Scala analysis: xen15-chalmers-triadic-reversed-diamond-24-19-tetrachord
Tetrachord 19/18 * 432/361 * 19/18 of triadic reversed diamond for M=24/19, 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: 24/19 404.441985 smaller undevicesimal major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 19/18 93.6030 undevicesimal semitone 1: 19/18 93.6030 undevicesimal semitone 2: 432/361 310.8390 3: 19/18 93.6030 undevicesimal semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 19/18 93.603 cents undevicesimal semitone 1: 1 432/361 310.839 cents 2: 1 361/324 187.206 cents two (undevicesimal semitone) 2: 2 24/19 404.442 cents smaller undevicesimal 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 : 93.6 404.4 498.0 93.6 : 310.8 404.4 498.0 404.4: 93.6 187.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 93.6030 .. 310.8390 cents 7776/6859, 217.2360 cents 19/18, 93.6030 cents 2: 187.2060 .. 404.4420 cents 7776/6859, 217.2360 cents 130321/139968,-123.6329 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 : 432/361, 310.8390 cents Average / Smallest step : 1.773607 Largest / Average step : 1.872355 Largest / Smallest step : 3.320822 Median interval of one step : 19/18, 93.6030 cents, amount: 2 Most common interval of one step : 19/18, 93.6030 cents, amount: 2 Least squares average step : 171.18728 cents, oct.: 513.56185 cents Scale is not proper Scale has Myhill's property chromas: 7776/6859, 217.2360 cents and 139968/130321, 123.6329 cents, ratio: 1.757104 generators: 1 of 93.60301 cents and 2 of 404.44198 cents ET pair of linear temperament : 32&266 Scale is distributional even Scale is a mode of a 282-tone equal temperament with octave 4/3 degrees: 53 229 282 generators: 53 and 229 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : SLS Scale is a Constant Structure, by a margin of 93.60301 cents Scale diversity : 1.022449 Lumma stability : 0.375882 Lumma impropriety factor : 0.248236 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 : 19/18, 93.6030 cents Most common intervals : 19/18, 93.6030 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 19 Odd number limit : 361 (O: 361 U: 361) Highest odd numerator or denominator: 19 Scale harmonicity : 0.012467 Average absolute harmonicity : 0.088052 Specific harmonicity : 0.065226 Fundamental : 1/342, -8.4179 octaves, 0.7650 Hz. Guide tone : 456, 8.8329 octaves, 119301.258 Hz. Exponens Consonantiae : 1.559520E+05, 17.25074 octaves Euler's gradus suavitatis : 47 Sum of Mann's harmonic distance : 43.5, average 14.50000 Mersenne's string divisions : 11137 Sum of van Prooijen's expressibility: 3.03463, average 1.01154 Sum of Tenney's harmonic distance : 6.27217, average 2.09072 Vogel's harmonic complexity : 25.33333 Wille's k value : 180 Wilson's harmonic complexity : 47 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 19.15346, average 3.19224 Lattice compactness (without 2's) : 11.90611, average 1.98435 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.33333 6 3: -2 .. 1 -0.66667 4 1 19: -1 .. 1 0.00000 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 11 28| Scale is JI-epimorphic with val: <7 11 30| Scale is weakly epimorphic with val: <7 11 31| = patent Scale is weakly epimorphic with val: <7 11 33| Scale is weakly epimorphic with val: <7 11 34|
FIT/MODE
3: 0 2 1 N G T3 SD: 68.3253 c. M: 93.6030 c. 4: 1 2 1 P M ME I SD: 25.2365 c. M:-30.9082 c. 5: 1 3 1 N M DE I SD: 4.9039 c. M: 6.0060 c. 11: 2 7 2 N M DE I SD: 2.4898 c. M:-3.0494 c. 16: 3 10 3 N M DE I SD: 0.1793 c. M:-0.2196 c. 85: 16 53 16 N M DE I SD: 0.1197 c. M: 0.1466 c. 101: 19 63 19 N M DE I SD: 0.0724 c. M:-0.0886 c. 117: 22 73 22 N M DE I SD: 0.0379 c. M:-0.0465 c. 133: 25 83 25 N M DE I SD: 0.0118 c. M:-0.0145 c. 149: 28 93 28 N M DE I SD: 0.0087 c. M: 0.0107 c. 282: 53 176 53 N M DE I SD: 0.0010 c. M:-0.0012 c. 995: 187 621 187 N M DE I SD: 0.0005 c. M:-0.0006 c. 1277: 240 797 240 N M DE I SD: 0.0002 c. M:-0.0002 c. 1559: 293 973 293 N M DE I SD: 0.0000 c. M: 0.0001 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: 18.1283 cents 5 x 6:7 S SD: 61.2786 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 70.4712 cents 8:9:10:11 H SD: 41.2772 cents 9:10:11:12 H SD: 35.1796 cents 10:11 x 13 SD: 41.8906 cents 11:12:14:15 S SD: 23.4219 cents 12:13:15:16 SD: 16.1620 cents 15:16:19:20 SD: 6.2512 cents 33:35:42:44 SD: 5.1533 cents 34:36:43:45 SD: 4.6712 cents 38:40:48:51 S SD: 4.1088 cents 39:41:49:52 SD: 3.8775 cents 53:56:67:71 SD: 2.8122 cents 54:57:68:72 SD: 1.7839 cents 57:60:72:76 S SD: 1.6008 cents 72:76:91:96 SD: 0.3339 cents 198:209:250:264 SD: 0.2429 cents 270:285:341:360 SD: 0.0891 cents 342:361:432:456 SD: 0.0000 cents