Scala analysis: 531_M39
Miscellaneous tetrachord 17/16 * 32/31 * 62/51
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: 34/31 159.919837 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 62/51 338.1252 1: 17/16 104.9554 17th harmonic 2: 32/31 54.9644 Greek enharmonic 1/4-tone 3: 62/51 338.1252
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 32/31 54.964 cents Greek enharmonic 1/4-tone 1: 1 17/16 104.955 cents 17th harmonic 1: 1 62/51 338.125 cents 2: 1 34/31 159.920 cents 2: 1 64/51 393.090 cents 2: 1 31/24 443.081 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 : 105.0 159.9 498.0 105.0: 55.0 393.1 498.0 159.9: 338.1 443.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.9644 .. 338.1252 cents 961/816, 283.1607 cents 32/31, 54.9644 cents 2: 159.9198 .. 443.0806 cents 961/816, 283.1607 cents 867/961,-178.2053 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 32/31, 54.9644 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 62/51, 338.1252 cents Average / Smallest step : 3.020408 Largest / Average step : 2.036715 Largest / Smallest step : 6.151709 Median interval of one step : 17/16, 104.9554 cents, amount: 1 Least squares average step : 137.06643 cents, oct.: 411.19930 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 54.96443 cents Scale diversity : 0.811649 Lumma stability : 0.220721 Lumma impropriety factor : 0.357810 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 : 527/512, 49.9910 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 31 Odd number limit : 51 (O: 31 U: 51) Highest odd numerator or denominator: 31 Scale harmonicity : 0.025784 Fundamental : 1/1488, -10.5392 octaves, 0.1758 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 1.011840E+05, 16.62662 octaves Euler's gradus suavitatis : 55 Sum of Mann's harmonic distance : 52.5, average 17.50000 Mersenne's string divisions : 15015 Sum of van Prooijen's expressibility: 3.19893, average 1.06631 Sum of Tenney's harmonic distance : 6.53659, average 2.17886 Vogel's harmonic complexity : 37.66667 Wille's k value : 790 Wilson's harmonic complexity : 51 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 20.66985, average 3.44498 Lattice compactness (without 2's) : 5.82843, average 0.97140 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.33333 7 3: -1 .. 0 -0.33333 1 1 17: 0 .. 1 0.66667 2 1 31: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is weakly epimorphic with val: <6 10 27 35| Scale is weakly epimorphic with val: <6 10 27 38| Scale is weakly epimorphic with val: <6 10 31 34| Scale is weakly epimorphic with val: <6 11 27 34| Scale is weakly epimorphic with val: <6 11 27 37| Scale is weakly epimorphic with val: <6 11 32 35| Scale is weakly epimorphic with val: <7 10 30 34| Scale is weakly epimorphic with val: <7 10 31 33| Scale is weakly epimorphic with val: <7 10 31 36| Scale is weakly epimorphic with val: <7 10 31 39| Scale is weakly epimorphic with val: <7 10 33 37| Scale is weakly epimorphic with val: <7 11 27 33| Scale is weakly epimorphic with val: <7 11 27 36| Scale is weakly epimorphic with val: <7 11 27 39| Scale is JI-epimorphic with val: <7 11 29 34| Scale is weakly epimorphic with val: <7 11 29 37| Scale is weakly epimorphic with val: <7 11 30 33| Scale is weakly epimorphic with val: <7 11 30 36| = patent Scale is weakly epimorphic with val: <7 11 30 39| Scale is weakly epimorphic with val: <7 11 32 34| Scale is weakly epimorphic with val: <7 11 32 37| Scale is weakly epimorphic with val: <7 11 33 33| Scale is weakly epimorphic with val: <7 11 33 36| Scale is weakly epimorphic with val: <7 11 33 39| Scale is weakly epimorphic with val: <7 12 29 33| Scale is weakly epimorphic with val: <7 12 31 34| Scale is weakly epimorphic with val: <7 12 31 37| Scale is weakly epimorphic with val: <7 12 32 36| Scale is weakly epimorphic with val: <8 11 30 35| Scale is weakly epimorphic with val: <8 11 33 38| Scale is weakly epimorphic with val: <8 12 28 33| Scale is weakly epimorphic with val: <8 12 31 36|
FIT/MODE
3: 1 0 2 N G T3 SD: 35.4280 c. M:-61.0596 c. 4: 1 0 3 N G T3 SD: 23.3538 c. M: 35.4086 c. 5: 1 1 3 N M DE S SD: 22.8978 c. M:-39.2982 c. 6: 1 1 4 N M DE S SD: 13.1512 c. M: 21.9479 c. 9: 2 1 6 N T3 SD: 4.8264 c. M:-6.0952 c. 15: 3 2 10 N T3 SD: 4.6810 c. M:-6.0952 c. 19: 4 2 13 N T3 SD: 1.5268 c. M: 2.6425 c. 28: 6 3 19 N T3 SD: 1.0255 c. M:-1.7685 c. 47: 10 5 32 N T3 SD: 0.8089 c. M:-1.0116 c. 53: 11 6 36 N T3 SD: 0.9218 c. M: 1.5876 c. 62: 13 7 42 N T3 SD: 0.5243 c. M:-0.7398 c. 81: 17 9 55 N T3 SD: 0.2487 c. M: 0.4274 c. 109: 23 12 74 N T3 SD: 0.0789 c. M:-0.1367 c. 190: 40 21 129 N T3 SD: 0.0612 c. M: 0.1038 c. 299: 63 33 203 N T3 SD: 0.0118 c. M: 0.0162 c. 707: 149 78 480 N T3 SD: 0.0072 c. M: 0.0101 c. 1006: 212 111 683 N T3 SD: 0.0062 c. M: 0.0108 c. 1305: 275 144 886 N T3 SD: 0.0067 c. M: 0.0111 c. 1604: 338 177 1089 N T3 SD: 0.0074 c. M: 0.0114 c. 1713: 361 189 1163 N T3 SD: 0.0063 c. M: 0.0105 c. 2292: 483 253 1556 N T3 SD: 0.0063 c. M:-0.0108 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: 88.5775 cents 6 x 7:8 S SD: 53.4755 cents 7 x 8:9 S SD: 47.5427 cents 8 x 9:11 SD: 34.5440 cents 9 x 10:12 S SD: 11.2419 cents 10 x 11:13 SD: 22.0625 cents 11 x 12:15 S SD: 19.9989 cents 12 x 13:16 SD: 10.6736 cents 13:14 x 17 SD: 20.4634 cents 14:15 x 19 SD: 16.9472 cents 15:16 x 20 S SD: 3.3879 cents 24 x 26:32 SD: 10.6736 cents 25 x 27:33 SD: 15.9271 cents 26:28:29:35 SD: 13.6133 cents 27:29:30:36 SD: 9.7601 cents 28:30:31:37 SD: 8.9214 cents 29:31:32:39 SD: 7.0036 cents 30:32:33:40 SD: 2.8238 cents 51:54:56:68 SD: 2.1080 cents 63:67:69:84 SD: 0.9717 cents 114:121:125:152 SD: 0.6142 cents 144:153:158:192 SD: 0.2357 cents 207:220:227:276 SD: 0.1833 cents 321:341:352:428 SD: 0.1496 cents 351:373:385:468 SD: 0.1081 cents 465:494:510:620 SD: 0.0730 cents