Scala analysis: xen15-chalmers-triadic-diamond-64-51-tetrachord
Upper tetrachord 17/16 * 8192/7803 * 153/128 of triadic diamond for M=64/51, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 17/16 104.955410 17th harmonic 2: 512/459 189.179588 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 153/128 308.8654 1: 17/16 104.9554 17th harmonic 2: 8192/7803 84.2242 3: 153/128 308.8654
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 8192/7803 84.224 cents 1: 1 17/16 104.955 cents 17th harmonic 1: 1 153/128 308.865 cents 2: 1 512/459 189.180 cents 2: 1 64/51 393.090 cents 2: 1 2601/2048 413.821 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 : 105.0 189.2 498.0 105.0: 84.2 393.1 498.0 189.2: 308.9 413.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.2242 .. 308.8654 cents 1193859/1048576, 224.6412 cents 8192/7803, 84.2242 cents 2: 189.1796 .. 413.8208 cents 1193859/1048576, 224.6412 cents 65536/70227,-119.6858 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 8192/7803, 84.2242 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 153/128, 308.8654 cents Average / Smallest step : 1.971109 Largest / Average step : 1.860467 Largest / Smallest step : 3.667182 Median interval of one step : 17/16, 104.9554 cents, amount: 1 Least squares average step : 141.24640 cents, oct.: 423.73920 cents Scale is not proper Scale has trivalence property 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 84.22418 cents Scale diversity : 1.037321 Lumma stability : 0.338219 Lumma impropriety factor : 0.240311 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 : 132651/131072, 20.7312 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 224.6412 cents: 2 -- Rational properties -- Prime limit : 17 Odd number limit : 7803 (O: 2601 U: 7803) Highest odd numerator or denominator: 459 Scale harmonicity : 0.012310 Average absolute harmonicity : 0.088273 Specific harmonicity : 0.064419 Fundamental : 1/7344, -12.8424 octaves, 0.0356 Hz. Guide tone : 8704, 13.0875 octaves, 2277188.920 Hz. Exponens Consonantiae : 6.392218E+07, 25.92981 octaves Euler's gradus suavitatis : 52 Sum of Mann's harmonic distance : 505.5, average 168.50000 Mersenne's string divisions : 224301 Sum of van Prooijen's expressibility: 4.36938, average 1.45646 Sum of Tenney's harmonic distance : 8.88483, average 2.96161 Vogel's harmonic complexity : 28.33333 Wille's k value : 3901 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 42.90219, average 7.15036 Lattice compactness (without 2's) : 12.41811, average 2.06969 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 9 2.33333 15 3: -3 .. 0 -1.33333 4 1 17: -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 30| Scale is weakly epimorphic with val: <7 10 31|
FIT/MODE
3: 1 0 2 N G T3 SD: 37.7044 c. M:-61.0596 c. 4: 1 1 2 P M ME S SD: 36.3483 c. M:-59.8429 c. 5: 1 1 3 N M DE S SD: 6.5664 c. M:-10.0384 c. 13: 3 2 8 N T3 SD: 5.9219 c. M:-9.9781 c. 18: 4 3 11 N T3 SD: 4.2041 c. M:-5.7213 c. 19: 4 3 12 N T3 SD: 3.2853 c. M: 5.6893 c. 23: 5 4 14 N T3 SD: 3.8108 c. M:-5.7076 c. 24: 5 4 15 N T3 SD: 1.5547 c. M: 2.4127 c. 29: 6 5 18 N T3 SD: 1.1143 c. M: 1.9116 c. 42: 9 7 26 N T3 SD: 1.0696 c. M:-1.7685 c. 47: 10 8 29 N T3 SD: 1.0740 c. M:-1.5611 c. 61: 13 10 38 N T3 SD: 1.0556 c. M: 1.3921 c. 66: 14 11 41 N T3 SD: 0.5012 c. M:-0.6905 c. 71: 15 12 44 N T3 SD: 0.1982 c. M:-0.2654 c. 166: 35 28 103 N T3 SD: 0.0989 c. M: 0.1625 c. 171: 36 29 106 N T3 SD: 0.0987 c. M:-0.1358 c. 237: 50 40 147 N T3 SD: 0.0733 c. M:-0.1174 c. 266: 56 45 165 N T3 SD: 0.0730 c. M: 0.1038 c. 337: 71 57 209 N T3 SD: 0.0164 c. M: 0.0260 c. 745: 157 126 462 N T3 SD: 0.0062 c. M:-0.0107 c. 1082: 228 183 671 N T3 SD: 0.0046 c. M: 0.0069 c. 1827: 385 309 1133 N T3 SD: 0.0043 c. M:-0.0066 c. 1993: 420 337 1236 N T3 SD: 0.0044 c. M: 0.0075 c. 2330: 491 394 1445 N T3 SD: 0.0048 c. M: 0.0080 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: 76.0383 cents 6 x 7:8 S SD: 38.8457 cents 7 x 8:9 S SD: 37.8405 cents 8 x 9:11 SD: 27.6360 cents 9 x 10:12 S SD: 3.3879 cents 10 x 11:13 SD: 25.0280 cents 11 x 12:15 S SD: 27.3824 cents 12:13 x 16 SD: 16.8086 cents 15:16:17:20 SD: 9.4431 cents 17:18:19:23 SD: 8.7318 cents 18:19:20:24 S SD: 4.4069 cents 33:35:37:44 SD: 3.1376 cents 51:54:57:68 SD: 2.2954 cents 78:83:87:104 SD: 0.8708 cents 96:102:107:128 SD: 0.4581 cents 207:220:231:276 SD: 0.2948 cents 225:239:251:300 SD: 0.1575 cents 303:322:338:404 SD: 0.1142 cents 528:561:589:704 SD: 0.0320 cents