Scala analysis: xen12-chalmers-tritriadic-dm-3-11-27
Tritriadic D->M scale built from 3:11:27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 27/22 354.547060 neutral third, Zalzal wosta of al-Farabi 3: 243/176 558.457062 4: 121/81 694.815881 two (undecimal neutral third) 5: 44/27 845.452940 neutral sixth 6: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 9/8 203.9100 major whole tone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 9/8 203.9100 major whole tone 4: 21296/19683 136.3588 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 9/8 203.9100 major whole tone 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 21296/19683 136.359 cents 1: 3 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 3 9/8 203.910 cents major whole tone 2: 1 7744/6561 286.996 cents two (2nd undecimal neutral second) 2: 1 2662/2187 340.269 cents 2: 5 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 3 968/729 490.906 cents 3: 2 162/121 505.184 cents 3: 2 243/176 558.457 cents 4: 2 352/243 641.543 cents 4: 2 121/81 694.816 cents two (undecimal neutral third) 4: 3 729/484 709.094 cents two (neutral third, Zalzal wosta of al-Farabi) 5: 5 44/27 845.453 cents neutral sixth 5: 1 2187/1331 859.731 cents 5: 1 6561/3872 913.004 cents 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 3 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 19683/10648 1063.641 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 : 203.9 354.5 558.5 694.8 845.5 1049.4 1200.0 203.9 : 150.6 354.5 490.9 641.5 845.5 996.1 1200.0 354.5 : 203.9 340.3 490.9 694.8 845.5 1049.4 1200.0 558.5 : 136.4 287.0 490.9 641.5 845.5 996.1 1200.0 694.8 : 150.6 354.5 505.2 709.1 859.7 1063.6 1200.0 845.5 : 203.9 354.5 558.5 709.1 913.0 1049.4 1200.0 1049.4: 150.6 354.5 505.2 709.1 845.5 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 136.3588 .. 203.9100 cents 177147/170368, 67.5512 cents 21296/19683, 136.3588 cents 2: 286.9959 .. 354.5471 cents 177147/170368, 67.5512 cents 61952/59049, 83.0859 cents 3: 490.9059 .. 558.4571 cents 177147/170368, 67.5512 cents 21296/19683, 136.3588 cents 4: 641.5429 .. 709.0941 cents 177147/170368, 67.5512 cents 61952/59049, 83.0859 cents 5: 845.4529 .. 913.0041 cents 177147/170368, 67.5512 cents 21296/19683, 136.3588 cents 6: 996.0900 .. 1063.6412 cents 177147/170368, 67.5512 cents 61952/59049, 83.0859 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 21296/19683, 136.3588 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.257187 Largest / Average step : 1.189475 Largest / Smallest step : 1.495393 Median interval of one step : 12/11, 150.6371 cents, amount: 3 Least squares average step : 173.50772 cents, oct.: 1214.55406 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACBAB Step pattern size order : LMLSMLM Scale is a Constant Structure, by a margin of 83.08588 cents Scale diversity : 1.306351 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.662244 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 : 59049/58564, 14.2782 cents Most common intervals : 27/22, 354.5471 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 150.637 354.547 cents Most common triad is 0.0 354.547 845.453 cents, amount: 3 Number of recognisable fifths : 5, average 703.3828 cents 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 : 11 27 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% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 67.5512 cents: 1 -- Rational properties -- Prime limit : 11 Odd number limit : 19683 (O: 19683 U: 19683) Highest odd numerator or denominator: 243 Scale harmonicity : 0.011828 Average absolute harmonicity : 0.183923 Specific harmonicity : 0.066932 Fundamental : 1/14256, -13.7993 octaves, 0.0184 Hz. Guide tone : 117612, 16.8437 octaves, 30770305.986 Hz. Exponens Consonantiae : 1.676677E+09, 30.64296 octaves Euler's gradus suavitatis : 55 Sum of Mann's harmonic distance : 389.0, average 55.57143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.32675, average 1.33239 Sum of Tenney's harmonic distance : 18.44890, average 2.63556 Vogel's harmonic complexity : 30.14286 Wille's k value : 9841 Wilson's harmonic complexity : 60 Rectangular lattice diameter : 12 Triangular lattice diameter : 9 Lattice compactness : 133.32604, average 4.76164 Lattice compactness (without 2's) : 108.82875, average 3.88674 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.85714 12 1 3: -4 .. 5 0.28571 18 1 11: -1 .. 2 0.28571 6 5 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 24 / 7 = 3.42857 Scale is weakly epimorphic with val: <7 10 25| Scale is JI-epimorphic with val: <7 11 24| = patent Scale is weakly epimorphic with val: <7 12 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 23.2827 c. M: 44.1713 c. Lebeng 10: 2 1 2 1 1 2 1 P M ME S SD: 25.8032 c. M:-41.5429 c. 13: 2 2 2 1 2 2 2 SP M ME I SD: 24.9207 c. M: 48.6620 c. Horthatian 16: 3 2 2 2 2 3 2 P D3 S SD: 19.9781 c. M: 33.4571 c. 17: 3 2 3 2 2 3 2 SP M ME S SD: 6.7387 c. M:-11.0665 c. 24: 4 3 4 3 3 4 3 SP M ME S SD: 4.7123 c. M: 8.4571 c. Neutral Hypodorian, Iced Dark Lydian 41: 7 5 7 5 5 7 5 SP M DE S SD: 3.8769 c. M:-7.6231 c. 47: 8 6 8 5 6 8 6 SP T3 SD: 3.0176 c. M: 5.4542 c. 54: 9 7 9 6 7 9 7 SP T3 SD: 3.4859 c. M: 5.9270 c. 64: 11 8 11 7 8 11 8 SP T3 SD: 2.0411 c. M:-4.0429 c. 71: 12 9 12 8 9 12 9 SP T3 SD: 1.0435 c. M: 1.8581 c. 88: 15 11 15 10 11 15 11 SP T3 SD: 0.4810 c. M:-0.6387 c. 159: 27 20 27 18 20 27 20 SP T3 SD: 0.2385 c. M: 0.4763 c. 247: 42 31 42 28 31 42 31 SP T3 SD: 0.1260 c. M:-0.2474 c. 406: 69 51 69 46 51 69 51 SP T3 SD: 0.1354 c. M: 0.2346 c. 518: 88 65 88 59 65 88 65 SP T3 SD: 0.1070 c. M:-0.1648 c. 589: 100 74 100 67 74 100 74 SP T3 SD: 0.1237 c. M: 0.2228 c. 606: 103 76 103 69 76 103 76 SP T3 SD: 0.1170 c. M:-0.2336 c. 677: 115 85 115 77 85 115 85 SP T3 SD: 0.0557 c. M: 0.1114 c. 765: 130 96 130 87 96 130 96 SP T3 SD: 0.0437 c. M:-0.0861 c. 836: 142 105 142 95 105 142 105 SP T3 SD: 0.0616 c. M: 0.0839 c. 924: 157 116 157 105 116 157 116 SP T3 SD: 0.0100 c. M: 0.0155 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: 3.5696 cents 3 x x 4 x 5 x 6 S SD: 23.9520 cents 4 x 5 x 6 x 7:8 S SD: 21.7174 cents 5 x 6:7 x 8:9:10 S SD: 12.8227 cents 6:7 x 8:9:10:11:12 S SD: 15.9673 cents 7:8:9:10 x 11:13:14 SD: 20.5327 cents 8:9:10:11:12:13:15:16 SD: 7.3526 cents 16:18:20:22:24:26:29:32 SD: 5.5820 cents 18:20:22:25:27:29:33:36 SD: 4.6537 cents 24:27:29:33:36:39:44:48 SD: 4.1678 cents 26:29:32:36:39:42:48:52 SD: 3.7713 cents 30:34:37:41:45:49:55:60 SD: 3.5410 cents 31:35:38:43:46:51:57:62 SD: 3.3088 cents 32:36:39:44:48:52:59:64 SD: 2.7403 cents 40:45:49:55:60:65:73:80 SD: 2.0137 cents 48:54:59:66:72:78:88:96 SD: 1.6495 cents 65:73:80:90:97:106:119:130 SD: 1.1757 cents 71:80:87:98:106:116:130:142 SD: 0.9088 cents 79:89:97:109:118:129:145:158 SD: 0.7010 cents 97:109:119:134:145:158:178:194 SD: 0.4510 cents 168:189:206:232:251:274:308:336 SD: 0.3026 cents 265:298:325:366:396:432:486:530 SD: 0.2622 cents 281:316:345:388:420:458:515:562 SD: 0.2158 cents 360:405:442:497:538:587:660:720 SD: 0.2026 cents 383:431:470:529:572:624:702:766 SD: 0.1572 cents 391:440:480:540:584:637:717:782 SD: 0.1569 cents 462:520:567:638:690:753:847:924 SD: 0.1437 cents 480:540:589:663:717:782:880:960 SD: 0.1300 cents 559:629:686:772:835:911:1025:1118 SD: 0.0932 cents