Scala analysis: xen15-chalmers-triadic-diamond-13-11-tetrachord
Upper tetrachord 104/99 * 363/338 * 13/11 of triadic diamond for M=13/11, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 104/99 85.299718 2: 44/39 208.835280 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 13/11 289.2097 tridecimal minor third 1: 104/99 85.2997 2: 363/338 123.5356 3: 13/11 289.2097 tridecimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 104/99 85.300 cents 1: 1 363/338 123.536 cents 1: 1 13/11 289.210 cents tridecimal minor third 2: 1 44/39 208.835 cents 2: 1 1352/1089 374.509 cents 2: 1 33/26 412.745 cents tridecimal major third 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 : 85.3 208.8 498.0 85.3 : 123.5 412.7 498.0 208.8: 289.2 374.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 85.2997 .. 289.2097 cents 9/8, 203.9100 cents 104/99, 85.2997 cents 2: 208.8353 .. 412.7453 cents 9/8, 203.9100 cents 484/507,-80.3744 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 104/99, 85.2997 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 13/11, 289.2097 cents Average / Smallest step : 1.946255 Largest / Average step : 1.742070 Largest / Smallest step : 3.390512 Median interval of one step : 363/338, 123.5356 cents, amount: 1 Least squares average step : 142.65038 cents, oct.: 427.95113 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1915-tone equal temperament with octave 4/3 degrees: 328 803 1915 Least number of segments generator : 958 of 249.153 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1293 of 336.278 cents and inv. generated superset size: 30 = 27 more = 1000.000% 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 80.37444 cents Scale diversity : 1.105135 Lumma stability : 0.342538 Lumma impropriety factor : 0.161380 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 : 35937/35152, 38.2358 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 13 Odd number limit : 1089 (O: 363 U: 1089) Highest odd numerator or denominator: 99 Scale harmonicity : 0.011235 Average absolute harmonicity : 0.085684 Specific harmonicity : 0.059922 Fundamental : 1/1287, -10.3298 octaves, 0.2033 Hz. Guide tone : 1144, 10.1599 octaves, 299299.647 Hz. Exponens Consonantiae : 1.472328E+06, 20.48967 octaves Euler's gradus suavitatis : 52 Sum of Mann's harmonic distance : 146.5, average 48.83333 Mersenne's string divisions : 16849 Sum of van Prooijen's expressibility: 4.06382, average 1.35461 Sum of Tenney's harmonic distance : 8.32637, average 2.77546 Vogel's harmonic complexity : 28.33333 Wille's k value : 214 Wilson's harmonic complexity : 54 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 15.33129, average 2.55522 Lattice compactness (without 2's) : 11.32780, average 1.88797 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -2 ..-1 -1.33333 4 1 11: -1 .. 1 0.00000 2 13: -1 .. 1 0.00000 2 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 10 23 25| Scale is weakly epimorphic with val: <7 10 24 25| Scale is weakly epimorphic with val: <7 10 24 26| Scale is weakly epimorphic with val: <7 10 25 26| Scale is weakly epimorphic with val: <7 10 25 27| Scale is weakly epimorphic with val: <7 10 26 27| Scale is weakly epimorphic with val: <7 10 26 28| Scale is weakly epimorphic with val: <7 10 27 28| Scale is weakly epimorphic with val: <7 10 27 29| Scale is weakly epimorphic with val: <8 11 23 25| Scale is weakly epimorphic with val: <8 11 24 25| Scale is weakly epimorphic with val: <8 11 24 26| Scale is weakly epimorphic with val: <8 11 25 26| Scale is weakly epimorphic with val: <8 11 25 27| Scale is weakly epimorphic with val: <8 11 26 27| Scale is weakly epimorphic with val: <8 11 26 28| Scale is weakly epimorphic with val: <8 11 27 28| Scale is weakly epimorphic with val: <8 11 27 29|
FIT/MODE
3: 0 1 2 N G T3 SD: 55.1048 c. M: 85.2997 c. 4: 1 1 2 P M ME S SD: 32.4169 c. M:-40.1872 c. 5: 1 1 3 N M DE S SD: 9.9540 c. M:-14.3093 c. 7: 1 2 4 N T3 SD: 8.5928 c. M: 14.1504 c. 12: 2 3 7 N T3 SD: 1.5262 c. M: 2.2922 c. 41: 7 10 24 N T3 SD: 1.3534 c. M: 2.3288 c. 52: 9 13 30 N T3 SD: 1.2014 c. M:-1.8761 c. 64: 11 16 37 N T3 SD: 0.7578 c. M:-1.2775 c. 69: 12 17 40 N T3 SD: 0.8108 c. M:-1.3168 c. 76: 13 19 44 N T3 SD: 0.5049 c. M:-0.8679 c. 81: 14 20 47 N T3 SD: 0.4692 c. M:-0.7821 c. 88: 15 22 51 N T3 SD: 0.4039 c. M:-0.5700 c. 93: 16 23 54 N T3 SD: 0.2229 c. M:-0.3854 c. 105: 18 26 61 N T3 SD: 0.0883 c. M: 0.1307 c. 286: 49 71 166 N T3 SD: 0.0796 c. M:-0.1346 c. 298: 51 74 173 N T3 SD: 0.0574 c. M:-0.0762 c. 391: 67 97 227 N T3 SD: 0.0442 c. M:-0.0634 c. 403: 69 100 234 N T3 SD: 0.0200 c. M: 0.0265 c. 508: 87 126 295 N T3 SD: 0.0060 c. M: 0.0093 c. 1915: 328 475 1112 N T3 SD: 0.0043 c. M:-0.0055 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: 68.0849 cents 6 x 7:8 S SD: 29.0178 cents 7 x 8:9 S SD: 33.4032 cents 8 x 9:11 SD: 26.7501 cents 9 x 10:12 S SD: 13.2158 cents 10 x 11:13 SD: 30.9932 cents 11 x 12:15 S SD: 35.0025 cents 12:13:14:16 S SD: 26.2597 cents 13:14:15:17 SD: 22.3424 cents 14:15:16:19 SD: 17.0089 cents 15:16:17:20 SD: 9.1910 cents 21:22:24:28 S SD: 7.6136 cents 23:24:26:31 SD: 7.4310 cents 24:25:27:32 SD: 5.1447 cents 38:40:43:51 SD: 4.3186 cents 39:41:44:52 SD: 0.4267 cents 180:189:203:240 SD: 0.3533 cents 219:230:247:292 SD: 0.2354 cents 258:271:291:344 SD: 0.1656 cents 297:312:335:396 SD: 0.1325 cents 336:353:379:448 SD: 0.1272 cents