Scala analysis: xen15-chalmers-triadic-diamond-32-25-tetrachord
Upper tetrachord 25/24 * 2048/1875 * 75/64 of triadic diamond for M=32/25, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 256/225 223.462571 Neapolitan diminished third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 75/64 274.5824 classic augmented second 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 2048/1875 152.7901 double diminished third 3: 75/64 274.5824 classic augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 2048/1875 152.790 cents double diminished third 1: 1 75/64 274.582 cents classic augmented second 2: 1 256/225 223.463 cents Neapolitan diminished third 2: 1 625/512 345.255 cents classic neutral third 2: 1 32/25 427.373 cents classic diminished fourth 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 : 70.7 223.5 498.0 70.7 : 152.8 427.4 498.0 223.5: 274.6 345.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 274.5824 cents 9/8, 203.9100 cents 25/24, 70.6724 cents 2: 223.4626 .. 427.3726 cents 9/8, 203.9100 cents 16384/16875,-51.1199 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 75/64, 274.5824 cents Average / Smallest step : 2.349077 Largest / Average step : 1.653962 Largest / Smallest step : 3.885284 Median interval of one step : 2048/1875, 152.7901 cents, amount: 1 Least squares average step : 143.69518 cents, oct.: 431.08555 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1656-tone equal temperament with octave 4/3 degrees: 235 743 1656 Least number of segments generator : 829 of 249.323 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 991 of 298.045 cents and inv. generated superset size: 69 = 66 more = 2300.000% 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 51.11986 cents Scale diversity : 1.032569 Lumma stability : 0.283799 Lumma impropriety factor : 0.102641 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 : 16875/16384, 51.1199 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle 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 : 5 Odd number limit : 1875 (O: 625 U: 1875) Highest odd numerator or denominator: 225 Scale harmonicity : 0.023847 Average absolute harmonicity : 0.102234 Specific harmonicity : 0.125195 Fundamental : 1/1800, -10.8138 octaves, 0.1453 Hz. Guide tone : 6400, 12.6439 octaves, 1674403.618 Hz. Exponens Consonantiae : 1.152000E+07, 23.45764 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 268.5, average 89.50000 Mersenne's string divisions : 23569 Sum of van Prooijen's expressibility: 4.22724, average 1.40908 Sum of Tenney's harmonic distance : 8.61775, average 2.87258 Vogel's harmonic complexity : 17.33333 Wille's k value : 937 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 37.99864, average 6.33311 Lattice compactness (without 2's) : 14.42367, average 2.40394 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 8 2.33333 13 3: -2 ..-1 -1.33333 4 1 5: -2 .. 2 0.00000 4 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 17| Scale is weakly epimorphic with val: <8 11 19|
FIT/MODE
3: 0 1 2 N G T3 SD: 52.5827 c. M: 70.6724 c. 4: 1 1 2 P M ME S SD: 34.4090 c. M:-53.8388 c. 5: 1 1 3 N M DE S SD: 21.7954 c. M:-28.9366 c. 6: 1 2 3 P T3 SD: 16.3856 c. M:-25.5599 c. 7: 1 2 4 N T3 SD: 5.7885 c. M: 10.0147 c. 13: 2 4 7 N T3 SD: 5.0470 c. M:-6.4044 c. 20: 3 6 11 N T3 SD: 2.3600 c. M:-4.0343 c. 22: 3 7 12 N T3 SD: 2.3193 c. M:-2.9215 c. 27: 4 8 15 N T3 SD: 2.1705 c. M:-3.1120 c. 29: 4 9 16 N T3 SD: 1.1471 c. M: 1.9766 c. 42: 6 13 23 N T3 SD: 1.0994 c. M:-1.8435 c. 49: 7 15 27 N T3 SD: 0.2885 c. M:-0.4769 c. 78: 11 24 43 N T3 SD: 0.2516 c. M: 0.4353 c. 127: 18 39 70 N T3 SD: 0.0626 c. M: 0.0834 c. 176: 25 54 97 N T3 SD: 0.0675 c. M:-0.0917 c. 303: 43 93 167 N T3 SD: 0.0477 c. M:-0.0824 c. 430: 61 132 237 N T3 SD: 0.0467 c. M:-0.0786 c. 437: 62 134 241 N T3 SD: 0.0485 c. M: 0.0831 c. 479: 68 147 264 N T3 SD: 0.0527 c. M:-0.0858 c. 486: 69 149 268 N T3 SD: 0.0407 c. M: 0.0597 c. 564: 80 173 311 N T3 SD: 0.0324 c. M: 0.0488 c. 613: 87 188 338 N T3 SD: 0.0203 c. M: 0.0329 c. 740: 105 227 408 N T3 SD: 0.0091 c. M: 0.0154 c. 867: 123 266 478 N T3 SD: 0.0091 c. M: 0.0155 c. 916: 130 281 505 N T3 SD: 0.0069 c. M:-0.0108 c. 1607: 228 493 886 N T3 SD: 0.0077 c. M: 0.0102 c. 1656: 235 508 913 N T3 SD: 0.0034 c. M:-0.0042 c. 1783: 253 547 983 N T3 SD: 0.0014 c. M: 0.0020 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: 62.5132 cents 6 x 7:8 S SD: 21.7042 cents 7 x 8:9 S SD: 31.7157 cents 8 x 9:11 SD: 28.3739 cents 9 x 10:12 S SD: 20.5294 cents 10 x 11:13 SD: 36.5327 cents 11 x 13:15 SD: 38.1980 cents 12:13:14:16 S SD: 26.8633 cents 13:14:15:17 SD: 23.6650 cents 14:15:16:19 SD: 19.3705 cents 15:16:17:20 SD: 13.8714 cents 20:21:23:27 SD: 10.5145 cents 21:22:24:28 S SD: 4.1737 cents 44:46:50:59 SD: 3.9488 cents 45:47:51:60 SD: 2.7319 cents 51:53:58:68 SD: 1.3851 cents 72:75:82:96 SD: 0.5633 cents 168:175:191:224 SD: 0.4430 cents 189:197:215:252 SD: 0.3817 cents 240:250:273:320 SD: 0.1409 cents 312:325:355:416 SD: 0.0217 cents