Scala analysis: xen11-chalmers-tetrachordal-08-11
Transposition and Inversion by 4/3A, 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: 9/7 435.084095 septimal major third, BP third 4: 4/3 498.044999 perfect fourth 5: 45/28 821.397809 septimale wide minor sixth 6: 81/49 870.168191 two (septimal major third, BP third) 7: 12/7 933.129094 septimal major sixth 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 28/27 62.9609 Archytas' 1/3-tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 135/112 323.3528 septimal wide minor third 4: 28/27 62.9609 Archytas' 1/3-tone 5: 135/112 323.3528 septimal wide minor third 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 28/27 62.9609 Archytas' 1/3-tone 8: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 3 28/27 62.961 cents Archytas' 1/3-tone 1: 1 7/6 266.871 cents septimal minor third 1: 2 135/112 323.353 cents septimal wide minor third 2: 2 16/15 111.731 cents minor diatonic semitone 2: 2 98/81 329.832 cents 2: 2 243/196 372.123 cents 2: 2 5/4 386.314 cents major third 3: 2 56/45 378.602 cents septimal narrow major third 3: 1 2744/2187 392.793 cents 3: 4 9/7 435.084 cents septimal major third, BP third 3: 1 675/448 709.667 cents 4: 2 1568/1215 441.563 cents 4: 2 4/3 498.045 cents perfect fourth 4: 2 3/2 701.955 cents perfect fifth 4: 2 1215/784 758.437 cents 5: 1 896/675 490.333 cents 5: 4 14/9 764.916 cents septimal minor sixth 5: 1 2187/1372 807.207 cents 5: 2 45/28 821.398 cents septimale wide minor sixth 6: 2 8/5 813.686 cents minor sixth 6: 2 392/243 827.877 cents 6: 2 81/49 870.168 cents two (septimal major third, BP third) 6: 2 15/8 1088.269 cents classic major seventh 7: 2 224/135 876.647 cents narrow septimal major sixth 7: 1 12/7 933.129 cents septimal major sixth 7: 3 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 : 63.0 111.7 435.1 498.0 821.4 870.2 933.1 1200.0 63.0 : 48.8 372.1 435.1 758.4 807.2 870.2 1137.0 1200.0 111.7 : 323.4 386.3 709.7 758.4 821.4 1088.3 1151.2 1200.0 435.1 : 63.0 386.3 435.1 498.0 764.9 827.9 876.6 1200.0 498.0 : 323.4 372.1 435.1 702.0 764.9 813.7 1137.0 1200.0 821.4 : 48.8 111.7 378.6 441.6 490.3 813.7 876.6 1200.0 870.2 : 63.0 329.8 392.8 441.6 764.9 827.9 1151.2 1200.0 933.1 : 266.9 329.8 378.6 702.0 764.9 1088.3 1137.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 323.3528 cents 75/64, 274.5824 cents 36/35, 48.7704 cents 2: 111.7313 .. 386.3137 cents 75/64, 274.5824 cents 1792/2025,-211.6215 cents 3: 378.6022 .. 709.6665 cents 30375/25088, 331.0643 cents 224/225,-7.7115 cents 4: 441.5631 .. 758.4369 cents 1476225/1229312, 316.8738 cents 702464/820125,-268.1034 cents 5: 490.3335 .. 821.3978 cents 30375/25088, 331.0643 cents 702464/820125,-268.1034 cents 6: 813.6863 .. 1088.2687 cents 75/64, 274.5824 cents 224/225,-7.7115 cents 7: 876.6472 .. 