Scala analysis: xen11-chalmers-tetrachordal-08-06
Transposition and Inversion by 2/A, 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: 135/112 323.352810 septimal wide minor third 4: 243/196 372.123191 5: 9/7 435.084095 septimal major third, BP third 6: 4/3 498.044999 perfect fourth 7: 27/14 1137.039096 septimal major seventh 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 28/27 62.9609 Archytas' 1/3-tone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 2025/1792 211.6215 4: 36/35 48.7704 septimal diesis, 1/4-tone 5: 28/27 62.9609 Archytas' 1/3-tone 6: 28/27 62.9609 Archytas' 1/3-tone 7: 81/56 638.9941 8: 28/27 62.9609 Archytas' 1/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 4 28/27 62.961 cents Archytas' 1/3-tone 1: 1 2025/1792 211.622 cents 1: 1 81/56 638.994 cents 2: 2 16/15 111.731 cents minor diatonic semitone 2: 2 784/729 125.922 cents two (Archytas' 1/3-tone) 2: 2 3645/3136 260.392 cents 2: 2 3/2 701.955 cents perfect fifth 3: 2 448/405 174.692 cents 3: 1 6561/5488 309.162 cents 3: 2 135/112 323.353 cents septimal wide minor third 3: 3 14/9 764.916 cents septimal minor sixth 4: 2 243/196 372.123 cents 4: 2 5/4 386.314 cents major third 4: 2 8/5 813.686 cents minor sixth 4: 2 392/243 827.877 cents 5: 3 9/7 435.084 cents septimal major third, BP third 5: 2 224/135 876.647 cents narrow septimal major sixth 5: 1 10976/6561 890.838 cents 5: 2 405/224 1025.308 cents 6: 2 4/3 498.045 cents perfect fourth 6: 2 6272/3645 939.608 cents 6: 2 729/392 1074.078 cents 6: 2 15/8 1088.269 cents classic major seventh 7: 1 112/81 561.006 cents 7: 1 3584/2025 988.378 cents 7: 4 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: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 63.0 111.7 323.4 372.1 435.1 498.0 1137.0 1200.0 63.0 : 48.8 260.4 309.2 372.1 435.1 1074.1 1137.0 1200.0 111.7 : 211.6 260.4 323.4 386.3 1025.3 1088.3 1151.2 1200.0 323.4 : 48.8 111.7 174.7 813.7 876.6 939.6 988.4 1200.0 372.1 : 63.0 125.9 764.9 827.9 890.8 939.6 1151.2 1200.0 435.1 : 63.0 702.0 764.9 827.9 876.6 1088.3 1137.0 1200.0 498.0 : 639.0 702.0 764.9 813.7 1025.3 1074.1 1137.0 1200.0 1137.0: 63.0 125.9 174.7 386.3 435.1 498.0 561.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 638.9941 cents 45/32, 590.2237 cents 36/35, 48.7704 cents 2: 111.7313 .. 701.9550 cents 45/32, 590.2237 cents 896/1215,-527.2628 cents 3: 174.6922 .. 764.9159 cents 45/32, 590.2237 cents 896/1215,-527.2628 cents 4: 372.1232 .. 827.8768 cents 76832/59049, 455.7536 cents 2187/2744,-392.7927 cents 5: 435.0841 .. 1025.3078 cents 45/32, 590.2237 cents 2187/2744,-392.7927 cents 6: 498.0450 .. 1088.2687 cents 45/32, 590.2237 cents 896/1215,-527.2628 cents 7: 561.0059 .. 