Scala analysis: xen12-chalmers-tritriadic-mt-1-21-23
Tritriadic M->T scale built from 1:21:23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 23/21 157.493440 2: 21/16 470.780907 narrow fourth 3: 23/16 628.274347 23rd harmonic 4: 32/21 729.219093 wide fifth 5: 441/256 941.561815 two (narrow fourth) 6: 483/256 1099.055255 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 512/483 100.9447 1: 23/21 157.4934 2: 441/368 313.2875 3: 23/21 157.4934 4: 512/483 100.9447 5: 9261/8192 212.3427 6: 23/21 157.4934 7: 512/483 100.9447
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 512/483 100.945 cents 1: 3 23/21 157.493 cents 1: 1 9261/8192 212.343 cents 1: 1 441/368 313.287 cents 2: 3 512/441 258.438 cents 2: 1 441/368 313.287 cents 2: 1 10143/8192 369.836 cents 2: 2 21/16 470.781 cents narrow fourth 3: 1 11776/9261 415.932 cents 3: 3 21/16 470.781 cents narrow fourth 3: 2 32/23 571.726 cents 23rd subharmonic 3: 1 23/16 628.274 cents 23rd harmonic 4: 1 32/23 571.726 cents 23rd subharmonic 4: 2 23/16 628.274 cents 23rd harmonic 4: 3 32/21 729.219 cents wide fifth 4: 1 9261/5888 784.068 cents 5: 2 32/21 729.219 cents wide fifth 5: 1 16384/10143 830.164 cents 5: 1 736/441 886.713 cents 5: 3 441/256 941.562 cents two (narrow fourth) 6: 1 736/441 886.713 cents 6: 1 16384/9261 987.657 cents 6: 3 42/23 1042.507 cents 6: 2 483/256 1099.055 cents 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 : 157.5 470.8 628.3 729.2 941.6 1099.1 1200.0 157.5 : 313.3 470.8 571.7 784.1 941.6 1042.5 1200.0 470.8 : 157.5 258.4 470.8 628.3 729.2 886.7 1200.0 628.3 : 100.9 313.3 470.8 571.7 729.2 1042.5 1200.0 729.2 : 212.3 369.8 470.8 628.3 941.6 1099.1 1200.0 941.6 : 157.5 258.4 415.9 729.2 886.7 987.7 1200.0 1099.1: 100.9 258.4 571.7 729.2 830.2 1042.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 100.9447 .. 313.2875 cents 9261/8192, 212.3427 cents 512/483, 100.9447 cents 2: 258.4382 .. 470.7809 cents 9261/8192, 212.3427 cents 188416/194481,-54.8493 cents 3: 415.9316 .. 628.2743 cents 9261/8192, 212.3427 cents 188416/194481,-54.8493 cents 4: 571.7257 .. 784.0684 cents 9261/8192, 212.3427 cents 512/529,-56.5487 cents 5: 729.2191 .. 941.5618 cents 9261/8192, 212.3427 cents 188416/194481,-54.8493 cents 6: 886.7125 .. 1099.0553 cents 9261/8192, 212.3427 cents 188416/194481,-54.8493 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 512/483, 100.9447 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 441/368, 313.2875 cents Average / Smallest step : 1.698242 Largest / Average step : 1.827510 Largest / Smallest step : 3.103554 Median interval of one step : 23/21, 157.4934 cents, amount: 3 Most common interval of one step : 23/21, 157.4934 cents, amount: 3 Least squares average step : 182.87782 cents, oct.: 1280.14476 cents Scale is not proper Step pattern alph. order: ABACDAC Step pattern size order : BDBACBA Scale is not a Constant Structure Scale diversity : 1.464597 Lumma stability : 0.168241 Lumma impropriety factor : 0.229955 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 : 4194304/4084101, 46.0955 cents Most common intervals : 21/16, 470.7809 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 157.493 729.219 cents Most common triad is 0.0 470.781 729.219 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 1 21 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 23 Odd number limit : 10143 (O: 10143 U: 10143) Highest odd numerator or denominator: 483 Scale harmonicity : 0.010645 Average absolute harmonicity : 0.171416 Specific harmonicity : 0.052301 Fundamental : 1/5376, -12.3923 octaves, 0.0487 Hz. Guide tone : 324576, 18.3082 octaves, 84917379.483 Hz. Exponens Consonantiae : 1.744921E+09, 30.70051 octaves Euler's gradus suavitatis : 60 Sum of Mann's harmonic distance : 806.0, average 115.14286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.69628, average 1.52804 Sum of Tenney's harmonic distance : 21.04940, average 3.00706 Vogel's harmonic complexity : 28.14286 Wille's k value : 5071 Wilson's harmonic complexity : 53 Rectangular lattice diameter : 7 Triangular lattice diameter : 6 Lattice compactness : 166.72698, average 5.95454 Lattice compactness (without 2's) : 54.93910, average 1.96211 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -8 .. 