Scala analysis: xen11-chalmers-tetrachordal-08-07
Transposition and Inversion by 9/8 & 3/2, 7 tones, Psi-Hypodorian 1
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: 45/32 590.223716 diatonic tritone 3: 81/56 638.994097 4: 3/2 701.955001 perfect fifth 5: 14/9 764.915905 septimal minor sixth 6: 8/5 813.686286 minor sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 5/4 386.3137 major third 1: 9/8 203.9100 major whole tone 2: 5/4 386.3137 major third 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 28/27 62.9609 Archytas' 1/3-tone 5: 28/27 62.9609 Archytas' 1/3-tone 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 5/4 386.3137 major 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 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: 1 784/729 125.922 cents two (Archytas' 1/3-tone) 2: 2 9/7 435.084 cents septimal major third, BP third 2: 2 45/32 590.224 cents diatonic tritone 3: 2 448/405 174.692 cents 3: 2 4/3 498.045 cents perfect fourth 3: 2 81/56 638.994 cents 3: 1 225/128 976.537 cents augmented sixth 4: 1 256/225 223.463 cents Neapolitan diminished third 4: 2 112/81 561.006 cents 4: 2 3/2 701.955 cents perfect fifth 4: 2 405/224 1025.308 cents 5: 2 64/45 609.776 cents 2nd tritone 5: 2 14/9 764.916 cents septimal minor sixth 5: 1 729/392 1074.078 cents 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 : 203.9 590.2 639.0 702.0 764.9 813.7 1200.0 203.9 : 386.3 435.1 498.0 561.0 609.8 996.1 1200.0 590.2 : 48.8 111.7 174.7 223.5 609.8 813.7 1200.0 639.0 : 63.0 125.9 174.7 561.0 764.9 1151.2 1200.0 702.0 : 63.0 111.7 498.0 702.0 1088.3 1137.0 1200.0 764.9 : 48.8 435.1 639.0 1025.3 1074.1 1137.0 1200.0 813.7 : 386.3 590.2 976.5 1025.3 1088.3 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 .. 590.2237 cents 675/512, 478.4924 cents 64/75,-274.5824 cents 3: 174.6922 .. 976.5374 cents 91125/57344, 801.8452 cents 14336/18225,-415.5315 cents 4: 223.4626 .. 1025.3078 cents 91125/57344, 801.8452 cents 32768/50625,-753.0749 cents 5: 609.7763 .. 1088.2687 cents 675/512, 478.4924 cents 14336/18225,-415.5315 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 : 165.82755 cents, oct.: 1160.79285 cents Scale is not proper Step pattern alph. order: ABCDDCB Step pattern size order : CDABBAD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.406363 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 : 245/243, 14.1905 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 : 729 (O: 729 U: 729) Highest odd numerator or denominator: 81 Scale harmonicity : 0.017430 Average absolute harmonicity : 0.237256 Specific harmonicity : 0.133351 Fundamental : 1/10080, -13.2992 octaves, 0.0260 Hz. Guide tone : 22680, 14.4691 octaves, 5933667.821 Hz. Exponens Consonantiae : 2.286144E+08, 27.76834 octaves Euler's gradus suavitatis : 41 Sum of Mann's harmonic distance : 137.5, average 19.64286 Mersenne's string divisions : 804308505 Sum of van Prooijen's expressibility: 6.64627, average 0.94947 Sum of Tenney's harmonic distance : 13.45398, average 1.92200 Vogel's harmonic complexity : 25.00000 Wille's k value : 7087 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 117.35038, average 4.19109 Lattice compactness (without 2's) : 67.47595, average 2.40986 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 3 -1.00000 17 1 3: -2 .. 4 1.00000 11 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: 15 / 7 = 2.14286 Scale is weakly epimorphic with val: <7 10 16 22| Scale is weakly epimorphic with val: <7 10 17 18| Scale is weakly epimorphic with val: <7 10 17 21| Scale is weakly epimorphic with val: <7 11 15 18| 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 11 18 21| Scale is weakly epimorphic with val: <7 12 15 18| Scale is weakly epimorphic with val: <7 12 15 19| Scale is weakly epimorphic with val: <7 12 17 18| Scale is weakly epimorphic with val: <7 12 17 19|
