Scala analysis: xen12-chalmers-tritriadic-mt-5-17-7
Tritriadic M->T scale built from 5:17:7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 20/17 281.358304 septendecimal augmented second 2: 119/100 301.153888 3: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 4: 289/200 637.283391 5: 28/17 863.870497 submajor sixth 6: 17/10 918.641696 septendecimal diminished seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 20/17 281.3583 septendecimal augmented second 1: 20/17 281.3583 septendecimal augmented second 2: 2023/2000 19.7956 3: 20/17 281.3583 septendecimal augmented second 4: 289/280 54.7712 5: 5600/4913 226.5871 6: 289/280 54.7712 7: 20/17 281.3583 septendecimal augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 2023/2000 19.796 cents 1: 2 289/280 54.771 cents 1: 1 5600/4913 226.587 cents 1: 3 20/17 281.358 cents septendecimal augmented second 2: 2 20/17 281.358 cents septendecimal augmented second 2: 2 119/100 301.154 cents 2: 2 17/14 336.130 cents supraminor third 2: 1 400/289 562.717 cents two (septendecimal augmented second) 3: 1 17/14 336.130 cents supraminor third 3: 1 4913/4000 355.925 cents 3: 2 400/289 562.717 cents two (septendecimal augmented second) 3: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 10/7 617.488 cents Euler's tritone 4: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 2 10/7 617.488 cents Euler's tritone 4: 2 289/200 637.283 cents 4: 1 8000/4913 844.075 cents 4: 1 28/17 863.870 cents submajor sixth 5: 1 289/200 637.283 cents 5: 2 28/17 863.870 cents submajor sixth 5: 2 200/119 898.846 cents 5: 2 17/10 918.642 cents septendecimal diminished seventh 6: 3 17/10 918.642 cents septendecimal diminished seventh 6: 1 4913/2800 973.413 cents 6: 2 560/289 1145.229 cents 6: 1 4000/2023 1180.204 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 : 281.4 301.2 582.5 637.3 863.9 918.6 1200.0 281.4 : 19.8 301.2 355.9 582.5 637.3 918.6 1200.0 301.2 : 281.4 336.1 562.7 617.5 898.8 1180.2 1200.0 582.5 : 54.8 281.4 336.1 617.5 898.8 918.6 1200.0 637.3 : 226.6 281.4 562.7 844.1 863.9 1145.2 1200.0 863.9 : 54.8 336.1 617.5 637.3 918.6 973.4 1200.0 918.6 : 281.4 562.7 582.5 863.9 918.6 1145.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 19.7956 .. 281.3583 cents 40000/34391, 261.5627 cents 2023/2000, 19.7956 cents 2: 281.3583 .. 562.7166 cents 20/17, 281.3583 cents 1/1, 0.0000 cents 3: 336.1295 .. 617.4878 cents 20/17, 281.3583 cents 4913/5600,-226.5871 cents 4: 582.5122 .. 863.8705 cents 20/17, 281.3583 cents 49/50,-34.9756 cents 5: 637.2834 .. 918.6417 cents 20/17, 281.3583 cents 4913/5600,-226.5871 cents 6: 918.6417 .. 