Scala analysis: xen12-chalmers-tritriadic-mt-27-9-5
Tritriadic M->T scale built from 27:9:5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 4/3 498.044999 perfect fourth 3: 40/27 680.448711 grave fifth 4: 3/2 701.955001 perfect fifth 5: 16/9 996.089998 Pythagorean minor seventh 6: 160/81 1178.493710 octave - syntonic comma 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 81/80 21.5063 syntonic comma, Didymus comma 1: 10/9 182.4037 minor whole tone 2: 6/5 315.6413 minor third 3: 10/9 182.4037 minor whole tone 4: 81/80 21.5063 syntonic comma, Didymus comma 5: 32/27 294.1350 Pythagorean minor third 6: 10/9 182.4037 minor whole tone 7: 81/80 21.5063 syntonic comma, Didymus comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 81/80 21.506 cents syntonic comma, Didymus comma 1: 3 10/9 182.404 cents minor whole tone 1: 1 32/27 294.135 cents Pythagorean minor third 1: 1 6/5 315.641 cents minor third 2: 3 9/8 203.910 cents major whole tone 2: 1 6/5 315.641 cents minor third 2: 1 320/243 476.539 cents grave fourth 2: 2 4/3 498.045 cents perfect fourth 3: 1 5/4 386.314 cents major third 3: 3 4/3 498.045 cents perfect fourth 3: 2 27/20 519.551 cents acute fourth 3: 1 40/27 680.449 cents grave fifth 4: 1 27/20 519.551 cents acute fourth 4: 2 40/27 680.449 cents grave fifth 4: 3 3/2 701.955 cents perfect fifth 4: 1 8/5 813.686 cents minor sixth 5: 2 3/2 701.955 cents perfect fifth 5: 1 243/160 723.461 cents acute fifth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 5/3 884.359 cents major sixth, BP sixth 6: 1 27/16 905.865 cents Pythagorean major sixth 6: 3 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 160/81 1178.494 cents octave - syntonic comma Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 182.4 498.0 680.4 702.0 996.1 1178.5 1200.0 182.4 : 315.6 498.0 519.6 813.7 996.1 1017.6 1200.0 498.0 : 182.4 203.9 498.0 680.4 702.0 884.4 1200.0 680.4 : 21.5 315.6 498.0 519.6 702.0 1017.6 1200.0 702.0 : 294.1 476.5 498.0 680.4 996.1 1178.5 1200.0 996.1 : 182.4 203.9 386.3 702.0 884.4 905.9 1200.0 1178.5: 21.5 203.9 519.6 702.0 723.5 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 315.6413 cents 32/27, 294.1350 cents 81/80, 21.5063 cents 2: 203.9100 .. 498.0450 cents 32/27, 294.1350 cents 15/16,-111.7313 cents 3: 386.3137 .. 680.4487 cents 32/27, 294.1350 cents 15/16,-111.7313 cents 4: 519.5513 .. 813.6863 cents 32/27, 294.1350 cents 729/800,-160.8974 cents 5: 701.9550 .. 996.0900 cents 32/27, 294.1350 cents 15/16,-111.7313 cents 6: 884.3587 .. 1178.4937 cents 32/27, 294.1350 cents 15/16,-111.7313 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 81/80, 21.5063 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 7.971090 Largest / Average step : 1.841241 Largest / Smallest step : 14.676697 Median interval of one step : 10/9, 182.4037 cents, amount: 3 Most common interval of one step : 10/9, 182.4037 cents, amount: 3 Least squares average step : 189.13623 cents, oct.: 1323.95361 cents Scale is not proper Step pattern alph. order: ABACDAC Step pattern size order : BDBACBA Scale is not a Constant Structure Scale diversity : 1.256667 Lumma stability : 0.035844 Lumma impropriety factor : 0.506519 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 : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 81/80, 21.5063 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 182.404 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale contains a complete diamond : 1 3 