FIT/MODE
7: 1 2 1 0 0 1 2 N S SD: 49.8992 c. M: 79.2016 c. 8: 1 3 0 0 1 0 3 N SD: 52.3664 c. M: 101.9550 c. 10: 2 3 0 1 0 1 3 N SD: 29.1647 c. M: 44.9159 c. 11: 2 3 1 0 1 0 4 N G SD: 32.0805 c. M: 50.0499 c. 12: 2 4 0 1 1 0 4 N S SD: 20.8855 c. M: 38.9941 c. 16: 3 5 1 0 1 1 5 N SD: 20.4025 c. M:-36.0059 c. 17: 3 5 1 1 1 1 5 N S SD: 16.8574 c. M:-33.3725 c. 19: 3 6 1 1 1 1 6 N S SD: 11.3037 c. M: 21.8027 c. 22: 4 7 1 1 1 1 7 N S SD: 9.3646 c. M:-15.5514 c. 24: 4 8 1 1 1 1 8 N S SD: 9.6037 c. M: 14.9159 c. 28: 5 9 1 1 2 1 9 N SD: 8.6577 c. M: 16.2407 c. 34: 6 11 1 2 2 1 11 N S SD: 6.7990 c. M:-11.5547 c. 41: 7 13 2 2 2 2 13 N S SD: 3.7479 c. M:-5.8259 c. 53: 9 17 2 3 3 2 17 N S SD: 2.7691 c. M: 5.0318 c. 75: 13 24 3 4 4 3 24 N S SD: 2.3887 c. M:-4.0900 c. 77: 13 25 3 4 4 3 25 N S SD: 1.6299 c. M: 3.2967 c. 118: 20 38 5 6 6 5 38 N S SD: 1.0825 c. M: 2.2040 c. 130: 22 42 5 7 7 5 42 N S SD: 1.1268 c. M: 2.0710 c. 152: 26 49 6 8 8 6 49 N S SD: 1.0072 c. M:-1.8815 c. 171: 29 55 7 9 9 7 55 N S SD: 0.3861 c. M: 0.7500 c. 248: 42 80 10 13 13 10 80 N S SD: 0.4549 c. M: 0.7831 c. 323: 55 104 13 17 17 13 104 N S SD: 0.3013 c. M:-0.4884 c. 419: 71 135 17 22 22 17 135 N S SD: 0.3240 c. M: 0.5687 c. 441: 75 142 18 23 23 18 142 N S SD: 0.2404 c. M:-0.4617 c. 494: 84 159 20 26 26 20 159 N S SD: 0.1315 c. M:-0.2663 c. 612: 104 197 25 32 32 25 197 N S SD: 0.1169 c. M:-0.2216 c. 665: 113 214 27 35 35 27 214 N S SD: 0.1318 c. M: 0.1971 c. 742: 126 239 30 39 39 30 239 N S SD: 0.1234 c. M: 0.2092 c. 783: 133 252 32 41 41 32 252 N S SD: 0.1122 c. M: 0.1854 c. 913: 155 294 37 48 48 37 294 N S SD: 0.1258 c. M: 0.2208 c. 935: 159 301 38 49 49 38 301 N S SD: 0.1035 c. M:-0.1542 c. 1106: 188 356 45 58 58 45 356 N S SD: 0.0439 c. M:-0.0683 c. 1848: 314 595 75 97 97 75 595 N S SD: 0.0280 c. M: 0.0499 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 4 x x x 5:6 S SD: 38.7176 cents 4:5 x x 6 x x 8 S SD: 60.8012 cents 5:6:7 x x x 8:10 S SD: 27.9993 cents 6:7:8 x 9 x 10:12 S SD: 26.4239 cents 7:8 x 10 x 11 x 14 SD: 9.7300 cents 8:9:11 x 12 x 13:16 SD: 9.4533 cents 9:10 x 13 x 14 x 18 SD: 5.4093 cents 10:11:14 x 15 x 16:20 SD: 7.9325 cents 11:12:15:16 x 17:18:22 SD: 14.3476 cents 12:14:17 x 18 x 19:24 SD: 13.3506 cents 13:15:18:19 x 20:21:26 SD: 10.0079 cents 14:16 x 20:21:22 x 28 SD: 7.7840 cents 15:17:21:22 x 23:24:30 SD: 6.2846 cents 16:18 x 23:24:25:26:32 SD: 4.9856 cents 17:19:24:25 x 26:27:34 SD: 7.4935 cents 18:20:25:26:27:28:29:36 SD: 4.6822 cents 19:21:27 x 29 x 30:38 SD: 10.3922 cents 20:23:28:29:30:31:32:40 SD: 5.6495 cents 21:24 x 30:32:33:34:42 SD: 8.6247 cents 22:25:31:32:33:34:35:44 SD: 3.5951 cents 30:34:42:43:45:47:48:60 SD: 3.5641 cents 32:36:45:46:48:50:51:64 SD: 2.1203 cents 40:45:56:58:60:62:64:80 SD: 1.5390 cents 56:63:79:81:84:87:90:112 SD: 1.3884 cents 72:81:101:104:108:112:115:144 SD: 0.8208 cents 110:124:155:159:165:171:176:220 SD: 0.7429 cents 128:144:180:185:192:199:205:256 SD: 0.3373 cents 248:279:349:359:372:386:397:496 SD: 0.3256 cents 280:315:394:405:420:436:448:560 SD: 0.2971 cents 288:324:405:417:432:448:461:576 SD: 0.2760 cents 320:360:450:463:480:498:512:640 SD: 0.1342 cents 448:504:630:648:672:697:717:896 SD: 0.0795 cents