1151.2296 cents 75/64, 274.5824 cents 1792/2025,-211.6215 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 : 135/112, 323.3528 cents Average / Smallest step : 3.075637 Largest / Average step : 2.155685 Largest / Smallest step : 6.630106 Median interval of one step : 28/27, 62.9609 cents, amount: 3 Most common interval of one step : 28/27, 62.9609 cents, amount: 3 Least squares average step : 142.37136 cents, oct.: 1138.97089 cents Scale is not proper Step pattern alph. order: ABCACBAD Step pattern size order : BADBDABC Scale is a Constant Structure, by a margin of 6.47900 cents Scale diversity : 1.201044 Lumma stability : 0.081284 Lumma impropriety factor : 0.629617 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 : 10976/10935, 6.4790 cents Most common intervals : 9/7, 435.0841 cents & inv., amount: 4 Most common triad is 0.0 435.084 764.916 cents, amount: 2 Number of recognisable fifths : 3, average 704.5255 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 : 2187 (O: 2187 U: 2187) Highest odd numerator or denominator: 81 Scale harmonicity : 0.014636 Average absolute harmonicity : 0.193082 Specific harmonicity : 0.103932 Fundamental : 1/26460, -14.6915 octaves, 0.0099 Hz. Guide tone : 45360, 15.4691 octaves, 11867335.642 Hz. Exponens Consonantiae : 1.200226E+09, 30.16066 octaves Euler's gradus suavitatis : 47 Sum of Mann's harmonic distance : 167.0, average 20.87500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.44561, average 1.05570 Sum of Tenney's harmonic distance : 17.06162, average 2.13270 Vogel's harmonic complexity : 29.12500 Wille's k value : 21262 Wilson's harmonic complexity : 52 Rectangular lattice diameter : 12 Triangular lattice diameter : 7 Lattice compactness : 133.71740, average 3.71437 Lattice compactness (without 2's) : 101.27984, average 2.81333 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.12500 13 1 3: -3 .. 4 0.50000 14 1 5: -1 .. 1 0.00000 2 1 7: -2 .. 1 -0.50000 6 5 Average exponent except 2's : 0 / 8 = 0.00000 Average absolute exponent except 2's: 22 / 8 = 2.75000 Scale is JI-epimorphic with val: <8 12 18 21| Scale is weakly epimorphic with val: <8 12 21 23| Scale is weakly epimorphic with val: <8 13 17 20| Scale is weakly epimorphic with val: <8 13 20 20| Scale is weakly epimorphic with val: <8 13 20 24| Scale is weakly epimorphic with val: <8 13 21 24| Scale is weakly epimorphic with val: <8 14 21 21|
FIT/MODE
8: 0 1 2 0 2 1 0 2 N D3 SD: 43.3654 c. M: 71.3978 c. 9: 0 1 2 1 2 1 0 2 N SD: 37.6740 c. M:-63.1651 c. 10: 1 0 3 0 3 0 1 2 N SD: 30.9093 c. M:-57.0391 c. 11: 1 0 3 1 3 0 1 2 N SD: 34.2712 c. M:-51.3295 c. 13: 1 0 4 0 4 0 1 3 N SD: 25.0305 c. M: 39.3990 c. 14: 1 0 4 1 4 0 1 3 N SD: 19.5025 c. M:-35.7450 c. 15: 1 0 4 1 4 1 1 3 N SD: 22.7220 c. M: 35.0841 c. 17: 1 1 4 1 5 0 1 4 N SD: 17.7001 c. M:-29.4452 c. 19: 1 1 5 1 5 1 1 4 N G SD: 9.4486 c. M:-14.5845 c. 22: 1 1 6 1 6 1 1 5 N G SD: 4.7636 c. M: 8.4154 c. 41: 2 2 11 2 11 2 2 9 N G SD: 4.2053 c. M:-7.8806 c. 55: 3 2 15 3 15 2 3 12 N SD: 3.8783 c. M:-7.6931 c. 57: 3 2 16 3 15 2 3 13 N SD: 5.4653 c. M:-7.2182 c. 58: 3 2 16 3 16 2 3 13 N SD: 3.8099 c. M: 8.2830 c. 63: 3 3 17 3 17 3 3 14 N G SD: 3.5205 c. M:-6.0223 c. 72: 4 3 19 4 19 3 4 16 N SD: 3.1556 c. M:-4.9354 c. 77: 4 3 21 4 21 3 4 17 N SD: 2.2546 c. M:-4.5762 c. 94: 5 4 25 5 25 4 5 21 N SD: 2.1459 c. M: 4.3765 c. 99: 5 4 27 5 27 4 5 22 N SD: 1.9363 c. M:-2.8446 c. 116: 6 5 31 6 31 5 6 26 N SD: 1.9605 c. M: 4.1564 c. 127: 7 5 34 7 34 5 7 28 N SD: 1.8394 c. M:-3.1808 c. 130: 7 5 35 7 35 5 7 29 N SD: 1.2346 