Scala analysis: xen12-chalmers-tritriadic-dm-13-23-7
Tritriadic D->M scale built from 13:23:7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/13 128.298245 2/3-tone 2: 28/23 340.551559 3: 392/299 468.849804 4: 529/364 647.195126 5: 23/14 859.448441 6: 23/13 987.746685 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 26/23 212.2533 1: 14/13 128.2982 2/3-tone 2: 26/23 212.2533 3: 14/13 128.2982 2/3-tone 4: 12167/10976 178.3453 5: 26/23 212.2533 6: 14/13 128.2982 2/3-tone 7: 26/23 212.2533
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 14/13 128.298 cents 2/3-tone 1: 1 12167/10976 178.345 cents 1: 3 26/23 212.253 cents 2: 1 12167/10192 306.644 cents 2: 5 28/23 340.552 cents 2: 1 6877/5488 390.599 cents 3: 2 392/299 468.850 cents 3: 3 529/392 518.897 cents 3: 2 728/529 552.805 cents 4: 2 529/364 647.195 cents 4: 3 784/529 681.103 cents 4: 2 299/196 731.150 cents 5: 1 10976/6877 809.401 cents 5: 5 23/14 859.448 cents 5: 1 20384/12167 893.356 cents 6: 3 23/13 987.747 cents 6: 1 21952/12167 1021.655 cents 6: 3 13/7 1071.702 cents 16/3-tone Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 128.3 340.6 468.8 647.2 859.4 987.7 1200.0 128.3 : 212.3 340.6 518.9 731.2 859.4 1071.7 1200.0 340.6 : 128.3 306.6 518.9 647.2 859.4 987.7 1200.0 468.8 : 178.3 390.6 518.9 731.2 859.4 1071.7 1200.0 647.2 : 212.3 340.6 552.8 681.1 893.4 1021.7 1200.0 859.4 : 128.3 340.6 468.8 681.1 809.4 987.7 1200.0 987.7 : 212.3 340.6 552.8 681.1 859.4 1071.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 128.2982 .. 212.2533 cents 169/161, 83.9551 cents 14/13, 128.2982 cents 2: 306.6436 .. 390.5986 cents 169/161, 83.9551 cents 279841/264992, 94.3903 cents 3: 468.8498 .. 552.8049 cents 169/161, 83.9551 cents 2151296/2056223, 78.2512 cents 4: 647.1951 .. 731.1502 cents 169/161, 83.9551 cents 279841/264992, 94.3903 cents 5: 809.4014 .. 893.3564 cents 169/161, 83.9551 cents 2151296/2056223, 78.2512 cents 6: 987.7467 .. 1071.7018 cents 169/161, 83.9551 cents 279841/264992, 94.3903 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 14/13, 128.2982 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 26/23, 212.2533 cents Average / Smallest step : 1.336172 Largest / Average step : 1.238144 Largest / Smallest step : 1.654374 Median interval of one step : 12167/10976, 178.3453 cents, amount: 1 Least squares average step : 167.34610 cents, oct.: 1171.42268 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACBAB Step pattern size order : SLSMLSL Scale is a Constant Structure, by a margin of 78.25117 cents Scale diversity : 1.403452 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.580225 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 : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 285376/279841, 33.9080 cents Most common intervals : 28/23, 340.5516 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 212.253 340.552 cents Most common triad is 0.0 340.552 859.448 cents, amount: 3 Number of recognisable fifths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 7 23 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 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 : 0.005427 Average absolute harmonicity : 0.157488 Specific harmonicity : 0.029235 Fundamental : 1/8372, -13.0314 octaves, 0.0313 Hz. Guide tone : 207368, 17.6618 octaves, 54252770.225 Hz. Exponens Consonantiae : 1.736085E+09, 30.69319 octaves Euler's gradus suavitatis : 102 Sum of Mann's harmonic distance : 869.0, average 124.14286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.39825, average 1.48546 Sum of Tenney's harmonic distance : 20.70703, average 2.95815 Vogel's harmonic complexity : 46.71429 Wille's k value : 6083 Wilson's harmonic complexity : 103 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 79.49113, average 2.83897 Lattice compactness (without 2's) : 56.12138, average 2.00433 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.57143 10 1 7: -1 .. 2 0.28571 6 13: -1 .. 