Scala analysis: xen11-chalmers-tetrachordal-08-08
Transposition and Inversion by 9/8 & 3/2, 7 tones, Psi-Hypodorian 2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 7/6 266.870906 septimal minor third 3: 6/5 315.641287 minor third 4: 3/2 701.955001 perfect fifth 5: 15/8 1088.268715 classic major seventh 6: 27/14 1137.039096 septimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 28/27 62.9609 Archytas' 1/3-tone 1: 9/8 203.9100 major whole tone 2: 28/27 62.9609 Archytas' 1/3-tone 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 5/4 386.3137 major third 5: 5/4 386.3137 major third 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 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: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 5/4 386.314 cents major third 2: 2 16/15 111.731 cents minor diatonic semitone 2: 2 7/6 266.871 cents septimal minor third 2: 2 9/7 435.084 cents septimal major third, BP third 2: 1 25/16 772.627 cents classic augmented fifth 3: 2 6/5 315.641 cents minor third 3: 1 98/81 329.832 cents 3: 2 4/3 498.045 cents perfect fourth 3: 2 45/28 821.398 cents septimale wide minor sixth 4: 2 56/45 378.602 cents septimal narrow major third 4: 2 3/2 701.955 cents perfect fifth 4: 1 81/49 870.168 cents two (septimal major third, BP third) 4: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 32/25 427.373 cents classic diminished fourth 5: 2 14/9 764.916 cents septimal minor sixth 5: 2 12/7 933.129 cents septimal major sixth 5: 2 15/8 1088.269 cents classic major seventh 6: 2 8/5 813.686 cents minor sixth 6: 1 16/9 996.090 cents Pythagorean minor 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: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 266.9 315.6 702.0 1088.3 1137.0 1200.0 203.9 : 63.0 111.7 498.0 884.4 933.1 996.1 1200.0 266.9 : 48.8 435.1 821.4 870.2 933.1 1137.0 1200.0 315.6 : 386.3 772.6 821.4 884.4 1088.3 1151.2 1200.0 702.0 : 386.3 435.1 498.0 702.0 764.9 813.7 1200.0 1088.3: 48.8 111.7 315.6 378.6 427.4 813.7 1200.0 1137.0: 63.0 266.9 329.8 378.6 764.9 1151.2 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 .. 772.6274 cents 375/256, 660.8961 cents 64/75,-274.5824 cents 3: 315.6413 .. 821.3978 cents 75/56, 505.7565 cents 96/125,-456.9861 cents 4: 378.6022 .. 884.3587 cents 75/56, 505.7565 cents 1568/2025,-442.7956 cents 5: 427.3726 .. 1088.2687 cents 375/256, 660.8961 cents 96/125,-456.9861 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 : 179.68553 cents, oct.: 1257.79869 cents Scale is not proper Step pattern alph. order: ABCDDCB Step pattern size order : CBADDAB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 7.71152 cents Scale diversity : 1.381734 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 24 = 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 : 225/224, 7.7115 cents Number of recognisable fifths : 2, average 701.9550 cents All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Limited inverse transpositions : 1 Inversional symmetry on degrees : 4 Inversional symmetry on intervals : 0-1 -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.020817 Average absolute harmonicity : 0.242637 Specific harmonicity : 0.162464 Fundamental : 1/840, -9.7142 octaves, 0.3115 Hz. Guide tone : 1890, 10.8842 octaves, 494472.318 Hz. Exponens Consonantiae : 1.587600E+06, 20.59842 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 56.5, average 8.07143 Mersenne's string divisions : 34386495 Sum of van Prooijen's expressibility: 5.58289, average 0.79756 Sum of Tenney's harmonic distance : 10.69356, average 1.52765 Vogel's harmonic complexity : 20.00000 Wille's k value : 787 Wilson's harmonic complexity : 36 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 79.29505, average 2.83197 Lattice compactness (without 2's) : 51.95699, average 1.85561 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.00000 11 1 3: -1 .. 3 1.00000 9 2 5: -1 .. 1 0.00000 2 2 7: -1 .. 1 0.00000 2 2 Average exponent except 2's : 7 / 7 = 1.00000 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 15 18| Scale is weakly epimorphic with val: <7 10 15 22| Scale is weakly epimorphic with val: <7 10 16 19| Scale is weakly epimorphic with val: <7 10 16 21| Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 16 21| Scale is weakly epimorphic with val: <7 12 15 20| Scale is weakly epimorphic with val: <7 12 15 21| Scale is weakly epimorphic with val: <7 12 17 18| Scale is weakly epimorphic with val: <7 12 18 18|
