Scala analysis: 521_M29
Miscellaneous tetrachord 68/55 * 55/54 * 18/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/55 367.323753 2: 34/27 399.090407 septendecimal major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 18/17 98.9546 Arabic lute index finger 1: 68/55 367.3238 2: 55/54 31.7667 telepathma 3: 18/17 98.9546 Arabic lute index finger
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 55/54 31.767 cents telepathma 1: 1 18/17 98.955 cents Arabic lute index finger 1: 1 68/55 367.324 cents 2: 1 55/51 130.721 cents 2: 1 34/27 399.090 cents septendecimal major third 2: 1 72/55 466.278 cents undecimal semi-diminished fourth 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 : 367.3 399.1 498.0 367.3: 31.8 130.7 498.0 399.1: 99.0 466.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.7667 .. 367.3238 cents 3672/3025, 335.5571 cents 55/54, 31.7667 cents 2: 130.7212 .. 466.2783 cents 3672/3025, 335.5571 cents 3025/3468,-236.6025 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 55/54, 31.7667 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 68/55, 367.3238 cents Average / Smallest step : 5.226078 Largest / Average step : 2.212594 Largest / Smallest step : 11.563187 Median interval of one step : 18/17, 98.9546 cents, amount: 1 Least squares average step : 189.97425 cents, oct.: 569.92276 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1223-tone equal temperament with octave 4/3 degrees: 902 980 1223 Least number of segments generator : 612 of 249.226 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 824 of 335.559 cents and inv. generated superset size: 20 = 17 more = 666.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LSM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 31.76665 cents Scale diversity : 0.550960 Lumma stability : 0.127565 Lumma impropriety factor : 0.475063 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 : 55/54, 31.7667 cents Number of recognisable fifths : 0 Number of recognisable fourths : 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 : 55 (O: 55 U: 55) Highest odd numerator or denominator: 55 Scale harmonicity : 0.015456 Average absolute harmonicity : 0.085828 Specific harmonicity : 0.070211 Fundamental : 1/1485, -10.5362 octaves, 0.1762 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 1.009800E+05, 16.62371 octaves Euler's gradus suavitatis : 39 Sum of Mann's harmonic distance : 95.5, average 31.83333 Mersenne's string divisions : 52521 Sum of van Prooijen's expressibility: 3.64885, average 1.21628 Sum of Tenney's harmonic distance : 7.61490, average 2.53830 Vogel's harmonic complexity : 28.66667 Wille's k value : 467 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 16.11204, average 2.68534 Lattice compactness (without 2's) : 13.44702, average 2.24117 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -3 .. 0 -1.33333 4 1 5: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 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: <6 10 15 23 27| Scale is weakly epimorphic with val: <6 10 15 25 31| Scale is weakly epimorphic with val: <6 10 15 26 27| Scale is weakly epimorphic with val: <6 10 16 24 31| Scale is weakly epimorphic with val: <6 10 16 25 27| Scale is weakly epimorphic with val: <6 10 17 23 31| Scale is weakly epimorphic with val: <6 10 17 24 27| Scale is weakly epimorphic with val: <6 10 17 27 27| Scale is weakly epimorphic with val: <6 10 18 23 27| Scale is weakly epimorphic with val: <6 10 18 26 27| Scale is weakly epimorphic with val: <6 10 19 25 27| Scale is weakly epimorphic with val: <6 11 15 23 29| Scale is weakly epimorphic with val: <6 11 15 25 30| Scale is weakly epimorphic with val: <6 11 15 26 32| Scale is weakly epimorphic with val: <6 11 16 24 30| Scale is weakly epimorphic with val: <6 11 16 25 32| Scale is weakly epimorphic with val: <6 11 16 27 30| Scale is weakly epimorphic with val: <6 11 17 23 30| Scale is weakly epimorphic with val: <6 11 