Scala analysis: xen12-chalmers-tritriadic-dm-23-19-7
Tritriadic D->M scale built from 23:19:7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 361/322 197.925779 2: 28/23 340.551559 3: 19/14 528.687110 4: 28/19 671.312890 5: 38/23 869.238669 6: 784/437 1011.864450 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 437/392 188.1356 1: 361/322 197.9258 2: 392/361 142.6258 3: 437/392 188.1356 4: 392/361 142.6258 5: 361/322 197.9258 6: 392/361 142.6258 7: 437/392 188.1356
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 392/361 142.626 cents 1: 2 437/392 188.136 cents 1: 2 361/322 197.926 cents 2: 3 23/19 330.761 cents 2: 3 28/23 340.552 cents 2: 1 6859/5488 386.061 cents 3: 1 9016/6859 473.387 cents 3: 1 10976/8303 483.177 cents 3: 5 19/14 528.687 cents 4: 5 28/19 671.313 cents 4: 1 8303/5488 716.823 cents 4: 1 6859/4508 726.613 cents 5: 1 10976/6859 813.939 cents 5: 3 23/14 859.448 cents 5: 3 38/23 869.239 cents 6: 2 644/361 1002.074 cents 6: 2 784/437 1011.864 cents 6: 3 361/196 1057.374 cents 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 : 197.9 340.6 528.7 671.3 869.2 1011.9 1200.0 197.9 : 142.6 330.8 473.4 671.3 813.9 1002.1 1200.0 340.6 : 188.1 330.8 528.7 671.3 859.4 1057.4 1200.0 528.7 : 142.6 340.6 483.2 671.3 869.2 1011.9 1200.0 671.3 : 197.9 340.6 528.7 726.6 869.2 1057.4 1200.0 869.2 : 142.6 330.8 528.7 671.3 859.4 1002.1 1200.0 1011.9: 188.1 386.1 528.7 716.8 859.4 1057.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 142.6258 .. 197.9258 cents 130321/126224, 55.3000 cents 392/361, 142.6258 cents 2: 330.7613 .. 386.0613 cents 130321/126224, 55.3000 cents 7406/6859, 132.8356 cents 3: 473.3871 .. 528.6871 cents 130321/126224, 55.3000 cents 49479808/47045881, 87.3258 cents 4: 671.3129 .. 726.6129 cents 130321/126224, 55.3000 cents 392/361, 142.6258 cents 5: 813.9387 .. 869.2387 cents 130321/126224, 55.3000 cents 49479808/47045881, 87.3258 cents 6: 1002.0742 .. 1057.3742 cents 130321/126224, 55.3000 cents 7406/6859, 132.8356 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 392/361, 142.6258 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 361/322, 197.9258 cents Average / Smallest step : 1.201947 Largest / Average step : 1.154567 Largest / Smallest step : 1.387728 Median interval of one step : 437/392, 188.1356 cents, amount: 2 Most common interval of one step : 392/361, 142.6258 cents, amount: 3 Least squares average step : 171.19801 cents, oct.: 1198.38609 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCBABC Step pattern size order : LSMSLSM Scale is a Constant Structure, by a margin of 87.32578 cents Scale diversity : 1.257780 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.723500 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 : 532/529, 9.7902 cents Most common intervals : 19/14, 528.6871 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 330.761 671.313 cents Most common triad is 0.0 528.687 671.313 cents, amount: 3 Number of recognisable fifths : 1, average 716.8227 cents Number of appreciable fifths : 0 Scale contains two identical disjunct tetrachords 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 19 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 23 Odd number limit : 8303 (O: 8303 U: 8303) Highest odd numerator or denominator: 437 Scale harmonicity : 0.005548 Average absolute harmonicity : 0.156154 Specific harmonicity : 0.028588 Fundamental : 1/6118, -12.5788 octaves, 0.0428 Hz. Guide tone : 283024, 18.1106 octaves, 74046313.994 Hz. Exponens Consonantiae : 1.731541E+09, 30.68941 octaves Euler's gradus suavitatis : 100 Sum of Mann's harmonic distance : 1049.5, average 149.92857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.47895, average 1.49699 Sum of Tenney's harmonic distance : 21.80238, average 3.11463 Vogel's harmonic complexity : 45.42857 Wille's k value : 4151 Wilson's harmonic complexity : 101 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 81.90707, average 2.92525 Lattice compactness (without 2's) : 56.12138, average 2.00433 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.14286 12 1 7: -1 .. 