1180.2044 cents 40000/34391, 261.5627 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 2023/2000, 19.7956 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 20/17, 281.3583 cents Average / Smallest step : 8.659940 Largest / Average step : 1.641257 Largest / Smallest step : 14.213185 Median interval of one step : 5600/4913, 226.5871 cents, amount: 1 Most common interval of one step : 20/17, 281.3583 cents, amount: 3 Least squares average step : 167.22528 cents, oct.: 1170.57694 cents Scale is not proper Step pattern alph. order: ABACDCA Step pattern size order : DADBCBD Scale is not a Constant Structure Scale diversity : 1.129735 Lumma stability : 0.032993 Lumma impropriety factor : 0.406792 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 : 2023/2000, 19.7956 cents Most common intervals : 20/17, 281.3583 cents & inv., amount: 5 Most common triad is 0.0 281.358 918.642 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 5 17 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 17 Odd number limit : 4913 (O: 4913 U: 4913) Highest odd numerator or denominator: 289 Scale harmonicity : 0.008010 Average absolute harmonicity : 0.166771 Specific harmonicity : 0.043737 Fundamental : 1/3400, -11.7313 octaves, 0.0769 Hz. Guide tone : 40460, 15.3042 octaves, 10585370.372 Hz. Exponens Consonantiae : 1.375640E+08, 27.03553 octaves Euler's gradus suavitatis : 72 Sum of Mann's harmonic distance : 416.0, average 59.42857 Mersenne's string divisions : 237742020 Sum of van Prooijen's expressibility: 9.07289, average 1.29613 Sum of Tenney's harmonic distance : 18.12211, average 2.58887 Vogel's harmonic complexity : 34.14286 Wille's k value : 2456 Wilson's harmonic complexity : 73 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 84.91706, average 3.03275 Lattice compactness (without 2's) : 56.50032, average 2.01787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.14286 11 1 5: -2 .. 1 -0.71429 7 7: 0 .. 1 0.42857 3 1 17: -1 .. 2 0.28571 6 5 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 15 18 28| Scale is weakly epimorphic with val: <7 15 19 30| Scale is weakly epimorphic with val: <7 15 20 32| Scale is weakly epimorphic with val: <7 15 21 27| Scale is weakly epimorphic with val: <7 16 18 27| Scale is weakly epimorphic with val: <7 16 19 29| Scale is weakly epimorphic with val: <7 16 20 31| Scale is weakly epimorphic with val: <7 16 21 26| Scale is weakly epimorphic with val: <7 16 22 28| Scale is weakly epimorphic with val: <7 17 18 26| Scale is weakly epimorphic with val: <7 17 19 28| Scale is weakly epimorphic with val: <7 17 20 30| Scale is weakly epimorphic with val: <7 17 21 32| Scale is weakly epimorphic with val: <7 17 22 27| Scale is weakly epimorphic with val: <7 18 19 27| Scale is weakly epimorphic with val: <7 18 20 29| Scale is weakly epimorphic with val: <7 18 21 31| Scale is weakly epimorphic with val: <7 18 22 26|
FIT/MODE
7: 2 0 1 1 1 0 2 N T3 I SD: 48.3278 c. M: 68.2265 c. 8: 2 0 2 0 2 0 2 N M DE I SD: 22.9831 c. M: 37.2834 c. 13: 3 0 3 1 2 1 3 N SD: 19.3560 c. M: 33.1013 c. 17: 4 0 4 1 3 1 4 N SD: 11.7054 c. M: 18.8009 c. 21: 5 0 5 1 4 1 5 N SD: 8.6217 c. M: 15.4396 c. 25: 6 0 6 1 5 1 6 N SD: 8.2818 c. M: 13.2834 c. 35: 8 1 8 2 6 2 8 N SD: 7.5643 c. M:-14.1452 c. 37: 9 0 9 2 7 1 9 N SD: 9.0857 c. M:-11.8052 c. 39: 9 1 9 2 7 2 9 N SD: 4.9373 c. M:-8.8705 c. 43: 10 1 10 2 8 2 10 N SD: 3.3674 c. M:-5.8229 c. 47: 11 1 11 2 9 2 11 N SD: 3.1384 c. M:-5.2291 c. 60: 14 1 14 3 11 3 14 N SD: 2.1939 