Scala analysis: xen15-chalmers-triadic-diamond-34-27-tetrachord
Upper tetrachord 18/17 * 2312/2187 * 81/68 of triadic diamond for M=34/27, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 18/17 98.954592 Arabic lute index finger 2: 272/243 195.180405 Persian whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 81/68 302.8646 Persian wosta 1: 18/17 98.9546 Arabic lute index finger 2: 2312/2187 96.2258 3: 81/68 302.8646 Persian wosta
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 2312/2187 96.226 cents 1: 1 18/17 98.955 cents Arabic lute index finger 1: 1 81/68 302.865 cents Persian wosta 2: 1 272/243 195.180 cents Persian whole tone 2: 1 34/27 399.090 cents septendecimal major third 2: 1 729/578 401.819 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 : 99.0 195.2 498.0 99.0 : 96.2 399.1 498.0 195.2: 302.9 401.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 96.2258 .. 302.8646 cents 177147/157216, 206.6388 cents 2312/2187, 96.2258 cents 2: 195.1804 .. 401.8192 cents 177147/157216, 206.6388 cents 18496/19683,-107.6842 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 2312/2187, 96.2258 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 81/68, 302.8646 cents Average / Smallest step : 1.725265 Largest / Average step : 1.824321 Largest / Smallest step : 3.147436 Median interval of one step : 18/17, 98.9546 cents, amount: 1 Least squares average step : 141.67503 cents, oct.: 425.02509 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1827-tone equal temperament with octave 4/3 degrees: 363 716 1827 Least number of segments generator : 914 of 249.159 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1462 of 398.545 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 96.22581 cents Scale diversity : 1.059422 Lumma stability : 0.386414 Lumma impropriety factor : 0.216214 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 : 19683/19652, 2.7288 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% Limited inverse transpositions with margin 206.6388 cents: 2 -- Rational properties -- Prime limit : 17 Odd number limit : 2187 (O: 729 U: 2187) Highest odd numerator or denominator: 243 Scale harmonicity : 0.012062 Average absolute harmonicity : 0.087598 Specific harmonicity : 0.063398 Fundamental : 1/4131, -12.0123 octaves, 0.0633 Hz. Guide tone : 2448, 11.2574 octaves, 640459.384 Hz. Exponens Consonantiae : 1.011269E+07, 23.26966 octaves Euler's gradus suavitatis : 51 Sum of Mann's harmonic distance : 278.5, average 92.83333 Mersenne's string divisions : 3605 Sum of van Prooijen's expressibility: 4.09318, average 1.36439 Sum of Tenney's harmonic distance : 8.38508, average 2.79503 Vogel's harmonic complexity : 30.33333 Wille's k value : 1093 Wilson's harmonic complexity : 55 Rectangular lattice diameter : 9 Triangular lattice diameter : 7 Lattice compactness : 26.93951, average 4.48992 Lattice compactness (without 2's) : 22.90058, average 3.81676 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 4 2.33333 7 3: -5 .. 2 -1.33333 8 1 17: -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: <8 11 27|
FIT/MODE
3: 0 1 2 N G T3 SD: 59.5613 c. M: 98.9546 c. 4: 1 1 2 P M ME S SD: 34.4099 c. M:-53.8421 c. 5: 1 1 3 N M DE S SD: 2.3615 c. M:-4.0376 c. 26: 5 5 16 N M DE S SD: 2.7827 c. M: 3.6246 c. 31: 6 6 19 N M DE S SD: 2.0210 c. M: 2.5588 c. 36: 7 7 22 N M DE S SD: 1.4946 c. M: 2.1125 c. 41: 8 8 25 N M DE S SD: 1.1292 c. M: 1.7751 c. 46: 9 9 28 N M DE S SD: 0.8887 c. M: 1.5110 c. 51: 10 10 31 N M DE S SD: 0.7536 c. M: 1.2987 c. 56: 11 11 34 N M DE S SD: 0.7058 c. M: 1.1243 c. 61: 12 12 37 N M DE S SD: 0.7195 c. M: 0.9785 c. 97: 19 19 59 N M DE S SD: 0.8089 c. M: 1.3994 c. 100: 20 19 61 N T3 SD: 0.6626 c. M: 0.9429 c. 105: 21 20 64 N T3 SD: 0.5557 c. M: 0.7057 c. 110: 22 21 67 N T3 SD: 0.4720 c. M:-0.6544 c. 115: 23 22 70 N T3 SD: 0.4140 c. M:-0.6544 c. 120: 24 23 73 N T3 SD: 0.3834 c. M:-0.6544 c. 125: 25 24 76 N T3 SD: 0.3791 c. M:-0.6544 c. 130: 26 25 79 N T3 SD: 0.3962 c. M:-0.6544 c. 135: 27 26 82 N T3 SD: 0.4280 c. M:-0.6544 c. 146: 29 28 89 N T3 SD: 0.4265 c. M: 0.7382 c. 151: 30 29 92 N T3 SD: 0.3349 c. M: 0.5800 c. 156: 31 30 95 N T3 SD: 0.2496 c. M: 0.4320 c. 161: 32 31 98 N T3 SD: 0.1705 c. M: 0.2932 c. 166: 33 32 101 N T3 SD: 0.0991 c. M: 0.1628 c. 171: 34 33 104 N T3 SD: 0.0475 c. M:-0.0719 c. 347: 69 67 211 N T3 SD: 0.0476 c. M:-0.0803 c. 518: 103 100 315 N T3 SD: 0.0448 c. M:-0.0775 c. 523: 104 101 318 N T3 SD: 0.0527 c. M:-0.0830 c. 559: 111 108 340 N T3 SD: 0.0487 c. M: 0.0608 c. 564: 112 109 343 N T3 SD: 0.0332 c. M: 0.0520 c. 569: 113 110 346 N T3 SD: 0.0272 c. M: 0.0458 c. 735: 146 142 447 N T3 SD: 0.0210 c. M: 0.0281 c. 740: 147 143 450 N T3 SD: 0.0108 c. M: 0.0186 c. 911: 181 176 554 N T3 SD: 0.0047 c. M: 0.0080 c. 1656: 329 320 1007 N T3 SD: 0.0060 c. M:-0.0075 c. 1827: 363 353 1111 N T3 SD: 0.0018 c. M:-0.0031 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: 73.5621 cents 6 x 7:8 S SD: 35.8453 cents 7 x 8:9 S SD: 36.2616 cents 8 x 9:11 SD: 26.9917 cents 9 x 10:12 S SD: 6.3883 cents 10 x 11:13 SD: 26.6072 cents 11 x 12:15 S SD: 29.5710 cents 12:13 x 16 SD: 19.8090 cents 14:15:16:19 SD: 17.1731 cents 15:16:17:20 SD: 8.3384 cents 18:19:20:24 S SD: 4.6174 cents 33:35:37:44 SD: 1.3677 cents 51:54:57:68 SD: 0.8743 cents 84:89:94:112 SD: 0.4105 cents 309:327:346:412 SD: 0.3733 cents 342:362:383:456 SD: 0.3362 cents 360:381:403:480 SD: 0.2724 cents 393:416:440:524 SD: 0.2084 cents 426:451:477:568 SD: 0.2083 cents 444:470:497:592 SD: 0.1451 cents 477:505:534:636 SD: 0.1045 cents 528:559:591:704 SD: 0.0619 cents 561:594:628:748 SD: 0.0454 cents