Scala analysis: xen15-chalmers-triadic-diamond-19-16-tetrachord
Upper tetrachord 19/18 * 384/361 * 19/16 of triadic diamond for M=19/16, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 19/18 93.603014 undevicesimal semitone 2: 64/57 200.531983 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 19/16 297.5130 19th harmonic 1: 19/18 93.6030 undevicesimal semitone 2: 384/361 106.9290 3: 19/16 297.5130 19th harmonic
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 19/18 93.603 cents undevicesimal semitone 1: 1 384/361 106.929 cents 1: 1 19/16 297.513 cents 19th harmonic 2: 1 64/57 200.532 cents 2: 1 361/288 391.116 cents 2: 1 24/19 404.442 cents smaller undevicesimal 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 : 93.6 200.5 498.0 93.6 : 106.9 404.4 498.0 200.5: 297.5 391.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 93.6030 .. 297.5130 cents 9/8, 203.9100 cents 19/18, 93.6030 cents 2: 200.5320 .. 404.4420 cents 9/8, 203.9100 cents 1024/1083,-96.9810 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 19/18, 93.6030 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 19/16, 297.5130 cents Average / Smallest step : 1.773607 Largest / Average step : 1.792085 Largest / Smallest step : 3.178456 Median interval of one step : 384/361, 106.9290 cents, amount: 1 Least squares average step : 142.05728 cents, oct.: 426.17185 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2208-tone equal temperament with octave 4/3 degrees: 415 889 2208 Least number of segments generator : 1105 of 249.248 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 2045 of 461.278 cents and inv. generated superset size: 31 = 28 more = 1033.333% 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 93.60301 cents Scale diversity : 1.087025 Lumma stability : 0.375882 Lumma impropriety factor : 0.194723 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 : 6912/6859, 13.3260 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% Limited inverse transpositions with margin 190.5840 cents: 2 -- Rational properties -- Prime limit : 19 Odd number limit : 361 (O: 361 U: 361) Highest odd numerator or denominator: 57 Scale harmonicity : 0.012416 Average absolute harmonicity : 0.087464 Specific harmonicity : 0.065672 Fundamental : 1/342, -8.4179 octaves, 0.7650 Hz. Guide tone : 1216, 10.2479 octaves, 318136.687 Hz. Exponens Consonantiae : 4.158720E+05, 18.66578 octaves Euler's gradus suavitatis : 48 Sum of Mann's harmonic distance : 82.5, average 27.50000 Mersenne's string divisions : 31339 Sum of van Prooijen's expressibility: 3.51175, average 1.17058 Sum of Tenney's harmonic distance : 7.17526, average 2.39175 Vogel's harmonic complexity : 24.33333 Wille's k value : 180 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 25.63817, average 4.27303 Lattice compactness (without 2's) : 9.30056, average 1.55009 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 6 2.33333 9 3: -2 ..-1 -1.33333 4 1 19: -1 .. 1 0.00000 2 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 10 29| Scale is weakly epimorphic with val: <7 10 30| Scale is weakly epimorphic with val: <8 11 33| Scale is weakly epimorphic with val: <8 11 34|
FIT/MODE
3: 0 1 2 N G T3 SD: 57.5990 c. M: 93.6030 c. 4: 1 1 2 P M ME S SD: 33.1996 c. M:-48.4905 c. 5: 1 1 3 N M DE S SD: 3.5496 c. M:-6.0060 c. 17: 3 4 10 N T3 SD: 4.2149 c. M: 5.7127 c. 22: 4 5 13 N T3 SD: 2.5578 c. M:-3.2137 c. 27: 5 6 16 N T3 SD: 1.5838 c. M:-2.3752 c. 32: 6 7 19 N T3 SD: 1.0462 c. M:-1.7988 c. 37: 7 8 22 N T3 SD: 0.8729 c. M:-1.3782 c. 42: 8 9 25 N T3 SD: 0.9510 c. M:-1.2627 c. 69: 13 15 41 N T3 SD: 0.9181 c. M:-1.5732 c. 75: 14 16 45 N T3 SD: 0.8425 c. M: 1.3140 c. 79: 15 17 47 N T3 SD: 0.8916 c. M:-1.2078 c. 80: 15 17 48 N T3 SD: 0.7691 c. M: 1.3140 c. 85: 16 18 51 N T3 SD: 0.7633 c. M: 1.3140 c. 97: 18 21 58 N T3 SD: 0.7024 c. M: 1.1823 c. 102: 19 22 61 N T3 SD: 0.5172 c. M: 0.8299 c. 107: 20 23 64 N T3 SD: 0.3685 c. M: 0.5105 c. 112: 21 24 67 N T3 SD: 0.2760 c. M: 0.4246 c. 117: 22 25 70 N T3 SD: 0.2684 c. M: 0.4626 c. 139: 26 30 83 N T3 SD: 0.2652 c. M: 0.4435 c. 144: 27 31 86 N T3 SD: 0.1330 c. M: 0.2196 c. 149: 28 32 89 N T3 SD: 0.0147 c. M:-0.0231 c. 899: 169 193 537 N T3 SD: 0.0160 c. M:-0.0228 c. 1048: 197 225 626 N T3 SD: 0.0142 c. M:-0.0180 c. 1197: 225 257 715 N T3 SD: 0.0131 c. M:-0.0175 c. 1309: 246 281 782 N T3 SD: 0.0122 c. M: 0.0204 c. 1346: 253 289 804 N T3 SD: 0.0124 c. M:-0.0181 c. 1458: 274 313 871 N T3 SD: 0.0098 c. M: 0.0159 c. 1607: 302 345 960 N T3 SD: 0.0080 c. M: 0.0123 c. 1756: 330 377 1049 N T3 SD: 0.0067 c. M: 0.0093 c. 1905: 358 409 1138 N T3 SD: 0.0057 c. M: 0.0072 c. 2054: 386 441 1227 N T3 SD: 0.0050 c. M: 0.0074 c. 2203: 414 473 1316 N T3 SD: 0.0047 c. M: 0.0076 c. 2208: 415 474 1319 N T3 SD: 0.0048 c. M:-0.0060 c. 2352: 442 505 1405 N T3 SD: 0.0046 c. M: 0.0078 c. 2357: 443 506 1408 N T3 SD: 0.0036 c. M:-0.0049 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: 71.3878 cents 6 x 7:8 S SD: 33.1695 cents 7 x 8:9 S SD: 35.0108 cents 8 x 9:11 SD: 26.6900 cents 9 x 10:12 S SD: 9.0641 cents 10 x 11:13 SD: 28.2107 cents 11 x 12:15 S SD: 31.6353 cents 12:13 x 16 SD: 22.4848 cents 14:15:16:19 SD: 16.8179 cents 15:16:17:20 SD: 8.0940 cents 18:19:20:24 S SD: 6.0428 cents 32:34:36:43 SD: 5.9796 cents 33:35:37:44 SD: 2.8741 cents 57:60:64:76 SD: 1.6008 cents 72:76:81:96 SD: 1.1260 cents 90:95:101:120 SD: 0.3006 cents 252:266:283:336 SD: 0.1073 cents 342:361:384:456 SD: 0.0000 cents