Scala analysis: xen12-chalmers-tritriadic-mt-21-25-17
Tritriadic M->T scale built from 21:25:17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/21 301.846520 BP second, quasi-equal minor third 2: 34/25 532.327982 3: 625/441 603.693041 two (BP second, quasi-equal minor third) 4: 34/21 834.174502 supraminor sixth 5: 42/25 898.153480 quasi-equal major sixth 6: 850/441 1136.021023 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 441/425 63.9790 1: 25/21 301.8465 BP second, quasi-equal minor third 2: 714/625 230.4815 3: 15625/14994 71.3651 4: 714/625 230.4815 5: 441/425 63.9790 6: 10625/9261 237.8675 7: 441/425 63.9790
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 441/425 63.979 cents 1: 1 15625/14994 71.365 cents 1: 2 714/625 230.481 cents 1: 1 10625/9261 237.868 cents 1: 1 25/21 301.847 cents BP second, quasi-equal minor third 2: 1 18522/15625 294.460 cents 2: 4 25/21 301.847 cents BP second, quasi-equal minor third 2: 1 21/17 365.825 cents submajor third 2: 1 34/25 532.328 cents 3: 2 21/17 365.825 cents submajor third 3: 2 34/25 532.328 cents 3: 1 882/625 596.307 cents 3: 2 625/441 603.693 cents two (BP second, quasi-equal minor third) 4: 2 882/625 596.307 cents 4: 1 625/441 603.693 cents two (BP second, quasi-equal minor third) 4: 2 25/17 667.672 cents 4: 2 34/21 834.175 cents supraminor sixth 5: 1 25/17 667.672 cents 5: 1 34/21 834.175 cents supraminor sixth 5: 4 42/25 898.153 cents quasi-equal major sixth 5: 1 15625/9261 905.540 cents 6: 1 42/25 898.153 cents quasi-equal major sixth 6: 1 18522/10625 962.132 cents 6: 2 625/357 969.519 cents 6: 1 29988/15625 1128.635 cents 6: 2 850/441 1136.021 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 301.8 532.3 603.7 834.2 898.2 1136.0 1200.0 301.8 : 230.5 301.8 532.3 596.3 834.2 898.2 1200.0 532.3 : 71.4 301.8 365.8 603.7 667.7 969.5 1200.0 603.7 : 230.5 294.5 532.3 596.3 898.2 1128.6 1200.0 834.2 : 64.0 301.8 365.8 667.7 898.2 969.5 1200.0 898.2 : 237.9 301.8 603.7 834.2 905.5 1136.0 1200.0 1136.0: 64.0 365.8 596.3 667.7 898.2 962.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 63.9790 .. 301.8465 cents 10625/9261, 237.8675 cents 441/425, 63.9790 cents 2: 294.4604 .. 532.3280 cents 10625/9261, 237.8675 cents 388962/390625,-7.3861 cents 3: 365.8255 .. 603.6930 cents 10625/9261, 237.8675 cents 525/578,-166.5025 cents 4: 596.3070 .. 834.1745 cents 10625/9261, 237.8675 cents 388962/390625,-7.3861 cents 5: 667.6720 .. 905.5396 cents 10625/9261, 237.8675 cents 525/578,-166.5025 cents 6: 898.1535 .. 1136.0210 cents 10625/9261, 237.8675 cents 388962/390625,-7.3861 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 441/425, 63.9790 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 25/21, 301.8465 cents Average / Smallest step : 2.679452 Largest / Average step : 1.760771 Largest / Smallest step : 4.717902 Median interval of one step : 714/625, 230.4815 cents, amount: 2 Least squares average step : 187.29409 cents, oct.: 1311.05866 cents Scale is not proper Scale is a mode of a 1463-tone equal temperament with octave 2/1 degrees: 368 649 736 1017 1095 1385 1463 Least number of segments generator : 732 of 600.410 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 872 of 715.243 cents and inv. generated superset size: 51 = 44 more = 728.571% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCBDED Step pattern