Scala analysis: xen12-chalmers-tritriadic-dm-5-9-11
Tritriadic D->M scale built from 5:9:11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 11/9 347.407941 undecimal neutral third 3: 121/90 512.412169 4: 81/55 670.188347 5: 18/11 852.592059 undecimal neutral sixth 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 10/9 182.4037 minor whole tone 3: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 1458/1331 157.7762 5: 10/9 182.4037 minor whole tone 6: 11/10 165.0042 Ptolemy's second, 4/5-tone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 1458/1331 157.776 cents 1: 3 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 3 10/9 182.404 cents minor whole tone 2: 1 729/605 322.780 cents 2: 1 1620/1331 340.180 cents 2: 5 11/9 347.408 cents undecimal neutral third 3: 3 162/121 505.184 cents 3: 2 121/90 512.412 cents 3: 2 110/81 529.812 cents 4: 2 81/55 670.188 cents 4: 2 180/121 687.588 cents 4: 3 121/81 694.816 cents two (undecimal neutral third) 5: 5 18/11 852.592 cents undecimal neutral sixth 5: 1 1331/810 859.820 cents 5: 1 1210/729 877.220 cents 6: 3 9/5 1017.596 cents just minor seventh, BP seventh 6: 3 20/11 1034.996 cents large minor seventh 6: 1 1331/729 1042.224 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 : 165.0 347.4 512.4 670.2 852.6 1017.6 1200.0 165.0 : 182.4 347.4 505.2 687.6 852.6 1035.0 1200.0 347.4 : 165.0 322.8 505.2 670.2 852.6 1017.6 1200.0 512.4 : 157.8 340.2 505.2 687.6 852.6 1035.0 1200.0 670.2 : 182.4 347.4 529.8 694.8 877.2 1042.2 1200.0 852.6 : 165.0 347.4 512.4 694.8 859.8 1017.6 1200.0 1017.6: 182.4 347.4 529.8 694.8 852.6 1035.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 157.7762 .. 182.4037 cents 6655/6561, 24.6275 cents 1458/1331, 157.7762 cents 2: 322.7804 .. 347.4079 cents 6655/6561, 24.6275 cents 6561/6050, 140.3767 cents 3: 505.1841 .. 529.8117 cents 6655/6561, 24.6275 cents 1458/1331, 157.7762 cents 4: 670.1883 .. 694.8159 cents 6655/6561, 24.6275 cents 6561/6050, 140.3767 cents 5: 852.5921 .. 877.2196 cents 6655/6561, 24.6275 cents 1458/1331, 157.7762 cents 6: 1017.5963 .. 1042.2238 cents 6655/6561, 24.6275 cents 6561/6050, 140.3767 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 1458/1331, 157.7762 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 1.086530 Largest / Average step : 1.064022 Largest / Smallest step : 1.156092 Median interval of one step : 11/10, 165.0042 cents, amount: 3 Least squares average step : 170.33106 cents, oct.: 1192.31740 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACBAB Step pattern size order : MLMSLML Scale is a Constant Structure, by a margin of 140.37669 cents Scale diversity : 1.126523 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.876862 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 : 14641/14580, 7.2281 cents Most common intervals : 11/9, 347.4079 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 182.404 347.408 cents Most common triad is 0.0 347.408 852.592 cents, amount: 3 Number of recognisable fifths : 5, average 691.9247 cents Number of appreciable fifths : 3, average 694.8159 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 : 9 11 Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval class 1 Limited transpositions with margin 24.6275 cents: 1 2 3 4 5 6 Limited inverse transpositions with margin 24.6275 cents: 1 2 3 4 5 6 -- Rational properties -- Prime limit : 11 Odd number limit : 1331 (O: 1331 U: 1331) Highest odd numerator or denominator: 121 Scale harmonicity : 0.012667 Average absolute harmonicity : 0.179481 Specific harmonicity : 0.069120 Fundamental : 1/990, -9.9513 octaves, 0.2643 Hz. Guide tone : 19602, 14.2587 octaves, 5128384.331 Hz. Exponens Consonantiae : 1.940598E+07, 24.21000 octaves Euler's gradus suavitatis : 49 Sum of Mann's harmonic distance : 217.0, average 31.00000 Mersenne's string divisions : 87379320 Sum of van Prooijen's expressibility: 8.06969, average 1.15281 Sum of Tenney's harmonic distance : 15.97381, average 2.28197 Vogel's harmonic complexity : 25.00000 Wille's k value : 665 Wilson's harmonic complexity : 56 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 90.15089, average 3.21967 Lattice compactness (without 2's) : 83.60828, average 2.98601 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 0.00000 4 1 3: -2 .. 