Scala analysis: xen12-chalmers-tritriadic-dm-1-3-11
Tritriadic D->M scale built from 1:3:11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 12/11 150.637059 undecimal neutral second, 3/4-tone 2: 121/96 400.680884 3: 11/8 551.317942 undecimal semi-augmented fourth 4: 3/2 701.955001 perfect fifth 5: 18/11 852.592059 undecimal 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: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 1331/1152 250.0438 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 121/108 196.7709 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 121/108 196.771 cents 1: 1 1331/1152 250.044 cents 2: 3 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 2: 2 11/9 347.408 cents undecimal neutral third 2: 2 121/96 400.681 cents 3: 1 1728/1331 451.911 cents 3: 3 4/3 498.045 cents perfect fourth 3: 3 11/8 551.318 cents undecimal semi-augmented fourth 4: 3 16/11 648.682 cents undecimal semi-diminished fifth 4: 3 3/2 701.955 cents perfect fifth 4: 1 1331/864 748.089 cents 5: 2 192/121 799.319 cents 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 3 121/72 898.726 cents 6: 1 2304/1331 949.956 cents 6: 1 216/121 1003.229 cents 6: 5 11/6 1049.363 cents undecimal neutral seventh, 21/4-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 : 150.6 400.7 551.3 702.0 852.6 1049.4 1200.0 150.6 : 250.0 400.7 551.3 702.0 898.7 1049.4 1200.0 400.7 : 150.6 301.3 451.9 648.7 799.3 950.0 1200.0 551.3 : 150.6 301.3 498.0 648.7 799.3 1049.4 1200.0 702.0 : 150.6 347.4 498.0 648.7 898.7 1049.4 1200.0 852.6 : 196.8 347.4 498.0 748.1 898.7 1049.4 1200.0 1049.4: 150.6 301.3 551.3 702.0 852.6 1003.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 250.0438 cents 14641/13824, 99.4068 cents 12/11, 150.6371 cents 2: 301.2741 .. 400.6809 cents 14641/13824, 99.4068 cents 165888/161051, 51.2303 cents 3: 451.9112 .. 551.3179 cents 14641/13824, 99.4068 cents 165888/161051, 51.2303 cents 4: 648.6821 .. 748.0888 cents 14641/13824, 99.4068 cents 128/121, 97.3641 cents 5: 799.3191 .. 898.7259 cents 14641/13824, 99.4068 cents 165888/161051, 51.2303 cents 6: 949.9562 .. 1049.3629 cents 14641/13824, 99.4068 cents 165888/161051, 51.2303 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 1331/1152, 250.0438 cents Average / Smallest step : 1.138024 Largest / Average step : 1.458589 Largest / Smallest step : 1.659909 Median interval of one step : 12/11, 150.6371 cents, amount: 5 Most common interval of one step : 12/11, 150.6371 cents, amount: 5 Least squares average step : 174.09222 cents, oct.: 1218.64553 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAAACA Step pattern size order : SLSSSMS Scale is a Constant Structure, by a margin of 51.23029 cents Scale diversity : 1.396184 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.502966 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 : 1331/1296, 46.1338 cents Most common intervals : 12/11, 150.6371 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 498.045 1049.363 cents Number of recognisable fifths : 3, average 701.9550 cents Best fifths form a closed circle Scale contains a complete diamond : 3 11 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 classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 -- Rational properties -- Prime limit : 11 Odd number limit : 1331 (O: 1331 U: 1331) Highest odd numerator or denominator: 121 Scale harmonicity : 0.014379 Average absolute harmonicity : 0.210425 Specific harmonicity : 0.081544 Fundamental : 1/1056, -10.0444 octaves, 0.2478 Hz. Guide tone : 4356, 12.0888 octaves, 1139640.962 