Scala analysis: xen11-chalmers-tetrachordal-08-14
Transposition and Inversion by B/A, 8 tones, an Octony
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 2: 28/27 62.960904 Archytas' 1/3-tone 3: 16/15 111.731285 minor diatonic semitone 4: 9/7 435.084095 septimal major third, BP third 5: 324/245 483.854477 6: 4/3 498.044999 perfect fourth 7: 48/35 546.815381 septimal semi-augmented fourth 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 35/24 653.1846 septimal semi-diminished fifth 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 245/243 14.1905 minor BP diesis, Sensamagic comma 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 135/112 323.3528 septimal wide minor third 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 245/243 14.1905 minor BP diesis, Sensamagic comma 7: 36/35 48.7704 septimal diesis, 1/4-tone 8: 35/24 653.1846 septimal semi-diminished fifth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 245/243 14.191 cents minor BP diesis, Sensamagic comma 1: 4 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 135/112 323.353 cents septimal wide minor third 1: 1 35/24 653.185 cents septimal semi-diminished fifth 2: 4 28/27 62.961 cents Archytas' 1/3-tone 2: 2 243/196 372.123 cents 2: 2 3/2 701.955 cents perfect fifth 3: 2 16/15 111.731 cents minor diatonic semitone 3: 2 5/4 386.314 cents major third 3: 1 2187/1715 420.894 cents 3: 2 245/162 716.146 cents 3: 1 54/35 750.725 cents septimal semi-augmented fifth 4: 4 9/7 435.084 cents septimal major third, BP third 4: 4 14/9 764.916 cents septimal minor sixth 5: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 5: 2 324/245 483.854 cents 5: 1 3430/2187 779.106 cents 5: 2 8/5 813.686 cents minor sixth 5: 2 15/8 1088.269 cents classic major seventh 6: 2 4/3 498.045 cents perfect fourth 6: 2 392/243 827.877 cents 6: 4 27/14 1137.039 cents septimal major seventh 7: 1 48/35 546.815 cents septimal semi-augmented fourth 7: 1 224/135 876.647 cents narrow septimal major sixth 7: 4 35/18 1151.230 cents septimal semi-diminished octave 7: 2 486/245 1185.809 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 3.71429 = 26/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 48.8 63.0 111.7 435.1 483.9 498.0 546.8 1200.0 48.8 : 14.2 63.0 386.3 435.1 449.3 498.0 1151.2 1200.0 63.0 : 48.8 372.1 420.9 435.1 483.9 1137.0 1185.8 1200.0 111.7 : 323.4 372.1 386.3 435.1 1088.3 1137.0 1151.2 1200.0 435.1 : 48.8 63.0 111.7 764.9 813.7 827.9 876.6 1200.0 483.9 : 14.2 63.0 716.1 764.9 779.1 827.9 1151.2 1200.0 498.0 : 48.8 702.0 750.7 764.9 813.7 1137.0 1185.8 1200.0 546.8 : 653.2 702.0 716.1 764.9 1088.3 1137.0 1151.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 14.1905 .. 653.1846 cents 81/56, 638.9941 cents 245/243, 14.1905 cents 2: 62.9609 .. 701.9550 cents 81/56, 638.9941 cents 32/45,-590.2237 cents 3: 111.7313 .. 750.7254 cents 81/56, 638.9941 cents 32/45,-590.2237 cents 4: 435.0841 .. 764.9159 cents 98/81, 329.8318 cents 5/6,-315.6413 cents 5: 449.2746 .. 