Scala analysis: xen12-chalmers-tritriadic-mt-19-21-17
Tritriadic M->T scale built from 19:21:17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/19 173.267891 2: 441/361 346.535782 3: 34/21 834.174502 supraminor sixth 4: 34/19 1007.442393 quasi-mean seventh 5: 38/21 1026.732109 6: 714/361 1180.710285 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 361/357 19.2897 1: 21/19 173.2679 2: 21/19 173.2679 3: 12274/9261 487.6387 4: 21/19 173.2679 5: 361/357 19.2897 6: 7497/6859 153.9782 7: 361/357 19.2897
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 361/357 19.290 cents 1: 1 7497/6859 153.978 cents 1: 3 21/19 173.268 cents 1: 1 12274/9261 487.639 cents 2: 2 21/19 173.268 cents 2: 2 19/17 192.558 cents quasi-meantone 2: 1 441/361 346.536 cents 2: 2 646/441 660.907 cents 3: 1 19/17 192.558 cents quasi-meantone 3: 2 441/361 346.536 cents 3: 1 21/17 365.825 cents submajor third 3: 1 13718/9261 680.196 cents 3: 2 34/21 834.175 cents supraminor sixth 4: 2 21/17 365.825 cents submajor third 4: 1 9261/6859 519.804 cents 4: 1 34/21 834.175 cents supraminor sixth 4: 2 722/441 853.464 cents 4: 1 34/19 1007.442 cents quasi-mean seventh 5: 2 441/323 539.093 cents 5: 1 722/441 853.464 cents 5: 2 34/19 1007.442 cents quasi-mean seventh 5: 2 38/21 1026.732 cents 6: 1 9261/6137 712.361 cents 6: 3 38/21 1026.732 cents 6: 1 13718/7497 1046.022 cents 6: 2 714/361 1180.710 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 : 173.3 346.5 834.2 1007.4 1026.7 1180.7 1200.0 173.3 : 173.3 660.9 834.2 853.5 1007.4 1026.7 1200.0 346.5 : 487.6 660.9 680.2 834.2 853.5 1026.7 1200.0 834.2 : 173.3 192.6 346.5 365.8 539.1 712.4 1200.0 1007.4: 19.3 173.3 192.6 365.8 539.1 1026.7 1200.0 1026.7: 154.0 173.3 346.5 519.8 1007.4 1180.7 1200.0 1180.7: 19.3 192.6 365.8 853.5 1026.7 1046.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 19.2897 .. 487.6387 cents 578/441, 468.3490 cents 361/357, 19.2897 cents 2: 173.2679 .. 660.9066 cents 12274/9261, 487.6387 cents 194481/233206,-314.3708 cents 3: 192.5576 .. 834.1745 cents 578/399, 641.6169 cents 441/578,-468.3490 cents 4: 365.8255 .. 1007.4424 cents 578/399, 641.6169 cents 441/578,-468.3490 cents 5: 539.0934 .. 1026.7321 cents 12274/9261, 487.6387 cents 441/578,-468.3490 cents 6: 712.3613 .. 1180.7103 cents 578/441, 468.3490 cents 194481/233206,-314.3708 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 361/357, 19.2897 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 12274/9261, 487.6387 cents Average / Smallest step : 8.887045 Largest / Average step : 2.844559 Largest / Smallest step : 25.279726 Median interval of one step : 21/19, 173.2679 cents, amount: 3 Most common interval of one step : 21/19, 173.2679 cents, amount: 3 Least squares average step : 200.11825 cents, oct.: 1400.82774 cents Scale is not proper Step pattern alph. order: AABACDC Step pattern size order : CCDCABA Scale is not a Constant Structure Scale diversity : 1.220259 Lumma stability : 0.032150 Lumma impropriety factor : 0.711220 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 : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 361/357, 19.2897 cents Most common intervals : 21/19, 173.2679 cents & inv., amount: 5 Most common triad is 0.0 173.268 1026.732 cents, amount: 3 Number of recognisable fifths : 1, average 712.3613 cents Scale contains a complete diamond : 19 21 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 19 Odd number limit : 9261 (O: 9261 U: 9261) Highest odd numerator or denominator: 441 Scale harmonicity : 0.005804 Average absolute harmonicity : 0.157087 