Scala analysis: xen11-chalmers-tetrachordal-08-10
Transposition and Inversion by 4/3B, 8 tones, an Octony
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: 25/16 772.627428 classic augmented fifth 6: 45/28 821.397809 septimale wide minor sixth 7: 5/3 884.358713 major sixth, BP sixth 8: 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: 16/15 111.7313 minor diatonic semitone 5: 75/64 274.5824 classic augmented second 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 28/27 62.9609 Archytas' 1/3-tone 8: 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 16/15 111.731 cents minor diatonic semitone 1: 2 75/64 274.582 cents classic augmented second 1: 1 6/5 315.641 cents minor third 2: 2 16/15 111.731 cents minor diatonic semitone 2: 2 135/112 323.353 cents septimal wide minor third 2: 2 56/45 378.602 cents septimal narrow major third 2: 2 5/4 386.314 cents major third 3: 2 5/4 386.314 cents major third 3: 2 32/25 427.373 cents classic diminished fourth 3: 2 9/7 435.084 cents septimal major third, BP third 3: 1 1568/1215 441.563 cents 3: 1 375/256 660.896 cents double augmented fourth 4: 2 896/675 490.333 cents 4: 2 4/3 498.045 cents perfect fourth 4: 2 3/2 701.955 cents perfect fifth 4: 2 675/448 709.667 cents 5: 1 512/375 539.104 cents double diminished fifth 5: 1 1215/784 758.437 cents 5: 2 14/9 764.916 cents septimal minor sixth 5: 2 25/16 772.627 cents classic augmented fifth 5: 2 8/5 813.686 cents minor sixth 6: 2 8/5 813.686 cents minor sixth 6: 2 45/28 821.398 cents septimale wide minor sixth 6: 2 224/135 876.647 cents narrow septimal major sixth 6: 2 15/8 1088.269 cents classic major seventh 7: 1 5/3 884.359 cents major sixth, BP sixth 7: 2 128/75 925.418 cents diminished seventh 7: 1 15/8 1088.269 cents classic major seventh 7: 2 27/14 1137.039 cents septimal major seventh 7: 2 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.57143 = 32/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 63.0 111.7 386.3 498.0 772.6 821.4 884.4 1200.0 63.0 : 48.8 323.4 435.1 709.7 758.4 821.4 1137.0 1200.0 111.7 : 274.6 386.3 660.9 709.7 772.6 1088.3 1151.2 1200.0 386.3 : 111.7 386.3 435.1 498.0 813.7 876.6 925.4 1200.0 498.0 : 274.6 323.4 386.3 702.0 764.9 813.7 1088.3 1200.0 772.6 : 48.8 111.7 427.4 490.3 539.1 813.7 925.4 1200.0 821.4 : 63.0 378.6 441.6 490.3 764.9 876.6 1151.2 1200.0 884.4 : 315.6 378.6 427.4 702.0 813.7 1088.3 1137.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 315.6413 cents 7/6, 266.8709 cents 36/35, 48.7704 cents 2: 111.7313 .. 386.3137 cents 75/64, 274.5824 cents 8/9,-203.9100 cents 3: 386.3137 .. 660.8961 cents 75/64, 274.5824 cents 1/1, 0.0000 cents 4: 490.3335 .. 709.6665 cents 455625/401408, 219.3330 cents 229376/253125,-170.5627 cents 5: 539.1039 .. 813.6863 cents 75/64, 274.5824 cents 229376/253125,-170.5627 cents 6: 813.6863 .. 1088.2687 cents 75/64, 274.5824 cents 1/1, 0.0000 cents 7: 884.3587 .. 