Scala analysis: xen12-chalmers-tritriadic-mt-5-15-27
Tritriadic M->T scale built from 5:15:27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 81/80 21.506290 syntonic comma, Didymus comma 2: 9/8 203.910002 major whole tone 3: 4/3 498.044999 perfect fourth 4: 27/20 519.551289 acute fourth 5: 3/2 701.955001 perfect fifth 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 81/80 21.5063 syntonic comma, Didymus comma 2: 10/9 182.4037 minor whole tone 3: 32/27 294.1350 Pythagorean minor third 4: 81/80 21.5063 syntonic comma, Didymus comma 5: 10/9 182.4037 minor whole tone 6: 6/5 315.6413 minor third 7: 10/9 182.4037 minor whole tone
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 : 21.5 203.9 498.0 519.6 702.0 1017.6 1200.0 21.5 : 182.4 476.5 498.0 680.4 996.1 1178.5 1200.0 203.9 : 294.1 315.6 498.0 813.7 996.1 1017.6 1200.0 498.0 : 21.5 203.9 519.6 702.0 723.5 905.9 1200.0 519.6 : 182.4 498.0 680.4 702.0 884.4 1178.5 1200.0 702.0 : 315.6 498.0 519.6 702.0 996.1 1017.6 1200.0 1017.6: 182.4 203.9 386.3 680.4 702.0 884.4 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 : 157.26442 cents, oct.: 1100.85096 cents Scale is not proper Step pattern alph. order: ABCABDB Step pattern size order : ABCABDB 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 0.0 519.551 701.955 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 n-1 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 : 0.257240 Specific harmonicity : 0.201892 Fundamental : 1/240, -7.9069 octaves, 1.0901 Hz. Guide tone : 324, 8.3399 octaves, 84766.683 Hz. Exponens Consonantiae : 7.776000E+04, 16.24674 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 127.0, average 18.14286 Mersenne's string divisions : 3859170 Sum of van Prooijen's expressibility: 6.20258, average 0.88608 Sum of Tenney's harmonic distance : 12.21288, average 1.74470 Vogel's harmonic complexity : 13.57143 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: -4 .. 2 -1.00000 13 1 3: -1 .. 4 1.57143 13 3 5: -1 .. 0 -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: 0 1 2 0 1 2 1 N T3 SD: 17.7010 c. M: 32.4814 c. 12: 0 2 3 0 2 3 2 N T3 SD: 12.9688 c. M: 21.5063 c. 19: 0 3 5 0 3 5 3 N T3 SD: 12.1259 c. M: 21.5063 c. 29: 1 4 7 1 4 8 4 N SD: 12.1378 c. M:-19.8730 c. 30: 1 4 7 1 5 7 5 N SD: 13.7237 c. M:-18.4937 c. 31: 0 5 8 0 5 8 5 N T3 SD: 12.0374 c. M: 21.5063 c. 32: 1 4 8 1 5 8 5 N SD: 10.7114 c. M: 16.4100 c. 34: 1 5 8 1 5 9 5 N SD: 7.7005 c. M:-13.7878 c. 39: 1 6 9 1 6 10 6 N SD: 6.5533 c. M:-11.4746 c. 41: 1 6 10 1 6 11 6 N SD: 4.7926 c. M:-7.7620 c. 46: 1 7 11 1 7 12 7 N SD: 2.9317 c. M:-4.7857 c. 53: 1 8 13 1 8 14 8 N SD: 0.7912 c. M:-1.2716 c. 118: 2 18 29 2 18 31 18 N SD: 0.6558 c. M: 1.1673 c. 164: 3 25 40 3 25 43 25 N SD: 0.5181 c. M:-0.9680 c. 171: 3 26 42 3 26 45 26 N SD: 