4 0.57143 12 5: -1 .. 0 -0.57143 4 1 11: -1 .. 2 0.28571 6 5 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 22 / 7 = 3.14286 Scale is weakly epimorphic with val: <7 10 15 24| Scale is weakly epimorphic with val: <7 10 16 26| Scale is weakly epimorphic with val: <7 10 18 23| Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 11 17 26| Scale is weakly epimorphic with val: <7 12 16 22| Scale is JI-epimorphic with val: <7 12 18 26|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 7.9974 c. M:-15.5259 c. Lebeng 31: 4 5 4 4 5 4 5 SP M ME S SD: 8.1138 c. M: 12.1238 c. Neutral Mixolydian 38: 5 6 5 5 6 5 6 SP M ME S SD: 5.3595 c. M: 7.1490 c. 45: 6 7 6 6 7 6 7 SP M ME S SD: 3.5802 c. M: 5.7455 c. 52: 7 8 7 7 8 7 8 SP M ME S SD: 2.4855 c. M: 4.7199 c. 59: 8 9 8 8 9 8 9 SP M ME S SD: 1.9852 c. M: 3.9376 c. 66: 9 10 9 9 10 9 10 SP M ME S SD: 1.9756 c. M: 3.3213 c. 86: 12 13 12 11 13 12 13 SP T3 SD: 1.9337 c. M:-3.8669 c. 93: 13 14 13 12 14 13 14 SP T3 SD: 1.9613 c. M:-3.7169 c. 100: 14 15 14 13 15 14 15 SP T3 SD: 2.1250 c. M:-3.5878 c. 117: 16 18 16 15 18 16 18 SP T3 SD: 1.7609 c. M: 3.5217 c. 124: 17 19 17 16 19 17 19 SP T3 SD: 1.2268 c. M: 2.4464 c. 131: 18 20 18 17 20 18 20 SP T3 SD: 0.7672 c. M: 1.4861 c. 138: 19 21 19 18 21 19 21 SP T3 SD: 0.4182 c. M:-0.6313 c. 145: 20 22 20 19 22 20 22 SP T3 SD: 0.3667 c. M:-0.6913 c. 204: 28 31 28 27 31 28 31 SP T3 SD: 0.3614 c. M: 0.6475 c. 283: 39 43 39 37 43 39 43 SP T3 SD: 0.3386 c. M:-0.6620 c. 328: 45 50 45 43 50 45 50 SP T3 SD: 0.3707 c. M: 0.6762 c. 335: 46 51 46 44 51 46 51 SP T3 SD: 0.2007 c. M: 0.3376 c. 342: 47 52 47 45 52 47 52 SP T3 SD: 0.0674 c. M: 0.1315 c. 487: 67 74 67 64 74 67 74 SP T3 SD: 0.0624 c. M:-0.1135 c. 822: 113 125 113 108 125 113 125 SP T3 SD: 0.0584 c. M: 0.1154 c. 829: 114 126 114 109 126 114 126 SP T3 SD: 0.0111 c. M:-0.0167 c. 2000: 275 304 275 263 304 275 304 SP T3 SD: 0.0079 c. M: 0.0122 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: 15.8833 cents 3 x x 4 x 5 x 6 S SD: 11.6215 cents 4 x 5 x 6 x 7:8 S SD: 17.5024 cents 5 x 6:7 x 8:9:10 S SD: 17.2474 cents 6 x 7:8:9:10:11:12 S SD: 16.4317 cents 7:8 x 9:10:11:13:14 SD: 24.1390 cents 8:9:10:11:12:13:14:16 S SD: 12.8366 cents 9:10:11:12:13:15:16:18 SD: 7.9639 cents 17:19:21:23:25:28:31:34 SD: 6.1552 cents 19:21:23:26:28:31:34:38 SD: 5.3680 cents 21:23:26:28:31:34:38:42 SD: 4.9509 cents 23:25:28:31:34:38:41:46 SD: 4.7255 cents 27:30:33:36:40:44:49:54 SD: 4.2059 cents 28:31:34:38:41:46:50:56 SD: 4.1747 cents 30:33:37:40:44:49:54:60 SD: 3.2361 cents 32:35:39:43:47:52:58:64 SD: 2.9740 cents 40:44:49:54:59:65:72:80 SD: 2.1145 cents 41:45:50:55:60:67:74:82 SD: 1.9814 cents 49:54:60:66:72:80:88:98 SD: 1.2554 cents 72:79:88:97:106:118:130:144 SD: 1.1769 cents 81:89:99:109:119:133:146:162 SD: 1.1511 cents 89:98:109:120:131:146:160:178 SD: 1.1483 cents 90:99:110:121:133:147:162:180 SD: 0.9628 cents 91:100:111:122:134:149:164:182 SD: 0.9523 cents 99:109:121:133:146:162:178:198 SD: 0.5274 cents 140:154:171:188:206:229:252:280 SD: 0.4104 cents 171:188:209:230:252:280:308:342 SD: 0.3260 cents 220:242:269:296:324:360:396:440 SD: 0.2120 cents 311:342:380:418:458:509:560:622 SD: 0.1598 cents 360:396:440:484:530:589:648:720 SD: 0.0930 cents 459:505:561:617:676:751:826:918 SD: 0.0924 cents 531:584:649:714:782:869:956:1062 SD: 0.0798 cents