Scala analysis: xen11-chalmers-tetrachordal-08-01
Transposition and Inversion by A, 6 tones, a Hexany
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 16/15 111.731285 minor diatonic semitone 3: 35/27 449.274618 septimal semi-diminished fourth, 9/4-tone 4: 4/3 498.044999 perfect fourth 5: 112/81 561.005903 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 81/56 638.9941 1: 28/27 62.9609 Archytas' 1/3-tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 175/144 337.5433 4: 36/35 48.7704 septimal diesis, 1/4-tone 5: 28/27 62.9609 Archytas' 1/3-tone 6: 81/56 638.9941
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 175/144 337.543 cents 1: 1 81/56 638.994 cents 2: 2 16/15 111.731 cents minor diatonic semitone 2: 2 5/4 386.314 cents major third 2: 2 3/2 701.955 cents perfect fifth 3: 1 9/7 435.084 cents septimal major third, BP third 3: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 3: 2 54/35 750.725 cents septimal semi-augmented fifth 3: 1 14/9 764.916 cents septimal minor sixth 4: 2 4/3 498.045 cents perfect fourth 4: 2 8/5 813.686 cents minor sixth 4: 2 15/8 1088.269 cents classic major seventh 5: 1 112/81 561.006 cents 5: 1 288/175 862.457 cents 5: 2 27/14 1137.039 cents septimal major seventh 5: 2 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.60000 = 18/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 63.0 111.7 449.3 498.0 561.0 1200.0 63.0 : 48.8 386.3 435.1 498.0 1137.0 1200.0 111.7 : 337.5 386.3 449.3 1088.3 1151.2 1200.0 449.3 : 48.8 111.7 750.7 813.7 862.5 1200.0 498.0 : 63.0 702.0 764.9 813.7 1151.2 1200.0 561.0 : 639.0 702.0 750.7 1088.3 1137.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 638.9941 cents 45/32, 590.2237 cents 36/35, 48.7704 cents 2: 111.7313 .. 701.9550 cents 45/32, 590.2237 cents 896/1215,-527.2628 cents 3: 435.0841 .. 764.9159 cents 98/81, 329.8318 cents 6/7,-266.8709 cents 4: 498.0450 .. 1088.2687 cents 45/32, 590.2237 cents 6/7,-266.8709 cents 5: 561.0059 .. 1151.2296 cents 45/32, 590.2237 cents 896/1215,-527.2628 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 81/56, 638.9941 cents Average / Smallest step : 4.100850 Largest / Average step : 3.194970 Largest / Smallest step : 13.102093 Median interval of one step : 28/27, 62.9609 cents, amount: 2 Least squares average step : 149.79623 cents, oct.: 898.77737 cents Scale is not proper Step pattern alph. order: ABCBAD Step pattern size order : BACABD Scale is a Constant Structure, by a margin of 48.77038 cents Scale diversity : 1.298499 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 Rothenberg efficiency : 0.466667 redundancy: 0.533333 Efficiency x scale size : 2.800000 Number of different interval sizes : 18 = 3.60000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.60000 = 18/5 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 245/243, 14.1905 cents Number of recognisable fifths : 2, average 701.9550 cents Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 16.6667% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval class 2 Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 5-6 -- Rational properties -- Prime limit : 7 Odd number limit : 175 (O: 175 U: 175) Highest odd numerator or denominator: 81 Scale harmonicity : 0.026488 Average absolute harmonicity : 0.236782 Specific harmonicity : 0.140443 Fundamental : 1/405, -8.6618 octaves, 0.6460 Hz. Guide tone : 560, 9.1293 octaves, 146510.317 Hz. Exponens Consonantiae : 2.268000E+05, 17.79106 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 175.5, average 29.25000 Mersenne's string divisions : 13820730 Sum of van Prooijen's expressibility: 6.53713, average 1.08952 Sum of Tenney's harmonic distance : 13.57208, average 2.26201 Vogel's harmonic complexity : 16.66667 Wille's k value : 262 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 68.46189, average 3.26009 Lattice compactness (without 2's) : 47.06061, average 2.24098 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 4 2.16667 13 1 3: -4 .. 0 -2.00000 12 1 5: -1 .. 1 0.00000 2 1 7: 0 .. 1 0.50000 3 3 Average exponent except 2's :-9 / 6 =-1.50000 Average absolute exponent except 2's: 17 / 6 = 2.83333 Scale is weakly epimorphic with val: <6 9 13 19| Scale is weakly epimorphic with val: <6 9 14 17| Scale is weakly epimorphic with val: <6 10 13 15| Scale is weakly epimorphic with val: <6 10 15 19| Scale is weakly epimorphic with val: <6 11 14 17| Scale is weakly epimorphic with val: <6 11 15 17|
