Scala analysis: xen12-chalmers-tritriadic-mt-27-23-17
Tritriadic M->T scale built from 27:23:17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 782/729 121.499752 2: 27/23 277.590655 vicesimotertial minor third 3: 34/27 399.090407 septendecimal major third 4: 1058/729 644.818689 5: 34/23 676.681062 6: 46/27 922.409345 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 27/23 277.5907 vicesimotertial minor third 1: 782/729 121.4998 2: 19683/17986 156.0909 3: 782/729 121.4998 4: 529/459 245.7283 5: 12393/12167 31.8624 6: 529/459 245.7283 7: 27/23 277.5907 vicesimotertial minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 12393/12167 31.862 cents 1: 2 782/729 121.500 cents 1: 1 19683/17986 156.091 cents 1: 2 529/459 245.728 cents 1: 1 27/23 277.591 cents vicesimotertial minor third 2: 4 27/23 277.591 cents vicesimotertial minor third 2: 1 24334/19683 367.228 cents 2: 1 34/27 399.090 cents septendecimal major third 2: 1 23/17 523.319 cents 3: 2 34/27 399.090 cents septendecimal major third 3: 2 23/17 523.319 cents 3: 2 729/529 555.181 cents two (vicesimotertial minor third) 3: 1 1058/729 644.819 cents 4: 1 729/529 555.181 cents two (vicesimotertial minor third) 4: 2 1058/729 644.819 cents 4: 2 34/23 676.681 cents 4: 2 27/17 800.910 cents septendecimal minor sixth 5: 1 34/23 676.681 cents 5: 1 27/17 800.910 cents septendecimal minor sixth 5: 1 19683/12167 832.772 cents 5: 4 46/27 922.409 cents 6: 1 46/27 922.409 cents 6: 2 918/529 954.272 cents 6: 1 35972/19683 1043.909 cents 6: 2 729/391 1078.500 cents 6: 1 24334/12393 1168.138 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 : 121.5 277.6 399.1 644.8 676.7 922.4 1200.0 121.5 : 156.1 277.6 523.3 555.2 800.9 1078.5 1200.0 277.6 : 121.5 367.2 399.1 644.8 922.4 1043.9 1200.0 399.1 : 245.7 277.6 523.3 800.9 922.4 1078.5 1200.0 644.8 : 31.9 277.6 555.2 676.7 832.8 954.3 1200.0 676.7 : 245.7 523.3 644.8 800.9 922.4 1168.1 1200.0 922.4 : 277.6 399.1 555.2 676.7 922.4 954.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.8624 .. 277.5907 cents 529/459, 245.7283 cents 12393/12167, 31.8624 cents 2: 277.5907 .. 523.3189 cents 529/459, 245.7283 cents 1/1, 0.0000 cents 3: 399.0904 .. 644.8187 cents 529/459, 245.7283 cents 578/621,-124.2285 cents 4: 555.1813 .. 800.9096 cents 529/459, 245.7283 cents 531441/559682,-89.6374 cents 5: 676.6811 .. 922.4093 cents 529/459, 245.7283 cents 578/621,-124.2285 cents 6: 922.4093 .. 1168.1376 cents 529/459, 245.7283 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 12393/12167, 31.8624 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 27/23, 277.5907 cents Average / Smallest step : 5.380283 Largest / Average step : 1.619279 Largest / Smallest step : 8.712178 Median interval of one step : 19683/17986, 156.0909 cents, amount: 1 Least squares average step : 155.50777 cents, oct.: 1088.55442 cents Scale is not proper Step pattern alph. order: ABACDCE Step pattern size order : BCBDADE Scale is not a Constant Structure Scale diversity : 1.383040 Lumma stability : 0.053104 Lumma impropriety factor : 0.281745 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 : 12393/12167, 31.8624 cents Most common intervals : 27/23, 277.5907 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 399.090 922.409 cents Most common triad is 0.0 277.591 922.409 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 23 27 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 23 Odd number limit : 19683 (O: 19683 U: 19683) Highest odd numerator or denominator: 729 Scale harmonicity : 0.005513 Average absolute harmonicity : 0.157122 Specific harmonicity : 0.029429 Fundamental : 1/16767, -14.0333 octaves, 0.0156 Hz. Guide tone : 485622, 18.8895 octaves, 127051130.273 Hz. Exponens Consonantiae : 8.142424E+09, 32.92281 octaves Euler's gradus suavitatis : 102 Sum of Mann's harmonic distance : 1771.0, average 253.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.38127, average 1.62590 Sum of Tenney's harmonic distance : 23.68744, average 3.38392 Vogel's harmonic complexity : 49.28571 Wille's k value : 9841 Wilson's harmonic complexity : 113 Rectangular lattice diameter : 13 Triangular lattice diameter : 9 Lattice compactness : 119.61932, average 4.27212 Lattice compactness (without 2's) : 117.25947, average 4.18784 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.85714 6 1 3: -6 .. 