Scala analysis: xen11-chalmers-tetrachordal-08-02
Transposition and Inversion by B, 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: 4/3 498.044999 perfect fourth 4: 48/35 546.815381 septimal semi-augmented fourth 5: 64/45 609.776284 2nd tritone 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 45/32 590.2237 diatonic tritone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 5/4 386.3137 major third 4: 36/35 48.7704 septimal diesis, 1/4-tone 5: 28/27 62.9609 Archytas' 1/3-tone 6: 45/32 590.2237 diatonic tritone
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 5/4 386.314 cents major third 1: 1 45/32 590.224 cents diatonic tritone 2: 2 16/15 111.731 cents minor diatonic semitone 2: 2 9/7 435.084 cents septimal major third, BP third 2: 2 35/24 653.185 cents septimal semi-diminished fifth 3: 1 324/245 483.854 cents 3: 2 4/3 498.045 cents perfect fourth 3: 2 3/2 701.955 cents perfect fifth 3: 1 245/162 716.146 cents 4: 2 48/35 546.815 cents septimal semi-augmented fourth 4: 2 14/9 764.916 cents septimal minor sixth 4: 2 15/8 1088.269 cents classic major seventh 5: 1 64/45 609.776 cents 2nd tritone 5: 1 8/5 813.686 cents minor sixth 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 : 63.0 111.7 498.0 546.8 609.8 1200.0 63.0 : 48.8 435.1 483.9 546.8 1137.0 1200.0 111.7 : 386.3 435.1 498.0 1088.3 1151.2 1200.0 498.0 : 48.8 111.7 702.0 764.9 813.7 1200.0 546.8 : 63.0 653.2 716.1 764.9 1151.2 1200.0 609.8 : 590.2 653.2 702.0 1088.3 1137.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 590.2237 cents 175/128, 541.4533 cents 36/35, 48.7704 cents 2: 111.7313 .. 653.1846 cents 175/128, 541.4533 cents 512/675,-478.4924 cents 3: 483.8545 .. 716.1455 cents 60025/52488, 232.2910 cents 7776/8575,-169.3301 cents 4: 546.8154 .. 1088.2687 cents 175/128, 541.4533 cents 7776/8575,-169.3301 cents 5: 609.7763 .. 1151.2296 cents 175/128, 541.4533 cents 512/675,-478.4924 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 : 45/32, 590.2237 cents Average / Smallest step : 4.100850 Largest / Average step : 2.951119 Largest / Smallest step : 12.102093 Median interval of one step : 28/27, 62.9609 cents, amount: 2 Least squares average step : 156.22749 cents, oct.: 937.36493 cents Scale is not proper Step pattern alph. order: ABCBAD Step pattern size order : BACABD Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.162009 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 : 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 = 16.6667% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 5-6 -- Rational properties -- Prime limit : 7 Odd number limit : 245 (O: 245 U: 245) Highest odd numerator or denominator: 45 Scale harmonicity : 0.022916 Average absolute harmonicity : 0.239887 Specific harmonicity : 0.142900 Fundamental : 1/945, -9.8842 octaves, 0.2769 Hz. Guide tone : 1344, 10.3923 octaves, 351624.760 Hz. Exponens Consonantiae : 1.270080E+06, 20.27649 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 144.0, average 24.00000 Mersenne's string divisions : 323927835 Sum of van Prooijen's expressibility: 6.28186, average 1.04698 Sum of Tenney's harmonic distance : 13.32365, average 2.22061 Vogel's harmonic complexity : 18.66667 Wille's k value : 472 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 71.58320, average 3.40872 Lattice compactness (without 2's) : 41.35145, average 1.96912 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 6 3.16667 19 1 3: -3 .. 1 -1.00000 8 1 5: -1 .. 0 -0.50000 3 2 7: -1 .. 1 0.00000 2 2 Average exponent except 2's :-9 / 6 =-1.50000 Average absolute exponent except 2's: 13 / 6 = 2.16667 Scale is JI-epimorphic with val: <6 9 13 16| Scale is weakly epimorphic with val: <6 9 13 19| Scale is weakly epimorphic with val: <6 10 13 16| Scale is weakly epimorphic with val: <6 10 13 17| Scale is weakly epimorphic with val: <6 10 15 15| Scale is weakly epimorphic with val: <6 10 15 16| Scale is weakly epimorphic with val: <6 11 15 17| Scale is weakly epimorphic with val: <6 11 15 18|
