Scala analysis: xen15-chalmers-triadic-diamond-23-20-tetrachord
Upper tetrachord 46/45 * 600/529 * 23/20 of triadic diamond for M=23/20, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 46/45 38.050632 23rd-partial chroma 2: 80/69 256.084366 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 23/20 241.9606 1: 46/45 38.0506 23rd-partial chroma 2: 600/529 218.0337 3: 23/20 241.9606
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 46/45 38.051 cents 23rd-partial chroma 1: 1 600/529 218.034 cents 1: 1 23/20 241.961 cents 2: 1 80/69 256.084 cents 2: 1 529/450 280.011 cents 2: 1 30/23 459.994 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 : 38.1 256.1 498.0 38.1 : 218.0 460.0 498.0 256.1: 242.0 280.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.0506 .. 241.9606 cents 9/8, 203.9100 cents 46/45, 38.0506 cents 2: 256.0844 .. 459.9944 cents 9/8, 203.9100 cents 1600/1587, 14.1237 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 46/45, 38.0506 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 23/20, 241.9606 cents Average / Smallest step : 4.363002 Largest / Average step : 1.457462 Largest / Smallest step : 6.358912 Median interval of one step : 600/529, 218.0337 cents, amount: 1 Least squares average step : 146.02531 cents, oct.: 438.07593 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 2081-tone equal temperament with octave 4/3 degrees: 159 1070 2081 Least number of segments generator : 1041 of 249.142 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1847 of 442.042 cents and inv. generated superset size: 32 = 29 more = 1066.667% 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 14.12373 cents Scale diversity : 0.576033 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.181158 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 : 1600/1587, 14.1237 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing 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 179.9831 cents: 1 -- Rational properties -- Prime limit : 23 Odd number limit : 529 (O: 529 U: 529) Highest odd numerator or denominator: 69 Scale harmonicity : 0.009407 Average absolute harmonicity : 0.083552 Specific harmonicity : 0.050012 Fundamental : 1/1035, -10.0154 octaves, 0.2528 Hz. Guide tone : 1840, 10.8455 octaves, 481391.040 Hz. Exponens Consonantiae : 1.904400E+06, 20.86091 octaves Euler's gradus suavitatis : 61 Sum of Mann's harmonic distance : 123.5, average 41.16667 Mersenne's string divisions : 13559 Sum of van Prooijen's expressibility: 3.96918, average 1.32306 Sum of Tenney's harmonic distance : 8.13709, average 2.71236 Vogel's harmonic complexity : 32.33333 Wille's k value : 264 Wilson's harmonic complexity : 62 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 17.93285, average 2.98881 Lattice compactness (without 2's) : 11.32780, average 1.88797 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 4 2.33333 7 3: -2 ..-1 -1.33333 4 1 5: -1 .. 