1151.2296 cents 7/6, 266.8709 cents 8/9,-203.9100 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 3.075637 Largest / Average step : 2.104275 Largest / Smallest step : 6.471987 Median interval of one step : 87.34609 cents, amount: 0 Least squares average step : 137.35088 cents, oct.: 1098.80704 cents Scale is not proper Step pattern alph. order: ABCDCBAE Step pattern size order : BADCDABE Scale is not a Constant Structure Scale diversity : 1.285908 Lumma stability : 0.081284 Lumma impropriety factor : 0.522628 Rothenberg efficiency : 0.387500 redundancy: 0.612500 Efficiency x scale size : 3.100000 Number of different interval sizes : 28 = 4.00000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.57143 = 32/7 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 10976/10935, 6.4790 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 4 Most common triad is 0.0 386.314 813.686 cents, amount: 2 Number of recognisable fifths : 4, average 705.8108 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 Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 7-8 -- Rational properties -- Prime limit : 7 Odd number limit : 1215 (O: 1215 U: 1215) Highest odd numerator or denominator: 45 Scale harmonicity : 0.016365 Average absolute harmonicity : 0.208826 Specific harmonicity : 0.126634 Fundamental : 1/15120, -13.8842 octaves, 0.0173 Hz. Guide tone : 25200, 14.6211 octaves, 6592964.246 Hz. Exponens Consonantiae : 3.810240E+08, 28.50531 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 113.5, average 14.18750 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.53367, average 0.94171 Sum of Tenney's harmonic distance : 14.81850, average 1.85231 Vogel's harmonic complexity : 26.12500 Wille's k value : 11812 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 137.03266, average 3.80646 Lattice compactness (without 2's) : 75.91990, average 2.10889 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 4 0.12500 17 1 3: -3 .. 2 -0.50000 8 1 5: -1 .. 2 0.50000 6 4 7: -1 .. 1 0.00000 2 2 Average exponent except 2's : 0 / 8 = 0.00000 Average absolute exponent except 2's: 16 / 8 = 2.00000 Scale is weakly epimorphic with val: <8 12 19 22| Scale is weakly epimorphic with val: <8 12 21 23| Scale is weakly epimorphic with val: <8 13 18 21| Scale is weakly epimorphic with val: <8 13 18 22| Scale is weakly epimorphic with val: <8 14 19 22|
FIT/MODE
8: 0 1 2 0 2 0 1 2 N T3 SD: 46.9669 c. M: 71.3978 c. 9: 1 0 2 1 2 0 1 2 N D3 SD: 36.1544 c. M:-70.3724 c. 10: 0 1 2 1 2 1 0 3 N SD: 35.5912 c. M: 62.9609 c. 12: 1 0 3 1 3 0 1 3 N D3 SD: 19.8508 c. M:-37.0391 c. 15: 1 0 4 1 4 0 1 4 N D3 SD: 19.4816 c. M: 31.7313 c. 17: 1 1 4 1 4 1 1 4 N M DE SD: 22.6578 c. M:-37.2157 c. 18: 1 1 4 1 5 0 1 5 N SD: 19.9137 c. M: 31.3783 c. 19: 1 1 4 2 4 1 1 5 N SD: 8.1877 c. M: 14.7327 c. 22: 1 1 5 2 5 1 1 6 N SD: 6.8501 c. M: 11.6314 c. 31: 2 1 7 3 7 1 2 8 N SD: 6.7641 c. M:-14.4585 c. 34: 2 1 8 3 8 1 2 9 N SD: 5.2808 c. M: 9.6331 c. 50: 3 2 11 5 11 2 3 13 N SD: 5.6425 c. M:-9.0391 c. 53: 3 2 12 5 12 2 3 14 N SD: 3.1278 c. M: 6.3035 c. 72: 4 3 16 7 16 3 4 19 N SD: 3.7041 c. M: 5.9608 c. 75: 4 3 17 7 17 3 4 20 N SD: 3.1669 c. M: 5.3978 c. 93: 5 4 21 9 21 4 5 24 N SD: 3.6515 c. M:-5.9639 c. 94: 5 4 21 9 21 4 5 25 N SD: 3.4974 c. M: 6.6700 c. 95: 5 4 22 8 22 4 5 