c. M: 2.4759 c. 149: 8 6 40 8 40 6 8 33 N SD: 0.8826 c. M:-1.4686 c. 152: 8 6 41 8 41 6 8 34 N SD: 1.0177 c. M: 1.7471 c. 171: 9 7 46 9 46 7 9 38 N SD: 0.2602 c. M:-0.5494 c. 364: 19 15 98 19 98 15 19 81 N SD: 0.2781 c. M: 0.5187 c. 494: 26 20 133 26 133 20 26 110 N SD: 0.2806 c. M: 0.5326 c. 535: 28 22 144 28 144 22 28 119 N SD: 0.2351 c. M: 0.4632 c. 549: 29 22 148 29 148 22 29 122 N SD: 0.2879 c. M:-0.4601 c. 571: 30 23 154 30 154 23 30 127 N SD: 0.1761 c. M: 0.3477 c. 742: 39 30 200 39 200 30 39 165 N SD: 0.0966 c. M:-0.1655 c. 913: 48 37 246 48 246 37 48 203 N SD: 0.0702 c. M:-0.1278 c. 935: 49 38 252 49 252 38 49 208 N SD: 0.0541 c. M: 0.0810 c. 1106: 58 45 298 58 298 45 58 246 N SD: 0.0309 c. M: 0.0597 c. 1848: 97 75 498 97 498 75 97 411 N SD: 0.0262 c. M: 0.0430 c. 2019: 106 82 544 106 544 82 106 449 N SD: 0.0217 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: 59.7214 cents 3 x x x 4 x 5 x 6 S SD: 4.7302 cents 4 x x 5 x 6 x 7:8 S SD: 33.4658 cents 5 x x 6:7:8 x 9:10 S SD: 33.8204 cents 6 x 7 x 8 x 10 x 12 S SD: 38.9468 cents 7 x 8:9 x 11 x 12:14 SD: 25.1239 cents 8 x 9:10:11:13 x 14:16 SD: 20.6517 cents 9 x 10 x 12:14:15 x 18 S SD: 18.3152 cents 10 x 11:13 x 16 x 17:20 SD: 11.7870 cents 11 x 12:14:15 x 18:19:22 SD: 10.2955 cents 12 x 13:15:16:19:20:21:24 SD: 10.3434 cents 13 x 14:17 x 21 x 22:26 SD: 8.2776 cents 14 x 15:18:19 x 23:24:28 SD: 5.5611 cents 15 x 16:19:20:24:25:26:30 SD: 5.1398 cents 16 x 17 x 21:26 x 27:32 SD: 8.7144 cents 17 x 18:22:23:27:28:29:34 SD: 5.4605 cents 18 x 19:23:24:29:30:31:36 SD: 3.8521 cents 19 x 20:24:25 x 31:33:38 SD: 9.1523 cents 20:21 x 26:27:32:33:34:40 SD: 5.6616 cents 21:22 x 27:28:34:35:36:42 SD: 3.7075 cents 22:23 x 28:29:35:36:38:44 SD: 5.8638 cents 24:25:26:31:32:39:40:41:48 SD: 4.7557 cents 25:26:27:32:33:40:41:43:50 SD: 4.2027 cents 27:28:29:35:36:43:45:46:54 SD: 3.7689 cents 28:29:30:36:37:45:46:48:56 SD: 2.5628 cents 45:47:48:58:60:72:74:77:90 SD: 2.2420 cents 46:48:49:59:61:74:76:79:92 SD: 1.9384 cents 49:51:52:63:65:79:81:84:98 SD: 1.8817 cents 56:58:60:72:75:90:93:96:112 S SD: 1.7128 cents 57:59:61:73:76:92:94:98:114 SD: 1.7055 cents 59:61:63:76:79:95:98:101:118 SD: 1.6807 cents 60:62:64:77:80:96:99:103:120 SD: 1.3931 cents 74:77:79:95:99:119:122:127:148 SD: 1.2709 cents 77:80:82:99:103:124:127:132:154 SD: 1.0972 cents 84:87:90:108:112:135:139:144:168 SD: 1.0271 cents 87:90:93:112:116:140:144:149:174 SD: 0.8796 cents 102:106:109:131:136:164:169:175:204 SD: 0.8409 cents 105:109:112:135:140:169:174:180:210 SD: 0.6604 cents 132:137:141:170:176:212:218:226:264 SD: 0.6282 cents 133:138:142:171:177:214:220:228:266 SD: 0.5517 cents 161:167:172:207:215:259:266:276:322 SD: 0.5338 cents 165:171:176:212:220:265:273:283:330 SD: 0.3345 cents 242:251:258:311:323:389:400:415:484 SD: 0.2845 cents 270:280:288:347:360:434:446:463:540 SD: 0.1968 cents 375:389:400:482:500:603:620:643:750 SD: 0.1576 cents 435:451:464:559:580:699:719:746:870 SD: 0.1538 cents 507:526:541:652:676:815:838:869:1014 SD: 0.1457 cents 539:559:575:693:719:866:891:924:1078 SD: 0.1217 cents 567:588:605:729:756:911:937:972:1134 SD: 0.1140 cents 570:591:608:733:760:916:942:977:1140 SD: 0.0888 cents