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 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.038860 Average absolute harmonicity : 0.253639 Specific harmonicity : 0.201892 Fundamental : 1/162, -7.3399 octaves, 1.6150 Hz. Guide tone : 480, 8.9069 octaves, 125580.271 Hz. Exponens Consonantiae : 7.776000E+04, 16.24674 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 183.5, average 26.21429 Mersenne's string divisions : 161066325 Sum of van Prooijen's expressibility: 6.20258, average 0.88608 Sum of Tenney's harmonic distance : 13.41700, average 1.91671 Vogel's harmonic complexity : 12.57143 Wille's k value : 121 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 95.25100, average 3.40182 Lattice compactness (without 2's) : 60.89015, average 2.17465 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 5 2.14286 17 1 3: -4 .. 1 -1.57143 13 3 5: 0 .. 1 0.42857 3 3 Average exponent except 2's :-8 / 7 =-1.14286 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 18| Scale is weakly epimorphic with val: <7 11 17| Scale is weakly epimorphic with val: <7 12 16|
FIT/MODE
7: 1 2 1 0 2 1 0 N T3 SD: 17.7010 c. M:-32.4814 c. 12: 2 3 2 0 3 2 0 N T3 SD: 12.9688 c. M:-21.5063 c. 19: 3 5 3 0 5 3 0 N T3 SD: 12.1259 c. M:-21.5063 c. 29: 4 8 4 1 7 4 1 N SD: 12.1378 c. M: 19.8730 c. 31: 5 8 5 0 8 5 0 N T3 SD: 12.0374 c. M:-21.5063 c. 32: 5 8 5 1 8 4 1 N SD: 10.7114 c. M:-16.4100 c. 34: 5 9 5 1 8 5 1 N SD: 7.7005 c. M: 13.7878 c. 39: 6 10 6 1 9 6 1 N SD: 6.5533 c. M: 11.4746 c. 41: 6 11 6 1 10 6 1 N SD: 4.7926 c. M: 7.7620 c. 46: 7 12 7 1 11 7 1 N SD: 2.9317 c. M: 4.7857 c. 53: 8 14 8 1 13 8 1 N SD: 0.7912 c. M: 1.2716 c. 118: 18 31 18 2 29 18 2 N SD: 0.6558 c. M:-1.1673 c. 164: 25 43 25 3 40 25 3 N SD: 0.5181 c. M: 0.9680 c. 171: 26 45 26 3 42 26 3 N SD: 0.2710 c. M:-0.4537 c. 224: 34 59 34 4 55 34 4 N SD: 0.1906 c. M:-0.3386 c. 335: 51 88 51 6 82 51 6 N SD: 0.1735 c. M:-0.2829 c. 388: 59 102 59 7 95 59 7 N SD: 0.1167 c. M: 0.2137 c. 506: 77 133 77 9 124 77 9 N SD: 0.1224 c. M:-0.2050 c. 559: 85 147 85 10 137 85 10 N SD: 0.0368 c. M:-0.0650 c. 612: 93 161 93 11 150 93 11 N SD: 0.0375 c. M: 0.0623 c. 1171: 178 308 178 21 287 178 21 N SD: 0.0102 c. M: 0.0183 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: 0.0000 cents 3 x 4 x x 5 x 6 S SD: 37.2438 cents 4 x 5 x 6:7 x 8 S SD: 28.7524 cents 5:6:7 x 8:9 x 10 S SD: 38.9016 cents 6:7:8 x 9:11 x 12 SD: 19.9727 cents 7:8:9:10:11:12 x 14 S SD: 24.0121 cents 8:9:11 x 12:14 x 16 SD: 12.7183 cents 9:10:12:13:14:16 x 18 S SD: 12.7859 cents 10:11:13 x 15:18 x 20 SD: 10.3661 cents 11:12:15:16:17:20 x 22 SD: 14.6407 cents 12:13:16 x 18:21 x 24 SD: 10.3237 cents 13:14:17:19:20:23 x 26 SD: 13.5389 cents 14:16:19 x 21:25 x 28 SD: 11.6223 cents 15:17:20:22:23:27 x 30 SD: 9.7017 cents 16:18:21 x 24:28 x 32 S SD: 8.8299 cents 17:19:23:25:26:30 x 34 SD: 7.8147 cents 18:20:24 x 27:32 x 36 SD: 0.0000 cents 19:21:25:28:29:34 x 38 SD: 6.9286 cents 20:22:27 x 30:36 x 40 SD: 7.0079 cents 21:23:28:31:32:37:41:42 SD: 6.4710 cents 22:24:29 x 33:39:43:44 SD: 6.9911 cents 23:26:31:34:35:41:45:46 SD: 6.6575 cents 24:27:32 x 36:43:47:48 SD: 4.9083 cents 26:29:35 x 39:46:51:52 SD: 3.8547 cents 27:30:36:40:41:48:53:54 SD: 3.4078 cents 35:39:47:52:53:62:69:70 SD: 3.2572 cents 36:40:48:53:54:64:71:72 SD: 1.5981 cents 54:60:72:80:81:96:107:108 SD: 0.7717 cents 90:100:120:133:135:160:178:180 SD: 0.6919 cents 108:120:144:160:162:192:213:216 SD: 0.3867 cents 162:180:216:240:243:288:320:324 SD: 0.0000 cents