Scala analysis: xen11-chalmers-tetrachordal-06-04
Transposition by 3/2, Dorian Mode
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: 4/3 498.044999 perfect fourth 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: 28/27 62.9609 Archytas' 1/3-tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 5/4 386.3137 major third 4: 9/8 203.9100 major whole 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 7/6 266.871 cents septimal minor third 2: 2 9/7 435.084 cents septimal major third, BP third 2: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 2: 1 45/32 590.224 cents diatonic tritone 3: 1 6/5 315.641 cents minor third 3: 4 4/3 498.045 cents perfect fourth 3: 1 81/56 638.994 cents 3: 1 35/24 653.185 cents septimal semi-diminished fifth 4: 1 48/35 546.815 cents septimal semi-augmented fourth 4: 1 112/81 561.006 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 64/45 609.776 cents 2nd tritone 5: 1 54/35 750.725 cents septimal semi-augmented fifth 5: 2 14/9 764.916 cents septimal minor sixth 5: 1 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: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 63.0 111.7 498.0 702.0 764.9 813.7 1200.0 63.0 : 48.8 435.1 639.0 702.0 750.7 1137.0 1200.0 111.7 : 386.3 590.2 653.2 702.0 1088.3 1151.2 1200.0 498.0 : 203.9 266.9 315.6 702.0 764.9 813.7 1200.0 702.0 : 63.0 111.7 498.0 561.0 609.8 996.1 1200.0 764.9 : 48.8 435.1 498.0 546.8 933.1 1137.0 1200.0 813.7 : 386.3 449.3 498.0 884.4 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: 315.6413 .. 653.1846 cents 175/144, 337.5433 cents 64/75,-274.5824 cents 4: 546.8154 .. 884.3587 cents 175/144, 337.5433 cents 1152/1225,-106.3692 cents 5: 609.7763 .. 1088.2687 cents 675/512, 478.4924 cents 64/75,-274.5824 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 : 154.96483 cents, oct.: 1084.75379 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : BADCBAD Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.578397 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 245/243, 14.1905 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Scale contains a complete diamond : 1 3 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 : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.030910 Average absolute harmonicity : 0.254199 Specific harmonicity : 0.174754 Fundamental : 1/270, -8.0768 octaves, 0.9690 Hz. Guide tone : 336, 8.3923 octaves, 87906.190 Hz. Exponens Consonantiae : 9.072000E+04, 16.46913 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 68.5, average 9.78571 Mersenne's string divisions : 10705695 Sum of van Prooijen's expressibility: 5.21491, average 0.74499 Sum of Tenney's harmonic distance : 11.11953, average 1.58850 Vogel's harmonic complexity : 14.71429 Wille's k value : 202 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 79.18553, average 2.82805 Lattice compactness (without 2's) : 50.57293, average 1.80618 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.71429 14 1 3: -3 .. 1 -0.85714 8 2 5: -1 .. 0 -0.28571 2 2 7: 0 .. 1 0.28571 2 2 Average exponent except 2's :-6 / 7 =-0.85714 Average absolute exponent except 2's: 12 / 7 = 1.71429 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 17 18|
FIT/MODE