1 0.00000 2 23: -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 15 30| Scale is weakly epimorphic with val: <7 10 15 31| Scale is weakly epimorphic with val: <7 10 16 31| Scale is weakly epimorphic with val: <7 10 16 32| Scale is weakly epimorphic with val: <7 10 17 32| Scale is weakly epimorphic with val: <7 10 17 33| Scale is weakly epimorphic with val: <7 10 18 33| Scale is weakly epimorphic with val: <7 10 18 34| Scale is weakly epimorphic with val: <7 10 19 34| Scale is weakly epimorphic with val: <7 10 19 35| Scale is weakly epimorphic with val: <8 11 15 32| Scale is weakly epimorphic with val: <8 11 15 33| Scale is weakly epimorphic with val: <8 11 16 33| Scale is weakly epimorphic with val: <8 11 16 34| Scale is weakly epimorphic with val: <8 11 17 34| Scale is weakly epimorphic with val: <8 11 17 35| Scale is weakly epimorphic with val: <8 11 18 35| Scale is weakly epimorphic with val: <8 11 18 36| Scale is weakly epimorphic with val: <8 11 19 36|
FIT/MODE
3: 0 1 2 N G T3 SD: 56.4516 c. M: 90.0694 c. 4: 0 2 2 P M DE S SD: 22.3437 c. M: 38.0506 c. 6: 0 3 3 P M DE S SD: 22.3437 c. M: 38.0506 c. 8: 1 3 4 P T3 SD: 14.5574 c. M:-24.2050 c. 9: 1 4 4 SP M DE S SD: 15.5298 c. M:-20.6073 c. 10: 1 4 5 P T3 SD: 7.9167 c. M:-11.7539 c. 12: 1 5 6 P T3 SD: 4.5385 c. M: 7.0619 c. 14: 1 6 7 P T3 SD: 4.3205 c. M: 7.0619 c. 23: 2 10 11 SP T3 SD: 3.7336 c. M:-5.2576 c. 25: 2 11 12 SP T3 SD: 1.9680 c. M:-2.8990 c. 27: 2 12 13 SP T3 SD: 1.4157 c. M:-2.1612 c. 37: 3 16 18 SP T3 SD: 1.3596 c. M:-2.3314 c. 39: 3 17 19 SP T3 SD: 0.4186 c. M: 0.6767 c. 66: 5 29 32 SP T3 SD: 0.3351 c. M:-0.4843 c. 103: 8 45 50 SP T3 SD: 0.3815 c. M:-0.6325 c. 105: 8 46 51 SP T3 SD: 0.0676 c. M: 0.1043 c. 249: 19 109 121 SP T3 SD: 0.0446 c. M: 0.0612 c. 354: 27 155 172 SP T3 SD: 0.0403 c. M: 0.0641 c. 562: 43 246 273 SP T3 SD: 0.0361 c. M:-0.0560 c. 667: 51 292 324 SP T3 SD: 0.0255 c. M:-0.0317 c. 706: 54 309 343 SP T3 SD: 0.0255 c. M:-0.0435 c. 772: 59 338 375 SP T3 SD: 0.0212 c. M:-0.0346 c. 811: 62 355 394 SP T3 SD: 0.0140 c. M:-0.0243 c. 916: 70 401 445 SP T3 SD: 0.0067 c. M:-0.0096 c. 1021: 78 447 496 SP T3 SD: 0.0066 c. M:-0.0113 c. 1165: 89 510 566 SP T3 SD: 0.0049 c. M: 0.0080 c. 2081: 159 911 1011 SP T3 SD: 0.0019 c. M:-0.0028 c. 2186: 167 957 1062 SP T3 SD: 0.0015 c. M: 0.0024 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: 51.6762 cents 6 x 7:8 S SD: 5.3933 cents 7 x 8:9 S SD: 33.8548 cents 8 x 9:11 SD: 37.2833 cents 9 x 10:12 S SD: 36.8403 cents 10 x 12:13 S SD: 36.9736 cents 11 x 13:15 SD: 25.5487 cents 17:18:20:23 SD: 23.5392 cents 18:19:21:24 SD: 18.8633 cents 19:20:22:25 SD: 18.5789 cents 20:21:23:27 SD: 17.6902 cents 21:22:24:28 S SD: 16.4168 cents 23:24:27:31 SD: 15.2108 cents 24:25:28:32 SD: 11.4530 cents 26:27:30:35 S SD: 10.9982 cents 27:28:31:36 SD: 10.0366 cents 30:31:35:40 SD: 7.2007 cents 32:33:37:43 SD: 6.9578 cents 33:34:38:44 SD: 6.0195 cents 36:37:42:48 SD: 4.7656 cents 38:39:44:51 SD: 4.4962 cents 39:40:45:52 SD: 3.3834 cents 44:45:51:59 SD: 3.2861 cents 45:46:52:60 SD: 1.9268 cents 81:83:94:108 SD: 1.4912 cents 87:89:101:116 SD: 0.8620 cents 132:135:153:176 SD: 0.3288 cents 138:141:160:184 SD: 0.2728 cents 270:276:313:360 SD: 0.0802 cents