Scala analysis: xen15-chalmers-triadic-diamond-35-27-tetrachord
Upper tetrachord 36/35 * 2450/2187 * 81/70 of triadic diamond for M=35/27, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 2: 280/243 245.364616 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 81/70 252.6804 Al-Hwarizmi's lute middle finger 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 2450/2187 196.5942 3: 81/70 252.6804 Al-Hwarizmi's lute middle finger
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 2450/2187 196.594 cents 1: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 280/243 245.365 cents 2: 1 1458/1225 301.451 cents 2: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 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 : 48.8 245.4 498.0 48.8 : 196.6 449.3 498.0 245.4: 252.7 301.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 252.6804 cents 9/8, 203.9100 cents 36/35, 48.7704 cents 2: 245.3646 .. 449.2746 cents 9/8, 203.9100 cents 19600/19683,-7.3158 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 81/70, 252.6804 cents Average / Smallest step : 3.404013 Largest / Average step : 1.522033 Largest / Smallest step : 5.181021 Median interval of one step : 2450/2187, 196.5942 cents, amount: 1 Least squares average step : 145.25962 cents, oct.: 435.77885 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1634-tone equal temperament with octave 4/3 degrees: 160 805 1634 Least number of segments generator : 819 of 249.632 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 821 of 250.242 cents and inv. generated superset size: 44 = 41 more = 1466.667% 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 7.31577 cents Scale diversity : 0.742378 Lumma stability : 0.195847 Lumma impropriety factor : 0.014689 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 : 19683/19600, 7.3158 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 : 7 Odd number limit : 2187 (O: 1225 U: 2187) Highest odd numerator or denominator: 243 Scale harmonicity : 0.018169 Average absolute harmonicity : 0.095401 Specific harmonicity : 0.095362 Fundamental : 1/8505, -13.0541 octaves, 0.0308 Hz. Guide tone : 2520, 11.2992 octaves, 659296.425 Hz. Exponens Consonantiae : 2.143260E+07, 24.35330 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 300.5, average 100.16667 Mersenne's string divisions : 259931 Sum of van Prooijen's expressibility: 4.40680, average 1.46893 Sum of Tenney's harmonic distance : 9.01232, average 3.00411 Vogel's harmonic complexity : 25.33333 Wille's k value : 1417 Wilson's harmonic complexity : 45 Rectangular lattice diameter : 11 Triangular lattice diameter : 7 Lattice compactness : 26.68964, average 4.44827 Lattice compactness (without 2's) : 23.75474, average 3.95912 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -5 .. 2 -1.33333 8 1 5: -1 .. 1 0.00000 2 7: -1 .. 1 0.00000 2 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 12 / 3 = 4.00000 Scale is weakly epimorphic with val: <8 11 15 19| Scale is weakly epimorphic with val: <8 11 15 20| Scale is weakly epimorphic with val: <8 11 16 18| Scale is weakly epimorphic with val: <8 11 16 19| Scale is weakly epimorphic with val: <8 11 17 18|
FIT/MODE
3: 0 1 2 N G T3 SD: 53.7739 c. M: 79.3496 c. 4: 0 2 2 P M DE S SD: 28.2367 c. M: 48.7704 c. 6: 1 2 3 P T3 SD: 19.8793 c. M:-34.2371 c. 7: 1 2 4 N T3 SD: 22.5055 c. M: 31.9168 c. 8: 1 3 4 P T3 SD: 8.0671 c. M:-13.4852 c. 10: 1 4 5 P T3 SD: 2.1947 c. M:-3.6579 c. 39: 4 15 20 N T3 SD: 2.0639 c. M: 2.7273 c. 41: 4 16 21 N T3 SD: 1.3987 c. M: 2.4158 c. 49: 5 19 25 N T3 SD: 1.4414 c. M:-2.0505 c. 51: 5 20 26 N T3 SD: 0.7080 c. M: 1.2249 c. 61: 6 24 31 N T3 SD: 0.2754 c. M: 0.4245 c. 71: 7 28 36 N T3 SD: 0.2108 c. M:-0.3326 c. 132: 13 52 67 N T3 SD: 0.1745 c. M:-0.2795 c. 193: 19 76 98 N T3 SD: 0.1940 c. M:-0.2600 c. 195: 19 77 99 N T3 SD: 0.1723 c. M: 0.2429 c. 205: 20 81 104 N T3 SD: 0.1046 c. M: 0.1806 c. 266: 26 105 135 N T3 SD: 0.0719 c. M: 0.0893 c. 276: 27 109 140 N T3 SD: 0.0398 c. M:-0.0489 c. 337: 33 133 171 N T3 SD: 0.0213 c. M: 0.0368 c. 613: 60 242 311 N T3 SD: 0.0128 c. M: 0.0221 c. 684: 67 270 347 N T3 SD: 0.0131 c. M:-0.0172 c. 950: 93 375 482 N T3 SD: 0.0108 c. M: 0.0144 c. 1021: 100 403 518 N T3 SD: 0.0056 c. M:-0.0097 c. 1358: 133 536 689 N T3 SD: 0.0069 c. M: 0.0096 c. 1634: 160 645 829 N T3 SD: 0.0013 c. M: 0.0022 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: 54.9398 cents 6 x 7:8 S SD: 10.7531 cents 7 x 8:9 S SD: 32.2701 cents 8 x 9:11 SD: 33.7509 cents 9 x 10:12 S SD: 31.4805 cents 10 x 12:13 S SD: 41.4125 cents 11 x 13:15 SD: 29.3089 cents 13:14:15:17 SD: 28.7913 cents 14:15:16:19 SD: 26.1085 cents 15:16:17:20 SD: 23.0615 cents 17:18:20:23 SD: 22.2430 cents 18:19:21:24 SD: 16.5747 cents 19:20:22:25 SD: 15.6329 cents 20:21:23:27 SD: 13.9378 cents 21:22:24:28 S SD: 11.5974 cents 24:25:28:32 SD: 10.2319 cents 25:26:29:33 SD: 9.4452 cents 26:27:30:35 S SD: 7.8498 cents 27:28:31:36 SD: 5.1611 cents 32:33:37:43 SD: 5.1374 cents 33:34:38:44 SD: 1.0406 cents 72:74:83:96 SD: 0.5146 cents 105:108:121:140 SD: 0.0589 cents