Scala analysis: xen11-chalmers-tetrachordal-06-09
Transposition by 4/3A
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: 9/7 435.084095 septimal major third, BP third 4: 4/3 498.044999 perfect fourth 5: 48/35 546.815381 septimal semi-augmented fourth 6: 12/7 933.129094 septimal major sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 28/27 62.9609 Archytas' 1/3-tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 135/112 323.3528 septimal wide minor third 4: 28/27 62.9609 Archytas' 1/3-tone 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 5/4 386.3137 major third 7: 7/6 266.8709 septimal minor third
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 7/6 266.871 cents septimal minor third 1: 1 135/112 323.353 cents septimal wide minor third 1: 1 5/4 386.314 cents major third 2: 2 16/15 111.731 cents minor diatonic semitone 2: 1 98/81 329.832 cents 2: 1 243/196 372.123 cents 2: 1 5/4 386.314 cents major third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 35/24 653.185 cents septimal semi-diminished fifth 3: 1 56/45 378.602 cents septimal narrow major third 3: 3 9/7 435.084 cents septimal major third, BP third 3: 1 4/3 498.045 cents perfect fourth 3: 1 3/2 701.955 cents perfect fifth 3: 1 245/162 716.146 cents 4: 1 324/245 483.854 cents 4: 1 4/3 498.045 cents perfect fourth 4: 1 3/2 701.955 cents perfect fifth 4: 3 14/9 764.916 cents septimal minor sixth 4: 1 45/28 821.398 cents septimale wide minor sixth 5: 1 48/35 546.815 cents septimal semi-augmented fourth 5: 1 14/9 764.916 cents septimal minor sixth 5: 1 8/5 813.686 cents minor sixth 5: 1 392/243 827.877 cents 5: 1 81/49 870.168 cents two (septimal major third, BP third) 5: 2 15/8 1088.269 cents classic major seventh 6: 1 8/5 813.686 cents minor sixth 6: 1 224/135 876.647 cents narrow septimal major sixth 6: 1 12/7 933.129 cents septimal major sixth 6: 2 27/14 1137.039 cents septimal major seventh 6: 2 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.33333 = 16/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 63.0 111.7 435.1 498.0 546.8 933.1 1200.0 63.0 : 48.8 372.1 435.1 483.9 870.2 1137.0 1200.0 111.7 : 323.4 386.3 435.1 821.4 1088.3 1151.2 1200.0 435.1 : 63.0 111.7 498.0 764.9 827.9 876.6 1200.0 498.0 : 48.8 435.1 702.0 764.9 813.7 1137.0 1200.0 546.8 : 386.3 653.2 716.1 764.9 1088.3 1151.2 1200.0 933.1 : 266.9 329.8 378.6 702.0 764.9 813.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 386.3137 cents 175/144, 337.5433 cents 36/35, 48.7704 cents 2: 111.7313 .. 653.1846 cents 175/128, 541.4533 cents 64/75,-274.5824 cents 3: 378.6022 .. 716.1455 cents 175/144, 337.5433 cents 64/75,-274.5824 cents 4: 483.8545 .. 821.3978 cents 175/144, 337.5433 cents 52488/60025,-232.2910 cents 5: 546.8154 .. 1088.2687 cents 175/128, 541.4533 cents 64/75,-274.5824 cents 6: 813.6863 .. 