Scala analysis: xen12-wilson-38-4C1-tetrany-12
3-5-9-11 4C1 Tetrany, Figure 38
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 3/2 701.955001 perfect fifth 2: 5/3 884.358713 major sixth, BP sixth 3: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 3/2 701.9550 perfect fifth 2: 10/9 182.4037 minor whole tone 3: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 10/9 182.404 cents minor whole tone 1: 1 3/2 701.955 cents perfect fifth 2: 1 6/5 315.641 cents minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 18/11 852.592 cents undecimal neutral sixth 2: 1 5/3 884.359 cents major sixth, BP sixth 3: 1 4/3 498.045 cents perfect fourth 3: 1 9/5 1017.596 cents just minor seventh, BP seventh 3: 1 20/11 1034.996 cents large minor seventh 3: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 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 : 702.0 884.4 1049.4 1200.0 702.0 : 182.4 347.4 498.0 1200.0 884.4 : 165.0 315.6 1017.6 1200.0 1049.4: 150.6 852.6 1035.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 701.9550 cents 11/8, 551.3179 cents 12/11, 150.6371 cents 2: 315.6413 .. 884.3587 cents 25/18, 568.7174 cents 4/5,-386.3137 cents 3: 498.0450 .. 1049.3629 cents 11/8, 551.3179 cents 4/5,-386.3137 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 3/2, 701.9550 cents Average / Smallest step : 1.991542 Largest / Average step : 2.339850 Largest / Smallest step : 4.659909 Median interval of one step : 173.70397 cents, amount: 0 Least squares average step : 347.29204 cents, oct.: 1389.16817 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : DCBA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 133.23757 cents Scale diversity : 1.537479 Lumma stability : 0.251062 Lumma impropriety factor : 0.473931 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 : 121/120, 14.3672 cents Number of recognisable fifths : 1, average 701.9550 cents All steps are superparticular (epimoric) Steps are strictly decreasing Length of longest harmonic part : 3 at degree 1 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 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 Limited inverse transpositions with margin 536.9508 cents: 1 -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.031333 Average absolute harmonicity : 0.357197 Specific harmonicity : 0.185193 Fundamental : 1/6, -2.5850 octaves, 43.6043 Hz. Guide tone : 330, 8.3663 octaves, 86336.437 Hz. Exponens Consonantiae : 1.980000E+03, 10.95128 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 16.5, average 4.12500 Mersenne's string divisions : 2040 Sum of van Prooijen's expressibility: 2.21748, average 0.55437 Sum of Tenney's harmonic distance : 4.07482, average 1.01870 Vogel's harmonic complexity : 7.00000 Wille's k value : 5 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 18.39569, average 1.83957 Lattice compactness (without 2's) : 13.54320, average 1.35432 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 -0.25000 3 1 3: -1 .. 1 -0.25000 3 1 5: 0 .. 1 0.25000 1 1 11: 0 .. 1 0.25000 1 1 Average exponent except 2's : 1 / 4 = 0.25000 Average absolute exponent except 2's: 5 / 4 = 1.25000 Scale is weakly epimorphic with val: <4 5 8 15| Scale is weakly epimorphic with val: <4 6 9 15| Scale is weakly epimorphic with val: <4 7 8 13|
FIT/MODE
4: 2 1 0 1 N D3 SD: 90.7590 c. M: 149.3629 c. 5: 3 1 0 1 N D3 SD: 59.2304 c. M: 89.3629 c. 6: 3 1 1 1 N M DE SD: 70.6185 c. M: 101.9550 c. 7: 4 1 1 1 N M DE SD: 18.9522 c. M: 27.2159 c. 15: 9 2 2 2 N M DE SD: 10.3957 c. M:-18.0450 c. 22: 13 3 3 3 N M DE SD: 9.4233 c. M: 12.9993 c. 24: 14 4 3 3 N SD: 7.8879 c. M:-15.6413 c. 26: 15 4 4 3 N SD: 8.6111 c. M:-12.1755 c. 27: 16 4 4 3 N SD: 10.0471 c. M:-17.3037 c. 31: 18 5 4 4 N SD: 4.4739 c. M:-5.9639 c. 34: 20 5 5 4 N SD: 5.2190 c. M:-9.4606 c. 38: 22 6 5 5 N SD: 5.1185 c. M: 7.2577 c. 41: 24 6 6 5 N SD: 3.8243 c. M: 6.3099 c. 46: 27 7 6 6 N SD: 3.4316 c. M: 5.8847 c. 53: 31 8 7 7 N SD: 3.9836 c. M: 7.8535 c. 56: 33 8 8 7 N SD: 3.8991 c. M: 5.7873 c. 58: 34 9 8 7 N SD: 4.0010 c. M:-5.8095 c. 65: 38 10 9 8 N SD: 1.7369 c. M:-2.9448 c. 72: 42 11 10 9 N SD: 1.1488 c. M: 1.9550 c. 87: 51 13 12 11 N SD: 1.2219 c. M: 1.6001 c. 111: 65 17 15 14 N SD: 1.1829 c. M:-2.1278 c. 118: 69 18 16 15 N SD: 0.9808 c. M: 1.9053 c. 152: 89 23 21 19 N SD: 0.4705 c. M:-0.6766 c. 224: 131 34 31 28 N SD: 0.3935 c. M:-0.6371 c. 270: 158 41 37 34 N SD: 0.2754 c. M: 0.4741 c. 335: 196 51 46 42 N SD: 0.2388 c. M:-0.4174 c. 342: 200 52 47 43 N SD: 0.1731 c. M: 0.2401 c. 494: 289 75 68 62 N SD: 0.0831 c. M: 0.1482 c. 677: 396 103 93 85 N SD: 0.0695 c. M:-0.1317 c. 829: 485 126 114 104 N SD: 0.0782 c. M:-0.0957 c. 901: 527 137 124 113 N SD: 0.0769 c. M:-0.1376 c. 1019: 596 155 140 128 N SD: 0.0696 c. M: 0.0990 c. 1171: 685 178 161 147 N SD: 0.0084 c. M:-0.0136 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2:3 x x 4 S SD: 0.0000 cents 3 x 5 x 6 SD: 0.0000 cents 4:6 x 7:8 S SD: 26.8457 cents 5 x 8:9:10 SD: 25.8279 cents 6:9:10:11:12 S SD: 0.0000 cents