FIT/MODE
6: 0 0 2 0 1 3 N SD: 89.1732 c. M: 146.8154 c. 7: 0 1 2 0 1 3 N SD: 49.3565 c. M:-75.9380 c. 8: 0 1 2 1 0 4 N SD: 42.1526 c. M: 62.9609 c. 9: 1 0 3 0 1 4 N SD: 40.9928 c. M:-70.3724 c. 10: 1 0 3 1 0 5 N SD: 33.0949 c. M:-57.0391 c. 11: 1 0 4 0 1 5 N SD: 32.6311 c. M:-47.4095 c. 13: 1 0 4 1 1 6 N SD: 25.6385 c. M: 36.5065 c. 14: 1 0 5 0 1 7 N SD: 20.8651 c. M: 32.5297 c. 15: 1 0 5 1 1 7 N SD: 21.2530 c. M: 31.7313 c. 17: 1 1 5 1 1 8 N D3 SD: 17.8505 c. M:-29.4452 c. 18: 1 1 5 1 1 9 N D3 SD: 17.0407 c. M: 31.3783 c. 19: 1 1 6 1 1 9 N D3 SD: 14.1834 c. M:-21.8027 c. 20: 1 1 6 1 1 10 N D3 SD: 9.5288 c. M: 18.0450 c. 22: 1 1 7 1 1 11 N D3 SD: 6.1392 c. M: 9.7763 c. 41: 2 2 13 2 2 20 N D3 SD: 5.1333 c. M:-9.2822 c. 51: 3 2 16 2 3 25 N SD: 4.9049 c. M:-7.6273 c. 53: 3 2 17 2 3 26 N SD: 2.6108 c. M:-4.9636 c. 55: 3 2 18 2 3 27 N SD: 2.2569 c. M:-3.7732 c. 75: 4 3 24 3 4 37 N SD: 1.6541 c. M: 2.8154 c. 77: 4 3 25 3 4 38 N SD: 1.5044 c. M: 2.6404 c. 116: 6 5 37 5 6 57 N SD: 1.2736 c. M:-2.0618 c. 118: 6 5 38 5 6 58 N SD: 1.2571 c. M:-2.3372 c. 130: 7 5 42 5 7 64 N SD: 1.2230 c. M: 2.2000 c. 149: 8 6 48 6 8 73 N SD: 1.3450 c. M:-2.3043 c. 152: 8 6 49 6 8 75 N SD: 1.2786 c. M: 2.0785 c. 169: 9 7 54 7 9 83 N SD: 1.0162 c. M:-1.8782 c. 171: 9 7 55 7 9 84 N SD: 0.4563 c. M:-0.7500 c. 246: 13 10 79 10 13 121 N SD: 0.3830 c. M: 0.4840 c. 248: 13 10 80 10 13 122 N SD: 0.2332 c. M: 0.4410 c. 364: 19 15 117 15 19 179 N SD: 0.2872 c. M:-0.4374 c. 419: 22 17 135 17 22 206 N SD: 0.1762 c. M:-0.2844 c. 494: 26 20 159 20 26 243 N SD: 0.1373 c. M: 0.2567 c. 612: 32 25 197 25 32 301 N SD: 0.1340 c. M:-0.2434 c. 665: 35 27 214 27 35 327 N SD: 0.1192 c. M:-0.1970 c. 742: 39 30 239 30 39 365 N SD: 0.1129 c. M: 0.1847 c. 858: 45 35 276 35 45 422 N SD: 0.0887 c. M:-0.1568 c. 913: 48 37 294 37 48 449 N SD: 0.0752 c. M:-0.1278 c. 935: 49 38 301 38 49 460 N SD: 0.0870 c. M: 0.1506 c. 1106: 58 45 356 45 58 544 N SD: 0.0231 c. M: 0.0341 c. 2019: 106 82 650 82 106 993 N SD: 0.0234 c. M:-0.0406 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x x x 3:4 S SD: 46.0894 cents 3 x x 4 x x 6 S SD: 0.0000 cents 4 x x 5 x 6:8 S SD: 48.2825 cents 5 x x x x 7:10 SD: 13.6320 cents 6 x 7:8 x 9:12 S SD: 45.1146 cents 7 x 8:9 x 10:14 SD: 33.8102 cents 8 x 9 x 11 x 16 SD: 30.7629 cents 9 x 10:12 x 13:18 SD: 18.8995 cents 10 x 11:13 x 14:20 SD: 18.5447 cents 11 x 12 x 15:16:22 SD: 13.9746 cents 12 x 13:16 x 17:24 SD: 6.9209 cents 13 x 14:17:18 x 26 SD: 10.2440 cents 14 x 15 x 19:20:28 SD: 5.2890 cents 15 x 16:20 x 21:30 SD: 6.8160 cents 16 x 17:21:22:23:32 SD: 6.7873 cents 17 x 18 x 23:24:34 SD: 7.4102 cents 18 x 19:24:25:26:36 SD: 7.8200 cents 19 x 20:25:26:27:38 SD: 6.5364 cents 20:21 x 27 x 28:40 SD: 10.2114 cents 21:22 x 28:29:30:42 SD: 4.5252 cents 22:23 x 29:30:31:44 SD: 6.1402 cents 24:25:26:32:33:34:48 SD: 4.8480 cents 26:27:28:35:36:37:52 SD: 4.8020 cents 27:28:29:36:37:38:54 SD: 3.6284 cents 29:30:31:39:40:41:58 SD: 3.5640 cents 30:31:32:40:41:43:60 SD: 2.6674 cents 45:47:48:60:62:64:90 SD: 2.4482 cents 48:50:51:64:66:68:96 SD: 2.1831 cents 54:56:58:72:74:77:108 SD: 2.1448 cents 57:59:61:76:78:81:114 SD: 1.2846 cents 75:78:80:100:103:107:150 SD: 1.2840 cents 78:81:83:104:107:111:156 SD: 0.8216 cents 105:109:112:140:144:149:210 SD: 0.7088 cents 132:137:141:176:181:188:264 SD: 0.6264 cents 135:140:144:180:185:192:270 SD: 0.2227 cents 433:449:462:577:594:616:866 SD: 0.2217 cents 436:452:465:581:598:620:872 SD: 0.2013 cents 495:513:528:660:679:704:990 SD: 0.1970 cents 509:528:543:679:698:724:1018 SD: 0.1723 cents 540:560:576:720:741:768:1080 SD: 0.1669 cents 568:589:606:757:779:808:1136 SD: 0.1570 cents 571:592:609:761:783:812:1142 SD: 0.1555 cents 597:619:637:796:819:849:1194 SD: 0.1401 cents