Scala analysis: xen15-chalmers-triadic-reversed-diamond-81-64-tetrachord
Tetrachord 256/243 * 19683/16384 * 256/243 of triadic reversed diamond for M=81/64, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 256/243 90.224996 limma, Pythagorean minor second 2: 81/64 407.820003 Pythagorean major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 256/243 90.2250 limma, Pythagorean minor second 1: 256/243 90.2250 limma, Pythagorean minor second 2: 19683/16384 317.5950 Pythagorean augmented second 3: 256/243 90.2250 limma, Pythagorean minor second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 256/243 90.225 cents limma, Pythagorean minor second 1: 1 19683/16384 317.595 cents Pythagorean augmented second 2: 1 65536/59049 180.450 cents Pythagorean diminished third 2: 2 81/64 407.820 cents Pythagorean major third 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 : 90.2 407.8 498.0 90.2 : 317.6 407.8 498.0 407.8: 90.2 180.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 317.5950 cents 4782969/4194304, 227.3700 cents 256/243, 90.2250 cents 2: 180.4500 .. 407.8200 cents 4782969/4194304, 227.3700 cents 1073741824/1162261467,-137.1450 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 19683/16384, 317.5950 cents Average / Smallest step : 1.840011 Largest / Average step : 1.913050 Largest / Smallest step : 3.520034 Median interval of one step : 256/243, 90.2250 cents, amount: 2 Most common interval of one step : 256/243, 90.2250 cents, amount: 2 Least squares average step : 171.42857 cents, oct.: 514.28571 cents Scale is not proper Scale has Myhill's property chromas: 4782969/4194304, 227.3700 cents and 1162261467/1073741824, 137.1450 cents, ratio: 1.657880 generators: 1 of 90.22500 cents and 2 of 407.82000 cents ET pair of linear temperament : 22&254 Scale is distributional even Scale is a mode of a 138-tone equal temperament with octave 4/3 degrees: 25 113 138 generators: 25 and 113 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 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 0.989125 Lumma stability : 0.362317 Lumma impropriety factor : 0.275367 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 : 256/243, 90.2250 cents Most common intervals : 256/243, 90.2250 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 : 59049 (O: 19683 U: 59049) Highest odd numerator or denominator: 243 Scale harmonicity : 0.026316 Average absolute harmonicity : 0.107053 Specific harmonicity : 0.134831 Fundamental : 1/15552, -13.9248 octaves, 0.0168 Hz. Guide tone : 20736, 14.3399 octaves, 5425067.722 Hz. Exponens Consonantiae : 3.224863E+08, 28.26466 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 325.5, average 108.50000 Mersenne's string divisions : 506485 Sum of van Prooijen's expressibility: 4.77121, average 1.59040 Sum of Tenney's harmonic distance : 9.58769, average 3.19590 Vogel's harmonic complexity : 20.33333 Wille's k value : 9841 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 9 Triangular lattice diameter : 9 Lattice compactness : 52.16955, average 8.69493 Lattice compactness (without 2's) : 28.00000, average 4.66667 Number of different primes : 2 Prime exponents' range, average, count, tones@limit: 2: -6 .. 8 1.33333 16 3: -5 .. 4 -0.66667 10 3 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is JI-epimorphic with val: <7 11| = patent
FIT/MODE
3: 0 2 1 N G T3 SD: 68.0311 c. M: 90.2250 c. 4: 1 2 1 P M ME I SD: 27.9946 c. M: 34.2863 c. 5: 1 3 1 N M DE I SD: 7.6620 c. M: 9.3840 c. 6: 1 4 1 N M DE I SD: 5.8931 c. M: 7.2175 c. 11: 2 7 2 N M DE I SD: 0.2683 c. M: 0.3286 c. 72: 13 46 13 N M DE I SD: 0.2451 c. M: 0.3002 c. 83: 15 53 15 N M DE I SD: 0.1771 c. M: 0.2169 c. 94: 17 60 17 N M DE I SD: 0.1249 c. M: 0.1530 c. 105: 19 67 19 N M DE I SD: 0.0837 c. M: 0.1026 c. 116: 21 74 21 N M DE I SD: 0.0504 c. M: 0.0617 c. 127: 23 81 23 N M DE I SD: 0.0228 c. M: 0.0279 c. 138: 25 88 25 N M DE I SD: 0.0004 c. M: 0.0005 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: 21.5063 cents 5 x 6:7 S SD: 62.5132 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 71.7809 cents 8:9:10:11 H SD: 42.4589 cents 9:10:11:12 H SD: 36.7371 cents 10:11 x 13 SD: 43.3391 cents 11:12:14:15 S SD: 24.1687 cents 12:13:15:16 SD: 17.6384 cents 14:15:18:19 S SD: 16.7861 cents 15:16:19:20 SD: 7.1845 cents 18:19:23:24 SD: 5.6286 cents 33:35:42:44 SD: 5.0485 cents 37:39:47:49 SD: 4.4575 cents 38:40:48:51 S SD: 3.9765 cents 42:44:53:56 SD: 3.6489 cents 53:56:67:71 SD: 3.2731 cents 54:57:68:72 SD: 3.1201 cents 56:59:71:75 SD: 2.7646 cents 57:60:72:76 S SD: 1.2220 cents 75:79:95:100 SD: 0.4833 cents 132:139:167:176 SD: 0.3351 cents 207:218:262:276 SD: 0.1990 cents 354:373:448:472 SD: 0.1036 cents 429:452:543:572 SD: 0.0804 cents 561:591:710:748 SD: 0.0175 cents