Scala analysis: xen15-chalmers-triadic-diamond-14-11-tetrachord
Upper tetrachord 22/21 * 392/363 * 33/28 of triadic diamond for M=14/11, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 22/21 80.537035 undecimal minor semitone 2: 112/99 213.597962 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 33/28 284.4470 undecimal minor third 1: 22/21 80.5370 undecimal minor semitone 2: 392/363 133.0609 3: 33/28 284.4470 undecimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 392/363 133.061 cents 1: 1 33/28 284.447 cents undecimal minor third 2: 1 112/99 213.598 cents 2: 1 121/98 364.984 cents 2: 1 14/11 417.508 cents undecimal diminished fourth or major third Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 80.5 213.6 498.0 80.5 : 133.1 417.5 498.0 213.6: 284.4 365.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 284.4470 cents 9/8, 203.9100 cents 22/21, 80.5370 cents 2: 213.5980 .. 417.5080 cents 9/8, 203.9100 cents 3136/3267,-70.8491 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 33/28, 284.4470 cents Average / Smallest step : 2.061350 Largest / Average step : 1.713382 Largest / Smallest step : 3.531879 Median interval of one step : 392/363, 133.0609 cents, amount: 1 Least squares average step : 142.99057 cents, oct.: 428.97171 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1849-tone equal temperament with octave 4/3 degrees: 299 793 1849 Least number of segments generator : 925 of 249.157 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1636 of 440.672 cents and inv. generated superset size: 43 = 40 more = 1433.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 70.84907 cents Scale diversity : 1.095683 Lumma stability : 0.323413 Lumma impropriety factor : 0.142254 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 1372/1331, 52.5239 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 11 Odd number limit : 363 (O: 121 U: 363) Highest odd numerator or denominator: 99 Scale harmonicity : 0.015090 Average absolute harmonicity : 0.090619 Specific harmonicity : 0.080078 Fundamental : 1/693, -9.4367 octaves, 0.3775 Hz. Guide tone : 1232, 10.2668 octaves, 322322.696 Hz. Exponens Consonantiae : 8.537760E+05, 19.70350 octaves Euler's gradus suavitatis : 41 Sum of Mann's harmonic distance : 130.5, average 43.50000 Mersenne's string divisions : 63511 Sum of van Prooijen's expressibility: 3.79498, average 1.26499 Sum of Tenney's harmonic distance : 7.78868, average 2.59623 Vogel's harmonic complexity : 22.33333 Wille's k value : 181 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 17.54693, average 2.92449 Lattice compactness (without 2's) : 11.32780, average 1.88797 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 4 2.33333 7 3: -2 ..-1 -1.33333 4 1 7: -1 .. 1 0.00000 2 11: -1 .. 1 0.00000 2 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 10 18 23| Scale is weakly epimorphic with val: <7 10 18 24| Scale is weakly epimorphic with val: <7 10 19 24| Scale is weakly epimorphic with val: <7 10 19 25| Scale is weakly epimorphic with val: <7 10 20 25| Scale is weakly epimorphic with val: <7 10 20 26| Scale is weakly epimorphic with val: <7 10 21 26| Scale is weakly epimorphic with val: <7 10 21 27| Scale is weakly epimorphic with val: <7 10 22 27| Scale is weakly epimorphic with val: <8 11 18 24| Scale is weakly epimorphic with val: <8 11 18 25| Scale is weakly epimorphic with val: <8 11 19 25| Scale is weakly epimorphic with val: <8 11 19 26| Scale is weakly epimorphic with val: <8 11 20 26| Scale is weakly epimorphic with val: <8 11 20 27| Scale is weakly epimorphic with val: <8 11 21 27|
FIT/MODE
3: 0 1 2 N G T3 SD: 54.0073 c. M: 80.5370 c. 4: 1 1 2 P M ME S SD: 32.6018 c. M:-43.9742 c. 5: 1 1 3 N M DE S SD: 13.7904 c. M:-19.0720 c. 7: 1 2 4 N T3 SD: 5.4207 c. M: 9.3877 c. 12: 2 3 7 N T3 SD: 3.7886 c. M: 6.0792 c. 19: 3 5 11 N T3 SD: 2.5015 c. M: 3.8948 c. 30: 5 8 17 N T3 SD: 1.9182 c. M:-2.4705 c. 37: 6 10 21 N T3 SD: 1.0319 c. M:-1.7728 c. 44: 7 12 25 N T3 SD: 1.1326 c. M:-1.4669 c. 49: 8 13 28 N T3 SD: 0.4566 c. M:-0.7764 c. 56: 9 15 32 N T3 SD: 0.2981 c. M: 0.4941 c. 105: 17 28 60 N T3 SD: 0.1038 c. M: 0.1501 c. 161: 26 43 92 N T3 SD: 0.1066 c. M: 0.1501 c. 247: 40 66 141 N T3 SD: 0.1048 c. M:-0.1379 c. 266: 43 71 152 N T3 SD: 0.0880 c. M: 0.1501 c. 303: 49 81 173 N T3 SD: 0.0490 c. M:-0.0847 c. 359: 58 96 205 N T3 SD: 0.0504 c. M: 0.0729 c. 408: 66 109 233 N T3 SD: 0.0219 c. M:-0.0291 c. 464: 75 124 265 N T3 SD: 0.0198 c. M: 0.0341 c. 569: 92 152 325 N T3 SD: 0.0155 c. M: 0.0251 c. 872: 141 233 498 N T3 SD: 0.0080 c. M:-0.0131 c. 977: 158 261 558 N T3 SD: 0.0046 c. M:-0.0066 c. 1441: 233 385 823 N T3 SD: 0.0039 c. M: 0.0065 c. 1849: 299 494 1056 N T3 SD: 0.0023 c. M:-0.0038 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 x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 66.2336 cents 6 x 7:8 S SD: 26.6365 cents 7 x 8:9 S SD: 32.6841 cents 8 x 9:11 SD: 27.0733 cents 9 x 10:12 S SD: 15.5971 cents 10 x 11:13 SD: 32.7205 cents 11 x 12:15 S SD: 37.0059 cents 12:13:14:16 S SD: 26.2597 cents 13:14:15:17 SD: 22.5512 cents 14:15:16:19 SD: 17.5167 cents 15:16:17:20 SD: 10.4489 cents 21:22:24:28 S SD: 5.8587 cents 24:25:27:32 SD: 4.6088 cents 39:41:44:52 SD: 2.5647 cents 45:47:51:60 SD: 2.0316 cents 60:63:68:80 SD: 1.6662 cents 84:88:95:112 SD: 0.1840 cents 357:374:404:476 SD: 0.1732 cents 441:462:499:588 SD: 0.1051 cents 525:550:594:700 SD: 0.0589 cents