1088.2687 cents 81/56, 638.9941 cents 5/6,-315.6413 cents 6: 498.0450 .. 1137.0391 cents 81/56, 638.9941 cents 32/45,-590.2237 cents 7: 546.8154 .. 1185.8095 cents 81/56, 638.9941 cents 32/45,-590.2237 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 245/243, 14.1905 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 35/24, 653.1846 cents Average / Smallest step : 10.570435 Largest / Average step : 4.354564 Largest / Smallest step : 46.029638 Median interval of one step : 36/35, 48.7704 cents, amount: 4 Most common interval of one step : 36/35, 48.7704 cents, amount: 4 Least squares average step : 103.36016 cents, oct.: 826.88127 cents Scale is not proper Step pattern alph. order: ABACABAD Step pattern size order : BABCBABD Scale is a Constant Structure, by a margin of 14.19052 cents Scale diversity : 1.176342 Lumma stability : 0.023651 Lumma impropriety factor : 0.895065 Rothenberg efficiency : 0.421429 redundancy: 0.578571 Efficiency x scale size : 3.371429 Number of different interval sizes : 26 = 3.71429 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 3.71429 = 26/7 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 245/243, 14.1905 cents Number of recognisable fifths : 4, average 709.0503 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 = 12.5000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 7-8 -- Rational properties -- Prime limit : 7 Odd number limit : 2187 (O: 2187 U: 2187) Highest odd numerator or denominator: 245 Scale harmonicity : 0.016688 Average absolute harmonicity : 0.189227 Specific harmonicity : 0.102149 Fundamental : 1/6615, -12.6915 octaves, 0.0396 Hz. Guide tone : 9072, 13.1472 octaves, 2373467.128 Hz. Exponens Consonantiae : 6.001128E+07, 25.83873 octaves Euler's gradus suavitatis : 41 Sum of Mann's harmonic distance : 417.5, average 52.18750 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.51612, average 1.18952 Sum of Tenney's harmonic distance : 19.66368, average 2.45796 Vogel's harmonic complexity : 25.62500 Wille's k value : 4252 Wilson's harmonic complexity : 47 Rectangular lattice diameter : 11 Triangular lattice diameter : 7 Lattice compactness : 129.28319, average 3.59120 Lattice compactness (without 2's) : 101.73282, average 2.82591 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 4 2.12500 17 1 3: -3 .. 4 0.50000 14 1 5: -1 .. 0 -0.50000 4 1 7: -2 .. 1 -0.50000 6 5 Average exponent except 2's :-4 / 8 =-0.50000 Average absolute exponent except 2's: 24 / 8 = 3.00000 Scale is weakly epimorphic with val: <8 13 17 21| Scale is weakly epimorphic with val: <8 13 18 20| Scale is weakly epimorphic with val: <8 13 18 22| Scale is weakly epimorphic with val: <8 14 17 22| Scale is weakly epimorphic with val: <8 14 17 24| Scale is weakly epimorphic with val: <8 14 19 22| Scale is weakly epimorphic with val: <8 14 19 24| Scale is weakly epimorphic with val: <8 14 21 22| Scale is weakly epimorphic with val: <8 14 21 24|
FIT/MODE
