 5.8286 cents 22:24:29:30:32:40:43:44 SD: 4.9504 cents 23:25:31 x 34:42:45:46 SD: 5.0731 cents 24:26:32:33:35:44:47:48 SD: 3.7027 cents 26:28:35 x 38:47:51:52 SD: 3.5134 cents 27:29:36:37:40:49:53:54 SD: 2.9771 cents 28:30:37:38:41:51:55:56 SD: 2.9644 cents 38:41:51:52:56:69:74:76 SD: 2.5619 cents 39:42:52:53:57:71:76:78 SD: 1.5548 cents 66:71:88:90:97:120:129:132 SD: 0.5283 cents 159:171:212:217:233:289:311:318 SD: 0.3118 cents 225:242:300:307:330:409:440:450 SD: 0.1565 cents 330:355:440:450:484:600:645:660 SD: 0.1360 cents 489:526:652:667:717:889:956:978 SD: 0.1238 cents 555:597:740:757:814:1009:1085:1110 SD: 0.1028 cents