7: 0 1 2 1 0 1 2 N T3 SD: 48.1319 c. M: 79.2016 c. 8: 0 1 2 2 0 0 3 N SD: 45.2353 c. M: 63.6863 c. 9: 0 1 3 1 1 0 3 N SD: 34.5160 c. M: 62.9609 c. 10: 1 0 3 2 0 1 3 N SD: 30.8983 c. M:-57.0391 c. 11: 1 0 4 1 1 0 4 N SD: 36.1286 c. M: 50.0499 c. 12: 1 0 4 2 1 0 4 N SD: 20.4778 c. M:-37.0391 c. 15: 1 0 5 3 1 0 5 N SD: 21.9306 c. M:-35.0841 c. 16: 1 0 6 2 1 1 5 N SD: 21.7050 c. M: 36.7313 c. 17: 1 1 5 3 1 1 5 N SD: 17.7413 c. M:-33.3725 c. 19: 1 1 6 3 1 1 6 N SD: 7.7507 c. M:-14.5845 c. 22: 1 1 7 4 1 1 7 N SD: 5.3650 c. M: 8.4154 c. 41: 2 2 13 7 2 2 13 N SD: 3.7425 c. M:-5.8259 c. 53: 3 2 17 9 3 2 17 N SD: 2.7457 c. M:-4.9636 c. 72: 4 3 23 12 4 3 23 N SD: 2.8706 c. M:-4.9354 c. 74: 4 3 24 12 4 3 24 N SD: 3.0716 c. M:-4.6577 c. 75: 4 3 24 13 4 3 24 N SD: 1.8663 c. M:-3.0841 c. 77: 4 3 25 13 4 3 25 N SD: 1.7207 c. M: 3.2967 c. 96: 5 4 31 16 5 4 31 N SD: 1.4972 c. M: 2.4159 c. 99: 5 4 32 17 5 4 32 N SD: 1.6439 c. M: 2.6404 c. 118: 6 5 38 20 6 5 38 N SD: 1.1216 c. M: 2.2040 c. 130: 7 5 42 22 7 5 42 N SD: 1.0311 c. M:-1.6545 c. 149: 8 6 48 25 8 6 48 N SD: 0.9709 c. M:-1.4686 c. 152: 8 6 49 26 8 6 49 N SD: 0.7019 c. M: 1.2050 c. 171: 9 7 55 29 9 7 55 N SD: 0.2785 c. M:-0.5494 c. 323: 17 13 104 55 17 13 104 N SD: 0.2320 c. M:-0.4092 c. 419: 22 17 135 71 22 17 135 N SD: 0.2155 c. M: 0.3211 c. 441: 23 18 142 75 23 18 142 N SD: 0.1980 c. M: 0.3759 c. 494: 26 20 159 84 26 20 159 N SD: 0.1340 c. M:-0.2663 c. 590: 31 24 190 100 31 24 190 N SD: 0.1716 c. M:-0.2601 c. 612: 32 25 197 104 32 25 197 N SD: 0.1155 c. M: 0.2158 c. 665: 35 27 214 113 35 27 214 N SD: 0.1318 c. M:-0.1970 c. 742: 39 30 239 126 39 30 239 N SD: 0.1117 c. M: 0.2092 c. 783: 41 32 252 133 41 32 252 N SD: 0.1061 c. M: 0.1649 c. 913: 48 37 294 155 48 37 294 N SD: 0.0810 c. M:-0.1278 c. 935: 49 38 301 159 49 38 301 N SD: 0.0569 c. M:-0.0771 c. 1106: 58 45 356 188 58 45 356 N SD: 0.0318 c. M:-0.0569 c. 1848: 97 75 595 314 97 75 595 N SD: 0.0280 c. M: 0.0499 c. 2019: 106 82 650 343 106 82 650 N SD: 0.0219 c. M:-0.0406 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 x x 5:6 S SD: 23.5575 cents 4 x x 5:6 x x 8 S SD: 37.2438 cents 5 x x 7 x x 8:10 SD: 28.1557 cents 6 x 7:8:9 x 10:12 S SD: 34.0957 cents 7 x 8:9 x 11 x 14 SD: 34.0400 cents 8 x 9:11:12 x 13:16 SD: 21.9594 cents 9 x 10:12 x 14 x 18 SD: 17.6681 cents 10 x 11:13:15 x 16:20 SD: 13.7973 cents 11 x 12:15 x 17:18:22 SD: 13.6648 cents 12 x 13:16:18 x 19:24 SD: 6.4779 cents 13 x 14:17 x 20:21:26 SD: 9.0443 cents 14 x 15:19:21:22 x 28 SD: 7.2314 cents 15 x 16:20 x 23:24:30 SD: 4.9821 cents 16 x 17:21:24:25:26:32 SD: 6.6021 cents 17 x 18:23 x 26:27:34 SD: 8.5471 cents 18 x 19:24:27:28:29:36 SD: 3.6216 cents 19 x 20:25:29 x 30:38 SD: 9.9679 cents 20:21 x 27:30:31:32:40 SD: 5.1731 cents 21:22 x 28:32:33:34:42 SD: 7.0335 cents 22:23 x 29:33:34:35:44 SD: 4.7489 cents 27:28:29:36:41:42:43:54 SD: 3.6682 cents 30:31:32:40:45:47:48:60 SD: 1.9702 cents 48:50:51:64:72:75:77:96 SD: 1.9437 cents 58:60:62:77:87:90:93:116 SD: 1.5660 cents 60:62:64:80:90:93:96:120 S SD: 1.2514 cents 78:81:83:104:117:121:125:156 SD: 1.0437 cents 90:93:96:120:135:140:144:180 S SD: 0.8849 cents 106:110:113:141:159:165:170:212 SD: 0.8702 cents 108:112:115:144:162:168:173:216 SD: 0.5163 cents 162:168:173:216:243:252:259:324 SD: 0.3439 cents 240:249:256:320:360:373:384:480 SD: 0.2470 cents 270:280:288:360:405:420:432:540 S SD: 0.0000 cents