3 -2.14286 21 17: 0 .. 1 0.42857 3 1 23: -1 .. 2 0.28571 6 5 Average exponent except 2's :-10 / 7 =-1.42857 Average absolute exponent except 2's: 30 / 7 = 4.28571 Scale is weakly epimorphic with val: <7 10 26 29| Scale is weakly epimorphic with val: <7 10 27 31| Scale is weakly epimorphic with val: <7 10 28 33| Scale is weakly epimorphic with val: <7 10 29 35| Scale is weakly epimorphic with val: <7 10 31 32| Scale is weakly epimorphic with val: <7 10 32 34| Scale is weakly epimorphic with val: <7 11 27 35| Scale is weakly epimorphic with val: <7 11 28 30| Scale is weakly epimorphic with val: <7 11 29 32| = patent Scale is weakly epimorphic with val: <7 11 30 34| Scale is weakly epimorphic with val: <7 12 26 30| Scale is weakly epimorphic with val: <7 12 27 32| Scale is weakly epimorphic with val: <7 12 28 34| Scale is weakly epimorphic with val: <7 12 30 31| Scale is weakly epimorphic with val: <7 12 31 33| Scale is weakly epimorphic with val: <7 12 32 35|
FIT/MODE
7: 1 1 0 2 0 1 2 N T3 SD: 47.7023 c. M: 65.2665 c. 8: 1 1 1 1 1 1 2 P M ME S SD: 41.0449 c. M:-73.3189 c. 9: 1 1 1 2 0 2 2 N T3 SD: 11.6934 c. M:-21.8480 c. 21: 2 3 2 4 1 4 5 N SD: 8.7049 c. M: 16.2473 c. 30: 3 4 3 6 1 6 7 N SD: 2.6436 c. M: 4.8187 c. 39: 4 5 4 8 1 8 9 N SD: 0.9295 c. M:-1.5772 c. 108: 11 14 11 22 3 22 25 N SD: 0.6282 c. M:-1.0967 c. 147: 15 19 15 30 4 30 34 N SD: 0.5970 c. M:-0.9492 c. 229: 23 30 23 47 6 47 53 N SD: 0.5677 c. M: 0.9757 c. 268: 27 35 27 55 7 55 62 N SD: 0.3823 c. M: 0.6042 c. 307: 31 40 31 63 8 63 71 N SD: 0.2671 c. M: 0.4596 c. 337: 34 44 34 69 9 69 78 N SD: 0.2452 c. M: 0.4315 c. 346: 35 45 35 71 9 71 80 N SD: 0.2158 c. M: 0.3805 c. 376: 38 49 38 77 10 77 87 N SD: 0.1250 c. M: 0.2232 c. 415: 42 54 42 85 11 85 96 N SD: 0.0355 c. M: 0.0546 c. 869: 88 113 88 178 23 178 201 N SD: 0.0331 c. M:-0.0605 c. 1284: 130 167 130 263 34 263 297 N SD: 0.0274 c. M: 0.0455 c. 1353: 137 176 137 277 36 277 313 N SD: 0.0216 c. M:-0.0373 c. 1768: 179 230 179 362 47 362 409 N SD: 0.0123 c. M: 0.0223 c. 2183: 221 284 221 447 58 447 505 N SD: 0.0105 c. M: 0.0180 c. 2222: 225 289 225 455 59 455 514 N SD: 0.0069 c. M:-0.0124 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 12.6370 cents 3 x x 4 x x 5:6 S SD: 35.3394 cents 4 x x 5 x 6:7:8 S SD: 13.5935 cents 5 x 6 x 7 x 9:10 SD: 29.9901 cents 6 x 7:8 x 9:10:12 S SD: 21.9030 cents 7 x 8:9:10 x 12:14 S SD: 13.1331 cents 8 x 9:10 x 12:14:16 S SD: 18.3143 cents 9:10 x 11:13 x 15:18 SD: 17.7713 cents 10:11:12:13 x 15:17:20 SD: 13.9762 cents 11:12:13:14:16 x 19:22 SD: 7.2722 cents 13:14:15:16:19 x 22:26 SD: 8.8032 cents 15:16:18:19 x 22:26:30 SD: 8.6974 cents 16:17:19:20:23:24:27:32 SD: 6.4207 cents 17:18:20:21 x 25:29:34 SD: 6.9023 cents 19:20:22:24 x 28:32:38 SD: 7.6182 cents 22:24:26:28:32:33:37:44 SD: 7.1112 cents 23:25:27:29:33:34:39:46 SD: 4.4887 cents 24:26:28:30:35 x 41:48 SD: 4.2873 cents 26:28:31:33:38 x 44:52 SD: 5.8695 cents 27:29:32:34:39:40:46:54 SD: 2.7108 cents 28:30:33:35:41 x 48:56 SD: 3.9690 cents 30:32:35:38 x 44:51:60 SD: 3.7766 cents 31:33:36:39:45:46:53:62 SD: 3.5247 cents 38:41:45:48:55:56:65:76 SD: 3.0540 cents 40:43:47:50:58:59:68:80 SD: 2.0740 cents 53:57:62:67:77:78:90:106 SD: 2.0037 cents 57:61:67:72:83:84:97:114 SD: 1.5406 cents 58:62:68:73:84:86:99:116 SD: 1.3806 cents 69:74:81:87:100:102:118:138 SD: 1.0457 cents 97:104:114:122:141:143:165:194 SD: 0.9732 cents 108:116:127:136:157:160:184:216 SD: 0.8580 cents 109:117:128:137:158:161:186:218 SD: 0.7328 cents 138:148:162:174:200:204:235:276 SD: 0.4860 cents 166:178:195:209:241:245:283:332 SD: 0.4772 cents 178:191:209:224:258:263:303:356 SD: 0.4429 cents 219:235:257:276:318:324:373:438 SD: 0.3391 cents 259:278:304:326:376:383:441:518 SD: 0.2655 cents 317:340:372:399:460:469:540:634 SD: 0.2584 cents 328:352:385:413:476:485:559:656 SD: 0.1558 cents 483:518:567:608:701:714:823:966 SD: 0.1112 cents 563:604:661:709:817:832:959:1126 SD: 0.1046 cents