Scala analysis: xen11-chalmers-tetrachordal-06-05
Transposition by 2/B
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: 5/4 386.313714 major third 4: 4/3 498.044999 perfect fourth 5: 15/8 1088.268715 classic major seventh 6: 35/18 1151.229619 septimal semi-diminished octave 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 75/64 274.5824 classic augmented second 4: 16/15 111.7313 minor diatonic semitone 5: 45/32 590.2237 diatonic tritone 6: 28/27 62.9609 Archytas' 1/3-tone 7: 36/35 48.7704 septimal diesis, 1/4-tone
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 16/15 111.731 cents minor diatonic semitone 1: 1 75/64 274.582 cents classic augmented second 1: 1 45/32 590.224 cents diatonic tritone 2: 3 16/15 111.731 cents minor diatonic semitone 2: 1 135/112 323.353 cents septimal wide minor third 2: 1 5/4 386.314 cents major third 2: 1 35/24 653.185 cents septimal semi-diminished fifth 2: 1 3/2 701.955 cents perfect fifth 3: 1 192/175 160.502 cents septimal 4/5-tone 3: 1 448/405 174.692 cents 3: 1 5/4 386.314 cents major third 3: 1 9/7 435.084 cents septimal major third, BP third 3: 1 3/2 701.955 cents perfect fifth 3: 1 14/9 764.916 cents septimal minor sixth 3: 1 225/128 976.537 cents augmented sixth 4: 1 256/225 223.463 cents Neapolitan diminished third 4: 1 9/7 435.084 cents septimal major third, BP third 4: 1 4/3 498.045 cents perfect fourth 4: 1 14/9 764.916 cents septimal minor sixth 4: 1 8/5 813.686 cents minor sixth 4: 1 405/224 1025.308 cents 4: 1 175/96 1039.498 cents 5: 1 4/3 498.045 cents perfect fourth 5: 1 48/35 546.815 cents septimal semi-augmented fourth 5: 1 8/5 813.686 cents minor sixth 5: 1 224/135 876.647 cents narrow septimal major sixth 5: 3 15/8 1088.269 cents classic major seventh 6: 1 64/45 609.776 cents 2nd tritone 6: 1 128/75 925.418 cents diminished seventh 6: 1 15/8 1088.269 cents classic major seventh 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: 7 Average number of different intervals per interval class: 5.66667 = 17/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 63.0 111.7 386.3 498.0 1088.3 1151.2 1200.0 63.0 : 48.8 323.4 435.1 1025.3 1088.3 1137.0 1200.0 111.7 : 274.6 386.3 976.5 1039.5 1088.3 1151.2 1200.0 386.3 : 111.7 702.0 764.9 813.7 876.6 925.4 1200.0 498.0 : 590.2 653.2 702.0 764.9 813.7 1088.3 1200.0 1088.3: 63.0 111.7 174.7 223.5 498.0 609.8 1200.0 1151.2: 48.8 111.7 160.5 435.1 546.8 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 .. 701.9550 cents 45/32, 590.2237 cents 512/675,-478.4924 cents 3: 160.5017 .. 976.5374 cents 13125/8192, 816.0358 cents 128/175,-541.4533 cents 4: 223.4626 .. 1039.4983 cents 13125/8192, 816.0358 cents 32768/50625,-753.0749 cents 5: 498.0450 .. 1088.2687 cents 45/32, 590.2237 cents 128/175,-541.4533 cents 6: 609.7763 .. 1151.2296 cents 175/128, 541.4533 cents 512/675,-478.4924 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 : 45/32, 590.2237 cents Average / Smallest step : 3.515014 Largest / Average step : 3.442972 Largest / Smallest step : 12.102093 Median interval of one step : 28/27, 62.9609 cents, amount: 2 Least squares average step : 172.75904 cents, oct.: 1209.31329 cents Scale is not proper Step pattern alph. order: ABCDEAB Step pattern size order : BADCEBA Scale is not a Constant Structure Scale diversity : 1.638891 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 : 7 Mean interval variety : 5.66667 = 17/3 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 245/243, 14.1905 cents Most common intervals : 16/15, 111.7313 cents & inv., amount: 4 Number of recognisable fifths : 2, average 701.9550 cents Scale contains a complete diamond : 1 15 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% 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 -- Rational properties -- Prime limit : 7 Odd number limit : 405 (O: 405 U: 405) Highest odd numerator or denominator: 35 Scale harmonicity : 0.024538 Average absolute harmonicity : 0.226496 Specific harmonicity : 0.140588 Fundamental : 1/1080, -10.0768 octaves, 0.2422 Hz. Guide tone : 1680, 10.7142 octaves, 439530.950 Hz. Exponens Consonantiae : 1.814400E+06, 20.79106 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 90.5, average 12.92857 Mersenne's string divisions : 130938885 Sum of van Prooijen's expressibility: 6.50371, average 0.92910 Sum of Tenney's harmonic distance : 12.81850, average 1.83121 Vogel's harmonic complexity : 18.28571 Wille's k value : 1012 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 101.04815, average 3.60886 Lattice compactness (without 2's) : 54.83409, average 1.95836 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.42857 15 1 3: -3 .. 