Scala analysis: xen12-chalmers-tritriadic-dm-1-21-23
Tritriadic D->M 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: 441/368 313.287467 3: 21/16 470.780907 narrow fourth 4: 23/16 628.274347 23rd harmonic 5: 529/336 785.767787 6: 42/23 1042.506560 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 23/21 157.4934 1: 23/21 157.4934 2: 9261/8464 155.7940 3: 23/21 157.4934 4: 23/21 157.4934 5: 23/21 157.4934 6: 14112/12167 256.7388 7: 23/21 157.4934
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 9261/8464 155.794 cents 1: 5 23/21 157.493 cents 1: 1 14112/12167 256.739 cents 2: 2 441/368 313.287 cents 2: 3 529/441 314.987 cents 2: 2 672/529 414.232 cents 3: 3 21/16 470.781 cents narrow fourth 3: 1 12167/9261 472.480 cents 3: 3 32/23 571.726 cents 23rd subharmonic 4: 3 23/16 628.274 cents 23rd harmonic 4: 1 18522/12167 727.520 cents 4: 3 32/21 729.219 cents wide fifth 5: 2 529/336 785.768 cents 5: 3 882/529 885.013 cents 5: 2 736/441 886.713 cents 6: 1 12167/7056 943.261 cents 6: 5 42/23 1042.507 cents 6: 1 16928/9261 1044.206 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 : 157.5 313.3 470.8 628.3 785.8 1042.5 1200.0 157.5 : 155.8 313.3 470.8 628.3 885.0 1042.5 1200.0 313.3 : 157.5 315.0 472.5 729.2 886.7 1044.2 1200.0 470.8 : 157.5 315.0 571.7 729.2 886.7 1042.5 1200.0 628.3 : 157.5 414.2 571.7 729.2 885.0 1042.5 1200.0 785.8 : 256.7 414.2 571.7 727.5 885.0 1042.5 1200.0 1042.5: 157.5 315.0 470.8 628.3 785.8 943.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 155.7940 .. 256.7388 cents 512/483, 100.9447 cents 9261/8464, 155.7940 cents 2: 313.2875 .. 414.2322 cents 512/483, 100.9447 cents 529/512, 56.5487 cents 3: 470.7809 .. 571.7257 cents 512/483, 100.9447 cents 529/512, 56.5487 cents 4: 628.2743 .. 729.2191 cents 512/483, 100.9447 cents 529/512, 56.5487 cents 5: 785.7678 .. 886.7125 cents 512/483, 100.9447 cents 529/512, 56.5487 cents 6: 943.2612 .. 1044.2060 cents 512/483, 100.9447 cents 529/512, 56.5487 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 9261/8464, 155.7940 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 14112/12167, 256.7388 cents Average / Smallest step : 1.100354 Largest / Average step : 1.497643 Largest / Smallest step : 1.647937 Median interval of one step : 23/21, 157.4934 cents, amount: 5 Most common interval of one step : 23/21, 157.4934 cents, amount: 5 Least squares average step : 166.38133 cents, oct.: 1164.66934 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAAACA Step pattern size order : MSMMMLM Scale is a Constant Structure, by a margin of 56.54869 cents Scale diversity : 1.261602 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.495276 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 : 194672/194481, 1.6994 cents Most common intervals : 23/21, 157.4934 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 571.726 1042.507 cents Most common triad is 0.0 157.493 1042.507 cents, amount: 3 Number of recognisable fifths : 0 Best fifths form a closed circle Best major thirds form a closed circle Scale contains a complete diamond : 21 23 Formal octave complements present : 3 = 42.8571% Limited inverse transpositions with margin 100.9447 cents: 4 -- Rational properties -- Prime limit : 23 Odd number limit : 12167 (O: 12167 U: 12167) Highest odd numerator or denominator: 529 Scale harmonicity : 0.005878 Average absolute harmonicity : 0.162925 Specific harmonicity : 0.032865 Fundamental : 1/7728, -12.9159 octaves, 0.0339 Hz. Guide tone : 466578, 18.8318 octaves, 122068733.007 Hz. Exponens Consonantiae : 3.605715E+09, 31.74764 octaves Euler's gradus suavitatis : 96 Sum of Mann's harmonic distance : 931.0, average 133.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.77530, average 1.53933 Sum of Tenney's harmonic distance : 21.52222, average 3.07460 Vogel's harmonic complexity : 44.42857 Wille's k value : 6083 Wilson's harmonic complexity : 99 Rectangular lattice diameter : 9 Triangular lattice diameter : 6 Lattice compactness : 111.01405, average 3.96479 Lattice compactness (without 2's) : 62.53166, average 2.23327 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -2.00000 18 1 3: -1 .. 