Scala analysis: xen15-chalmers-triadic-diamond-16-13-tetrachord
Upper tetrachord 13/12 * 512/507 * 39/32 of triadic diamond for M=16/13, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 13/12 138.572661 tridecimal 2/3-tone 2: 128/117 155.562336 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 39/32 342.4827 39th harmonic, Zalzal wosta of Ibn Sina 1: 13/12 138.5727 tridecimal 2/3-tone 2: 512/507 16.9897 tridecimal neutral third comma 3: 39/32 342.4827 39th harmonic, Zalzal wosta of Ibn Sina
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 512/507 16.990 cents tridecimal neutral third comma 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 1 128/117 155.562 cents 2: 1 16/13 359.472 cents tridecimal neutral third 2: 1 169/128 481.055 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 : 138.6 155.6 498.0 138.6: 17.0 359.5 498.0 155.6: 342.5 481.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 16.9897 .. 342.4827 cents 19773/16384, 325.4930 cents 512/507, 16.9897 cents 2: 155.5623 .. 481.0553 cents 19773/16384, 325.4930 cents 4096/4563,-186.9203 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 512/507, 16.9897 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 39/32, 342.4827 cents Average / Smallest step : 9.771523 Largest / Average step : 2.062962 Largest / Smallest step : 20.158281 Median interval of one step : 13/12, 138.5727 cents, amount: 1 Least squares average step : 138.84517 cents, oct.: 416.53550 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1319-tone equal temperament with octave 4/3 degrees: 367 412 1319 Least number of segments generator : 660 of 249.211 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 682 of 257.518 cents and inv. generated superset size: 14 = 11 more = 466.667% 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 16.98968 cents Scale diversity : 0.516511 Lumma stability : 0.068225 Lumma impropriety factor : 0.375308 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 : 512/507, 16.9897 cents Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 481.0553 cents Number of appreciable 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 : 13 Odd number limit : 507 (O: 169 U: 507) Highest odd numerator or denominator: 117 Scale harmonicity : 0.017053 Average absolute harmonicity : 0.093522 Specific harmonicity : 0.089926 Fundamental : 1/468, -8.8704 octaves, 0.5590 Hz. Guide tone : 1664, 10.7004 octaves, 435344.941 Hz. Exponens Consonantiae : 7.787520E+05, 19.57080 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 138.5, average 46.16667 Mersenne's string divisions : 1225 Sum of van Prooijen's expressibility: 3.65925, average 1.21975 Sum of Tenney's harmonic distance : 7.44770, average 2.48257 Vogel's harmonic complexity : 19.33333 Wille's k value : 253 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 30.62690, average 5.10448 Lattice compactness (without 2's) : 9.30056, average 1.55009 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 7 2.33333 11 3: -2 ..-1 -1.33333 4 1 13: -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 26| Scale is weakly epimorphic with val: <7 10 27| Scale is weakly epimorphic with val: <8 11 30|