17 24 32| Scale is weakly epimorphic with val: <6 11 17 26 30| Scale is weakly epimorphic with val: <6 11 18 23 32| Scale is weakly epimorphic with val: <6 11 18 25 30| Scale is weakly epimorphic with val: <6 11 19 24 30| Scale is weakly epimorphic with val: <6 11 19 27 30| Scale is weakly epimorphic with val: <7 10 15 24 28| Scale is weakly epimorphic with val: <7 10 15 27 31| Scale is weakly epimorphic with val: <7 10 16 23 28| Scale is weakly epimorphic with val: <7 10 16 26 31| Scale is weakly epimorphic with val: <7 10 17 25 31| Scale is weakly epimorphic with val: <7 10 18 24 31| Scale is weakly epimorphic with val: <7 10 19 23 31| Scale is weakly epimorphic with val: <7 11 15 23 28| Scale is weakly epimorphic with val: <7 11 15 23 31| Scale is weakly epimorphic with val: <7 11 15 24 27| Scale is weakly epimorphic with val: <7 11 15 24 30| Scale is weakly epimorphic with val: <7 11 15 24 33| Scale is JI-epimorphic with val: <7 11 15 26 28| Scale is weakly epimorphic with val: <7 11 15 26 31| Scale is weakly epimorphic with val: <7 11 15 27 27| Scale is weakly epimorphic with val: <7 11 15 27 30| Scale is weakly epimorphic with val: <7 11 15 27 33| Scale is weakly epimorphic with val: <7 11 16 23 27| Scale is weakly epimorphic with val: <7 11 16 23 30| Scale is weakly epimorphic with val: <7 11 16 23 33| Scale is JI-epimorphic with val: <7 11 16 25 28| Scale is weakly epimorphic with val: <7 11 16 25 31| Scale is weakly epimorphic with val: <7 11 16 26 27| Scale is weakly epimorphic with val: <7 11 16 26 30| Scale is weakly epimorphic with val: <7 11 16 26 33| Scale is JI-epimorphic with val: <7 11 17 24 28| Scale is weakly epimorphic with val: <7 11 17 24 31| Scale is weakly epimorphic with val: <7 11 17 25 27| Scale is weakly epimorphic with val: <7 11 17 25 30| = patent Scale is weakly epimorphic with val: <7 11 17 25 33| Scale is weakly epimorphic with val: <7 11 17 27 28| Scale is weakly epimorphic with val: <7 11 17 27 31| Scale is JI-epimorphic with val: <7 11 18 23 28| Scale is weakly epimorphic with val: <7 11 18 23 31| Scale is weakly epimorphic with val: <7 11 18 24 27| Scale is weakly epimorphic with val: <7 11 18 24 30| Scale is weakly epimorphic with val: <7 11 18 24 33| Scale is weakly epimorphic with val: <7 11 18 26 28| Scale is weakly epimorphic with val: <7 11 18 26 31| Scale is weakly epimorphic with val: <7 11 18 27 27| Scale is weakly epimorphic with val: <7 11 18 27 30| Scale is weakly epimorphic with val: <7 11 18 27 33| Scale is weakly epimorphic with val: <7 11 19 23 27| Scale is weakly epimorphic with val: <7 11 19 23 30| Scale is weakly epimorphic with val: <7 11 19 23 33| Scale is weakly epimorphic with val: <7 11 19 25 28| Scale is weakly epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 26 27| Scale is weakly epimorphic with val: <7 11 19 26 30| Scale is weakly epimorphic with val: <7 11 19 26 33| Scale is weakly epimorphic with val: <7 12 15 23 27| Scale is weakly epimorphic with val: <7 12 15 24 32| Scale is weakly epimorphic with val: <7 12 15 26 30| Scale is weakly epimorphic with val: <7 12 15 27 32| Scale is weakly epimorphic with val: <7 12 16 23 32| Scale is weakly epimorphic with val: <7 12 16 25 30| Scale is weakly epimorphic with val: <7 12 16 26 32| Scale is weakly epimorphic with val: <7 12 17 24 30| Scale is weakly epimorphic with val: <7 12 17 25 32| Scale is weakly epimorphic with val: <7 12 17 27 33| Scale is weakly epimorphic with val: <7 12 18 23 30| Scale is weakly epimorphic with val: <7 12 18 24 32| Scale is weakly epimorphic with val: <7 12 18 26 33| Scale is weakly epimorphic with val: <7 12 18 27 32| Scale is weakly epimorphic with val: <7 12 19 23 32| Scale is weakly epimorphic with val: <7 12 19 25 33| Scale is weakly epimorphic with val: <7 12 19 26 32| Scale is weakly epimorphic with val: <8 11 15 25 28| Scale is weakly epimorphic with val: <8 11 15 27 29| Scale is weakly epimorphic with val: <8 11 16 24 28| Scale is weakly epimorphic with val: <8 11 16 26 29| Scale is weakly epimorphic with val: <8 11 16 27 28| Scale is weakly epimorphic with val: <8 11 17 23 28| Scale is weakly epimorphic with val: <8 11 17 25 29| Scale is weakly epimorphic with val: <8 11 17 26 28| Scale is weakly epimorphic with val: <8 11 18 24 29| Scale is weakly epimorphic with val: <8 11 18 25 28| Scale is weakly epimorphic with val: <8 11 18 27 32| Scale is weakly epimorphic with val: <8 11 19 23 29| Scale is weakly epimorphic with val: <8 11 19 24 28| Scale is weakly epimorphic with val: <8 11 19 26 32| Scale is weakly epimorphic with val: <8 11 19 27 28| Scale is weakly epimorphic with val: <8 12 15 24 31| Scale is weakly epimorphic with val: <8 12 15 25 27| Scale is weakly epimorphic with val: <8 12 15 27 31| Scale is weakly epimorphic with val: <8 12 16 23 31| Scale is weakly epimorphic with val: <8 12 16 24 27| Scale is weakly epimorphic with val: <8 12 16 26 31| Scale is weakly epimorphic with val: <8 12 16 27 30| Scale is weakly epimorphic with val: <8 12 17 23 27| Scale is weakly epimorphic with val: <8 12 17 25 31| Scale is weakly epimorphic with val: <8 12 17 26 30| Scale is weakly epimorphic with val: <8 12 18 24 31| Scale is weakly epimorphic with val: <8 12 18 25 30| Scale is weakly epimorphic with val: <8 12 18 27 31| Scale is weakly epimorphic with val: <8 12 19 23 31| Scale is weakly epimorphic with val: <8 12 19 24 30| Scale is weakly epimorphic with val: <8 12 19 26 31| Scale is weakly epimorphic with val: <8 12 19 27 33|
FIT/MODE
3: 2 0 1 N G T3 SD: 43.7521 c. M: 67.0604 c. 4: 3 0 1 N G T3 SD: 15.1845 c. M: 25.5567 c. 9: 7 0 2 N G T3 SD: 13.4064 c. M:-20.0446 c. 10: 7 1 2 N T3 SD: 10.7986 c. M: 18.6923 c. 11: 8 1 2 N T3 SD: 5.6769 c. M:-8.4010 c. 15: 11 1 3 N T3 SD: 1.2648 c. M: 2.0908 c. 46: 34 3 9 N T3 SD: 0.9862 c. M:-1.5110 c. 50: 37 3 10 N T3 SD: 0.8042 c. M:-1.2295 c. 61: 45 4 12 N T3 SD: 0.5672 c. M:-0.9785 c. 65: 48 4 13 N T3 SD: 0.4629 c. M: 0.6544 c. 76: 56 5 15 N T3 SD: 0.4276 c. M:-0.6562 c. 80: 59 5 16 N T3 SD: 0.3779 c. M: 0.6544 c. 91: 67 6 18 N T3 SD: 0.4443 c. M: 0.6313 c. 95: 70 6 19 N T3 SD: 0.4266 c. M: 0.6544 c. 111: 82 7 22 N T3 SD: 0.3745 c. M:-0.6014 c. 126: 93 8 25 N T3 SD: 0.1802 c. M:-0.2809 c. 141: 104 9 28 N T3 SD: 0.0343 c. M:-0.0520 c. 438: 323 28 87 N T3 SD: 0.0301 c. M: 0.0440 c. 579: 427 37 115 N T3 SD: 0.0247 c. M:-0.0337 c. 644: 475 41 128 N T3 SD: 0.0246 c. M: 0.0357 c. 720: 531 46 143 N T3 SD: 0.0233 c. M:-0.0373 c. 785: 579 50 156 N T3 SD: 0.0181 c. M:-0.0241 c. 800: 590 51 159 N T3 SD: 0.0205 c. M: 0.0319 c. 926: 683 59 184 N T3 SD: 0.0152 c. M:-0.0248 c. 941: 694 60 187 N T3 SD: 0.0123 c. M: 0.0193 c. 1082: 798 69 215 N T3 SD: 0.0062 c. M: 0.0100 c. 1223: 902 78 243 N T3 SD: 0.0016 c. M: 0.0028 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 5 x S SD: 12.7767 cents 5:6 x 7 S SD: 49.5121 cents 6:7 x 8 S SD: 50.2264 cents 7 x 9 x SD: 35.9937 cents 8 x 10:11 S SD: 27.3918 cents 9:11 x 12 SD: 9.9579 cents 10:12 x 13 S SD: 33.8830 cents 11 x 14:15 SD: 21.5225 cents 12 x 15:16 S SD: 6.3883 cents 13:16 x 17 SD: 17.2610 cents 15 x 19:20 SD: 5.0769 cents 16 x 20:21 S SD: 15.0547 cents 17:21 x 23 SD: 12.6592 cents 18:22:23:24 SD: 10.7259 cents 20 x 25:27 SD: 12.5076 cents 21:26 x 28 SD: 1.2115 cents 24 x 30:32 S SD: 6.3883 cents 25:31 x 33 SD: 9.0636 cents 26:32:33:35 SD: 7.6199 cents 27:33:34:36 SD: 6.6386 cents 28 x 35:37 SD: 10.0539 cents 29:36:37:39 SD: 9.3344 cents 30:37:38:40 SD: 3.6689 cents 32 x 40:43 SD: 9.2838 cents 33:41:42:44 SD: 6.7567 cents 34:42:43:45 SD: 4.9589 cents 36 x 45:48 S SD: 6.3883 cents 38:47:48:51 SD: 4.1895 cents 39:48:49:52 SD: 2.9254 cents 42:52:53:56 SD: 1.4557 cents 81:100:102:108 SD: 0.8388 cents 93:115:117:124 SD: 0.5553 cents 123:152:155:164 SD: 0.4974 cents 135:167:170:180 SD: 0.3142 cents 216:267:272:288 SD: 0.1179 cents 351:434:442:468 SD: 0.0484 cents 567:701:714:756 SD: 0.0150 cents