2 0.28571 6 7: -1 .. 2 0.28571 6 1 23: -1 .. 2 0.28571 6 5 Average exponent except 2's : 6 / 7 = 0.85714 Average absolute exponent except 2's: 18 / 7 = 2.57143 Scale is weakly epimorphic with val: <7 10 19 34| Scale is weakly epimorphic with val: <7 10 20 33| Scale is JI-epimorphic with val: <7 10 21 32| Scale is weakly epimorphic with val: <7 10 22 31| Scale is weakly epimorphic with val: <7 11 18 34| Scale is weakly epimorphic with val: <7 11 19 33| Scale is JI-epimorphic with val: <7 11 20 32| = patent Scale is weakly epimorphic with val: <7 11 21 31| Scale is weakly epimorphic with val: <7 11 22 30| Scale is weakly epimorphic with val: <7 12 18 33| Scale is JI-epimorphic with val: <7 12 19 32| Scale is weakly epimorphic with val: <7 12 20 31| Scale is weakly epimorphic with val: <7 12 21 30| Scale is weakly epimorphic with val: <7 12 22 29|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 40.6187 c. M:-71.3751 c. Lebeng 8: 1 1 1 1 1 2 1 P M ME S SD: 19.9981 c. M: 35.7678 c. 15: 2 2 2 2 2 3 2 SP M ME S SD: 8.3037 c. M:-14.2322 c. 23: 3 3 3 3 3 5 3 SP M DE S SD: 1.6120 c. M: 3.1591 c. 61: 8 8 8 8 8 13 8 SP M DE S SD: 0.9836 c. M:-1.4666 c. 84: 11 11 11 11 11 18 11 SP M DE S SD: 0.5004 c. M:-0.9982 c. 107: 14 14 14 14 14 23 14 SP M DE S SD: 0.4841 c. M:-0.7312 c. 191: 25 25 25 25 25 41 25 SP M DE S SD: 0.4542 c. M:-0.8487 c. 365: 48 47 48 48 48 78 48 SP T3 SD: 0.4841 c. M: 0.9587 c. 380: 50 49 50 50 50 81 50 SP T3 SD: 0.4034 c. M: 0.6559 c. 403: 53 52 53 53 53 86 53 SP T3 SD: 0.3418 c. M: 0.6324 c. 426: 56 55 56 56 56 91 56 SP T3 SD: 0.3078 c. M: 0.6114 c. 449: 59 58 59 59 59 96 59 SP T3 SD: 0.3002 c. M: 0.5926 c. 464: 61 60 61 61 61 99 61 SP T3 SD: 0.2670 c. M:-0.4391 c. 472: 62 61 62 62 62 101 62 SP T3 SD: 0.3135 c. M: 0.5756 c. 487: 64 63 64 64 64 104 64 SP T3 SD: 0.2091 c. M: 0.3511 c. 510: 67 66 67 67 67 109 67 SP T3 SD: 0.1768 c. M: 0.3463 c. 533: 70 69 70 70 70 114 70 SP T3 SD: 0.1745 c. M: 0.3419 c. 556: 73 72 73 73 73 119 73 SP T3 SD: 0.1963 c. M: 0.3378 c. 571: 75 74 75 75 75 122 75 SP T3 SD: 0.1275 c. M:-0.2217 c. 594: 78 77 78 78 78 127 78 SP T3 SD: 0.0859 c. M: 0.1562 c. 617: 81 80 81 81 81 132 81 SP T3 SD: 0.0836 c. M: 0.1594 c. 678: 89 88 89 89 89 145 89 SP T3 SD: 0.0365 c. M:-0.0729 c. 701: 92 91 92 92 92 150 92 SP T3 SD: 0.0208 c. M: 0.0331 c. 1379: 181 179 181 181 181 295 181 SP T3 SD: 0.0120 c. M:-0.0190 c. 2080: 273 270 273 273 273 445 273 SP T3 SD: 0.0091 c. M: 0.0182 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: 36.8403 cents 3 x x 4 x 5 x 6 S SD: 34.0971 cents 4 x 5 x 6 x 7:8 S SD: 31.8105 cents 5 x 6 x 7:8:9:10 S SD: 11.8316 cents 6 x 7:8:9 x 11:12 SD: 18.3016 cents 7:8 x 9:10:11:13:14 SD: 14.6084 cents 8:9:10 x 12:13:15:16 SD: 22.3663 cents 9:10:11:12:13:14:16:18 S SD: 10.2887 cents 10:11:12:13:14:16:18:20 S SD: 8.8416 cents 16:18:19:21:23:25:29:32 SD: 7.4822 cents 19:21:23:25:27:30:35:38 SD: 4.9966 cents 23:25:28:30:33:36:42:46 SD: 4.8355 cents 25:27:30:33:36:39:46:50 SD: 4.7940 cents 29:32:35:38:42:46:53:58 SD: 3.6764 cents 30:33:36:39:43:47:55:60 SD: 3.1345 cents 35:38:42:46:50:55:64:70 SD: 2.7565 cents 41:45:49:54:59:65:75:82 SD: 2.1595 cents 45:49:54:59:65:71:82:90 SD: 2.0554 cents 51:56:61:67:73:80:93:102 SD: 1.6551 cents 61:67:73:80:88:96:111:122 SD: 1.4800 cents 64:70:77:84:92:101:117:128 SD: 1.2204 cents 80:88:96:105:115:126:146:160 SD: 1.1379 cents 87:95:104:114:125:137:159:174 SD: 1.0731 cents 96:105:115:126:138:151:175:192 SD: 0.6010 cents 115:126:138:151:165:181:210:230 SD: 0.5977 cents 137:150:164:180:197:216:250:274 SD: 0.5501 cents 157:172:188:206:226:247:287:314 SD: 0.5150 cents 160:175:192:210:230:252:292:320 SD: 0.5065 cents 167:183:200:219:240:263:305:334 SD: 0.3108 cents 263:288:315:345:378:414:480:526 SD: 0.2433 cents 272:298:326:357:391:428:497:544 SD: 0.2218 cents 327:358:392:429:470:515:597:654 SD: 0.1978 cents 368:403:441:483:529:579:672:736 SD: 0.1653 cents 409:448:490:537:588:644:747:818 SD: 0.1262 cents 505:553:605:663:726:795:922:1010 SD: 0.1228 cents 569:623:682:747:818:896:1039:1138 SD: 0.1193 cents 599:656:718:786:861:943:1094:1198 SD: 0.0985 cents