Hz. Exponens Consonantiae : 4.599936E+06, 22.13318 octaves Euler's gradus suavitatis : 44 Sum of Mann's harmonic distance : 156.5, average 22.35714 Mersenne's string divisions : 701260455 Sum of van Prooijen's expressibility: 6.72548, average 0.96078 Sum of Tenney's harmonic distance : 13.32550, average 1.90364 Vogel's harmonic complexity : 22.14286 Wille's k value : 665 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 96.12873, average 3.43317 Lattice compactness (without 2's) : 51.25493, average 1.83053 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -0.85714 14 1 3: -1 .. 2 0.28571 6 1 11: -1 .. 2 0.28571 6 5 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 12 / 7 = 1.71429 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: 28.9433 c. M: 57.8237 c. Lebeng 8: 1 2 1 1 1 1 1 P M ME S SD: 36.5649 c. M:-49.3191 c. 9: 1 2 1 1 1 2 1 P M ME I SD: 26.5490 c. M: 52.5921 c. 10: 1 2 2 1 1 2 1 P D3 S SD: 30.2048 c. M:-48.6821 c. 14: 2 3 1 2 2 2 2 P T3 SD: 21.7069 c. M: 37.0322 c. 15: 2 3 2 2 2 2 2 SP M ME S SD: 13.7736 c. M:-27.4079 c. Miller's Porcupine-7 Major 17: 2 4 2 2 2 3 2 P T3 SD: 11.5037 c. M:-22.8485 c. 21: 3 4 3 2 3 3 3 SP T3 SD: 14.8994 c. M:-20.7915 c. 22: 3 4 3 3 3 3 3 SP M ME S SD: 13.0082 c. M:-20.1352 c. Miller's Porcupine-7 Major 24: 3 5 3 3 3 4 3 SP T3 SD: 1.3915 c. M: 2.5921 c. 87: 11 18 11 11 11 14 11 SP T3 SD: 1.3028 c. M:-2.5804 c. 111: 14 23 14 14 14 18 14 SP T3 SD: 0.7729 c. M:-1.4620 c. 135: 17 28 17 17 17 22 17 SP T3 SD: 0.4746 c. M:-0.7413 c. 159: 20 33 20 20 20 26 20 SP T3 SD: 0.3491 c. M: 0.6809 c. 183: 23 38 23 23 23 30 23 SP T3 SD: 0.3578 c. M: 0.6809 c. 311: 39 65 39 39 39 51 39 SP T3 SD: 0.3217 c. M:-0.6053 c. 335: 42 70 42 42 42 55 42 SP T3 SD: 0.2566 c. M:-0.5131 c. 359: 45 75 45 45 45 59 45 SP T3 SD: 0.2330 c. M:-0.4333 c. 383: 48 80 48 48 48 63 48 SP T3 SD: 0.2454 c. M: 0.3727 c. 446: 56 93 56 56 56 73 56 SP T3 SD: 0.2067 c. M:-0.3227 c. 470: 59 98 59 59 59 77 59 SP T3 SD: 0.1301 c. M:-0.1739 c. 494: 62 103 62 62 62 81 62 SP T3 SD: 0.0703 c. M:-0.1288 c. 518: 65 108 65 65 65 85 65 SP T3 SD: 0.0580 c. M:-0.0913 c. 653: 82 136 82 82 82 107 82 SP T3 SD: 0.0526 c. M:-0.0879 c. 677: 85 141 85 85 85 111 85 SP T3 SD: 0.0460 c. M: 0.0900 c. 1147: 144 239 144 144 144 188 144 SP T3 SD: 0.0358 c. M:-0.0671 c. 1171: 147 244 147 147 147 192 147 SP T3 SD: 0.0066 c. M:-0.0126 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 20.6751 cents 4 x 5 x 6 x 7:8 S SD: 20.4521 cents 5 x 6:7 x 8:9:10 S SD: 20.7148 cents 6:7 x 8:9:10:11:12 S SD: 21.9579 cents 7:8:9:10 x 11:13:14 SD: 22.0235 cents 8:9:10:11:12:13:15:16 SD: 9.7976 cents 11:12:14:15:17:18:20:22 SD: 8.2895 cents 14:15:18:19:21:23:26:28 SD: 8.0999 cents 16:17:20:22:24:26:29:32 SD: 7.6000 cents 18:20:23:25:27:29:33:36 SD: 7.2811 cents 19:21:24:26:29:31:35:38 SD: 5.7068 cents 22:24:28:30:33:36:40:44 S SD: 3.7688 cents 24:26:30:33:36:39:44:48 SD: 3.1864 cents 30:33:38:41:45:49:55:60 SD: 2.8600 cents 34:37:43:47:51:56:62:68 SD: 2.6774 cents 42:46:53:58:63:69:77:84 SD: 1.7735 cents 54:59:68:74:81:88:99:108 SD: 1.3903 cents 66:72:83:91:99:108:121:132 SD: 0.8800 cents 88:96:111:121:132:144:161:176 SD: 0.5442 cents 154:168:194:212:231:252:282:308 SD: 0.4338 cents 176:192:222:242:264:288:323:352 SD: 0.3158 cents 242:264:305:333:363:396:444:484 SD: 0.2632 cents 264:288:333:363:396:432:484:528 SD: 0.1857 cents 330:360:416:454:495:540:605:660 SD: 0.1412 cents 552:602:696:759:828:903:1012:1104 SD: 0.1380 cents 584:637:736:803:876:956:1071:1168 SD: 0.1297 cents 594:648:749:817:891:972:1089:1188 SD: 0.1280 cents