25 N SD: 2.8600 c. M: 5.4134 c. 96: 5 4 22 9 22 4 5 25 N SD: 2.0768 c. M:-3.6022 c. 99: 5 4 23 9 23 4 5 26 N SD: 2.0692 c. M:-3.1301 c. 115: 6 5 26 11 26 5 6 30 N SD: 2.0347 c. M:-3.0513 c. 118: 6 5 27 11 27 5 6 31 N SD: 1.0913 c. M:-2.3310 c. 137: 7 6 31 13 31 6 7 36 N SD: 1.4527 c. M:-2.1373 c. 140: 7 6 32 13 32 6 7 37 N SD: 1.4077 c. M: 2.9609 c. 149: 8 6 34 14 34 6 8 39 N SD: 0.9743 c. M:-1.5473 c. 152: 8 6 35 14 35 6 8 40 N SD: 0.6601 c. M: 1.2050 c. 171: 9 7 39 16 39 7 9 45 N SD: 0.3759 c. M: 0.6976 c. 323: 17 13 74 30 74 13 17 85 N SD: 0.2005 c. M: 0.3452 c. 494: 26 20 113 46 113 20 26 130 N SD: 0.1643 c. M: 0.3452 c. 612: 32 25 140 57 140 25 32 161 N SD: 0.1040 c. M: 0.2158 c. 764: 40 31 175 71 175 31 40 201 N SD: 0.1218 c. M: 0.2130 c. 783: 41 32 179 73 179 32 41 206 N SD: 0.1138 c. M: 0.2136 c. 913: 48 37 209 85 209 37 48 240 N SD: 0.1244 c. M:-0.2094 c. 935: 49 38 214 87 214 38 49 246 N SD: 0.0540 c. M: 0.0806 c. 1696: 89 69 388 158 388 69 89 446 N SD: 0.0482 c. M:-0.0752 c. 2019: 106 82 462 188 462 82 106 531 N SD: 0.0253 c. M:-0.0406 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x 4 S SD: 35.3362 cents 3 x x x 4 x x 5:6 S SD: 0.0000 cents 4 x x 5 x 6 x 7:8 S SD: 27.5333 cents 5 x x 6:7 x 8 x 10 S SD: 27.6007 cents 6 x x x 8:9 x 10:12 S SD: 17.6681 cents 7 x 8:9 x 11 x 12:14 SD: 27.6557 cents 8 x 9:10:11 x 13 x 16 SD: 21.6341 cents 9 x 10:11:12:14 x 15:18 S SD: 13.5069 cents 10 x 11 x 13 x 16:17:20 SD: 15.4841 cents 11 x 12:14:15:17:18 x 22 SD: 12.1725 cents 12 x 13:15:16:19 x 20:24 SD: 5.8838 cents 13 x 14:16:17:20:21:22:26 SD: 8.5982 cents 14 x 15:18:19:22 x 23:28 SD: 10.6651 cents 15 x 16:19:20:23:24:25:30 SD: 5.8019 cents 16 x 17:20:21:25:26:27:32 SD: 5.7458 cents 17 x 18:21:23 x 27:28:34 SD: 7.5670 cents 18 x 19:23:24:28:29:30:36 SD: 6.1515 cents 19 x 20:24:25:30:31:32:38 SD: 7.4506 cents 20:21 x 25:27:31:32:33:40 SD: 5.4970 cents 21:22 x 26:28:33:34:35:42 SD: 4.1501 cents 22:23 x 28:29:34:35:37:44 SD: 7.1077 cents 23:24:25:29:31:36:37:38:46 SD: 5.5825 cents 24:25:26:30:32:38:39:40:48 SD: 5.1108 cents 25:26:27:31:33:39:40:42:50 SD: 4.4025 cents 27:28:29:34:36:42:43:45:54 SD: 3.0978 cents 28:29:30:35:37:44:45:47:56 SD: 2.9437 cents 33:34:35:41:44:52:53:55:66 SD: 2.9331 cents 43:45:46:54:57:67:69:72:86 SD: 2.8906 cents 44:46:47:55:59:69:71:73:88 SD: 2.6474 cents 45:47:48:56:60:70:72:75:90 SD: 2.2715 cents 48:50:51:60:64:75:77:80:96 SD: 1.3444 cents 75:78:80:94:100:117:121:125:150 SD: 1.2351 cents 76:79:81:95:101:119:122:127:152 SD: 1.1802 cents 84:87:90:105:112:131:135:140:168 SD: 1.0843 cents 87:90:93:109:116:136:140:145:174 SD: 0.9138 cents 105:109:112:131:140:164:169:175:210 SD: 0.5730 cents 132:137:141:165:176:206:212:220:264 SD: 0.4640 cents 135:140:144:169:180:211:217:225:270 SD: 0.3286 cents 240:249:256:300:320:375:386:400:480 SD: 0.1871 cents 300:311:320:375:400:469:482:500:600 SD: 0.1530 cents 405:420:432:506:540:633:651:675:810 SD: 0.1296 cents 432:448:461:540:576:675:694:720:864 SD: 0.1294 cents 537:557:573:671:716:839:863:895:1074 SD: 0.1200 cents 540:560:576:675:720:844:868:900:1080 SD: 0.0733 cents