Scala analysis: xen12-chalmers-tritriadic-mt-21-23-19
Tritriadic M->T scale built from 21:23:19
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 23/21 157.493440 2: 529/441 314.986880 3: 38/23 869.238669 4: 38/21 1026.732109 5: 42/23 1042.506560 6: 874/441 1184.225549 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 441/437 15.7745 1: 23/21 157.4934 2: 23/21 157.4934 3: 16758/12167 554.2518 4: 23/21 157.4934 5: 441/437 15.7745 6: 10051/9261 141.7190 7: 441/437 15.7745
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 441/437 15.774 cents 1: 1 10051/9261 141.719 cents 1: 3 23/21 157.493 cents 1: 1 16758/12167 554.252 cents 2: 2 23/21 157.493 cents 2: 2 21/19 173.268 cents 2: 1 529/441 314.987 cents 2: 2 798/529 711.745 cents 3: 1 21/19 173.268 cents 3: 2 529/441 314.987 cents 3: 1 23/19 330.761 cents 3: 1 18522/12167 727.520 cents 3: 2 38/23 869.239 cents 4: 2 23/19 330.761 cents 4: 1 12167/9261 472.480 cents 4: 1 38/23 869.239 cents 4: 2 882/529 885.013 cents 4: 1 38/21 1026.732 cents 5: 2 529/399 488.255 cents 5: 1 882/529 885.013 cents 5: 2 38/21 1026.732 cents 5: 2 42/23 1042.507 cents 6: 1 12167/8379 645.748 cents 6: 3 42/23 1042.507 cents 6: 1 18522/10051 1058.281 cents 6: 2 874/441 1184.226 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 : 157.5 315.0 869.2 1026.7 1042.5 1184.2 1200.0 157.5 : 157.5 711.7 869.2 885.0 1026.7 1042.5 1200.0 315.0 : 554.3 711.7 727.5 869.2 885.0 1042.5 1200.0 869.2 : 157.5 173.3 315.0 330.8 488.3 645.7 1200.0 1026.7: 15.8 157.5 173.3 330.8 488.3 1042.5 1200.0 1042.5: 141.7 157.5 315.0 472.5 1026.7 1184.2 1200.0 1184.2: 15.8 173.3 330.8 885.0 1042.5 1058.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 15.7745 .. 554.2518 cents 722/529, 538.4773 cents 441/437, 15.7745 cents 2: 157.4934 .. 711.7452 cents 16758/12167, 554.2518 cents 279841/351918,-396.7583 cents 3: 173.2679 .. 869.2387 cents 722/483, 695.9708 cents 529/722,-538.4773 cents 4: 330.7613 .. 1026.7321 cents 722/483, 695.9708 cents 529/722,-538.4773 cents 5: 488.2548 .. 1042.5066 cents 16758/12167, 554.2518 cents 529/722,-538.4773 cents 6: 645.7482 .. 1184.2255 cents 722/529, 538.4773 cents 279841/351918,-396.7583 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 441/437, 15.7745 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 16758/12167, 554.2518 cents Average / Smallest step : 10.867482 Largest / Average step : 3.233135 Largest / Smallest step : 35.136042 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 : 201.57141 cents, oct.: 1410.99989 cents Scale is not proper Step pattern alph. order: AABACDC Step pattern size order : CCDCABA Scale is not a Constant Structure Scale diversity : 1.229443 Lumma stability : 0.026291 Lumma impropriety factor : 0.737511 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 : 441/437, 15.7745 cents Most common intervals : 23/21, 157.4934 cents & inv., amount: 5 Most common triad is 0.0 157.493 1042.507 cents, amount: 3 Number of recognisable fifths : 2, average 711.7452 cents Scale contains a complete diamond : 21 23 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 23 Odd number limit : 12167 (O: 12167 U: 12167) Highest odd numerator or denominator: 529 Scale harmonicity : 0.004994 Average absolute harmonicity : 