FIT/MODE
7: 1 1 0 2 2 1 0 N SD: 46.8451 c. M:-75.9862 c. 9: 1 1 0 3 3 0 1 N S SD: 44.7913 c. M: 70.5767 c. 10: 2 0 1 3 3 0 1 N SD: 33.0361 c. M: 57.0391 c. 11: 2 0 1 3 4 0 1 N G SD: 31.8304 c. M: 48.6891 c. 12: 2 1 0 4 4 0 1 N S SD: 20.2513 c. M: 37.0391 c. 15: 3 0 1 5 5 0 1 N SD: 22.8859 c. M:-36.0900 c. 17: 3 1 0 6 5 1 1 N SD: 18.3230 c. M: 33.2883 c. 18: 3 1 1 6 5 1 1 N SD: 16.0059 c. M:-31.3783 c. 19: 3 1 1 6 6 1 1 N S SD: 9.8273 c. M: 14.5845 c. 22: 4 1 1 7 7 1 1 N S SD: 8.4683 c. M:-14.2718 c. 31: 5 2 1 10 10 1 2 N S SD: 7.6992 c. M: 14.4585 c. 34: 6 2 1 11 11 1 2 N S SD: 7.6832 c. M:-15.4820 c. 39: 7 2 1 13 12 2 2 N SD: 8.1026 c. M:-11.4746 c. 41: 7 2 2 13 13 2 2 N S SD: 3.7993 c. M:-6.3099 c. 53: 9 3 2 17 17 2 3 N S SD: 2.7239 c. M: 4.9636 c. 72: 12 4 3 23 23 3 4 N S SD: 2.8858 c. M: 4.9354 c. 76: 13 4 3 24 25 3 4 N SD: 2.8747 c. M: 7.2182 c. 77: 13 4 3 25 25 3 4 N S SD: 2.0314 c. M: 3.9530 c. 94: 16 5 4 30 30 4 5 N S SD: 1.8778 c. M:-3.5076 c. 99: 17 5 4 32 32 4 5 N S SD: 1.6292 c. M:-2.6404 c. 118: 20 6 5 38 38 5 6 N S SD: 1.2164 c. M: 2.4641 c. 130: 22 7 5 42 42 5 7 N S SD: 1.0972 c. M: 1.7951 c. 152: 26 8 6 49 49 6 8 N S SD: 0.9415 c. M:-1.5501 c. 171: 29 9 7 55 55 7 9 N S SD: 0.2941 c. M: 0.5494 c. 441: 75 23 18 142 142 18 23 N S SD: 0.1881 c. M:-0.3759 c. 494: 84 26 20 159 159 20 26 N S SD: 0.1680 c. M:-0.3356 c. 612: 104 32 25 197 197 25 32 N S SD: 0.1144 c. M:-0.2158 c. 665: 113 35 27 214 214 27 35 N S SD: 0.1318 c. M: 0.1970 c. 783: 133 41 32 252 252 32 41 N S SD: 0.1141 c. M: 0.2042 c. 913: 155 48 37 294 294 37 48 N S SD: 0.1208 c. M: 0.1977 c. 935: 159 49 38 301 301 38 49 N S SD: 0.0875 c. M:-0.1542 c. 1106: 188 58 45 356 356 45 58 N S SD: 0.0493 c. M:-0.0911 c. 1848: 314 97 75 595 595 75 97 N S SD: 0.0296 c. M: 0.0569 c. 2019: 343 106 82 650 650 82 106 N S SD: 0.0293 c. M: 0.0467 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4:5 x x 6 S SD: 85.9859 cents 4 x x 5:6 x x 8 S SD: 23.5575 cents 5 x x 6:8:9 x 10 S SD: 33.0515 cents 6 x 7 x 9:11 x 12 SD: 9.7264 cents 7:8 x x 11:13 x 14 SD: 21.6564 cents 8:9 x 10:12:15 x 16 S SD: 14.1345 cents 9:10 x 11:14:17 x 18 SD: 14.9652 cents 10:11 x 12:15:19 x 20 SD: 9.0321 cents 11:12:13 x 17 x 21:22 SD: 15.8959 cents 12 x 14 x 18 x 23:24 SD: 2.6799 cents 13 x 15:16:20:24:25:26 SD: 11.7297 cents 14:16 x 17:21:26:27:28 SD: 6.3192 cents 15:17 x 18:23:28:29:30 SD: 6.8491 cents 16:18 x 19:24:30:31:32 SD: 3.3023 cents 17:19:20 x 26:32:33:34 SD: 6.7536 cents 18:20:21:22:27:34:35:36 SD: 6.1217 cents 20 x 23:24:30:38:39:40 SD: 6.4814 cents 21:24 x 25:32:39:41:42 SD: 8.1695 cents 22:25:26 x 33:41:42:44 SD: 5.8249 cents 23:26:27:28:35:43:44:46 SD: 5.7971 cents 24:27:28:29:36:45:46:48 SD: 2.2966 cents 27:30 x 32:41:51:52:54 SD: 6.5514 cents 28:32:33:34:42:53:54:56 SD: 5.9613 cents 29:33:34:35:44:54:56:58 SD: 4.7427 cents 30:34:35:36:45:56:58:60 SD: 2.2175 cents 40:45:47:48:60:75:77:80 SD: 1.8190 cents 54:61:63:65:81:101:104:108 SD: 1.4497 cents 66:74:77:79:99:124:127:132 SD: 1.2825 cents 72:81:84:86:108:135:139:144 SD: 1.1755 cents 80:90:93:96:120:150:154:160 SD: 0.9966 cents 90:101:105:108:135:169:174:180 SD: 0.9380 cents 96:108:112:115:144:180:185:192 SD: 0.4702 cents 120:135:140:144:180:225:231:240 SD: 0.4584 cents 144:162:168:173:216:270:278:288 SD: 0.3828 cents 210:236:245:252:315:394:405:420 SD: 0.3053 cents 240:270:280:288:360:450:463:480 SD: 0.0763 cents 600:675:700:720:900:1125:1157:1200 SD: 0.0305 cents