1151.2296 cents 175/144, 337.5433 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 3.515014 Largest / Average step : 2.253497 Largest / Smallest step : 7.921072 Median interval of one step : 28/27, 62.9609 cents, amount: 2 Least squares average step : 145.11934 cents, oct.: 1015.83536 cents Scale is not proper Step pattern alph. order: ABCABDE Step pattern size order : BADBAEC Scale is not a Constant Structure Scale diversity : 1.400919 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.33333 = 16/3 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 10976/10935, 6.4790 cents Most common intervals : 9/7, 435.0841 cents & inv., amount: 4 Number of recognisable fifths : 3, average 706.6852 cents Number of appreciable 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 = 14.2857% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 7 Odd number limit : 245 (O: 245 U: 245) Highest odd numerator or denominator: 35 Scale harmonicity : 0.022571 Average absolute harmonicity : 0.216262 Specific harmonicity : 0.130589 Fundamental : 1/945, -9.8842 octaves, 0.2769 Hz. Guide tone : 1008, 9.9773 octaves, 263718.570 Hz. Exponens Consonantiae : 9.525600E+05, 19.86145 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 107.0, average 15.28571 Mersenne's string divisions : 903431760 Sum of van Prooijen's expressibility: 6.42798, average 0.91828 Sum of Tenney's harmonic distance : 13.58787, average 1.94112 Vogel's harmonic complexity : 19.28571 Wille's k value : 607 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 8 Triangular lattice diameter : 5 Lattice compactness : 87.25832, average 3.11637 Lattice compactness (without 2's) : 61.30731, average 2.18955 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 4 2.14286 15 1 3: -3 .. 2 -0.14286 9 1 5: -1 .. 0 -0.28571 2 1 7: -1 .. 1 -0.28571 4 4 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is weakly epimorphic with val: <7 10 15 22| Scale is weakly epimorphic with val: <7 10 16 21| Scale is weakly epimorphic with val: <7 12 15 21| Scale is weakly epimorphic with val: <7 12 18 18|
FIT/MODE
7: 0 1 2 0 0 2 2 N SD: 54.6372 c. M:-79.2016 c. 8: 0 1 2 0 1 2 2 N SD: 41.2060 c. M: 62.9609 c. 9: 0 1 2 1 0 3 2 N SD: 31.8225 c. M: 62.9609 c. 10: 1 0 3 0 1 3 2 N SD: 36.2837 c. M:-57.0391 c. 11: 1 0 3 1 0 4 2 N SD: 31.0684 c. M:-48.6891 c. 12: 0 1 3 1 0 4 3 N SD: 35.1032 c. M: 62.9609 c. 13: 1 0 4 0 1 4 3 N SD: 22.1087 c. M: 36.5065 c. 14: 1 0 4 1 0 5 3 N SD: 19.4701 c. M: 32.5297 c. 17: 1 1 4 1 1 5 4 N SD: 15.2779 c. M:-29.4452 c. 19: 1 1 5 1 1 6 4 N SD: 11.8545 c. M:-21.6057 c. 22: 1 1 6 1 1 7 5 N SD: 4.8770 c. M: 8.4154 c. 41: 2 2 11 2 2 13 9 N SD: 4.8103 c. M:-9.2822 c. 53: 3 2 14 3 2 17 12 N SD: 3.5006 c. M:-4.9636 c. 55: 3 2 15 3 2 18 12 N SD: 2.8397 c. M:-5.0527 c. 72: 4 3 19 4 3 23 16 N SD: 2.8072 c. M:-4.9354 c. 75: 4 3 20 4 3 24 17 N SD: 2.6479 c. M: 5.1291 c. 77: 4 3 21 4 3 25 17 N SD: 