Scala analysis: xen11-chalmers-tetrachordal-06-08
Transposition by 4/3B
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: 35/27 449.274618 septimal semi-diminished fourth, 9/4-tone 5: 4/3 498.044999 perfect fourth 6: 5/3 884.358713 major sixth, BP sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 6/5 315.6413 minor third 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: 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: 6/5 315.6413 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 75/64 274.582 cents classic augmented second 1: 1 6/5 315.641 cents minor third 1: 1 5/4 386.314 cents major third 2: 2 16/15 111.731 cents minor diatonic semitone 2: 1 135/112 323.353 cents septimal wide minor third 2: 1 175/144 337.543 cents 2: 1 56/45 378.602 cents septimal narrow major third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 3/2 701.955 cents perfect fifth 3: 3 5/4 386.314 cents major third 3: 1 32/25 427.373 cents classic diminished fourth 3: 1 4/3 498.045 cents perfect fourth 3: 1 54/35 750.725 cents septimal semi-augmented fifth 3: 1 14/9 764.916 cents septimal minor sixth 4: 1 9/7 435.084 cents septimal major third, BP third 4: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 4: 1 3/2 701.955 cents perfect fifth 4: 1 25/16 772.627 cents classic augmented fifth 4: 3 8/5 813.686 cents minor sixth 5: 1 4/3 498.045 cents perfect fourth 5: 1 14/9 764.916 cents septimal minor sixth 5: 1 45/28 821.398 cents septimale wide minor sixth 5: 1 288/175 862.457 cents 5: 1 224/135 876.647 cents narrow septimal major sixth 5: 2 15/8 1088.269 cents classic major seventh 6: 1 8/5 813.686 cents minor sixth 6: 1 5/3 884.359 cents major sixth, BP sixth 6: 1 128/75 925.418 cents diminished 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: 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 : 63.0 111.7 386.3 449.3 498.0 884.4 1200.0 63.0 : 48.8 323.4 386.3 435.1 821.4 1137.0 1200.0 111.7 : 274.6 337.5 386.3 772.6 1088.3 1151.2 1200.0 386.3 : 63.0 111.7 498.0 813.7 876.6 925.4 1200.0 449.3 : 48.8 435.1 750.7 813.7 862.5 1137.0 1200.0 498.0 : 386.3 702.0 764.9 813.7 1088.3 1151.2 1200.0 884.4 : 315.6 378.6 427.4 702.0 764.9 813.7 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 .. 701.9550 cents 45/32, 590.2237 cents 64/75,-274.5824 cents 3: 386.3137 .. 764.9159 cents 56/45, 378.6022 cents 5/6,-315.6413 cents 4: 435.0841 .. 813.6863 cents 56/45, 378.6022 cents 81/98,-329.8318 cents 5: 498.0450 .. 1088.2687 cents 45/32, 590.2237 cents 5/6,-315.6413 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 : 138.84886 cents, oct.: 971.94202 cents Scale is not proper Step pattern alph. order: ABCABDE Step pattern size order : BACBAED Scale is not a Constant Structure Scale diversity : 1.274547 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 : 225/224, 7.7115 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 4 Number of recognisable fifths : 2, average 701.9550 cents Length of longest harmonic part : 2 at degree 5 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 : 175 (O: 175 U: 175) Highest odd numerator or denominator: 35 Scale harmonicity : 0.026965 Average absolute harmonicity : 0.229994 Specific harmonicity : 0.149802 Fundamental : 1/540, -9.0768 octaves, 0.4845 Hz. Guide tone : 560, 9.1293 octaves, 146510.317 Hz. Exponens Consonantiae : 3.024000E+05, 18.20610 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 87.5, average 12.50000 Mersenne's string divisions : 859320 Sum of van Prooijen's expressibility: 6.02658, average 0.86094 Sum of Tenney's harmonic distance : 12.09150, average 1.72736 Vogel's harmonic complexity : 16.57143 Wille's k value : 337 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 86.55212, average 3.09115 Lattice compactness (without 2's) : 53.56445, average 1.91302 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.00000 11 1 3: -3 .. 0 -1.28571 9 1 5: -1 .. 1 0.28571 4 3 7: 0 .. 1 0.28571 2 2 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 15 / 7 = 2.14286