size order : ECBCADA Scale is not a Constant Structure Scale diversity : 1.207295 Lumma stability : 0.106632 Lumma impropriety factor : 0.295969 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 : 5 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 390625/388962, 7.3861 cents Most common intervals : 25/21, 301.8465 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 532.328 898.153 cents Most common triad is 0.0 301.847 898.153 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 21 25 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 17 Odd number limit : 15625 (O: 15625 U: 15625) Highest odd numerator or denominator: 625 Scale harmonicity : 0.009227 Average absolute harmonicity : 0.165058 Specific harmonicity : 0.047222 Fundamental : 1/11025, -13.4285 octaves, 0.0237 Hz. Guide tone : 446250, 18.7675 octaves, 116750408.516 Hz. Exponens Consonantiae : 4.919906E+09, 32.19598 octaves Euler's gradus suavitatis : 66 Sum of Mann's harmonic distance : 1293.5, average 184.78571 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.95636, average 1.56519 Sum of Tenney's harmonic distance : 22.83967, average 3.26281 Vogel's harmonic complexity : 33.71429 Wille's k value : 7812 Wilson's harmonic complexity : 77 Rectangular lattice diameter : 13 Triangular lattice diameter : 6 Lattice compactness : 95.39719, average 3.40704 Lattice compactness (without 2's) : 92.12203, average 3.29007 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.71429 5 1 3: -2 .. 1 -0.71429 7 5: -2 .. 4 0.57143 12 7: -2 .. 1 -0.71429 7 3 17: 0 .. 1 0.42857 3 3 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 29 / 7 = 4.14286 Scale is weakly epimorphic with val: <7 10 15 18 29| Scale is weakly epimorphic with val: <7 10 15 19 26| Scale is weakly epimorphic with val: <7 10 15 21 27| Scale is weakly epimorphic with val: <7 10 15 22 31| Scale is weakly epimorphic with val: <7 10 16 18 30| Scale is weakly epimorphic with val: <7 10 16 19 27| Scale is weakly epimorphic with val: <7 10 16 20 31| Scale is weakly epimorphic with val: <7 10 16 21 28| Scale is weakly epimorphic with val: <7 10 17 18 31| Scale is weakly epimorphic with val: <7 10 17 19 28| Scale is weakly epimorphic with val: <7 10 17 20 32| Scale is weakly epimorphic with val: <7 10 17 21 29| Scale is weakly epimorphic with val: <7 10 17 22 26| Scale is weakly epimorphic with val: <7 10 18 18 32| Scale is weakly epimorphic with val: <7 10 18 20 26| Scale is weakly epimorphic with val: <7 10 18 21 30| Scale is weakly epimorphic with val: <7 10 18 22 27| Scale is weakly epimorphic with val: <7 11 15 18 26| Scale is weakly epimorphic with val: <7 11 15 20 27| Scale is weakly epimorphic with val: <7 11 15 21 31| Scale is weakly epimorphic with val: <7 11 15 22 28| Scale is weakly epimorphic with val: <7 11 16 18 27| Scale is weakly epimorphic with val: <7 11 16 19 31| Scale is weakly epimorphic with val: <7 11 16 20 28| Scale is weakly epimorphic with val: <7 11 16 22 29| Scale is weakly epimorphic with val: <7 11 17 18 28| Scale is weakly epimorphic with val: <7 11 17 19 32| Scale is weakly epimorphic with val: <7 11 17 20 29| Scale is weakly epimorphic with val: <7 11 17 21 26| Scale is weakly epimorphic with val: <7 11 17 22 30| Scale is weakly epimorphic with val: <7 11 18 19 26| Scale is weakly epimorphic with val: <7 11 18 20 30| Scale