2 0.28571 6 19: -1 .. 2 0.28571 6 2 23: -1 .. 0 -0.57143 4 4 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 18 27 33| Scale is JI-epimorphic with val: <7 18 28 30| Scale is weakly epimorphic with val: <7 18 29 34| Scale is weakly epimorphic with val: <7 18 30 31| Scale is weakly epimorphic with val: <7 18 31 35| Scale is weakly epimorphic with val: <7 19 27 30| Scale is weakly epimorphic with val: <7 19 28 34| Scale is JI-epimorphic with val: <7 19 29 31| Scale is weakly epimorphic with val: <7 19 30 35| Scale is weakly epimorphic with val: <7 19 31 32| Scale is weakly epimorphic with val: <7 20 28 31| Scale is weakly epimorphic with val: <7 20 29 35| Scale is JI-epimorphic with val: <7 20 30 32| = patent Scale is weakly epimorphic with val: <7 20 32 33| Scale is weakly epimorphic with val: <7 21 27 31| Scale is weakly epimorphic with val: <7 21 29 32| Scale is JI-epimorphic with val: <7 21 31 33| Scale is weakly epimorphic with val: <7 21 33 34| Scale is weakly epimorphic with val: <7 22 27 35| Scale is weakly epimorphic with val: <7 22 28 32| Scale is weakly epimorphic with val: <7 22 30 33| Scale is JI-epimorphic with val: <7 22 32 34|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 14.8692 c. M: 26.4972 c. Lebeng 18: 3 2 3 2 3 2 3 SP M ME I SD: 5.9397 c. M: 11.8644 c. 25: 4 3 4 3 4 3 4 SP M ME I SD: 3.7636 c. M: 5.9258 c. 59: 10 7 9 7 10 7 9 SP T3 SD: 3.9891 c. M:-5.4641 c. 66: 11 8 10 8 11 8 10 SP T3 SD: 3.4728 c. M:-6.3174 c. 77: 13 9 12 9 13 9 12 SP T3 SD: 2.4891 c. M:-4.6716 c. 84: 14 10 13 10 14 10 13 SP T3 SD: 1.7031 c. M:-2.4213 c. 102: 17 12 16 12 17 12 16 SP T3 SD: 1.0402 c. M:-2.0742 c. 109: 18 13 17 13 18 13 17 SP T3 SD: 0.5226 c. M:-0.9796 c. 127: 21 15 20 15 21 15 20 SP T3 SD: 0.4650 c. M: 0.8408 c. 134: 22 16 21 16 22 16 21 SP T3 SD: 0.4558 c. M: 0.9109 c. 236: 39 28 37 28 39 28 37 SP T3 SD: 0.1911 c. M:-0.3793 c. 261: 43 31 41 31 43 31 41 SP T3 SD: 0.2300 c. M: 0.3702 c. 345: 57 41 54 41 57 41 54 SP T3 SD: 0.2438 c. M:-0.3351 c. 363: 60 43 57 43 60 43 57 SP T3 SD: 0.2433 c. M:-0.4213 c. 370: 61 44 58 44 61 44 58 SP T3 SD: 0.0447 c. M: 0.0879 c. 606: 100 72 95 72 100 72 95 SP T3 SD: 0.0492 c. M:-0.0940 c. 976: 161 116 153 116 161 116 153 SP T3 SD: 0.0174 c. M:-0.0250 c. 1346: 222 160 211 160 222 160 211 SP T3 SD: 0.0114 c. M:-0.0226 c. 2213: 365 263 347 263 365 263 347 SP T3 SD: 0.0132 c. M: 0.0253 c. 2322: 383 276 364 276 383 276 364 SP T3 SD: 0.0120 c. M:-0.0219 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: 15.3211 cents 3 x x 4 x 5 x 6 S SD: 11.3898 cents 4 x 5 x 6 x 7:8 S SD: 17.4740 cents 5 x 6:7 x 8:9:10 S SD: 16.2930 cents 6:7 x 8:9:10:11:12 S SD: 15.1530 cents 7:8 x x 10:12:13:14 S SD: 21.6010 cents 8:9:10:11:12:13:14:16 S SD: 11.3008 cents 9:10:11:12:13:15:16:18 SD: 7.7038 cents 14:16:17:19:21:23:25:28 SD: 6.7383 cents 17:19:21:23:25:28:31:34 SD: 5.5963 cents 19:21:23:26:28:31:34:38 SD: 5.3458 cents 23:26:28:31:34:38:41:46 SD: 3.1912 cents 34:38:41:46:50:56:61:68 SD: 2.7484 cents 40:45:49:54:59:66:72:80 SD: 2.3736 cents 42:47:51:57:62:69:75:84 SD: 2.0168 cents 50:56:61:68:74:83:90:100 SD: 1.9408 cents 59:66:72:80:87:97:106:118 SD: 1.5269 cents 64:72:78:87:94:106:115:128 SD: 1.4775 cents 73:82:89:99:108:121:131:146 SD: 1.4040 cents 74:83:90:100:109:122:133:148 SD: 1.2967 cents 82:92:100:111:121:135:147:164 SD: 1.2362 cents 83:93:101:113:122:137:149:166 SD: 1.0641 cents 92:103:112:125:136:152:165:184 SD: 0.8898 cents 101:113:123:137:149:167:181:202 SD: 0.6809 cents 106:119:129:144:156:175:190:212 SD: 0.6114 cents 156:175:190:212:230:258:280:312 SD: 0.4843 cents 165:185:201:224:243:273:296:330 SD: 0.4293 cents 190:213:231:258:280:314:341:380 SD: 0.3724 cents 198:222:241:269:292:327:355:396 SD: 0.3701 cents 207:232:252:281:305:342:371:414 SD: 0.2680 cents 330:370:402:448:486:545:592:660 SD: 0.2611 cents 331:371:403:449:488:547:594:662 SD: 0.1951 cents 414:464:504:562:610:684:743:828 SD: 0.1387 cents 437:490:532:593:644:722:784:874 SD: 0.0468 cents