8: 0 0 0 3 0 0 0 5 N D3 SD: 63.1235 c. M: 111.7313 c. 9: 0 0 1 2 1 0 0 5 N SD: 38.5930 c. M: 62.9609 c. 10: 0 0 1 2 1 0 0 6 N SD: 45.8985 c. M: 75.0841 c. 11: 0 1 0 3 0 1 0 6 N SD: 33.5783 c. M: 48.7704 c. 12: 0 0 1 3 1 0 0 7 N SD: 35.6499 c. M: 62.9609 c. 15: 0 1 0 4 1 0 1 8 N SD: 26.0311 c. M: 48.7704 c. 16: 1 0 1 4 1 0 0 9 N G SD: 26.0177 c. M:-41.1455 c. 17: 1 0 1 4 1 0 1 9 N SD: 15.7144 c. M:-29.4452 c. 19: 1 0 1 5 1 0 1 10 N SD: 13.4456 c. M:-21.6057 c. 20: 1 0 1 5 1 0 1 11 N SD: 10.1100 c. M: 18.0450 c. 22: 1 0 1 6 1 0 1 12 N SD: 5.1880 c. M: 8.4154 c. 50: 2 1 2 13 2 1 2 27 N SD: 5.4473 c. M:-9.0391 c. 52: 2 1 2 14 2 1 2 28 N SD: 5.1720 c. M:-9.6473 c. 53: 2 1 2 14 2 1 2 29 N SD: 4.2560 c. M: 8.3828 c. 55: 2 1 2 15 2 1 2 30 N SD: 3.0027 c. M: 5.1340 c. 72: 3 1 3 19 3 1 3 39 N SD: 2.6670 c. M:-4.9354 c. 74: 3 1 3 20 3 1 3 40 N SD: 2.8195 c. M:-4.6577 c. 75: 3 1 3 20 3 1 3 41 N SD: 2.1858 c. M: 3.8545 c. 77: 3 1 3 21 3 1 3 42 N SD: 1.4095 c. M: 2.6404 c. 147: 6 2 6 39 6 2 6 80 N SD: 1.6933 c. M:-2.5544 c. 149: 6 2 6 40 6 2 6 81 N SD: 0.8789 c. M:-1.4686 c. 171: 7 2 7 46 7 2 7 93 N SD: 0.3424 c. M:-0.5530 c. 248: 10 3 10 67 10 3 10 135 N SD: 0.2792 c. M: 0.4410 c. 419: 17 5 17 113 17 5 17 228 N SD: 0.1630 c. M:-0.2844 c. 590: 24 7 24 159 24 7 24 321 N SD: 0.1809 c. M:-0.3033 c. 665: 27 8 27 179 27 8 27 362 N SD: 0.1434 c. M: 0.2455 c. 687: 28 8 28 185 28 8 28 374 N SD: 0.1181 c. M: 0.2284 c. 764: 31 9 31 206 31 9 31 416 N SD: 0.1341 c. M: 0.2185 c. 836: 34 10 34 225 34 10 34 455 N SD: 0.1321 c. M:-0.2304 c. 858: 35 10 35 231 35 10 35 467 N SD: 0.1105 c. M:-0.1807 c. 913: 37 11 37 246 37 11 37 497 N SD: 0.0990 c. M: 0.1743 c. 935: 38 11 38 252 38 11 38 509 N SD: 0.0533 c. M: 0.0774 c. 1106: 45 13 45 298 45 13 45 602 N SD: 0.0329 c. M:-0.0542 c. 2019: 82 24 82 544 82 24 82 1099 N SD: 0.0281 c. M: 0.0506 c. 2190: 89 26 89 590 89 26 89 1192 N SD: 0.0324 c. M:-0.0528 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3:4 S SD: 77.5698 cents 3 x x x x x 4 x 6 S SD: 0.0000 cents 4 x x x 5 x x 6:8 S SD: 54.2083 cents 5 x x x 6 x x 7:10 SD: 41.5543 cents 6 x x 7 x x 8 x 12 S SD: 51.7132 cents 7 x x 8:9 x x 10:14 SD: 34.6962 cents 8 x x 9:10 x x 11:16 SD: 26.0957 cents 9 x x 10 x x 12 x 18 S SD: 23.5575 cents 10 x x 11:13 x x 14:20 SD: 16.7299 cents 11 x x 12:14 x x 15:22 SD: 10.9541 cents 12 x x 13:15 x 16 x 24 SD: 13.9172 cents 13 x x 14 x 17 x 18:26 SD: 7.6089 cents 14 x x 15:18 x x 19:28 SD: 4.9251 cents 15 x x 16:19 x 20:21:30 SD: 8.8135 cents 16 x x 17 x 21 x 22:32 SD: 3.8495 cents 17 x x 18:22 x x 23:34 SD: 7.2566 cents 18 x x 19:23 x 24:25:36 SD: 6.0770 cents 19 x x 20:24:25 x 26:38 SD: 7.8882 cents 20 x 21 x 26 x 27 x 40 SD: 8.9826 cents 21 x 22 x 27 x 28:29:42 SD: 4.2542 cents 22 x 23 x 28:29 x 30:44 SD: 5.0335 cents 23 x 24:25 x 30:31:32:46 SD: 8.6910 cents 24 x 25:26:31 x 32:33:48 SD: 4.8994 cents 25 x 26:27:32:33 x 34:50 SD: 4.6145 cents 26 x 27:28:33:34:35:36:52 SD: 5.8996 cents 27 x 28:29:35 x 36:37:54 SD: 3.1033 