5 -2.57143 30 1 3: -1 .. 2 0.28571 6 7: -1 .. 2 0.28571 6 3 23: 0 .. 1 0.42857 3 3 Average exponent except 2's : 7 / 7 = 1.00000 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is weakly epimorphic with val: <7 10 19 32| Scale is weakly epimorphic with val: <7 10 20 29| Scale is weakly epimorphic with val: <7 10 21 33| Scale is weakly epimorphic with val: <7 10 22 30| Scale is weakly epimorphic with val: <7 11 18 32| Scale is weakly epimorphic with val: <7 11 19 29| Scale is weakly epimorphic with val: <7 11 20 33| Scale is weakly epimorphic with val: <7 11 21 30| Scale is weakly epimorphic with val: <7 11 22 34| Scale is weakly epimorphic with val: <7 12 18 29| Scale is weakly epimorphic with val: <7 12 19 33| Scale is weakly epimorphic with val: <7 12 20 30| Scale is weakly epimorphic with val: <7 12 21 34| Scale is weakly epimorphic with val: <7 12 22 31|
FIT/MODE
7: 1 2 1 0 2 0 1 N T3 SD: 53.2078 c. M:-87.0096 c. 8: 1 2 1 1 1 1 1 P M ME S SD: 28.9163 c. M: 49.0553 c. 10: 1 3 1 1 2 1 1 N T3 SD: 20.9702 c. M: 37.4934 c. 13: 2 3 2 1 2 2 1 N G T3 S SD: 15.3176 c. M:-27.1219 c. 15: 2 4 2 1 3 2 1 N SD: 12.4923 c. M:-20.9447 c. 23: 3 6 3 2 4 3 2 N SD: 1.9338 c. M: 3.4031 c. 61: 8 16 8 5 11 8 5 N SD: 1.6541 c. M:-2.7005 c. 84: 11 22 11 7 15 11 7 N SD: 0.7192 c. M:-1.2953 c. 107: 14 28 14 9 19 14 9 N SD: 0.3064 c. M:-0.4943 c. 237: 31 62 31 20 42 31 20 N SD: 0.3008 c. M: 0.5314 c. 344: 45 90 45 29 61 45 29 N SD: 0.2887 c. M: 0.5167 c. 357: 47 93 47 30 63 47 30 N SD: 0.2833 c. M:-0.4898 c. 418: 55 109 55 35 74 55 35 N SD: 0.2861 c. M:-0.4663 c. 441: 58 115 58 37 78 58 37 N SD: 0.1976 c. M:-0.3297 c. 464: 61 121 61 39 82 61 39 N SD: 0.1499 c. M:-0.2652 c. 548: 72 143 72 46 97 72 46 N SD: 0.1284 c. M:-0.2148 c. 571: 75 149 75 48 101 75 48 N SD: 0.0701 c. M:-0.1248 c. 678: 89 177 89 57 120 89 57 N SD: 0.0334 c. M:-0.0598 c. 701: 92 183 92 59 124 92 59 N SD: 0.0326 c. M: 0.0538 c. 1272: 167 332 167 107 225 167 107 N SD: 0.0333 c. M:-0.0537 c. 1379: 181 360 181 116 244 181 116 N SD: 0.0070 c. M:-0.0120 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: 13.6320 cents 3 x 4 x x 5 x 6 S SD: 21.1227 cents 4 x 5 x 6:7 x 8 S SD: 23.2128 cents 5 x x 7:8:9 x 10 SD: 30.6290 cents 6:7:8 x 9:10:11:12 S SD: 23.0890 cents 7:8:9:10:11:12:13:14 H SD: 14.6223 cents 8:9 x x 12:14:15:16 S SD: 12.2597 cents 9:10:12:13:14:16:17:18 S SD: 10.7713 cents 10:11:13:14:15:17:19:20 SD: 8.8539 cents 16:18:21:23:24:28:30:32 SD: 8.7569 cents 17:19:22:24:26:29:32:34 SD: 8.0144 cents 18:20:24:26:27:31:34:36 SD: 6.6715 cents 19:21:25:27:29:33:36:38 SD: 4.3521 cents 23:25:30:33:35:40:43:46 SD: 4.1078 cents 25:27:33:36:38:43:47:50 SD: 3.9351 cents 29:32:38:42:44:50:55:58 SD: 3.1349 cents 32:35:42:46:49:55:60:64 SD: 2.0625 cents 44:48:58:63:67:76:83:88 SD: 1.8792 cents 51:56:67:73:78:88:96:102 SD: 1.6987 cents 54:59:71:78:82:93:102:108 SD: 1.6712 cents 55:60:72:79:84:95:104:110 SD: 1.5703 cents 61:67:80:88:93:105:115:122 SD: 1.1823 cents 73:80:96:105:111:126:138:146 SD: 1.0127 cents 96:105:126:138:146:165:181:192 SD: 0.8314 cents 105:115:138:151:160:181:198:210 SD: 0.4102 cents 176:193:231:253:268:303:332:352 SD: 0.3869 cents 220:241:289:316:335:379:415:440 SD: 0.3458 cents 231:253:303:332:352:398:436:462 SD: 0.1907 cents 336:368:441:483:512:579:634:672 SD: 0.0837 cents