Scala analysis: xen12-wilson-08-4C1-tetrany-11
3-7-9-15 4C1 Tetrany, Figure 8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 2: 5/4 386.313714 major third 3: 3/2 701.955001 perfect fifth 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 4/3 498.0450 perfect fourth 1: 7/6 266.8709 septimal minor third 2: 15/14 119.4428 major diatonic semitone 3: 6/5 315.6413 minor third 4: 4/3 498.0450 perfect fourth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 7/6 266.871 cents septimal minor third 1: 1 6/5 315.641 cents minor third 1: 1 4/3 498.045 cents perfect fourth 2: 1 5/4 386.314 cents major third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 14/9 764.916 cents septimal minor sixth 2: 1 8/5 813.686 cents minor sixth 3: 1 3/2 701.955 cents perfect fifth 3: 1 5/3 884.359 cents major sixth, BP sixth 3: 1 12/7 933.129 cents septimal major sixth 3: 1 28/15 1080.557 cents grave major seventh 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 0.0 : 266.9 386.3 702.0 1200.0 266.9 : 119.4 435.1 933.1 1200.0 386.3 : 315.6 813.7 1080.6 1200.0 702.0 : 498.0 764.9 884.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 119.4428 .. 498.0450 cents 56/45, 378.6022 cents 15/14, 119.4428 cents 2: 386.3137 .. 813.6863 cents 32/25, 427.3726 cents 15/16,-111.7313 cents 3: 701.9550 .. 1080.5572 cents 56/45, 378.6022 cents 15/16,-111.7313 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 15/14, 119.4428 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 4/3, 498.0450 cents Average / Smallest step : 2.511662 Largest / Average step : 1.660150 Largest / Smallest step : 4.169736 Median interval of one step : 291.25610 cents, amount: 0 Least squares average step : 264.84544 cents, oct.: 1059.38178 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : BACD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 62.96090 cents Scale diversity : 1.676079 Lumma stability : 0.199071 Lumma impropriety factor : 0.186219 Rothenberg efficiency : 0.500000 redundancy: 0.500000 Efficiency x scale size : 2.000000 Number of different interval sizes : 12 = 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 : 36/35, 48.7704 cents Number of recognisable fifths : 1, 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 = 25.0000% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Limited inverse transpositions with margin 378.6022 cents: 3 -- Rational properties -- Prime limit : 7 Odd number limit : 15 (O: 15 U: 15) Highest odd numerator or denominator: 7 Scale harmonicity : 0.039970 Average absolute harmonicity : 0.365861 Specific harmonicity : 0.244915 Fundamental : 1/12, -3.5850 octaves, 21.8021 Hz. Guide tone : 210, 7.7142 octaves, 54941.369 Hz. Exponens Consonantiae : 2.520000E+03, 11.29921 octaves Euler's gradus suavitatis : 18 Sum of Mann's harmonic distance : 15.0, average 3.75000 Mersenne's string divisions : 585 Sum of van Prooijen's expressibility: 2.02119, average 0.50530 Sum of Tenney's harmonic distance : 4.00346, average 1.00087 Vogel's harmonic complexity : 7.25000 Wille's k value : 7 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 20.19829, average 2.01983 Lattice compactness (without 2's) : 12.21076, average 1.22108 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.75000 5 1 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.25000 1 1 7: 0 .. 1 0.25000 1 1 Average exponent except 2's : 2 / 4 = 0.50000 Average absolute exponent except 2's: 4 / 4 = 1.00000 Scale is weakly epimorphic with val: <4 5 10 12| Scale is JI-epimorphic with val: <4 7 10 12|
FIT/MODE
4: 1 0 1 2 N D3 SD: 68.8157 c. M: 101.9550 c. 5: 1 1 1 2 P M ME SD: 49.5600 c. M:-93.6863 c. 7: 1 1 2 3 N SD: 53.0600 c. M: 95.4423 c. 8: 2 1 2 3 P G D3 SD: 43.1909 c. M:-63.6863 c. 9: 2 1 2 4 N D3 SD: 18.9250 c. M: 35.2883 c. 10: 2 1 3 4 N SD: 20.8571 c. M: 26.8709 c. 12: 3 1 3 5 N D3 SD: 17.9490 c. M:-33.1291 c. 15: 3 2 4 6 N SD: 17.5712 c. M: 26.8709 c. 18: 4 2 5 7 N SD: 17.1169 c. M:-31.3783 c. 19: 4 2 5 8 N SD: 8.7910 c. M: 14.2393 c. 22: 5 2 6 9 N SD: 5.1339 c. M:-7.1359 c. 31: 7 3 8 13 N SD: 3.3256 c. M: 5.1808 c. 41: 9 4 11 17 N SD: 3.3956 c. M: 5.8259 c. 50: 11 5 13 21 N SD: 3.5020 c. M: 5.9550 c. 53: 12 5 14 22 N SD: 2.5144 c. M:-4.8272 c. 68: 15 7 18 28 N SD: 2.4395 c. M:-3.9274 c. 72: 16 7 19 30 N SD: 1.7851 c. M: 2.9804 c. 94: 21 9 25 39 N SD: 1.7767 c. M: 3.3350 c. 99: 22 10 26 41 N SD: 0.9549 c. M:-1.5651 c. 130: 29 13 34 54 N SD: 0.8290 c. M:-1.3786 c. 140: 31 14 37 58 N SD: 0.7923 c. M: 1.1566 c. 149: 33 15 39 62 N SD: 0.8552 c. M: 1.2839 c. 152: 34 15 40 63 N SD: 0.8860 c. M:-1.5501 c. 171: 38 17 45 71 N SD: 0.2256 c. M: 0.3488 c. 441: 98 44 116 183 N SD: 0.1179 c. M: 0.2042 c. 612: 136 61 161 254 N SD: 0.1040 c. M: 0.2042 c. 665: 148 66 175 276 N SD: 0.1232 c. M:-0.1968 c. 742: 165 74 195 308 N SD: 0.1107 c. M:-0.2092 c. 764: 170 76 201 317 N SD: 0.1070 c. M:-0.1448 c. 913: 203 91 240 379 N SD: 0.0758 c. M:-0.1047 c. 935: 208 93 246 388 N SD: 0.0559 c. M:-0.0810 c. 1106: 246 110 291 459 N SD: 0.0380 c. M: 0.0569 c. 1376: 306 137 362 571 N SD: 0.0420 c. M:-0.0799 c. 1547: 344 154 407 642 N SD: 0.0305 c. M:-0.0489 c. 1848: 411 184 486 767 N SD: 0.0259 c. M:-0.0499 c. 2019: 449 201 531 838 N SD: 0.0145 c. M: 0.0234 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x x 3:4 S SD: 0.0000 cents 3 x 4:5:6 S SD: 71.3014 cents 4 x 5:6:8 S SD: 0.0000 cents 5:6 x 8:10 S SD: 40.6372 cents 6:7:8:9:12 S SD: 27.9328 cents 7:8:9:11:14 SD: 25.1732 cents 8:9:10:12:16 S SD: 15.7402 cents 9 x 11:14:18 SD: 24.6706 cents 10:12:13:15:20 SD: 20.9000 cents 11:13:14:17:22 SD: 16.0919 cents 12:14:15:18:24 S SD: 0.0000 cents