1151.2296 cents 45/32, 590.2237 cents 896/1215,-527.2628 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 : 81/56, 638.9941 cents Average / Smallest step : 3.075637 Largest / Average step : 4.259961 Largest / Smallest step : 13.102093 Median interval of one step : 28/27, 62.9609 cents, amount: 4 Most common interval of one step : 28/27, 62.9609 cents, amount: 4 Least squares average step : 124.84284 cents, oct.: 998.74270 cents Scale is not proper Step pattern alph. order: ABCBAADA Step pattern size order : BACABBDB Scale is a Constant Structure, by a margin of 36.92934 cents Scale diversity : 1.531726 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 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 : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 245/243, 14.1905 cents Most common intervals : 28/27, 62.9609 cents & inv., amount: 4 Most common triad is 0.0 62.961 1137.039 cents, amount: 2 Number of recognisable fifths : 2, average 701.9550 cents Scale contains a complete diamond : 7 27 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 37.5000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 6-7 -- Rational properties -- Prime limit : 7 Odd number limit : 6561 (O: 6561 U: 6561) Highest odd numerator or denominator: 243 Scale harmonicity : 0.013700 Average absolute harmonicity : 0.189837 Specific harmonicity : 0.093892 Fundamental : 1/105840, -16.6915 octaves, 0.0025 Hz. Guide tone : 136080, 17.0541 octaves, 35602006.926 Hz. Exponens Consonantiae : 1.440271E+10, 33.74562 octaves Euler's gradus suavitatis : 51 Sum of Mann's harmonic distance : 419.5, average 52.43750 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.98612, average 1.24827 Sum of Tenney's harmonic distance : 19.87319, average 2.48415 Vogel's harmonic complexity : 31.75000 Wille's k value : 63787 Wilson's harmonic complexity : 55 Rectangular lattice diameter : 13 Triangular lattice diameter : 8 Lattice compactness : 164.29784, average 4.56383 Lattice compactness (without 2's) : 119.35525, average 3.31542 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 4 0.25000 16 1 3: -3 .. 5 1.00000 18 1 5: -1 .. 1 0.00000 2 1 7: -2 .. 1 -0.50000 6 5 Average exponent except 2's : 4 / 8 = 0.50000 Average absolute exponent except 2's: 26 / 8 = 3.25000 Scale is weakly epimorphic with val: <8 12 18 23| 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 14 17 21| Scale is weakly epimorphic with val: <8 14 20 21|
FIT/MODE
8: 0 1 1 0 1 0 5 0 N SD: 46.9981 c. M: 72.1232 c. 9: 0 1 1 1 0 1 4 1 N SD: 44.5107 c. M: 70.3724 c. 10: 1 0 2 0 1 0 6 0 N SD: 37.2810 c. M:-62.9609 c. 11: 1 0 2 0 1 1 5 1 N SD: 32.6710 c. M:-47.4095 c. 14: 1 0 3 0 1 1 7 1 N SD: 20.1724 c. M: 29.2660 c. 16: 1 0 3 1 1 1 8 1 N SD: 19.8171 c. M: 36.7313 c. 17: 1 1 3 0 1 1 9 1 N SD: 17.2327 c. M:-29.5884 c. 19: 1 1 3 1 1 1 10 1 N D3 SD: 7.2280 c. M:-14.5845 c. 22: 1 1 4 1 1 1 12 1 N D3 SD: 6.2303 c. M:-9.6950 c. 36: 2 1 7 1 2 2 19 2 N SD: 6.1376 c. M: 11.7313 c. 41: 2 2 7 2 2 2 22 2 N D3 SD: 4.4070 c. M:-8.3646 c. 55: 3 2 10 2 3 3 29 3 N SD: 2.5525 c. M:-3.9199 c. 74: 4 3 13 3 4 4 39 4 N SD: 2.2740 c. M:-4.6577 c. 75: 4 3 13 3 4 4 40 4 N SD: 2.3497 c. M: 4.1232 c. 77: 4 3 14 3 4 4 41 4 N SD: 1.8975 c. M:-3.9199 c. 96: 5 4 17 4 5 5 51 5 N SD: 1.6456 c. M:-2.8768 