Scala analysis: 332_C25
Chromatic tetrachord 52/51 * 9/8 * 136/117
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 52/51 33.617251 2: 39/34 237.527253 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 136/117 260.5177 1: 52/51 33.6173 2: 9/8 203.9100 major whole tone 3: 136/117 260.5177
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 52/51 33.617 cents 1: 1 9/8 203.910 cents major whole tone 1: 1 136/117 260.518 cents 2: 1 39/34 237.527 cents 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 17/13 464.428 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 : 33.6 237.5 498.0 33.6 : 203.9 464.4 498.0 237.5: 260.5 294.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.6173 .. 260.5177 cents 578/507, 226.9005 cents 52/51, 33.6173 cents 2: 237.5273 .. 464.4277 cents 578/507, 226.9005 cents 4563/4624,-22.9905 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 52/51, 33.6173 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 136/117, 260.5177 cents Average / Smallest step : 4.938387 Largest / Average step : 1.569242 Largest / Smallest step : 7.749525 Median interval of one step : 9/8, 203.9100 cents, amount: 1 Least squares average step : 143.05763 cents, oct.: 429.17288 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1126-tone equal temperament with octave 4/3 degrees: 76 537 1126 Least number of segments generator : 565 of 249.907 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1107 of 489.641 cents and inv. generated superset size: 36 = 33 more = 1200.000% 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 22.99049 cents Scale diversity : 0.599810 Lumma stability : 0.134997 Lumma impropriety factor : 0.046161 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 : 4624/4563, 22.9905 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 17 Odd number limit : 117 (O: 39 U: 117) Highest odd numerator or denominator: 51 Scale harmonicity : 0.016500 Average absolute harmonicity : 0.083241 Specific harmonicity : 0.067015 Fundamental : 1/102, -6.6724 octaves, 2.5650 Hz. Guide tone : 156, 7.2854 octaves, 40813.588 Hz. Exponens Consonantiae : 1.591200E+04, 13.95783 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 91.5, average 30.50000 Mersenne's string divisions : 52633 Sum of van Prooijen's expressibility: 3.77576, average 1.25859 Sum of Tenney's harmonic distance : 7.62530, average 2.54177 Vogel's harmonic complexity : 18.33333 Wille's k value : 58 Wilson's harmonic complexity : 36 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 15.77457, average 2.62909 Lattice compactness (without 2's) : 10.32780, average 1.72130 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 1.00000 5 3: -1 .. 1 -0.33333 3 1 13: 0 .. 1 0.66667 2 17: -1 .. 