Scala analysis: xen15-chalmers-triadic-reversed-diamond-8192-6561-tetrachord
Tetrachord 2187/2048 * 16777216/14348907 * 2187/2048 of triadic reversed diamond for M=8192/6561, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 2187/2048 113.685006 apotome 2: 8192/6561 384.359993 Pythagorean diminished fourth 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 2187/2048 113.6850 apotome 1: 2187/2048 113.6850 apotome 2: 16777216/14348907 270.6750 Pythagorean double diminished fourth 3: 2187/2048 113.6850 apotome
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 2187/2048 113.685 cents apotome 1: 1 16777216/14348907 270.675 cents Pythagorean double diminished fourth 2: 1 4782969/4194304 227.370 cents Pythagorean double augmented prime 2: 2 8192/6561 384.360 cents Pythagorean diminished fourth Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 113.7 384.4 498.0 113.7: 270.7 384.4 498.0 384.4: 113.7 227.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 113.6850 .. 270.6750 cents 156.98998 cents 2187/2048, 113.6850 cents 2: 227.3700 .. 384.3600 cents 156.98998 cents -43.30497 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 2187/2048, 113.6850 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 16777216/14348907, 270.6750 cents Average / Smallest step : 1.460307 Largest / Average step : 1.630425 Largest / Smallest step : 2.380921 Median interval of one step : 2187/2048, 113.6850 cents, amount: 2 Most common interval of one step : 2187/2048, 113.6850 cents, amount: 2 Least squares average step : 169.75286 cents, oct.: 509.25857 cents Scale is not proper Scale has Myhill's property chromas: 156.98998 cents and 43.30497 cents, ratio: 3.625218 generators: 1 of 113.68501 cents and 2 of 384.35999 cents ET pair of linear temperament : 26&44 Scale is distributional even Scale is a mode of a 92-tone equal temperament with octave 4/3 degrees: 21 71 92 generators: 21 and 71 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : SLS Interval vector is [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ] Scale is a Constant Structure, by a margin of 43.30497 cents Scale diversity : 1.123295 Lumma stability : 0.456525 Lumma impropriety factor : 0.086950 Rothenberg efficiency : 0.888889 redundancy: 0.111111 Efficiency x scale size : 2.666667 Number of different interval sizes : 4 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 43.30497 cents Most common intervals : 2187/2048, 113.6850 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 3 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 3 Odd number limit : 14348907 (O: 4782969 U: 14348907) Highest odd numerator or denominator: 6561 Scale harmonicity : 0.015625 Average absolute harmonicity : 0.092373 Specific harmonicity : 0.081355 Fundamental : 1/13436928, -23.6797 octaves, 0.0000 Hz. Guide tone : 17915904, 24.0947 octaves, 4687258511.878 Hz. Exponens Consonantiae : 2.407347E+14, 47.77444 octaves Euler's gradus suavitatis : 55 Sum of Mann's harmonic distance : 9497.5, average 3165.83333 Mersenne's string divisions : 62478955 Sum of van Prooijen's expressibility: 7.63394, average 2.54465 Sum of Tenney's harmonic distance : 15.46072, average 5.15357 Vogel's harmonic complexity : 34.33333 Wille's k value : 7174453 Wilson's harmonic complexity : 45 Rectangular lattice diameter : 15 Triangular lattice diameter : 15 Lattice compactness : 87.14350, average 14.52392 Lattice compactness (without 2's) : 46.00000, average 7.66667 Number of different primes : 2 Prime exponents' range, average, count, tones@limit: 2: -11 .. 13 1.33333 26 3: -8 .. 7 -0.66667 16 3 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 16 / 3 = 5.33333
FIT/MODE
3: 1 1 1 SP B ME I SD: 42.7273 c. M: 52.3300 c. 4: 1 2 1 P M ME I SD: 8.8396 c. M: 10.8262 c. 9: 2 5 2 N M DE I SD: 2.4563 c. M: 3.0083 c. 13: 3 7 3 N M DE I SD: 1.0194 c. M: 1.2485 c. 22: 5 12 5 N M DE I SD: 0.4025 c. M: 0.4930 c. 35: 8 19 8 N M DE I SD: 0.1256 c. M: 0.1539 c. 57: 13 31 13 N M DE I SD: 0.0782 c. M: 0.0958 c. 92: 21 50 21 N M DE I SD: 0.0007 c. M: 0.0008 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x 5 x S SD: 1.9537 cents 5 x 6:7 S SD: 54.4449 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 63.9856 cents 8:9:10:11 H SD: 34.9323 cents 9:10:11:12 H SD: 26.0079 cents 11:12:14:15 S SD: 21.0235 cents 12:13:15:16 SD: 8.3214 cents 15:16:19:20 SD: 8.3203 cents 27:29:34:36 SD: 5.9398 cents 28:30:35:37 SD: 5.5583 cents 32:34:40:43 SD: 5.3907 cents 33:35:41:44 SD: 4.8663 cents 43:46:54:57 SD: 4.8429 cents 44:47:55:59 SD: 3.3380 cents 45:48:56:60 S SD: 2.0267 cents 57:61:71:76 SD: 1.8558 cents 60:64:75:80 SD: 0.9210 cents 105:112:131:140 SD: 0.7910 cents 117:125:146:156 SD: 0.4329 cents 177:189:221:236 SD: 0.0403 cents