is weakly epimorphic with val: <7 11 18 21 27| Scale is weakly epimorphic with val: <7 11 18 22 31| Scale is weakly epimorphic with val: <7 12 15 19 27| Scale is weakly epimorphic with val: <7 12 15 20 31| Scale is weakly epimorphic with val: <7 12 15 21 28| Scale is weakly epimorphic with val: <7 12 15 22 32| Scale is weakly epimorphic with val: <7 12 16 18 31| Scale is weakly epimorphic with val: <7 12 16 19 28| Scale is weakly epimorphic with val: <7 12 16 21 29| Scale is weakly epimorphic with val: <7 12 16 22 26| Scale is weakly epimorphic with val: <7 12 17 18 32| Scale is weakly epimorphic with val: <7 12 17 19 29| Scale is weakly epimorphic with val: <7 12 17 20 26| Scale is weakly epimorphic with val: <7 12 17 21 30| Scale is weakly epimorphic with val: <7 12 18 18 26| Scale is weakly epimorphic with val: <7 12 18 19 30| Scale is weakly epimorphic with val: <7 12 18 20 27| Scale is weakly epimorphic with val: <7 12 18 21 31| Scale is weakly epimorphic with val: <7 12 18 22 28|
FIT/MODE
7: 2 1 1 1 0 2 0 N T3 SD: 46.3490 c. M:-82.0212 c. 8: 2 2 0 2 0 2 0 N M DE S SD: 43.1381 c. M:-67.6720 c. 10: 2 2 1 2 0 2 1 N T3 S SD: 43.3111 c. M: 61.8465 c. 12: 3 2 1 2 1 2 1 N T3 SD: 22.4594 c. M: 36.0210 c. 16: 4 3 1 3 1 3 1 N T3 SD: 6.3222 c. M: 11.0210 c. 20: 5 4 1 4 1 4 1 N T3 SD: 4.2943 c. M:-7.6720 c. 36: 9 7 2 7 2 7 2 N T3 SD: 2.0494 c. M: 3.6930 c. 92: 23 18 5 18 5 18 5 N T3 SD: 2.0138 c. M: 3.6930 c. 95: 24 18 6 18 5 19 5 N SD: 1.4382 c. M:-2.6227 c. 111: 28 21 7 21 6 22 6 N SD: 1.4623 c. M: 2.5983 c. 115: 29 22 7 22 6 23 6 N SD: 0.9069 c. M:-1.5244 c. 131: 33 25 8 25 7 26 7 N SD: 0.6102 c. M: 1.0303 c. 151: 38 29 9 29 8 30 8 N SD: 0.2281 c. M:-0.4028 c. 318: 80 61 19 61 17 63 17 N SD: 0.1455 c. M: 0.2525 c. 338: 85 65 20 65 18 67 18 N SD: 0.1218 c. M:-0.2164 c. 469: 118 90 28 90 25 93 25 N SD: 0.0867 c. M:-0.1449 c. 505: 127 97 30 97 27 100 27 N SD: 0.1020 c. M: 0.1794 c. 620: 156 119 37 119 33 123 33 N SD: 0.0959 c. M:-0.1779 c. 656: 165 126 39 126 35 130 35 N SD: 0.0261 c. M: 0.0454 c. 807: 203 155 48 155 43 160 43 N SD: 0.0216 c. M:-0.0385 c. 1463: 368 281 87 281 78 290 78 N SD: 0.0016 c. M:-0.0028 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x 4 S SD: 49.1310 cents 3 x 4 x x 5 x 6 S SD: 12.3181 cents 4:5 x 6 x 7 x 8 S SD: 36.8991 cents 5:6 x 7:8 x x 10 S SD: 8.1344 cents 6:7:8:9 x 10 x 12 S SD: 22.1308 cents 7:8 x 10:11:12 x 14 S SD: 19.0570 cents 8:10:11 x 13 x 15:16 SD: 19.8151 cents 9:11:12:13 x 15:17:18 SD: 12.6368 cents 10:12 x 14:16:17:19:20 SD: 7.6278 cents 11:13:15:16:18 x 21:22 SD: 8.8482 cents 13:15:18 x 21:22:25:26 SD: 10.6487 cents 14:17:19:20:23:24:27:28 SD: 8.1341 cents 15:18:20:21:24:25:29:30 SD: 7.0743 cents 16:19:22:23:26:27:31:32 SD: 4.8755 cents 22:26:30:31:36:37:42:44 SD: 4.2796 cents 26:31:35:37:42:44:50:52 SD: 3.3870 cents 31:37:42:44:50:52:60:62 SD: 1.8756 cents 53:63:72:75:86:89:102:106 SD: 0.8985 cents 84:100:114:119:136:141:162:168 SD: 0.5880 cents 137:163:186:194:222:230:264:274 SD: 0.5669 cents 147:175:200:208:238:247:283:294 SD: 0.5030 cents 153:182:208:217:248:257:295:306 SD: 0.4140 cents 178:212:242:252:288:299:343:356 SD: 0.3456 cents 194:231:264:275:314:326:374:388 SD: 0.1990 cents 247:294:336:350:400:415:476:494 SD: 0.1110 cents 441:525:600:625:714:741:850:882 SD: 0.1067 cents 525:625:714:744:850:882:1012:1050 SD: 0.0281 cents