Specific harmonicity : 0.030464 Fundamental : 1/7581, -12.8882 octaves, 0.0345 Hz. Guide tone : 284886, 18.1200 octaves, 74533460.796 Hz. Exponens Consonantiae : 2.159721E+09, 31.00820 octaves Euler's gradus suavitatis : 96 Sum of Mann's harmonic distance : 1043.5, average 149.07143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.44736, average 1.49248 Sum of Tenney's harmonic distance : 22.08109, average 3.15444 Vogel's harmonic complexity : 45.28571 Wille's k value : 4630 Wilson's harmonic complexity : 104 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 71.01044, average 2.53609 Lattice compactness (without 2's) : 67.06225, average 2.39508 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.71429 5 1 3: -1 .. 2 0.28571 6 7: -1 .. 2 0.28571 6 17: 0 .. 1 0.42857 3 1 19: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 22 / 7 = 3.14286 Scale is weakly epimorphic with val: <7 10 18 26 31| Scale is weakly epimorphic with val: <7 10 18 27 33| Scale is weakly epimorphic with val: <7 10 18 29 30| Scale is weakly epimorphic with val: <7 10 18 30 32| Scale is weakly epimorphic with val: <7 10 19 26 30| Scale is weakly epimorphic with val: <7 10 19 27 32| Scale is weakly epimorphic with val: <7 10 19 30 31| Scale is weakly epimorphic with val: <7 10 19 31 33| Scale is weakly epimorphic with val: <7 10 20 26 29| Scale is weakly epimorphic with val: <7 10 20 27 31| Scale is weakly epimorphic with val: <7 10 20 28 33| Scale is weakly epimorphic with val: <7 10 20 31 32| Scale is weakly epimorphic with val: <7 10 21 26 28| Scale is weakly epimorphic with val: <7 10 21 27 30| Scale is weakly epimorphic with val: <7 10 21 28 32| Scale is weakly epimorphic with val: <7 10 21 32 33| Scale is weakly epimorphic with val: <7 10 22 26 27| Scale is weakly epimorphic with val: <7 10 22 27 29| Scale is weakly epimorphic with val: <7 10 22 28 31| Scale is weakly epimorphic with val: <7 10 22 29 33| Scale is weakly epimorphic with val: <7 11 18 26 30| Scale is weakly epimorphic with val: <7 11 18 27 32| Scale is weakly epimorphic with val: <7 11 18 30 31| Scale is weakly epimorphic with val: <7 11 18 31 33| Scale is weakly epimorphic with val: <7 11 19 26 29| Scale is weakly epimorphic with val: <7 11 19 27 31| Scale is weakly epimorphic with val: <7 11 19 28 33| Scale is weakly epimorphic with val: <7 11 19 31 32| Scale is weakly epimorphic with val: <7 11 20 26 28| Scale is weakly epimorphic with val: <7 11 20 27 30| Scale is weakly epimorphic with val: <7 11 20 28 32| Scale is weakly epimorphic with val: <7 11 20 32 33| Scale is weakly epimorphic with val: <7 11 21 26 27| Scale is weakly epimorphic with val: <7 11 21 27 29| Scale is weakly epimorphic with val: <7 11 21 28 31| Scale is weakly epimorphic with val: <7 11 21 29 33| Scale is weakly epimorphic with val: <7 11 22 27 28| Scale is weakly epimorphic with val: <7 11 22 28 30| Scale is weakly epimorphic with val: <7 11 22 29 32| Scale is weakly epimorphic with val: <7 12 18 26 29| Scale is weakly epimorphic with val: <7 12 18 27 31| Scale is weakly epimorphic with val: <7 12 18 28 33| Scale is weakly epimorphic with val: <7 12 18 31 32| Scale is weakly epimorphic with val: <7 12 19 26 28| Scale is weakly epimorphic with val: <7 12 19 27 30| Scale is weakly epimorphic with val: <7 12 19 28 32| Scale is weakly epimorphic with val: <7 12 19 32 33| Scale is weakly epimorphic with val: <7 12 20 26 27| Scale is weakly epimorphic with val: <7 12 20 27 29| Scale is weakly epimorphic with val: <7 12 20 28 31| Scale is weakly epimorphic with val: <7 12 20 29 33| Scale is weakly epimorphic with val: <7 12 21 27 28| Scale is weakly epimorphic with val: <7 12 21 28 30| Scale is weakly epimorphic with val: <7 12 21 29 32| Scale is weakly epimorphic with val: <7 12 22 26 32| Scale is weakly epimorphic with val: <7 12 22 28 29| Scale is weakly epimorphic with val: <7 12 22 29 31| Scale is weakly epimorphic with val: <7 12 22 30 33|
