Scala analysis: xen12-wilson-08-4C3-tetrany-11
3-7-9-15 4C3 Tetrany, Figure 8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 5/4 386.313714 major third 3: 5/3 884.358713 major sixth, BP sixth 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 15/14 119.4428 major diatonic semitone 2: 7/6 266.8709 septimal minor third 3: 4/3 498.0450 perfect fourth 4: 6/5 315.6413 minor third
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 : 119.4 386.3 884.4 1200.0 119.4 : 266.9 764.9 1080.6 1200.0 386.3 : 498.0 813.7 933.1 1200.0 884.4 : 315.6 435.1 702.0 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 : 278.17155 cents, oct.: 1112.68618 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : ABDC 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 Limited inverse transpositions with margin 378.6022 cents: 1 -- Rational properties -- Prime limit : 7 Odd number limit : 15 (O: 15 U: 15) Highest odd numerator or denominator: 15 Scale harmonicity : 0.039970 Average absolute harmonicity : 0.319619 Specific harmonicity : 0.217625 Fundamental : 1/84, -6.3923 octaves, 3.1146 Hz. Guide tone : 30, 4.9069 octaves, 7848.767 Hz. Exponens Consonantiae : 2.520000E+03, 11.29921 octaves Euler's gradus suavitatis : 18 Sum of Mann's harmonic distance : 24.5, average 6.12500 Mersenne's string divisions : 2088 Sum of van Prooijen's expressibility: 2.57403, average 0.64351 Sum of Tenney's harmonic distance : 5.10037, average 1.27509 Vogel's harmonic complexity : 13.50000 Wille's k value : 52 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 20.60797, average 2.06080 Lattice compactness (without 2's) : 12.94281, average 1.29428 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.50000 4 1 3: -1 .. 1 0.00000 2 5: 0 .. 1 0.75000 3 2 7: -1 .. 0 -0.25000 1 1 Average exponent except 2's : 2 / 4 = 0.50000 Average absolute exponent except 2's: 6 / 4 = 1.50000 Scale is weakly epimorphic with val: <4 5 10 12| Scale is JI-epimorphic with val: <4 7 10 12|
FIT/MODE
4: 0 1 2 1 N D3 SD: 74.0967 c. M: 119.4428 c. 6: 1 1 2 2 P D3 S SD: 58.7222 c. M: 84.3587 c. 7: 1 1 3 2 N SD: 36.5092 c. M:-51.9858 c. 8: 1 2 3 2 P G D3 SD: 36.1744 c. M:-63.6863 c. 9: 1 2 4 2 N D3 SD: 26.3570 c. M:-48.9746 c. 10: 1 2 4 3 N SD: 25.7896 c. M: 44.3587 c. 12: 1 3 5 3 N D3 SD: 14.2301 c. M: 19.4428 c. 18: 2 4 7 5 N SD: 13.1650 c. M: 17.6920 c. 19: 2 4 8 5 N SD: 5.0379 c. M: 7.3663 c. 31: 3 7 13 8 N SD: 3.4337 c. M:-5.9639 c. 49: 5 11 20 13 N SD: 3.4268 c. M:-5.5230 c. 50: 5 11 21 13 N SD: 2.1750 c. M:-3.6413 c. 72: 7 16 30 19 N SD: 2.1001 c. M: 2.9804 c. 80: 8 18 33 21 N SD: 1.8915 c. M:-3.6863 c. 99: 10 22 41 26 N SD: 1.2062 c. M:-1.7693 c. 121: 12 27 50 32 N SD: 0.9140 c. M: 1.7141 c. 140: 14 31 58 37 N SD: 0.8551 c. M: 1.5016 c. 152: 15 34 63 40 N SD: 0.5799 c. M: 1.0218 c. 171: 17 38 71 45 N SD: 0.2028 c. M: 0.3488 c. 441: 44 98 183 116 N SD: 0.1482 c. M:-0.2851 c. 593: 59 132 246 156 N SD: 0.1030 c. M:-0.1956 c. 612: 61 136 254 161 N SD: 0.0877 c. M:-0.1650 c. 764: 76 170 317 201 N SD: 0.0608 c. M:-0.0737 c. 935: 93 208 388 246 N SD: 0.0584 c. M: 0.0845 c. 1205: 120 268 500 317 N SD: 0.0530 c. M:-0.0763 c. 1376: 137 306 571 362 N SD: 0.0349 c. M: 0.0564 c. 1547: 154 344 642 407 N SD: 0.0351 c. M: 0.0665 c. 1578: 157 351 655 415 N SD: 0.0365 c. M:-0.0519 c. 1848: 184 411 767 486 N SD: 0.0423 c. M:-0.0569 c. 2019: 201 449 838 531 N SD: 0.0241 c. M:-0.0395 c. 2190: 218 487 909 576 N SD: 0.0146 c. M:-0.0248 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x x 3:4 S SD: 91.2019 cents 3 x 4:5:6 S SD: 37.2438 cents 4 x 5:7:8 SD: 28.1557 cents 5 x 6:8:10 S SD: 33.3153 cents 6 x 8:10:12 S SD: 37.2438 cents 7:8:9:12:14 S SD: 32.8262 cents 8:9:10:13:16 SD: 23.7906 cents 9:10:11:15:18 SD: 18.5029 cents 11:12:14:18:22 SD: 13.5906 cents 12:13:15:20:24 SD: 4.7825 cents 27:29:34:45:54 SD: 3.3678 cents 28:30:35:47:56 SD: 3.0805 cents 40:43:50:67:80 SD: 2.5950 cents 44:47:55:73:88 SD: 2.3693 cents 55:59:69:92:110 SD: 2.2827 cents 56:60:70:93:112 SD: 1.5485 cents 68:73:85:113:136 SD: 1.5310 cents 69:74:86:115:138 SD: 1.3240 cents 72:77:90:120:144 SD: 0.8022 cents 84:90:105:140:168 S SD: 0.0000 cents