0 -0.57143 4 1 23: -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 JI-epimorphic with val: <7 18 24 30| Scale is weakly epimorphic with val: <7 18 26 34| Scale is weakly epimorphic with val: <7 18 27 29| Scale is weakly epimorphic with val: <7 18 28 31| Scale is weakly epimorphic with val: <7 18 29 33| Scale is weakly epimorphic with val: <7 19 24 29| Scale is JI-epimorphic with val: <7 19 25 31| Scale is weakly epimorphic with val: <7 19 27 35| Scale is weakly epimorphic with val: <7 19 28 30| Scale is weakly epimorphic with val: <7 19 29 32| Scale is weakly epimorphic with val: <7 20 24 35| Scale is weakly epimorphic with val: <7 20 25 30| Scale is JI-epimorphic with val: <7 20 26 32| = patent Scale is weakly epimorphic with val: <7 20 28 29| Scale is weakly epimorphic with val: <7 20 29 31| Scale is weakly epimorphic with val: <7 21 24 34| Scale is weakly epimorphic with val: <7 21 25 29| Scale is weakly epimorphic with val: <7 21 26 31| Scale is JI-epimorphic with val: <7 21 27 33| Scale is weakly epimorphic with val: <7 21 29 30| Scale is weakly epimorphic with val: <7 22 24 33| Scale is weakly epimorphic with val: <7 22 25 35| Scale is weakly epimorphic with val: <7 22 26 30| Scale is weakly epimorphic with val: <7 22 27 32| Scale is JI-epimorphic with val: <7 22 28 34|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 31.8157 c. M:-45.4359 c. Lebeng 10: 1 2 1 1 2 1 2 P M ME S SD: 23.7455 c. M: 47.1951 c. 11: 1 2 1 2 2 1 2 P M ME S SD: 16.3275 c. M: 32.4862 c. 15: 2 2 2 2 3 1 3 SP D3 S SD: 19.9847 c. M:-31.7018 c. 17: 2 3 2 2 3 2 3 SP M ME S SD: 13.3801 c. M:-25.2678 c. 18: 2 3 2 3 3 2 3 SP M ME S SD: 9.7366 c. M:-19.4715 c. 21: 2 4 2 3 4 2 4 SP T3 SD: 11.6935 c. M: 18.6237 c. 28: 3 5 3 4 5 3 5 SP T3 SD: 2.3995 c. M: 4.3380 c. 46: 5 8 5 7 8 5 8 SP T3 SD: 2.5791 c. M:-4.9788 c. 67: 7 12 7 10 12 7 12 SP T3 SD: 2.1306 c. M: 3.1782 c. 74: 8 13 8 11 13 8 13 SP T3 SD: 1.0863 c. M:-1.4535 c. 102: 11 18 11 15 18 11 18 SP T3 SD: 0.8702 c. M:-1.7384 c. 113: 12 20 12 17 20 12 20 SP T3 SD: 0.8209 c. M: 1.5932 c. 141: 15 25 15 21 25 15 25 SP T3 SD: 0.4530 c. M: 0.7647 c. 215: 23 38 23 32 38 23 38 SP T3 SD: 0.1237 c. M:-0.2467 c. 458: 49 81 49 68 81 49 81 SP T3 SD: 0.0733 c. M:-0.1458 c. 599: 64 106 64 89 106 64 106 SP T3 SD: 0.0718 c. M: 0.1167 c. 673: 72 119 72 100 119 72 119 SP T3 SD: 0.0586 c. M:-0.0952 c. 814: 87 144 87 121 144 87 144 SP T3 SD: 0.0302 c. M: 0.0537 c. 1029: 110 182 110 153 182 110 182 SP T3 SD: 0.0270 c. M: 0.0451 c. 1272: 136 225 136 189 225 136 225 SP T3 SD: 0.0147 c. M: 0.0253 c. 1487: 159 263 159 221 263 159 263 SP T3 SD: 0.0105 c. M:-0.0140 c. 2301: 246 407 246 342 407 246 407 SP T3 SD: 0.0051 c. M: 0.0102 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: 27.3799 cents 3 x x 4 x 5 x 6 S SD: 12.7927 cents 4 x 5 x 6 x 7:8 S SD: 18.4574 cents 5 x 6 x 7:8:9:10 S SD: 17.6517 cents 6 x 7:8:9:10:11:12 S SD: 19.5056 cents 7:8 x 9:10 x 12:14 S SD: 24.9713 cents 8:9:10:11:12:13:14:16 S SD: 19.3396 cents 9:10:11:12:13:15:16:18 SD: 9.7193 cents 13:14:16:17:19:21:23:26 SD: 5.2016 cents 22:24:27:29:32:36:39:44 SD: 4.1511 cents 26:28:32:34:38:43:46:52 SD: 3.5185 cents 36:39:44:47:52:59:64:72 SD: 2.8721 cents 38:41:46:50:55:62:67:76 SD: 2.7605 cents 42:45:51:55:61:69:74:84 SD: 1.7772 cents 51:55:62:67:74:84:90:102 SD: 1.2052 cents 64:69:78:84:93:105:113:128 SD: 0.7725 cents 106:114:129:139:154:174:188:212 SD: 0.7336 cents 129:139:157:169:187:212:228:258 SD: 0.7210 cents 142:153:173:186:206:233:251:284 SD: 0.6619 cents 152:164:185:199:221:250:269:304 SD: 0.6597 cents 157:169:191:206:228:258:278:314 SD: 0.4018 cents 170:183:207:223:247:279:301:340 SD: 0.3689 cents 221:238:269:290:321:363:391:442 SD: 0.2691 cents 286:308:348:375:416:470:506:572 SD: 0.2586 cents 322:347:392:422:468:529:570:644 SD: 0.2312 cents 350:377:426:459:509:575:619:700 SD: 0.2176 cents 364:392:443:477:529:598:644:728 SD: 0.1342 cents 428:461:521:561:622:703:757:856 SD: 0.1155 cents 585:630:712:767:850:961:1035:1170 SD: 0.0830 cents