cents 28 x 29:30:36:37 x 38:56 SD: 3.3115 cents 29 x 30:31:37:38:39:40:58 SD: 3.9952 cents 30 x 31:32:39 x 40:41:60 SD: 3.4983 cents 31:32 x 33:40:41 x 43:62 SD: 3.6353 cents 32:33 x 34:41:42:43:44:64 SD: 3.1140 cents 33:34 x 35:42 x 44:45:66 SD: 3.7713 cents 34:35 x 36:44:45 x 47:68 SD: 3.6633 cents 35:36 x 37:45:46:47:48:70 SD: 3.2193 cents 36:37 x 38:46 x 48:49:72 SD: 4.1374 cents 37:38 x 39:48:49 x 51:74 SD: 4.5780 cents 38:39 x 41:49:50:51:52:76 SD: 3.6491 cents 39:40 x 42:50 x 52:53:78 SD: 3.9885 cents 40:41 x 43:51:53 x 55:80 SD: 3.5710 cents 42:43:44:45:54 x 56:58:84 SD: 3.4300 cents 43:44:45:46:55:57 x 59:86 SD: 3.0357 cents 45:46:47:48:58 x 60:62:90 SD: 2.6685 cents 46:47:48:49:59:61 x 63:92 SD: 2.4713 cents 49:50:51:52:63:65 x 67:98 SD: 2.7235 cents 52:53:54:55:67:69 x 71:104 SD: 3.4266 cents 53 x 55:57:68:70:71:73:106 SD: 2.6504 cents 54 x 56:58:69:71:72:74:108 SD: 2.7132 cents 55 x 57:59:71:73 x 75:110 SD: 2.8050 cents 56 x 58:60:72:74:75:77:112 SD: 1.7254 cents 57 x 59:61:73:75:76:78:114 SD: 1.9140 cents 58 x 60:62:75:77 x 80:116 SD: 2.7590 cents 59 x 61:63:76:78:79:81:118 SD: 1.4196 cents 60 x 62:64:77:79:80:82:120 SD: 1.7052 cents 61:63 x 65:78:81 x 84:122 SD: 2.6010 cents 62:64 x 66:80:82:83:85:124 SD: 1.6772 cents 63:65 x 67:81:83:84:86:126 SD: 1.8207 cents 64:66 x 68:82 x 85:88:128 SD: 2.1643 cents 65:67 x 69:84:86:87:89:130 SD: 2.0910 cents 66:68 x 70:85:87:88:91:132 SD: 2.1732 cents 67:69 x 71:86 x 89:92:134 SD: 2.2855 cents 69:71:72:74:89:91:92:95:138 SD: 2.1752 cents 70:72:73:75:90 x 93:96:140 SD: 1.9780 cents 71:73:74:76:91:94:95:97:142 SD: 1.8834 cents 72:74:75:77:93:95:96:99:144 SD: 1.6829 cents 73:75:76:78:94 x 97:100:146 SD: 1.4606 cents 75:77:78:80:96:99:100:103:150 SD: 1.3124 cents 76:78:79:81:98 x 101:104:152 SD: 1.4674 cents 77:79:80:82:99:102:103:106:154 SD: 1.3704 cents 78:80:81:83:100:103:104:107:156 SD: 1.1071 cents 88 x 91:94:113:116:117:121:176 SD: 1.5045 cents 89 x 92:95:114:118:119:122:178 SD: 1.5557 cents 90 x 93:96:116:119:120:123:180 SD: 1.3772 cents 91 x 94:97:117:120:121:125:182 SD: 1.4465 cents 92:95 x 98:118:122:123:126:184 SD: 1.5603 cents 93:96 x 99:120:123:124:128:186 SD: 1.6120 cents 94:97 x 100:121:124:125:129:188 SD: 1.4164 cents 99:102:103:106:127:131:132:136:198 SD: 1.2959 cents 102:105:106:109:131:135:136:140:204 SD: 0.7166 cents 105:108:109:112:135:139:140:144:210 SD: 0.3134 cents 242:249:251:258:311:320:323:332:484 SD: 0.2914 cents 347:357:360:370:446:459:463:476:694 SD: 0.2263 cents 375:386:389:400:482:496:500:514:750 SD: 0.2221 cents 452:465:469:482:581:598:603:620:904 SD: 0.2159 cents 462:475:479:493:594:611:616:634:924 SD: 0.1931 cents 490:504:508:523:630:648:653:672:980 SD: 0.1877 cents 493:507:511:526:634:652:657:676:986 SD: 0.1797 cents 567:583:588:605:729:750:756:778:1134 SD: 0.1596 cents 570:586:591:608:733:754:760:782:1140 SD: 0.1557 cents 595:612:617:635:765:787:793:816:1190 SD: 0.1513 cents 598:615:620:638:769:791:797:820:1196 SD: 0.1366 cents