Scala analysis: xen15-chalmers-triadic-diamond-56-45-tetrachord
Upper tetrachord 15/14 * 6272/6075 * 135/112 of triadic diamond for M=56/45, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 448/405 174.692189 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 135/112 323.3528 septimal wide minor third 1: 15/14 119.4428 major diatonic semitone 2: 6272/6075 55.2494 3: 135/112 323.3528 septimal wide minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 6272/6075 55.249 cents 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 135/112 323.353 cents septimal wide minor third 2: 1 448/405 174.692 cents 2: 1 56/45 378.602 cents septimal narrow major third 2: 1 2025/1568 442.796 cents 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 : 119.4 174.7 498.0 119.4: 55.2 378.6 498.0 174.7: 323.4 442.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 55.2494 .. 323.3528 cents 820125/702464, 268.1034 cents 6272/6075, 55.2494 cents 2: 174.6922 .. 442.7956 cents 820125/702464, 268.1034 cents 50176/54675,-148.6606 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 6272/6075, 55.2494 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 135/112, 323.3528 cents Average / Smallest step : 3.004830 Largest / Average step : 1.947732 Largest / Smallest step : 5.852605 Median interval of one step : 15/14, 119.4428 cents, amount: 1 Least squares average step : 140.21158 cents, oct.: 420.63475 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1893-tone equal temperament with octave 4/3 degrees: 454 664 1893 Least number of segments generator : 947 of 249.154 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1297 of 341.238 cents and inv. generated superset size: 38 = 35 more = 1266.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 55.24938 cents Scale diversity : 0.871336 Lumma stability : 0.221865 Lumma impropriety factor : 0.298488 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 : 6272/6075, 55.2494 cents 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 : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 7 Odd number limit : 6075 (O: 2025 U: 6075) Highest odd numerator or denominator: 405 Scale harmonicity : 0.018620 Average absolute harmonicity : 0.097801 Specific harmonicity : 0.096512 Fundamental : 1/5670, -12.4691 octaves, 0.0461 Hz. Guide tone : 6720, 12.7142 octaves, 1758123.799 Hz. Exponens Consonantiae : 3.810240E+07, 25.18338 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 444.5, average 148.16667 Mersenne's string divisions : 173159 Sum of van Prooijen's expressibility: 4.26067, average 1.42022 Sum of Tenney's harmonic distance : 8.66013, average 2.88671 Vogel's harmonic complexity : 23.33333 Wille's k value : 3037 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 9 Triangular lattice diameter : 7 Lattice compactness : 29.70906, average 4.95151 Lattice compactness (without 2's) : 18.48537, average 3.08089 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 6 2.33333 9 3: -4 .. 1 -1.33333 6 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: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <7 10 17 18| Scale is weakly epimorphic with val: <7 10 18 18| Scale is weakly epimorphic with val: <7 10 18 19| Scale is weakly epimorphic with val: <7 10 19 19| Scale is weakly epimorphic with val: <7 10 19 20| Scale is weakly epimorphic with val: <8 11 18 18| Scale is weakly epimorphic with val: <8 11 19 19|
FIT/MODE
3: 1 0 2 N G T3 SD: 27.3512 c. M:-46.5722 c. 5: 1 1 3 N M DE S SD: 18.2108 c. M:-24.5258 c. 6: 1 1 4 N M DE S SD: 21.6243 c. M: 36.4353 c. 8: 2 1 5 N T3 SD: 7.5606 c. M:-12.0747 c. 9: 2 1 6 N T3 SD: 7.1213 c. M: 8.7661 c. 12: 3 1 8 N T3 SD: 5.8018 c. M: 8.6772 c. 17: 4 2 11 N T3 SD: 1.4460 c. M: 2.2557 c. 37: 9 4 24 N T3 SD: 0.9982 c. M:-1.7033 c. 46: 11 5 30 N T3 SD: 0.8657 c. M: 1.4591 c. 54: 13 6 35 N T3 SD: 0.4110 c. M:-0.5459 c. 71: 17 8 46 N T3 SD: 0.4057 c. M:-0.6758 c. 100: 24 11 65 N T3 SD: 0.2232 c. M: 0.3764 c. 117: 28 13 76 N T3 SD: 0.1737 c. M: 0.2526 c. 154: 37 17 100 N T3 SD: 0.1292 c. M:-0.2174 c. 171: 41 19 111 N T3 SD: 0.0386 c. M:-0.0604 c. 442: 106 49 287 N T3 SD: 0.0222 c. M: 0.0384 c. 613: 147 68 398 N T3 SD: 0.0083 c. M: 0.0108 c. 1397: 335 155 907 N T3 SD: 0.0069 c. M: 0.0118 c. 1722: 413 191 1118 N T3 SD: 0.0041 c. M:-0.0070 c. 1893: 454 210 1229 N T3 SD: 0.0037 c. M:-0.0051 c. 2335: 560 259 1516 N T3 SD: 0.0024 c. M: 0.0032 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: 82.1604 cents 6 x 7:8 S SD: 46.0894 cents 7 x 8:9 S SD: 42.2915 cents 8 x 9:11 SD: 30.3796 cents 9 x 10:12 S SD: 3.8558 cents 10 x 11:13 SD: 22.4445 cents 11 x 12:15 S SD: 22.8709 cents 12:13 x 16 SD: 9.5649 cents 13:14 x 17 SD: 17.3820 cents 14:15 x 19 SD: 15.3211 cents 15:16:17:20 SD: 14.2322 cents 16:17:18:21 S SD: 14.1692 cents 17:18:19:23 SD: 12.3725 cents 18:19:20:24 S SD: 8.9887 cents 21 x 23:28 SD: 8.5994 cents 22 x 24:29 SD: 15.5734 cents 23:25 x 31 SD: 15.5790 cents 24:26:27:32 SD: 11.6411 cents 25:27:28:33 SD: 10.3040 cents 26:28:29:35 SD: 7.8812 cents 27:29:30:36 SD: 2.9382 cents 56:60:62:75 SD: 2.6198 cents 57:61:63:76 SD: 0.8255 cents 84:90:93:112 SD: 0.5058 cents 141:151:156:188 SD: 0.2941 cents 321:344:355:428 SD: 0.1786 cents 405:434:448:540 SD: 0.0950 cents 462:495:511:616 SD: 0.0586 cents 546:585:604:728 SD: 0.0283 cents