0.155508 Specific harmonicity : 0.026546 Fundamental : 1/10143, -13.3082 octaves, 0.0258 Hz. Guide tone : 422142, 18.6874 octaves, 110443139.387 Hz. Exponens Consonantiae : 4.281786E+09, 31.99557 octaves Euler's gradus suavitatis : 110 Sum of Mann's harmonic distance : 1258.5, average 179.78571 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 : 22.76731, average 3.25247 Vogel's harmonic complexity : 51.28571 Wille's k value : 6083 Wilson's harmonic complexity : 118 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 71.61829, average 2.55780 Lattice compactness (without 2's) : 67.57878, average 2.41353 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 7: -2 .. 1 -0.71429 7 19: 0 .. 1 0.42857 3 1 23: -1 .. 2 0.28571 6 5 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 23 / 7 = 3.28571 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 18 31 34| Scale is weakly epimorphic with val: <7 10 19 27 32| Scale is weakly epimorphic with val: <7 10 19 28 34| 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 19 32 35| 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 29 35| Scale is weakly epimorphic with val: <7 10 20 31 32| Scale is weakly epimorphic with val: <7 10 20 32 34| 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 29 34| Scale is weakly epimorphic with val: <7 10 21 32 33| Scale is weakly epimorphic with val: <7 10 21 33 35| 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 10 22 30 35| Scale is weakly epimorphic with val: <7 10 22 33 34| Scale is weakly epimorphic with val: <7 11 18 27 32| Scale is weakly epimorphic with val: <7 11 18 28 34| 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 18 32 35| 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 29 35| Scale is weakly epimorphic with val: <7 11 19 31 32| Scale is weakly epimorphic with val: <7 11 19 32 34| 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 29 34| Scale is weakly epimorphic with val: <7 11 20 32 33| Scale is weakly epimorphic with val: <7 11 20 33 35| 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 21 30 35| Scale is weakly epimorphic with val: <7 11 21 33 34| Scale is weakly epimorphic with val: <7 11 22 27 35| 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 11 22 30 34| 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 29 35| Scale is weakly epimorphic with val: <7 12 18 31 32| Scale is weakly epimorphic with val: <7 12 18 32 34| 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 29 34| Scale is weakly epimorphic with val: <7 12 19 32 33| Scale is weakly epimorphic with val: <7 12 19 33 35| 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 20 30 35| Scale is weakly epimorphic with val: <7 12 20 33 34| Scale is weakly epimorphic with val: <7 12 21 27 35| 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 21 30 34| 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| Scale is weakly epimorphic with val: <7 12 22 31 35|
FIT/MODE