FIT/MODE
7: 0 1 1 1 0 2 2 N T3 S SD: 45.7434 c. M:-65.0111 c. 8: 0 1 2 0 0 3 2 N SD: 41.4695 c. M:-63.6863 c. 9: 0 1 2 0 1 3 2 N SD: 39.0783 c. M: 62.9609 c. 10: 1 0 2 1 0 3 3 N SD: 32.1861 c. M:-57.0391 c. 12: 1 0 3 1 0 4 3 N SD: 25.4063 c. M:-50.7254 c. 13: 1 0 3 1 0 5 3 N SD: 25.3900 c. M:-38.7182 c. 15: 1 0 4 1 0 5 4 N SD: 19.9040 c. M: 31.7313 c. 16: 1 1 3 1 1 5 4 N SD: 19.6730 c. M:-38.2687 c. 18: 1 1 4 1 0 6 5 N SD: 17.9992 c. M: 31.3783 c. 19: 1 1 4 1 1 6 5 N SD: 7.2755 c. M:-14.5845 c. 22: 1 1 5 1 1 7 6 N SD: 8.0259 c. M: 12.9110 c. 34: 2 1 8 2 1 11 9 N SD: 5.4341 c. M:-9.5489 c. 43: 2 2 10 2 2 14 11 N SD: 4.9474 c. M:-8.6645 c. 53: 3 2 12 3 2 17 14 N SD: 2.4854 c. M:-4.9636 c. 72: 4 3 16 4 3 23 19 N SD: 2.7353 c. M:-4.9354 c. 75: 4 3 17 4 3 24 20 N SD: 2.1149 c. M: 4.3587 c. 77: 4 3 18 4 3 25 20 N SD: 2.4329 c. M:-3.9530 c. 94: 5 4 21 5 4 30 25 N SD: 2.3992 c. M: 3.5076 c. 96: 5 4 22 5 4 31 25 N SD: 1.5319 c. M:-3.1413 c. 99: 5 4 23 5 4 32 26 N SD: 1.5578 c. M: 2.6404 c. 118: 6 5 27 6 5 38 31 N SD: 1.0234 c. M: 1.9440 c. 149: 8 6 34 8 6 48 39 N SD: 1.2136 c. M:-1.7321 c. 152: 8 6 35 8 6 49 40 N SD: 0.6297 c. M: 1.2050 c. 171: 9 7 39 9 7 55 45 N SD: 0.2797 c. M:-0.5494 c. 323: 17 13 74 17 13 104 85 N SD: 0.1906 c. M: 0.2762 c. 441: 23 18 101 23 18 142 116 N SD: 0.1964 c. M: 0.3759 c. 494: 26 20 113 26 20 159 130 N SD: 0.1107 c. M:-0.1970 c. 612: 32 25 140 32 25 197 161 N SD: 0.1289 c. M: 0.2550 c. 665: 35 27 152 35 27 214 175 N SD: 0.1237 c. M:-0.1970 c. 764: 40 31 175 40 31 246 201 N SD: 0.1171 c. M: 0.2130 c. 913: 48 37 209 48 37 294 240 N SD: 0.1359 c. M:-0.2325 c. 935: 49 38 214 49 38 301 246 N SD: 0.0645 c. M: 0.0806 c. 1106: 58 45 253 58 45 356 291 N SD: 0.0561 c. M: 0.0911 c. 1429: 75 58 327 75 58 460 376 N SD: 0.0531 c. M: 0.1040 c. 1525: 80 62 349 80 62 491 401 N SD: 0.0487 c. M:-0.1003 c. 1696: 89 69 388 89 69 546 446 N SD: 0.0456 c. M:-0.0752 c. 1848: 97 75 423 97 75 595 486 N SD: 0.0449 c. M:-0.0760 c. 2019: 106 82 462 106 82 650 531 N SD: 0.0323 c. M:-0.0567 c. 2190: 115 89 501 115 89 705 576 N SD: 0.0359 c. M:-0.0528 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3:4 S SD: 91.2019 cents 3 x x x x 4:5:6 S SD: 0.0000 cents 4 x x 5 x x 7:8 SD: 28.1557 cents 5 x x 6 x 7:8:10 S SD: 32.7146 cents 6 x x x x 8:10:12 S SD: 0.0000 cents 7 x 8 x 9 x 12:14 S SD: 32.4485 cents 8 x 9:10 x 11:13:16 SD: 23.0270 cents 9 x 10:11 x 12:15:18 S SD: 16.1347 cents 10 x 11 x 13 x 17:20 SD: 15.8858 cents 11 x 12:14 x 15:18:22 SD: 14.1556 cents 12 x 13:15 x 16:20:24 SD: 5.3683 cents 13 x 14:16:17 x 22:26 SD: 8.7708 cents 14 x 15 x 18:19:23:28 SD: 8.5330 cents 15 x 16:19 x 20:25:30 SD: 4.5861 cents 16 x 17:20:21 x 27:32 SD: 6.2320 cents 17 x 18:21:22:23:28:34 SD: 6.7701 cents 18 x 19 x 23:24:30:36 SD: 6.1617 cents 19 x 20:24 x 25:32:38 SD: 8.2677 cents 20:21 x 25:26:27:33:40 SD: 5.8977 cents 21:22 x 26:27:28:35:42 SD: 4.6689 cents 22:23 x 28 x 29:37:44 SD: 8.4992 cents 23:24:25:29:30:31:38:46 SD: 6.5428 cents 24:25:26:30:31:32:40:48 SD: 4.0865 cents 27:28:29:34:35:36:45:54 SD: 2.5022 cents 47:49:50:59:61:63:78:94 SD: 2.4864 cents 48:50:51:60:62:64:80:96 SD: 1.7128 cents 57:59:61:71:74:76:95:114 SD: 1.3304 cents 60:62:64:75:78:80:100:120 SD: 1.1318 cents 75:78:80:94:97:100:125:150 SD: 1.1189 cents 87:90:93:109:113:116:145:174 SD: 1.1023 cents 104:108:111:130:135:139:173:208 SD: 0.9120 cents 105:109:112:131:136:140:175:210 SD: 0.5716 cents 108:112:115:135:140:144:180:216 SD: 0.4297 cents 135:140:144:169:175:180:225:270 SD: 0.3661 cents 165:171:176:206:214:220:275:330 SD: 0.3637 cents 192:199:205:240:249:256:320:384 SD: 0.2992 cents 240:249:256:300:311:320:400:480 SD: 0.1414 cents 300:311:320:375:389:400:500:600 SD: 0.1131 cents 432:448:461:540:560:576:720:864 SD: 0.1073 cents 540:560:576:675:700:720:900:1080 SD: 0.0000 cents