FIT/MODE
3: 1 0 2 N G T3 SD: 16.9543 c. M:-27.4423 c. 7: 2 0 5 N G T3 SD: 7.9542 c. M: 13.2638 c. 10: 3 0 7 N G T3 SD: 7.1956 c. M:-10.8408 c. 15: 4 1 10 N T3 SD: 6.8907 c. M:-10.4527 c. 16: 4 1 11 N T3 SD: 8.1185 c. M: 14.0614 c. 17: 5 0 12 N G T3 SD: 6.9524 c. M: 9.0785 c. 18: 5 1 12 N T3 SD: 6.0363 c. M:-10.4527 c. 19: 5 1 13 N T3 SD: 4.4465 c. M: 7.5082 c. 22: 6 1 15 N T3 SD: 2.3071 c. M:-2.9065 c. 25: 7 1 17 N T3 SD: 2.2588 c. M:-3.8121 c. 29: 8 1 20 N T3 SD: 0.8922 c. M: 1.1809 c. 32: 9 1 22 N T3 SD: 0.8686 c. M:-1.5025 c. 54: 15 2 37 N T3 SD: 0.7219 c. M:-1.2296 c. 61: 17 2 42 N T3 SD: 0.2825 c. M: 0.4336 c. 115: 32 4 79 N T3 SD: 0.2007 c. M:-0.3474 c. 144: 40 5 99 N T3 SD: 0.1382 c. M: 0.2268 c. 176: 49 6 121 N T3 SD: 0.0672 c. M:-0.0876 c. 320: 89 11 220 N T3 SD: 0.0541 c. M:-0.0767 c. 381: 106 13 262 N T3 SD: 0.0059 c. M: 0.0090 c. 1319: 367 45 907 N T3 SD: 0.0041 c. M:-0.0059 c. 1700: 473 58 1169 N T3 SD: 0.0021 c. M:-0.0035 c. 2081: 579 71 1431 N T3 SD: 0.0012 c. M:-0.0019 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: 90.4986 cents 6 x 7:8 S SD: 55.6543 cents 7 x 8:9 S SD: 49.1966 cents 8 x 9:11 SD: 35.9705 cents 9 x 10:12 S SD: 13.4207 cents 10 x 11:13 SD: 22.4182 cents 11 x 12:15 S SD: 19.6081 cents 12:13 x 16 SD: 0.0000 cents 13:14 x 17 SD: 17.5761 cents 14:15 x 19 SD: 18.0616 cents 15:16 x 20 S SD: 13.4207 cents 18 x 20:24 S SD: 13.4207 cents 19 x 21:25 SD: 14.4853 cents 20 x 22:27 SD: 11.7438 cents 21 x 23:28 SD: 0.9656 cents 22 x 24:29 SD: 10.1948 cents 23:25 x 31 SD: 9.7943 cents 24:26 x 32 SD: 0.0000 cents 25:27 x 33 SD: 9.0995 cents 26:28 x 35 S SD: 9.7472 cents 30 x 33:40 SD: 4.7209 cents 31 x 34:41 SD: 7.3399 cents 32 x 35:43 SD: 6.7397 cents 33 x 36:44 SD: 2.4626 cents 34:37 x 45 SD: 7.4889 cents 35:38 x 47 SD: 6.4474 cents 36:39 x 48 SD: 0.0000 cents 37:40 x 49 SD: 6.1389 cents 39:42:43:52 SD: 5.6478 cents 42 x 46:56 SD: 0.9656 cents 43 x 47:57 SD: 5.1083 cents 44 x 48:59 SD: 5.4879 cents 45 x 49:60 SD: 4.0671 cents 46:50 x 61 SD: 5.5323 cents 47:51 x 63 SD: 4.8054 cents 50:54:55:67 SD: 4.6208 cents 51:55:56:68 SD: 3.3666 cents 54 x 59:72 SD: 1.1278 cents 55 x 60:73 SD: 4.6494 cents 56 x 61:75 SD: 5.3798 cents 57:62 x 76 SD: 3.4974 cents 58:63 x 77 SD: 4.3863 cents 60:65:66:80 SD: 3.1473 cents 62:67:68:83 SD: 3.0916 cents 63:68:69:84 SD: 2.2134 cents 66 x 72:88 SD: 2.4626 cents 67 x 73:89 SD: 4.7961 cents 68:74 x 91 SD: 5.0362 cents 69:75 x 92 SD: 2.8902 cents 72:78:79:96 SD: 1.6882 cents 78 x 85:104 SD: 3.3879 cents 79:86 x 105 SD: 5.0201 cents 80:87:88:107 SD: 4.2491 cents 81:88:89:108 SD: 2.9903 cents 82:89:90:109 SD: 2.7853 cents 83:90:91:111 SD: 2.2035 cents 84:91:92:112 SD: 0.6437 cents 90 x 98:120 SD: 4.0671 cents 91:99:100:121 SD: 3.8797 cents 92:100:101:123 SD: 3.1918 cents 93:101:102:124 SD: 2.0384 cents 94:102:103:125 SD: 2.0203 cents 95:103:104:127 SD: 1.6317 cents 96:104:105:128 SD: 0.1409 cents 276:299:302:368 SD: 0.0980 cents 372:403:407:496 SD: 0.0364 cents 468:507:512:624 SD: 0.0000 cents