1.4652 c. M: 2.6404 c. 99: 5 4 27 5 4 32 22 N SD: 1.5677 c. M: 2.6404 c. 116: 6 5 31 6 5 37 26 N SD: 1.4222 c. M: 2.0946 c. 130: 7 5 35 7 5 42 29 N SD: 1.2469 c. M: 2.2000 c. 149: 8 6 40 8 6 48 33 N SD: 0.9847 c. M:-1.4686 c. 171: 9 7 46 9 7 55 38 N SD: 0.3226 c. M:-0.5530 c. 364: 19 15 98 19 15 117 81 N SD: 0.2712 c. M:-0.4374 c. 419: 22 17 113 22 17 135 93 N SD: 0.2548 c. M:-0.5225 c. 441: 23 18 119 23 18 142 98 N SD: 0.2130 c. M: 0.3759 c. 494: 26 20 133 26 20 159 110 N SD: 0.2046 c. M: 0.3356 c. 590: 31 24 159 31 24 190 131 N SD: 0.2389 c. M:-0.4302 c. 612: 32 25 165 32 25 197 136 N SD: 0.1660 c. M:-0.2434 c. 665: 35 27 179 35 27 214 148 N SD: 0.1418 c. M:-0.1970 c. 742: 39 30 200 39 30 239 165 N SD: 0.1026 c. M: 0.1847 c. 913: 48 37 246 48 37 294 203 N SD: 0.0675 c. M:-0.1278 c. 935: 49 38 252 49 38 301 208 N SD: 0.0647 c. M: 0.0810 c. 1106: 58 45 298 58 45 356 246 N SD: 0.0252 c. M: 0.0369 c. 2019: 106 82 544 106 82 650 449 N SD: 0.0196 c. M:-0.0406 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 77.5698 cents 3 x x x 4 x 5:6 S SD: 16.2568 cents 4 x x 5 x 6:7:8 S SD: 41.6241 cents 5 x x 6 x 7:9:10 SD: 37.6460 cents 6 x 7 x 8 x 10:12 S SD: 40.6562 cents 7 x 8:9 x 10:12:14 S SD: 27.7569 cents 8 x 9:10 x 11:14:16 SD: 22.0635 cents 9 x 10 x 12 x 15:18 S SD: 21.4668 cents 10 x 11:13 x 14:17:20 SD: 13.6939 cents 11 x 12:14 x 15:19:22 SD: 9.1446 cents 12 x 13:15:16 x 21:24 SD: 13.2261 cents 13 x 14:17 x 18:22:26 SD: 8.7384 cents 14 x 15:18 x 19:24:28 SD: 3.9401 cents 15 x 16:19:20:21:26:30 SD: 8.0068 cents 16 x 17 x 21:22:27:32 SD: 7.8812 cents 17 x 18:22 x 23:29:34 SD: 6.0495 cents 18 x 19:23:24:25:31:36 SD: 5.2366 cents 19 x 20:24:25:26:33:38 SD: 8.3619 cents 20:21 x 26:27 x 34:40 SD: 7.7482 cents 21:22 x 27:28:29:36:42 SD: 3.5452 cents 22:23 x 28:29:30:38:44 SD: 5.6870 cents 24:25:26:31:32:33:41:48 SD: 4.2867 cents 27:28:29:35:36:37:46:54 SD: 3.0693 cents 32:33:34:41:43:44:55:64 SD: 2.8503 cents 45:47:48:58:60:62:77:90 SD: 2.2329 cents 46:48:49:59:61:63:79:92 SD: 2.2240 cents 48:50:51:62:64:66:82:96 SD: 2.1469 cents 49:51:52:63:65:67:84:98 SD: 2.1339 cents 56:58:60:72:75:77:96:112 SD: 1.7148 cents 57:59:61:73:76:78:98:114 SD: 1.6204 cents 59:61:63:76:79:81:101:118 SD: 1.4600 cents 60:62:64:77:80:82:103:120 SD: 1.3605 cents 78:81:83:100:104:107:134:156 SD: 1.1183 cents 87:90:93:112:116:119:149:174 SD: 1.1121 cents 102:106:109:131:136:140:175:204 SD: 0.7937 cents 105:109:112:135:140:144:180:210 SD: 0.2522 cents 270:280:288:347:360:370:463:540 SD: 0.2294 cents 374:388:399:481:499:513:641:748 SD: 0.2193 cents 375:389:400:482:500:514:643:750 SD: 0.1796 cents 434:450:463:558:579:595:744:868 SD: 0.1735 cents 480:498:512:617:640:658:823:960 SD: 0.1698 cents 511:530:545:657:681:701:876:1022 SD: 0.1474 cents 539:559:575:693:719:739:924:1078 SD: 0.1368 cents 570:591:608:733:760:782:977:1140 SD: 0.1182 cents