FIT/MODE
7: 1 1 3 1 0 1 0 N SD: 13.9713 c. M:-22.9684 c. 13: 2 2 5 2 0 2 0 N SD: 13.1983 c. M:-22.6950 c. 20: 3 3 8 3 0 3 0 N SD: 10.9261 c. M:-19.2897 c. 27: 4 4 11 4 0 4 0 N SD: 10.8103 c. M:-19.2897 c. 35: 5 5 14 5 1 4 1 N SD: 8.8347 c. M: 14.9960 c. 36: 5 5 15 5 1 4 1 N SD: 8.5755 c. M: 14.0436 c. 41: 6 6 16 6 1 5 1 N SD: 8.4452 c. M: 14.6623 c. 42: 6 6 17 6 1 5 1 N SD: 5.2540 c. M: 9.2817 c. 48: 7 7 19 7 1 6 1 N SD: 5.2122 c. M: 9.1745 c. 49: 7 7 20 7 1 6 1 N SD: 2.9508 c. M: 5.2001 c. 55: 8 8 22 8 1 7 1 N SD: 2.8414 c. M: 5.0836 c. 56: 8 8 23 8 1 7 1 N SD: 1.9761 c. M: 3.6786 c. 62: 9 9 25 9 1 8 1 N SD: 1.1832 c. M: 1.9164 c. 69: 10 10 28 10 1 9 1 N SD: 1.0718 c. M:-1.8984 c. 118: 17 17 48 17 2 15 2 N SD: 0.5992 c. M: 1.0493 c. 125: 18 18 51 18 2 16 2 N SD: 0.6192 c. M:-1.0255 c. 180: 26 26 73 26 3 23 3 N SD: 0.5126 c. M: 0.8412 c. 187: 27 27 76 27 3 24 3 N SD: 0.0296 c. M:-0.0501 c. 1676: 242 242 681 242 27 215 27 N SD: 0.0288 c. M: 0.0456 c. 1863: 269 269 757 269 30 239 30 N SD: 0.0229 c. M: 0.0360 c. 2050: 296 296 833 296 33 263 33 N SD: 0.0182 c. M: 0.0282 c. 2237: 323 323 909 323 36 287 36 N SD: 0.0142 c. M: 0.0219 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: 66.1098 cents 3 x 4:5 x x x 6 S SD: 53.2014 cents 4 x 5:6:7 x x 8 S SD: 35.8430 cents 5 x 6:8 x 9 x 10 S SD: 9.5450 cents 6 x 7:10 x 11 x 12 SD: 24.2089 cents 7:8:9:11 x 13 x 14 SD: 25.2089 cents 8:9:10:13:14 x x 16 SD: 12.7324 cents 9:10:11:15:16 x x 18 SD: 10.4529 cents 10:11:12:16 x 18 x 20 S SD: 7.8128 cents 11:12:13:18 x 20 x 22 SD: 12.9706 cents 12:13:15:19:21:22 x 24 SD: 13.2084 cents 13:14:16:21:23:24 x 26 SD: 10.2695 cents 14:15:17:23:25 x x 28 SD: 12.0954 cents 15:17:18:24 x 27 x 30 SD: 11.5636 cents 16:18:20:26 x 29 x 32 SD: 10.1384 cents 17:19:21:28:30:31 x 34 SD: 8.1418 cents 18:20:22:29:32:33 x 36 SD: 4.7071 cents 19:21:23:31:34 x x 38 SD: 4.1328 cents 20:22:24:32 x 36 x 40 S SD: 7.8128 cents 21:23:26:34 x 38 x 42 SD: 5.6128 cents 22:24:27:36:39:40 x 44 S SD: 5.8897 cents 23:25:28:37:41:42:45:46 SD: 5.7858 cents 24:27:29:39:43 x 47:48 SD: 6.7411 cents 25:28:31:40 x 45:49:50 SD: 7.3494 cents 26:29:32:42 x 47:51:52 SD: 4.2168 cents 27:30:33:44:48:49:53:54 SD: 3.3095 cents 29:32:35:47:52 x 57:58 SD: 4.0153 cents 30:33:37:49 x 54:59:60 SD: 4.5728 cents 31:34:38:50:55:56:61:62 SD: 3.3938 cents 32:35:39:52:57:58:63:64 SD: 3.2598 cents 35:39:43:57 x 63:69:70 SD: 3.7754 cents 36:40:44:58:64:65:71:72 SD: 2.5721 cents 37:41:45:60:66:67:73:74 SD: 1.6665 cents 40:44:49:65 x 72:79:80 SD: 2.4797 cents 45:50:55:73 x 81:89:90 SD: 2.2310 cents 47:52:57:76:84:85:93:94 SD: 1.8743 cents 48:53:59:78:86:87:95:96 SD: 1.8699 cents 57:63:70:92:102:103:113:114 SD: 1.6557 cents 58:64:71:94:104:105:115:116 SD: 1.0636 cents 85:94:104:138:152:154:168:170 SD: 0.8889 cents 86:95:105:139:154:156:170:172 SD: 0.7935 cents 94:104:115:152:168:170:186:188 SD: 0.6467 cents 95:105:116:154:170:172:188:190 SD: 0.3798 cents 189:209:231:306:338:342:374:378 SD: 0.2651 cents 257:284:314:416:460:465:508:514 SD: 0.1803 cents 352:389:430:570:630:637:696:704 SD: 0.0995 cents 446:493:545:722:798:807:882:892 SD: 0.0980 cents 541:598:661:876:968:979:1070:1082 SD: 0.0616 cents