0.2710 c. M: 0.4537 c. 224: 4 34 55 4 34 59 34 N SD: 0.1906 c. M: 0.3386 c. 335: 6 51 82 6 51 88 51 N SD: 0.1735 c. M: 0.2829 c. 388: 7 59 95 7 59 102 59 N SD: 0.1167 c. M:-0.2137 c. 506: 9 77 124 9 77 133 77 N SD: 0.1224 c. M: 0.2050 c. 559: 10 85 137 10 85 147 85 N SD: 0.0368 c. M: 0.0650 c. 612: 11 93 150 11 93 161 93 N SD: 0.0375 c. M:-0.0623 c. 1171: 21 178 287 21 178 308 178 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 x 3 x 4 S SD: 0.0000 cents 3 x x 4 x x 5:6 S SD: 44.4125 cents 4 x x 5 x 6:7:8 S SD: 30.4779 cents 5 x 6 x 7:8:9:10 S SD: 34.0187 cents 6 x 7:8 x 9:11:12 SD: 14.1042 cents 7 x 8:9 x 11:13:14 SD: 23.7664 cents 8 x 9 x 11:12:14:16 SD: 11.6407 cents 9 x 10:12 x 14:16:18 S SD: 13.9844 cents 10 x 11:13:14:15:18:20 SD: 14.3361 cents 11 x 12 x 15:17:20:22 SD: 15.6391 cents 12 x 14:16 x 18:22:24 SD: 14.1042 cents 13 x 15:17:18:20:23:26 SD: 14.7051 cents 14 x 16 x 19:21:25:28 SD: 6.3784 cents 15:16:17:20 x 23:27:30 SD: 16.4584 cents 16:17:18:21:22:24:29:32 SD: 13.4466 cents 17:18:19 x 23:26:31:34 SD: 14.6978 cents 18:19:20:24 x 27:32:36 SD: 13.0416 cents 19:20:21:25:26:29:34:38 SD: 12.4158 cents 20:21:23 x 27:30:36:40 SD: 12.2610 cents 21:22:24:28 x 32:38:42 SD: 11.8495 cents 22:23:25:29:30:33:40:44 SD: 9.4485 cents 23:24:26 x 31:35:41:46 SD: 10.1415 cents 24:25:27:32 x 36:43:48 SD: 8.3030 cents 25:26:28:33:34:38:45:50 SD: 8.0858 cents 26:27:29 x 35:39:47:52 SD: 7.8544 cents 27:28:30:36 x 41:49:54 SD: 8.8720 cents 28:29:32:37:38:42:50:56 SD: 7.5571 cents 29:30:33 x 39:44:52:58 SD: 7.9128 cents 30:31:34:40:41:45:54:60 SD: 6.1574 cents 31:32:35:41:42:47:56:62 SD: 6.0168 cents 32:33:36 x 43:48:58:64 SD: 5.8147 cents 34:35:38:45:46:51:61:68 SD: 4.8673 cents 35:36:39 x 47:53:63:70 SD: 6.1721 cents 36:37:41:48:49:54:65:72 SD: 5.2554 cents 37:38:42:49:50:56:67:74 SD: 5.2268 cents 38:39:43 x 51:57:68:76 SD: 4.8837 cents 39:40:44:52:53:59:70:78 SD: 4.2755 cents 40:41:45:53:54:60:72:80 SD: 3.4078 cents 41:42:46:55 x 62:74:82 SD: 4.5942 cents 42:43:47:56:57:63:76:84 SD: 3.5602 cents 44:45:50:59 x 66:79:88 SD: 4.4748 cents 45:46:51:60:61:68:81:90 SD: 3.6443 cents 46:47:52:61:62:69:83:92 SD: 2.9663 cents 47:48:53:63 x 71:85:94 SD: 3.8755 cents 48:49:54:64:65:72:86:96 SD: 2.4510 cents 54:55:61:72:73:81:97:108 SD: 1.8853 cents 63:64:71:84:85:95:113:126 SD: 1.8316 cents 64:65:72:85:86:96:115:128 SD: 1.7377 cents 66:67:74:88:89:99:119:132 SD: 1.1681 cents 72:73:81:96:97:108:130:144 SD: 0.9774 cents 80:81:90:107:108:120:144:160 SD: 0.7717 cents 144:146:162:192:194:216:259:288 SD: 0.6410 cents 152:154:171:203:205:228:274:304 SD: 0.6162 cents 154:156:173:205:208:231:277:308 SD: 0.5909 cents 160:162:180:213:216:240:288:320 SD: 0.3867 cents 234:237:263:312:316:351:421:468 SD: 0.2851 cents 240:243:270:320:324:360:432:480 SD: 0.0000 cents