c. M: 3.8705 c. 64: 15 1 15 3 12 3 15 N SD: 0.8344 c. M: 1.3705 c. 111: 26 2 26 5 21 5 26 N SD: 0.8836 c. M:-1.5488 c. 132: 31 2 31 6 25 6 31 N SD: 0.6694 c. M: 1.1539 c. 175: 41 3 41 8 33 8 41 N SD: 0.3226 c. M:-0.5604 c. 239: 56 4 56 11 45 11 56 N SD: 0.2073 c. M:-0.3735 c. 243: 57 4 57 11 46 11 57 N SD: 0.1875 c. M:-0.3270 c. 307: 72 5 72 14 58 14 72 N SD: 0.1042 c. M: 0.1767 c. 482: 113 8 113 22 91 22 113 N SD: 0.0513 c. M:-0.0909 c. 789: 185 13 185 36 149 36 185 N SD: 0.0114 c. M: 0.0210 c. 2060: 483 34 483 94 389 94 483 N SD: 0.0080 c. M:-0.0130 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: 32.3358 cents 3 x x 4 x 5 x 6 S SD: 28.9722 cents 4 x 5 x 6 x 7:8 S SD: 29.5308 cents 5 x 6:7 x 8:9:10 S SD: 22.3789 cents 6:7 x 8:9:10 x 12 S SD: 21.8603 cents 7:8 x x 10 x 12:14 S SD: 13.9647 cents 9 x 11 x 13:15 x 18 SD: 12.6482 cents 10 x 12:14 x 16:17:20 SD: 10.4467 cents 11:13 x 15:16:18:19:22 SD: 9.3598 cents 12:14 x 17 x 20 x 24 SD: 8.0987 cents 13:15 x 18:19:21:22:26 SD: 9.2436 cents 14:16:17 x 20:23:24:28 SD: 11.0089 cents 15 x 18:21:22:25:26:30 SD: 8.2051 cents 16 x 19:22:23:26:27:32 SD: 7.0230 cents 17:20 x 24:25:28:29:34 SD: 5.6987 cents 18:21 x 25:26:30:31:36 SD: 6.0689 cents 19:22:23:27 x 31:32:38 SD: 8.8690 cents 20 x 24:28:29:33:34:40 SD: 2.6624 cents 21 x 25:29:30:35:36:42 SD: 6.6342 cents 22:26 x 31:32:36:37:44 SD: 4.6871 cents 23:27 x 32:33:38:39:46 SD: 3.0273 cents 26 x 31:36:38:43:44:52 SD: 4.9377 cents 27 x 32:38:39:44:46:54 SD: 3.6764 cents 28:33 x 39:40:46:48:56 SD: 4.4387 cents 30:35:36:42:43:49:51:60 SD: 4.1073 cents 32 x 38:45:46:53:54:64 SD: 3.3745 cents 33:39 x 46:48:54:56:66 SD: 3.2691 cents 34:40 x 48:49:56:58:68 SD: 2.7218 cents 37 x 44:52:53:61:63:74 SD: 2.8134 cents 38 x 45:53:55:63:65:76 SD: 3.1838 cents 39:46 x 55:56:64:66:78 SD: 3.3377 cents 40:47:48:56:58:66:68:80 SD: 2.3030 cents 43 x 51:60:62:71:73:86 SD: 1.7057 cents 44:52 x 62:64:72:75:88 SD: 3.5967 cents 45:53:54:63:65:74:77:90 SD: 2.6680 cents 47:55:56:66:68:77:80:94 SD: 2.0809 cents 49 x 58:69:71:81:83:98 SD: 2.8276 cents 50:59:60:70:72:82:85:100 SD: 2.5875 cents 51:60:61:71:74:84:87:102 SD: 2.3003 cents 52:61:62:73:75:86:88:104 SD: 1.9250 cents 54 x 64:76:78:89:92:108 SD: 2.0322 cents 55:65 x 77:79:91:94:110 SD: 2.9639 cents 56:66:67:78:81:92:95:112 SD: 2.0736 cents 57:67:68:80:82:94:97:114 SD: 1.4769 cents 60 x 71:84:87:99:102:120 SD: 1.9713 cents 62:73:74:87:90:102:105:124 SD: 1.7739 cents 63:74:75:88:91:104:107:126 SD: 0.9250 cents 71:84 x 99:103:117:121:142 SD: 2.4099 cents 72:85:86:101:104:119:122:144 SD: 1.7957 cents 73:86:87:102:105:120:124:146 SD: 1.4351 cents 74:87:88:104:107:122:126:148 SD: 1.0964 cents 85:100:101:119:123:140:145:170 SD: 0.9942 cents 90:106:107:126:130:148:153:180 SD: 0.5406 cents 153:180:182:214:221:252:260:306 SD: 0.2837 cents 227:267:270:318:328:374:386:454 SD: 0.2272 cents 317:373:377:444:458:522:539:634 SD: 0.2077 cents 357:420:425:500:516:588:607:714 SD: 0.1595 cents 380:447:452:532:549:626:646:760 SD: 0.1312 cents 510:600:607:714:737:840:867:1020 SD: 0.0441 cents