7: 1 1 3 1 0 1 0 N SD: 14.9459 c. M:-27.8703 c. 15: 2 2 7 2 0 2 0 N SD: 9.0898 c. M:-15.7745 c. 37: 5 5 17 5 0 5 0 N SD: 8.8187 c. M:-15.7745 c. 39: 5 5 18 5 1 4 1 N SD: 8.3898 c. M: 14.9948 c. 42: 5 6 19 6 0 5 1 N SD: 10.1584 c. M: 14.6363 c. 43: 5 6 20 6 0 5 1 N SD: 9.8834 c. M: 17.9586 c. 45: 6 6 21 6 0 6 0 N SD: 9.0898 c. M:-15.7745 c. 46: 6 6 21 6 1 5 1 N SD: 6.2026 c. M: 10.3125 c. 47: 6 6 22 6 1 5 1 N SD: 5.8229 c. M: 9.7575 c. 53: 7 7 24 7 1 6 1 N SD: 5.2575 c. M: 8.8613 c. 54: 7 7 25 7 1 6 1 N SD: 3.6067 c. M: 6.4478 c. 61: 8 8 28 8 1 7 1 N SD: 2.4786 c. M: 3.8977 c. 69: 9 9 32 9 1 8 1 N SD: 1.1214 c. M: 1.9434 c. 76: 10 10 35 10 1 9 1 N SD: 0.5083 c. M: 0.8176 c. 145: 19 19 67 19 2 17 2 N SD: 0.4368 c. M: 0.7773 c. 160: 21 21 74 21 2 19 2 N SD: 0.5028 c. M:-0.7745 c. 221: 29 29 102 29 3 26 3 N SD: 0.3207 c. M: 0.5151 c. 236: 31 31 109 31 3 28 3 N SD: 0.2906 c. M:-0.5202 c. 305: 40 40 141 40 4 36 4 N SD: 0.1598 c. M:-0.2695 c. 381: 50 50 176 50 5 45 5 N SD: 0.0294 c. M:-0.0527 c. 838: 110 110 387 110 11 99 11 N SD: 0.0262 c. M:-0.0489 c. 1219: 160 160 563 160 16 144 16 N SD: 0.0154 c. M:-0.0254 c. 1600: 210 210 739 210 21 189 21 N SD: 0.0137 c. M:-0.0245 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: 83.6418 cents 3 x 4:5 x x x 6 S SD: 61.2272 cents 4 x 5 x 7 x x 8 SD: 30.6243 cents 5 x 6:8:9 x x 10 S SD: 14.0756 cents 6 x 7:10 x 11 x 12 SD: 12.7249 cents 7:8 x 12 x 13 x 14 S SD: 25.4499 cents 8:9:10:13:14:15 x 16 SD: 19.3747 cents 9:10:11:15:16 x x 18 SD: 10.6568 cents 10:11:12:17:18 x x 20 SD: 10.1606 cents 11:12:13:18 x 20 x 22 SD: 6.4653 cents 12:13:14:20 x 22 x 24 SD: 10.8605 cents 13:14:16:21 x 24 x 26 SD: 13.7247 cents 14:15:17:23:25:26 x 28 SD: 9.6737 cents 15:16:18:25:27 x x 30 SD: 9.8116 cents 16:18:19:26:29 x x 32 SD: 11.4756 cents 17:19:20:28 x 31 x 34 SD: 9.7879 cents 18:20:22:30 x 33 x 36 SD: 8.8256 cents 19:21:23:31:34:35 x 38 SD: 6.6038 cents 20:22:24:33:36:37 x 40 SD: 4.2584 cents 21:23:25:35:38 x x 42 SD: 4.0064 cents 22:24:26:36 x 40 x 44 SD: 6.4653 cents 23:25:28:38 x 42 x 46 SD: 5.7488 cents 24:26:29:40:43:44 x 48 SD: 5.4976 cents 25:27:30:41:45:46 x 50 SD: 5.2937 cents 26:28:31:43:47 x x 52 SD: 6.2235 cents 27:30:32:45:49 x x 54 SD: 7.2374 cents 28:31:34:46 x 51:55:56 SD: 5.6531 cents 29:32:35:48:52:53:57:58 SD: 3.9004 cents 30:33:36:50:54:55:59:60 SD: 3.4800 cents 31:34:37:51:56:57:61:62 SD: 2.9948 cents 32:35:38:53:58 x 63:64 SD: 3.6101 cents 33:36:40:55 x 60:65:66 SD: 4.6295 cents 34:37:41:56 x 62:67:68 SD: 3.0673 cents 35:38:42:58:63:64:69:70 SD: 2.9573 cents 38:42:46:63:69 x 75:76 SD: 4.1516 cents 39:43:47:64 x 71:77:78 SD: 3.3595 cents 40:44:48:66:72:73:79:80 SD: 1.9304 cents 41:45:49:68:74:75:81:82 SD: 1.7925 cents 44:48:53:73 x 80:87:88 SD: 2.4926 cents 45:49:54:74:81:82:89:90 SD: 2.3789 cents 46:50:55:76:83:84:91:92 SD: 2.2078 cents 49:54:59:81:89 x 97:98 SD: 2.3839 cents 50:55:60:83:90:91:99:100 SD: 2.2282 cents 51:56:61:84:92:93:101:102 SD: 1.4972 cents 55:60:66:91 x 100:109:110 SD: 1.7482 cents 61:67:73:101:110:111:121:122 SD: 1.6297 cents 63:69:76:104:114:115:125:126 SD: 1.4448 cents 64:70:77:106:116:117:127:128 SD: 1.1692 cents 74:81:89:122:134:135:147:148 SD: 1.0692 cents 75:82:90:124:136:137:149:150 SD: 0.9273 cents 95:104:114:157:172:173:188:190 SD: 0.8022 cents 104:114:125:172:188:190:206:208 SD: 0.6626 cents 115:126:138:190:208:210:228:230 SD: 0.1976 cents 316:346:379:522:572:577:626:632 SD: 0.1612 cents 420:460:504:694:760:767:832:840 SD: 0.1507 cents 431:472:517:712:780:787:854:862 SD: 0.0735 cents 546:598:655:902:988:997:1082:1092 SD: 0.0385 cents