Scala analysis: xen11-chalmers-tetrachordal-08-09
Transposition and Inversion by 1/1, 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: 5/4 386.313714 major third 4: 9/7 435.084095 septimal major third, BP third 5: 4/3 498.044999 perfect fourth 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 3/2 701.9550 perfect fifth 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: 36/35 48.7704 septimal diesis, 1/4-tone 5: 28/27 62.9609 Archytas' 1/3-tone 6: 3/2 701.9550 perfect fifth
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 3/2 701.955 cents perfect fifth 2: 2 16/15 111.731 cents minor diatonic semitone 2: 2 135/112 323.353 cents septimal wide minor third 2: 2 14/9 764.916 cents septimal minor sixth 3: 1 243/196 372.123 cents 3: 2 5/4 386.314 cents major third 3: 2 8/5 813.686 cents minor sixth 3: 1 392/243 827.877 cents 4: 2 9/7 435.084 cents septimal major third, BP third 4: 2 224/135 876.647 cents narrow septimal major sixth 4: 2 15/8 1088.269 cents classic major seventh 5: 1 4/3 498.045 cents perfect fourth 5: 1 128/75 925.418 cents diminished seventh 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 : 63.0 111.7 386.3 435.1 498.0 1200.0 63.0 : 48.8 323.4 372.1 435.1 1137.0 1200.0 111.7 : 274.6 323.4 386.3 1088.3 1151.2 1200.0 386.3 : 48.8 111.7 813.7 876.6 925.4 1200.0 435.1 : 63.0 764.9 827.9 876.6 1151.2 1200.0 498.0 : 702.0 764.9 813.7 1088.3 1137.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 701.9550 cents 35/24, 653.1846 cents 36/35, 48.7704 cents 2: 111.7313 .. 764.9159 cents 35/24, 653.1846 cents 32/45,-590.2237 cents 3: 372.1232 .. 827.8768 cents 76832/59049, 455.7536 cents 2187/2744,-392.7927 cents 4: 435.0841 .. 1088.2687 cents 35/24, 653.1846 cents 2187/2744,-392.7927 cents 5: 498.0450 .. 1151.2296 cents 35/24, 653.1846 cents 32/45,-590.2237 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 : 3/2, 701.9550 cents Average / Smallest step : 4.100850 Largest / Average step : 3.509775 Largest / Smallest step : 14.393059 Median interval of one step : 28/27, 62.9609 cents, amount: 2 Least squares average step : 141.49369 cents, oct.: 848.96215 cents Scale is not proper Step pattern alph. order: ABCBAD Step pattern size order : BACABD Scale is a Constant Structure, by a margin of 48.77038 cents Scale diversity : 1.354598 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 : 1, 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 : 243 (O: 243 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.018974 Average absolute harmonicity : 0.253864 Specific harmonicity : 0.142347 Fundamental : 1/3780, -11.8842 octaves, 0.0692 Hz. Guide tone : 5040, 12.2992 octaves, 1318592.849 Hz. Exponens Consonantiae : 1.905120E+07, 24.18338 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 60.5, average 10.08333 Mersenne's string divisions : 1718640 Sum of van Prooijen's expressibility: 4.73779, average 0.78963 Sum of Tenney's harmonic distance : 9.73931, average 1.62322 Vogel's harmonic complexity : 22.66667 Wille's k value : 2362 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 9 Triangular lattice diameter : 5 Lattice compactness : 70.67271, average 3.36537 Lattice compactness (without 2's) : 44.59114, average 2.12339 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.16667 11 1 3: -3 .. 2 -0.50000 7 1 5: -1 .. 1 0.00000 2 2 7: -1 .. 1 0.00000 2 2 Average exponent except 2's :-3 / 6 =-0.50000 Average absolute exponent except 2's: 11 / 6 = 1.83333 Scale is weakly epimorphic with val: <6 9 13 19| Scale is weakly epimorphic with val: <6 9 14 19| Scale is weakly epimorphic with val: <6 11 14 18| Scale is weakly epimorphic with val: <6 11 14 19| Scale is weakly epimorphic with val: <6 11 15 17|