c. 97: 5 4 17 4 5 5 52 5 N SD: 1.6240 c. M: 3.1996 c. 116: 6 5 20 5 6 6 62 6 N SD: 1.3969 c. M: 2.6632 c. 138: 7 6 24 6 7 7 74 7 N SD: 1.6618 c. M: 2.3928 c. 149: 8 6 26 6 8 8 79 8 N SD: 1.1845 c. M: 1.6534 c. 152: 8 6 27 6 8 8 81 8 N SD: 0.7077 c. M: 1.2050 c. 171: 9 7 30 7 9 9 91 9 N SD: 0.3072 c. M:-0.5494 c. 323: 17 13 57 13 17 17 172 17 N SD: 0.3065 c. M: 0.6062 c. 364: 19 15 64 15 19 19 194 19 N SD: 0.2832 c. M:-0.4043 c. 419: 22 17 74 17 22 22 223 22 N SD: 0.1787 c. M:-0.2844 c. 571: 30 23 101 23 30 30 304 30 N SD: 0.1750 c. M: 0.3477 c. 590: 31 24 104 24 31 31 314 31 N SD: 0.1315 c. M:-0.2601 c. 687: 36 28 121 28 36 36 366 36 N SD: 0.1318 c. M: 0.2284 c. 742: 39 30 131 30 39 39 395 39 N SD: 0.1032 c. M: 0.1555 c. 913: 48 37 161 37 48 48 486 48 N SD: 0.0933 c. M: 0.1626 c. 935: 49 38 165 38 49 49 498 49 N SD: 0.0630 c. M: 0.0771 c. 1106: 58 45 195 45 58 58 589 58 N SD: 0.0254 c. M: 0.0341 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x 4 S SD: 101.9550 cents 3 x x x x x 4 x 6 S SD: 0.0000 cents 4 x x x 5 x x x 8 SD: 7.0953 cents 5 x x 6 x x 7 x 10 SD: 28.2728 cents 6 x x 7 x x 8 x 12 S SD: 18.8273 cents 7 x x 8 x 9 x x 14 SD: 30.7262 cents 8 x 9 x 10 x 11:15:16 SD: 23.5922 cents 9 x 10:11 x x 12:17:18 SD: 16.5756 cents 10 x 11:12 x 13 x 19:20 SD: 12.5397 cents 11 x 12:13 x 14:15:21:22 SD: 11.5601 cents 12 x 13:14:15 x 16:23:24 SD: 10.8358 cents 13 x 14 x 16:17 x 25:26 SD: 7.2662 cents 14 x 15:17 x 18:19:27:28 SD: 5.6805 cents 15 x 16:18 x 19:20:29:30 SD: 4.5503 cents 16 x 17:19:20 x 21:31:32 SD: 6.9167 cents 17 x 18:20:21:22:23:33:34 SD: 7.6393 cents 18 x 19:22 x 23:24:35:36 SD: 5.8299 cents 19 x 20:23 x 24:25:37:38 SD: 8.0406 cents 20:21 x 24:25:26:27:39:40 SD: 6.2561 cents 21:22 x 25:26:27:28:41:42 SD: 5.0068 cents 22:23 x x 27:28:29:42:44 SD: 6.4853 cents 24:25:26:29:30:31:32:46:48 SD: 4.2909 cents 25:26:27:30:31:32:33:48:50 SD: 3.8894 cents 27:28:29:33 x 35:36:52:54 SD: 4.3547 cents 28:29:30:34:35:36:37:54:56 SD: 3.2357 cents 29:30:31:35:36:37:39:56:58 SD: 2.6367 cents 45:47:48:54:56:58:60:87:90 SD: 2.1277 cents 54:56:58:65:67:69:72:104:108 SD: 2.0596 cents 57:59:61:69:71:73:76:110:114 SD: 1.8136 cents 58:60:62:70:72:75:77:112:116 SD: 1.7727 cents 59:61:63:71:73:76:79:114:118 SD: 1.4031 cents 78:81:83:94:97:100:104:150:156 SD: 1.2493 cents 84:87:90:101:104:108:112:162:168 SD: 1.1747 cents 87:90:93:105:108:112:116:168:174 SD: 0.8983 cents 108:112:115:130:134:139:144:208:216 SD: 0.6282 cents 137:142:146:165:170:176:183:264:274 SD: 0.5791 cents 165:171:176:199:205:212:220:318:330 SD: 0.5369 cents 192:199:205:231:238:247:256:370:384 SD: 0.5148 cents 195:202:208:235:242:251:260:376:390 SD: 0.4084 cents 210:218:224:253:260:270:280:405:420 SD: 0.3852 cents 213:221:227:257:264:274:284:411:426 SD: 0.3538 cents 238:247:254:287:295:306:317:459:476 SD: 0.3203 cents 267:277:285:322:331:343:356:515:534 SD: 0.2780 cents 297:308:317:358:368:382:396:573:594 SD: 0.2200 cents 375:389:400:452:465:482:500:723:750 SD: 0.1155 cents