FIT/MODE
6: 0 0 2 0 1 3 N SD: 70.7216 c. M: 111.7313 c. 7: 0 1 2 0 0 4 N SD: 48.6498 c. M:-65.0111 c. 8: 0 1 2 0 1 4 N SD: 39.2809 c. M: 62.9609 c. 9: 0 1 2 1 0 5 N SD: 38.4486 c. M: 62.9609 c. 10: 1 0 3 0 1 5 N SD: 31.9167 c. M:-57.0391 c. 12: 1 0 4 0 1 6 N SD: 30.5694 c. M:-50.7254 c. 13: 1 0 4 0 1 7 N SD: 21.4977 c. M: 36.5065 c. 15: 1 0 5 0 1 8 N SD: 20.6877 c. M: 31.7313 c. 17: 1 1 4 1 1 9 N D3 SD: 16.4171 c. M:-29.4452 c. 19: 1 1 5 1 1 10 N D3 SD: 7.8659 c. M:-14.5845 c. 24: 1 1 7 1 1 13 N D3 SD: 8.4763 c. M: 12.9609 c. 32: 2 1 9 1 2 17 N SD: 6.5763 c. M:-12.0391 c. 34: 2 1 10 1 2 18 N SD: 5.9537 c. M:-9.5489 c. 41: 2 2 11 2 2 22 N D3 SD: 5.4391 c. M: 10.2502 c. 43: 2 2 12 2 2 23 N D3 SD: 3.7697 c. M: 7.1470 c. 53: 3 2 15 2 3 28 N SD: 3.2859 c. M:-5.0318 c. 72: 4 3 20 3 4 38 N SD: 3.5233 c. M:-5.6608 c. 75: 4 3 21 3 4 40 N SD: 1.1526 c. M: 2.0450 c. 96: 5 4 27 4 5 51 N SD: 1.1093 c. M:-1.9550 c. 118: 6 5 33 5 6 63 N SD: 1.2911 c. M: 1.9440 c. 152: 8 6 43 6 8 81 N SD: 0.6714 c. M: 1.2050 c. 171: 9 7 48 7 9 91 N SD: 0.3061 c. M:-0.5494 c. 246: 13 10 69 10 13 131 N SD: 0.3874 c. M: 0.4941 c. 323: 17 13 91 13 17 172 N SD: 0.1951 c. M: 0.2762 c. 419: 22 17 118 17 22 223 N SD: 0.2340 c. M:-0.3674 c. 494: 26 20 139 20 26 263 N SD: 0.1110 c. M:-0.1970 c. 665: 35 27 187 27 35 354 N SD: 0.1304 c. M:-0.1971 c. 783: 41 32 220 32 41 417 N SD: 0.1292 c. M: 0.2325 c. 860: 45 35 242 35 45 458 N SD: 0.0958 c. M: 0.1702 c. 935: 49 38 263 38 49 498 N SD: 0.0868 c. M: 0.1503 c. 1031: 54 42 290 42 54 549 N SD: 0.0640 c. M:-0.1121 c. 1106: 58 45 311 45 58 589 N SD: 0.0496 c. M: 0.0884 c. 1354: 71 55 381 55 71 721 N SD: 0.0410 c. M: 0.0622 c. 1429: 75 58 402 58 75 761 N SD: 0.0428 c. M: 0.0744 c. 1525: 80 62 429 62 80 812 N SD: 0.0322 c. M:-0.0534 c. 1600: 84 65 450 65 84 852 N SD: 0.0275 c. M: 0.0450 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x x x 3:4 S SD: 70.4745 cents 3 x x x 4 x 6 S SD: 0.0000 cents 4 x x 5 x 6:8 S SD: 51.4573 cents 5 x x x x 7:10 SD: 10.7531 cents 6 x 7 x 8 x 12 S SD: 51.7132 cents 7 x 8:9 x 10:14 SD: 33.2210 cents 8 x 9:10 x 11:16 SD: 28.0121 cents 9 x 10 x 12 x 18 S SD: 23.5575 cents 10 x 11:13 x 14:20 SD: 14.4155 cents 11 x 12:14 x 15:22 SD: 13.9226 cents 12 x 13 x 16:17:24 SD: 12.4599 cents 13 x 14:17 x 18:26 SD: 5.6443 cents 14 x 15:18:19 x 28 SD: 8.6595 cents 15 x 16:19:20:21:30 SD: 9.0883 cents 16 x 17:21 x 22:32 SD: 6.1354 cents 17 x 18:22:23:24:34 SD: 9.1783 cents 18 x 19:23:24:25:36 SD: 6.3518 cents 19 x 20 x 25:26:38 SD: 9.2713 cents 20:21 x 26:27:28:40 SD: 7.5152 cents 21:22 x 27:28:29:42 SD: 4.5395 cents 22:23 x x 29:30:44 SD: 8.5367 cents 23:24:25:30:31:32:46 SD: 6.9905 cents 24:25:26:31:32:33:48 SD: 5.0336 cents 26:27:28:34:35:36:52 SD: 4.6840 cents 27:28:29:35:36:37:54 SD: 3.2686 cents 31:32:33:40:41:43:62 SD: 3.1911 cents 44:46:47:57:59:61:88 SD: 2.9823 cents 45:47:48:58:60:62:90 SD: 2.8315 cents 47:49:50:61:63:65:94 SD: 2.3243 cents 57:59:61:74:76:79:114 SD: 1.3562 cents 60:62:64:78:80:83:120 SD: 1.3267 cents 78:81:83:101:104:108:156 SD: 0.9469 cents 102:106:109:132:136:141:204 SD: 0.9428 cents 105:109:112:136:140:145:210 SD: 0.5270 cents 135:140:144:175:180:187:270 SD: 0.5148 cents 162:168:173:210:216:224:324 SD: 0.3338 cents 165:171:176:214:220:228:330 SD: 0.3045 cents 240:249:256:311:320:332:480 SD: 0.2093 cents 300:311:320:389:400:415:600 SD: 0.1844 cents 402:417:429:521:536:556:804 SD: 0.1836 cents 405:420:432:525:540:560:810 SD: 0.0000 cents