0 -0.66667 2 2 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 26 27| Scale is weakly epimorphic with val: <6 10 27 28| Scale is weakly epimorphic with val: <6 10 28 29| Scale is weakly epimorphic with val: <6 10 29 30| Scale is weakly epimorphic with val: <6 10 30 31| Scale is weakly epimorphic with val: <6 11 25 27| Scale is weakly epimorphic with val: <6 11 26 28| Scale is weakly epimorphic with val: <6 11 27 29| Scale is weakly epimorphic with val: <6 11 28 30| Scale is weakly epimorphic with val: <6 11 29 31| Scale is weakly epimorphic with val: <6 11 30 32| Scale is weakly epimorphic with val: <7 10 26 27| Scale is weakly epimorphic with val: <7 10 27 28| Scale is weakly epimorphic with val: <7 10 28 29| Scale is weakly epimorphic with val: <7 10 29 30| Scale is weakly epimorphic with val: <7 10 30 31| Scale is JI-epimorphic with val: <7 11 25 27| Scale is weakly epimorphic with val: <7 11 25 30| Scale is weakly epimorphic with val: <7 11 25 33| Scale is JI-epimorphic with val: <7 11 26 28| Scale is weakly epimorphic with val: <7 11 26 31| Scale is JI-epimorphic with val: <7 11 27 29| Scale is weakly epimorphic with val: <7 11 27 32| Scale is JI-epimorphic with val: <7 11 28 30| Scale is weakly epimorphic with val: <7 11 28 33| Scale is JI-epimorphic with val: <7 11 29 31| Scale is JI-epimorphic with val: <7 11 30 32| Scale is weakly epimorphic with val: <8 11 25 27| Scale is weakly epimorphic with val: <8 11 26 28| Scale is weakly epimorphic with val: <8 11 27 29| Scale is weakly epimorphic with val: <8 11 28 30| Scale is weakly epimorphic with val: <8 11 29 31| Scale is weakly epimorphic with val: <8 11 30 32|
FIT/MODE
3: 0 1 2 N G T3 SD: 45.6221 c. M: 71.5123 c. 4: 0 2 2 P M DE S SD: 20.5123 c. M: 33.6173 c. 7: 0 3 4 N G T3 SD: 23.8742 c. M: 33.6173 c. 8: 1 3 4 P T3 SD: 17.8166 c. M:-28.6384 c. 10: 1 4 5 P T3 SD: 11.4625 c. M:-16.1872 c. 11: 1 4 6 N T3 SD: 9.3116 c. M:-11.6596 c. 12: 1 5 6 P T3 SD: 8.0486 c. M:-11.4952 c. 13: 1 5 7 N T3 SD: 5.1870 c. M: 7.6603 c. 15: 1 6 8 N T3 SD: 2.9578 c. M: 5.1063 c. 17: 1 7 9 N T3 SD: 3.0881 c. M: 4.3205 c. 27: 2 11 14 N T3 SD: 2.3013 c. M:-3.2750 c. 29: 2 12 15 N T3 SD: 1.7313 c. M:-2.9083 c. 42: 3 17 22 N T3 SD: 1.1494 c. M:-1.9574 c. 44: 3 18 23 N T3 SD: 0.2212 c. M:-0.3404 c. 134: 9 55 70 N T3 SD: 0.2212 c. M:-0.3450 c. 149: 10 61 78 N T3 SD: 0.1614 c. M: 0.2038 c. 193: 13 79 101 N T3 SD: 0.0789 c. M: 0.1172 c. 237: 16 97 124 N T3 SD: 0.0364 c. M: 0.0628 c. 281: 19 115 147 N T3 SD: 0.0368 c. M:-0.0584 c. 518: 35 212 271 N T3 SD: 0.0316 c. M: 0.0425 c. 608: 41 249 318 N T3 SD: 0.0242 c. M: 0.0320 c. 652: 44 267 341 N T3 SD: 0.0218 c. M:-0.0372 c. 801: 54 328 419 N T3 SD: 0.0242 c. M: 0.0412 c. 845: 57 346 442 N T3 SD: 0.0124 c. M: 0.0213 c. 889: 60 364 465 N T3 SD: 0.0064 c. M:-0.0105 c. 1126: 76 461 589 N T3 SD: 0.0029 c. M: 0.0049 c. 2015: 136 825 1054 N T3 SD: 0.0017 c. M: 0.0023 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: 57.5250 cents 6 x 7:8 S SD: 14.6718 cents 7 x 8:9 S SD: 31.6403 cents 8 x 9:11 SD: 31.4965 cents 9 x 10:12 S SD: 27.5618 cents 10 x 11:13 SD: 42.3697 cents 11 x 13:15 SD: 32.3448 cents 12 x 14:16 S SD: 14.6718 cents 25:26:29:33 SD: 14.3577 cents 26:27:30:35 S SD: 12.4050 cents 27:28:31:36 SD: 9.7965 cents 32:33:37:43 SD: 9.1819 cents 33:34:38:44 SD: 6.4240 cents 36:37:41:48 SD: 6.1828 cents 39:40:45:52 SD: 4.8148 cents 41:42:47:55 SD: 4.4418 cents 42:43:48:56 SD: 3.1807 cents 48:49:55:64 SD: 0.9279 cents 54:55:62:72 SD: 0.8250 cents 102:104:117:136 SD: 0.0000 cents