1 -0.85714 8 1 5: -1 .. 1 0.28571 4 3 7: 0 .. 1 0.28571 2 2 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 14 / 7 = 2.00000 Scale is weakly epimorphic with val: <7 11 15 18| Scale is weakly epimorphic with val: <7 12 17 19|
FIT/MODE
7: 0 1 1 1 3 1 0 N SD: 47.2416 c. M: 62.9609 c. 9: 1 0 2 1 4 1 0 N SD: 37.2189 c. M:-70.3724 c. 10: 1 0 2 1 5 1 0 N SD: 31.1374 c. M:-57.0391 c. 12: 1 0 3 1 6 1 0 N SD: 24.5439 c. M:-48.7704 c. 15: 1 0 4 1 8 0 1 N SD: 23.2757 c. M:-31.7313 c. 17: 1 0 4 2 8 1 1 N SD: 24.5622 c. M: 41.1430 c. 18: 1 1 4 1 9 1 1 N SD: 18.6671 c. M: 31.3783 c. 19: 1 1 4 2 9 1 1 N SD: 10.2735 c. M: 14.5845 c. 21: 1 1 5 2 10 1 1 N SD: 9.0085 c. M:-16.2407 c. 22: 1 1 5 2 11 1 1 N SD: 5.1995 c. M: 8.4154 c. 43: 2 2 10 4 21 2 2 N SD: 4.4442 c. M: 7.1470 c. 53: 3 2 12 5 26 3 2 N SD: 2.4827 c. M:-4.9636 c. 72: 4 3 16 7 35 4 3 N SD: 3.3094 c. M: 4.9354 c. 74: 4 3 17 7 36 4 3 N SD: 2.3891 c. M:-4.6577 c. 75: 4 3 17 7 37 4 3 N SD: 1.2735 c. M: 2.3137 c. 96: 5 4 22 9 47 5 4 N SD: 1.0781 c. M:-1.9550 c. 118: 6 5 27 11 58 6 5 N SD: 1.0831 c. M: 2.0771 c. 149: 8 6 34 14 73 8 6 N SD: 0.9379 c. M:-1.4686 c. 152: 8 6 35 14 75 8 6 N SD: 0.8980 c. M:-1.4020 c. 171: 9 7 39 16 84 9 7 N SD: 0.3642 c. M:-0.5494 c. 323: 17 13 74 30 159 17 13 N SD: 0.2576 c. M:-0.4732 c. 419: 22 17 96 39 206 22 17 N SD: 0.1672 c. M:-0.3211 c. 494: 26 20 113 46 243 26 20 N SD: 0.1103 c. M:-0.1970 c. 612: 32 25 140 57 301 32 25 N SD: 0.1268 c. M: 0.2492 c. 665: 35 27 152 62 327 35 27 N SD: 0.1238 c. M:-0.1970 c. 860: 45 35 197 80 423 45 35 N SD: 0.1213 c. M:-0.1979 c. 913: 48 37 209 85 449 48 37 N SD: 0.0892 c. M:-0.1395 c. 935: 49 38 214 87 460 49 38 N SD: 0.0562 c. M: 0.0771 c. 1106: 58 45 253 103 544 58 45 N SD: 0.0366 c. M: 0.0569 c. 1525: 80 62 349 142 750 80 62 N SD: 0.0280 c. M:-0.0534 c. 2019: 106 82 462 188 993 106 82 N SD: 0.0229 c. M:-0.0406 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: 101.9550 cents 3 x x x 4 x x 6 S SD: 0.0000 cents 4 x x 5 x x x 8 SD: 0.0000 cents 5 x x 6:7:9 x 10 SD: 32.7146 cents 6 x x x 8:11 x 12 SD: 12.9686 cents 7 x 8:9 x 13 x 14 SD: 32.5188 cents 8 x 9:10:11:15 x 16 SD: 21.2931 cents 9 x 10:11:12:17 x 18 SD: 16.3358 cents 10 x 11 x 13:19 x 20 SD: 18.1745 cents 11 x 12:14:15:21 x 22 SD: 14.1046 cents 12 x 13:15:16 x 23:24 SD: 7.3239 cents 13 x 14:16:17:24:25:26 SD: 9.4449 cents 14 x 15:18:19:26:27:28 SD: 10.3451 cents 15 x 16:19:20:28:29:30 SD: 4.3580 cents 16 x 17:20:21:30:31:32 SD: 4.7947 cents 17 x 18:21:23:32:33:34 SD: 5.9539 cents 18 x 19:23:24:34:35:36 SD: 7.3404 cents 19 x 20:24:25:36:37:38 SD: 6.9034 cents 20:21 x 25:27:38:39:40 SD: 6.4015 cents 21:22 x 26:28:39:41:42 SD: 5.0210 cents 22:23 x 28:29:41:43:44 SD: 6.9755 cents 23:24:25:29:31:43:45:46 SD: 6.2175 cents 24:25:26:30:32:45:47:48 SD: 4.3607 cents 27:28:29:34:36:51:53:54 SD: 3.8843 cents 29:30:31:36:39:54:56:58 SD: 3.7350 cents 31:32:33:39:41:58:60:62 SD: 3.1117 cents 32:33:34:40:43:60:62:64 SD: 2.7092 cents 47:49:50:59:63:88:91:94 SD: 2.4930 cents 48:50:51:60:64:90:93:96 SD: 1.7128 cents 56:58:60:70:75:105:109:112 SD: 1.6095 cents 57:59:61:71:76:107:111:114 SD: 1.3615 cents 72:75:77:90:96:135:140:144 SD: 1.2757 cents 75:78:80:94:100:141:146:150 SD: 1.2022 cents 87:90:93:109:116:163:169:174 SD: 1.0360 cents 103:107:110:129:137:193:200:206 SD: 1.0042 cents 104:108:111:130:139:195:202:208 SD: 0.7509 cents 105:109:112:131:140:197:204:210 SD: 0.5928 cents 164:170:175:205:219:308:319:328 SD: 0.5756 cents 165:171:176:206:220:309:321:330 SD: 0.4714 cents 192:199:205:240:256:360:373:384 SD: 0.3552 cents 240:249:256:300:320:450:467:480 SD: 0.2083 cents 375:389:400:469:500:703:729:750 SD: 0.1659 cents 432:448:461:540:576:810:840:864 SD: 0.1073 cents