Scala analysis: 385_D4
Diatonic tetrachord 32/31 * 9/8 * 31/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 32/31 54.964428 Greek enharmonic 1/4-tone 2: 36/31 258.874429 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 31/27 239.1706 1: 32/31 54.9644 Greek enharmonic 1/4-tone 2: 9/8 203.9100 major whole tone 3: 31/27 239.1706
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 32/31 54.964 cents Greek enharmonic 1/4-tone 1: 1 9/8 203.910 cents major whole tone 1: 1 31/27 239.171 cents 2: 1 36/31 258.874 cents 2: 1 32/27 294.135 cents Pythagorean minor third 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 : 55.0 258.9 498.0 55.0 : 203.9 443.1 498.0 258.9: 239.2 294.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.9644 .. 239.1706 cents 961/864, 184.2061 cents 32/31, 54.9644 cents 2: 258.8744 .. 443.0806 cents 961/864, 184.2061 cents 972/961, 19.7039 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 : 31/27, 239.1706 cents Average / Smallest step : 3.020408 Largest / Average step : 1.440656 Largest / Smallest step : 4.351370 Median interval of one step : 9/8, 203.9100 cents, amount: 1 Least squares average step : 147.63202 cents, oct.: 442.89606 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1314-tone equal temperament with octave 4/3 degrees: 145 683 1314 Least number of segments generator : 659 of 249.781 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1045 of 396.086 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 : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.70386 cents Scale diversity : 0.772690 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.260283 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 : 972/961, 19.7039 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 : 31 Odd number limit : 31 (O: 31 U: 31) Highest odd numerator or denominator: 31 Scale harmonicity : 0.076923 Fundamental : 1/93, -6.5392 octaves, 2.8132 Hz. Guide tone : 288, 8.1699 octaves, 75348.163 Hz. Exponens Consonantiae : 2.678400E+04, 14.70908 octaves Euler's gradus suavitatis : 42 Sum of Mann's harmonic distance : 68.5, average 22.83333 Mersenne's string divisions : 4221 Sum of van Prooijen's expressibility: 3.45984, average 1.15328 Sum of Tenney's harmonic distance : 7.12336, average 2.37445 Vogel's harmonic complexity : 17.33333 Wille's k value : 15 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 19.83232, average 3.30539 Lattice compactness (without 2's) : 9.00000, average 1.50000 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 2 .. 5 3.00000 9 3: -1 .. 2 0.33333 3 1 31: -1 .. 0 -0.66667 2 2 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is JI-epimorphic with val: <7 11 34| Scale is weakly epimorphic with val: <7 11 37| Scale is weakly epimorphic with val: <8 11 37|
FIT/MODE
3: 0 1 2 N G T3 SD: 62.3002 c. M: 92.8594 c. 4: 0 2 2 P M DE S SD: 32.2395 c. M: 54.9644 c. 6: 1 2 3 P T3 SD: 17.1608 c. M:-28.0431 c. 7: 1 3 3 SP M DE S SD: 17.5462 c. M:-25.7227 c. 8: 1 3 4 P T3 SD: 7.0763 c. M: 9.8519 c. 10: 1 4 5 P T3 SD: 6.4209 c. M: 9.8519 c. 17: 2 7 8 SP T3 SD: 3.4726 c. M:-4.7965 c. 19: 2 8 9 SP T3 SD: 2.3830 c. M:-3.2545 c. 27: 3 11 13 SP T3 SD: 0.4224 c. M: 0.6289 c. 73: 8 30 35 SP T3 SD: 0.3127 c. M: 0.3842 c. 100: 11 41 48 SP T3 SD: 0.1212 c. M: 0.1795 c. 127: 14 52 61 SP T3 SD: 0.0452 c. M: 0.0618 c. 679: 75 278 326 SP T3 SD: 0.0401 c. M:-0.0503 c. 706: 78 289 339 SP T3 SD: 0.0376 c. M:-0.0604 c. 779: 86 319 374 SP T3 SD: 0.0351 c. M:-0.0578 c. 806: 89 330 387 SP T3 SD: 0.0268 c. M:-0.0348 c. 833: 92 341 400 SP T3 SD: 0.0253 c. M:-0.0417 c. 906: 100 371 435 SP T3 SD: 0.0252 c. M:-0.0430 c. 933: 103 382 448 SP T3 SD: 0.0171 c. M:-0.0236 c. 960: 106 393 461 SP T3 SD: 0.0165 c. M:-0.0280 c. 1060: 117 434 509 SP T3 SD: 0.0099 c. M:-0.0150 c. 1187: 131 486 570 SP T3 SD: 0.0048 c. M:-0.0083 c. 1314: 145 538 631 SP T3 SD: 0.0034 c. M: 0.0051 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: 50.8851 cents 6 x 7:8 S SD: 3.9982 cents 7 x 8:9 S SD: 34.3925 cents 8 x 9:11 SD: 38.2724 cents 9 x 10:12 S SD: 38.2354 cents 10 x 12:13 S SD: 35.8596 cents 12:13:14:16 S SD: 27.9966 cents 13:14:15:17 SD: 27.1455 cents 14:15:16:19 SD: 25.5250 cents 15:16:17:20 SD: 23.5756 cents 16:17:19:21 SD: 22.9380 cents 17:18:20:23 SD: 18.4975 cents 18:19:21:24 SD: 13.1525 cents 21:22:24:28 S SD: 12.5666 cents 23:24:27:31 SD: 10.8058 cents 24:25:28:32 SD: 5.8754 cents 30:31:35:40 SD: 2.7324 cents 57:59:66:76 SD: 2.3132 cents 63:65:73:84 SD: 1.3054 cents 87:90:101:116 SD: 1.2560 cents 93:96:108:124 SD: 0.0000 cents