FIT/MODE
6: 0 0 2 0 0 4 N D3 SD: 67.6744 c. M: 111.7313 c. 9: 0 1 2 0 1 5 N G SD: 34.3856 c. M: 62.9609 c. 10: 1 0 2 1 0 6 N G SD: 32.5507 c. M:-57.0391 c. 11: 1 0 3 0 1 6 N SD: 33.8852 c. M:-50.0499 c. 12: 1 0 3 0 1 7 N SD: 22.1041 c. M:-37.0391 c. 14: 1 0 4 0 1 8 N SD: 23.4040 c. M:-42.2577 c. 15: 1 0 4 0 1 9 N SD: 22.5131 c. M: 35.0841 c. 16: 1 1 3 1 1 9 N D3 SD: 21.1601 c. M:-38.2687 c. 19: 1 1 4 1 1 11 N D3 SD: 7.8359 c. M:-14.5845 c. 22: 1 1 5 1 1 13 N D3 SD: 5.0093 c. M: 8.4154 c. 41: 2 2 9 2 2 24 N D3 SD: 4.0376 c. M: 5.8259 c. 53: 3 2 12 2 3 31 N SD: 2.9656 c. M:-4.9636 c. 55: 3 2 13 2 3 32 N SD: 3.4205 c. M:-6.4136 c. 72: 4 3 16 3 4 42 N SD: 2.9961 c. M:-4.9354 c. 74: 4 3 17 3 4 43 N SD: 2.7187 c. M:-4.6577 c. 75: 4 3 17 3 4 44 N SD: 1.8348 c. M: 3.0841 c. 96: 5 4 22 4 5 56 N SD: 1.4065 c. M:-2.4159 c. 118: 6 5 27 5 6 69 N SD: 1.2068 c. M:-2.2040 c. 130: 7 5 30 5 7 76 N SD: 1.1007 c. M:-1.6545 c. 149: 8 6 34 6 8 87 N SD: 0.9083 c. M:-1.4686 c. 152: 8 6 35 6 8 89 N SD: 0.7060 c. M: 1.2050 c. 171: 9 7 39 7 9 100 N SD: 0.2894 c. M:-0.5494 c. 323: 17 13 74 13 17 189 N SD: 0.2351 c. M: 0.4092 c. 419: 22 17 96 17 22 245 N SD: 0.2017 c. M:-0.3211 c. 494: 26 20 113 20 26 289 N SD: 0.1419 c. M: 0.2663 c. 590: 31 24 135 24 31 345 N SD: 0.1519 c. M:-0.2601 c. 612: 32 25 140 25 32 358 N SD: 0.1247 c. M: 0.2158 c. 665: 35 27 152 27 35 389 N SD: 0.1424 c. M:-0.1970 c. 742: 39 30 170 30 39 434 N SD: 0.1174 c. M:-0.2092 c. 783: 41 32 179 32 41 458 N SD: 0.1135 c. M:-0.1649 c. 913: 48 37 209 37 48 534 N SD: 0.0788 c. M:-0.1278 c. 935: 49 38 214 38 49 547 N SD: 0.0528 c. M: 0.0771 c. 1106: 58 45 253 45 58 647 N SD: 0.0314 c. M: 0.0569 c. 1848: 97 75 423 75 97 1081 N SD: 0.0301 c. M:-0.0499 c. 2019: 106 82 462 82 106 1181 N SD: 0.0216 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: 101.9550 cents 3 x x x x 4:6 S SD: 0.0000 cents 4 x x 5 x x 8 SD: 0.0000 cents 5 x x 6 x 7:10 SD: 36.7110 cents 6 x x x x 8:12 S SD: 0.0000 cents 7 x 8 x 9 x 14 SD: 39.8143 cents 8 x 9:10 x 11:16 SD: 26.6164 cents 9 x 10:11 x 12:18 S SD: 20.1684 cents 10 x 11 x 13 x 20 SD: 18.8678 cents 11 x 12 x 14:15:22 SD: 14.4400 cents 12 x 13:15 x 16:24 SD: 6.7103 cents 13 x 14:16:17 x 26 SD: 10.7703 cents 14 x 15 x 18:19:28 SD: 7.8994 cents 15 x 16:19 x 20:30 SD: 5.7326 cents 16 x 17:20 x 21:32 SD: 7.0234 cents 17 x 18:21:22:23:34 SD: 7.3457 cents 18 x 19 x 23:24:36 SD: 5.2651 cents 19 x 20:24 x 25:38 SD: 9.2880 cents 20:21 x 25:26:27:40 SD: 7.1861 cents 21:22 x 26:27:28:42 SD: 4.8307 cents 22:23 x x 28:29:44 SD: 7.4844 cents 24:25:26:30:31:32:48 SD: 4.8416 cents 26:27:28 x 33:35:52 SD: 6.4918 cents 27:28:29:34:35:36:54 SD: 3.7571 cents 28:29:30:35:36:37:56 SD: 2.9128 cents 45:47:48:56:58:60:90 SD: 2.5250 cents 48:50:51:60:62:64:96 SD: 2.1687 cents 56:58:60:70:72:75:112 SD: 1.8546 cents 60:62:64:75:77:80:120 SD: 1.1627 cents 104:108:111:130:134:139:208 SD: 1.0228 cents 105:109:112:131:135:140:210 SD: 0.6239 cents 108:112:115:135:139:144:216 SD: 0.5826 cents 164:170:175:205:211:219:328 SD: 0.5092 cents 165:171:176:206:212:220:330 SD: 0.4420 cents 192:199:205:240:247:256:384 SD: 0.3649 cents 273:283:291:341:351:364:546 SD: 0.3112 cents 297:308:317:371:382:396:594 SD: 0.2874 cents 300:311:320:375:386:400:600 SD: 0.2372 cents 375:389:400:469:482:500:750 SD: 0.1944 cents 480:498:512:600:617:640:960 SD: 0.1451 cents 540:560:576:675:694:720:1080 SD: 0.1188 cents