Scala analysis: 384_D4
Diatonic tetrachord 54/49 * 98/93 * 31/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 54/49 168.213190 Zalzal's mujannab 2: 36/31 258.874429 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 31/27 239.1706 1: 54/49 168.2132 Zalzal's mujannab 2: 98/93 90.6612 3: 31/27 239.1706
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 98/93 90.661 cents 1: 1 54/49 168.213 cents Zalzal's mujannab 1: 1 31/27 239.171 cents 2: 1 36/31 258.874 cents 2: 1 98/81 329.832 cents 2: 1 62/49 407.384 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 : 168.2 258.9 498.0 168.2: 90.7 329.8 498.0 258.9: 239.2 407.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.6612 .. 239.1706 cents 961/882, 148.5093 cents 98/93, 90.6612 cents 2: 258.8744 .. 407.3838 cents 961/882, 148.5093 cents 972/961, 19.7039 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 98/93, 90.6612 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 31/27, 239.1706 cents Average / Smallest step : 1.831157 Largest / Average step : 1.440656 Largest / Smallest step : 2.638069 Median interval of one step : 54/49, 168.2132 cents, amount: 1 Least squares average step : 155.72122 cents, oct.: 467.16365 cents Scale is strictly 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 19.70386 cents Scale diversity : 1.138952 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.403631 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 Best fifths form a closed circle Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 31 Odd number limit : 93 (O: 49 U: 93) Highest odd numerator or denominator: 49 Scale harmonicity : 0.030086 Fundamental : 1/4557, -12.1539 octaves, 0.0574 Hz. Guide tone : 108, 6.7549 octaves, 28255.561 Hz. Exponens Consonantiae : 4.921560E+05, 18.90876 octaves Euler's gradus suavitatis : 53 Sum of Mann's harmonic distance : 88.5, average 29.50000 Mersenne's string divisions : 48307 Sum of van Prooijen's expressibility: 3.65868, average 1.21956 Sum of Tenney's harmonic distance : 7.54944, average 2.51648 Vogel's harmonic complexity : 38.66667 Wille's k value : 1255 Wilson's harmonic complexity : 57 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 18.83822, average 3.13970 Lattice compactness (without 2's) : 16.31376, average 2.71896 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 3 1.33333 6 1 7: -2 .. 0 -0.66667 2 1 31: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 11 18 35| Scale is weakly epimorphic with val: <6 11 18 38| Scale is weakly epimorphic with val: <7 11 18 34| Scale is weakly epimorphic with val: <7 11 18 37| Scale is weakly epimorphic with val: <7 11 19 35| Scale is weakly epimorphic with val: <7 11 19 38| Scale is weakly epimorphic with val: <7 11 21 34| Scale is weakly epimorphic with val: <7 11 21 37| Scale is weakly epimorphic with val: <7 11 22 35| Scale is weakly epimorphic with val: <7 11 22 38| Scale is weakly epimorphic with val: <7 12 18 35| Scale is weakly epimorphic with val: <7 12 20 34| Scale is weakly epimorphic with val: <7 12 20 37| Scale is weakly epimorphic with val: <7 12 21 35| Scale is weakly epimorphic with val: <8 11 19 34| Scale is weakly epimorphic with val: <8 11 19 37| Scale is weakly epimorphic with val: <8 11 20 35| Scale is weakly epimorphic with val: <8 12 18 37| Scale is weakly epimorphic with val: <8 12 21 37|
FIT/MODE
3: 1 1 1 SP B ME I SD: 42.2555 c. M:-73.1556 c. 4: 1 1 2 P M ME S SD: 25.8645 c. M: 43.7019 c. 5: 2 1 2 SP M ME I SD: 29.1976 c. M:-39.9526 c. 6: 2 1 3 P T3 SD: 5.8279 c. M: 9.8519 c. 15: 5 3 7 SP T3 SD: 4.0983 c. M:-6.7496 c. 21: 7 4 10 SP T3 SD: 1.7183 c. M: 2.1982 c. 27: 9 5 13 SP T3 SD: 1.3200 c. M: 2.1982 c. 44: 15 8 21 SP T3 SD: 1.2427 c. M:-1.5749 c. 50: 17 9 24 SP T3 SD: 0.6509 c. M:-1.1221 c. 56: 19 10 27 SP T3 SD: 0.7084 c. M: 0.9583 c. 71: 24 13 34 SP T3 SD: 0.3953 c. M:-0.6701 c. 77: 26 14 37 SP T3 SD: 0.0898 c. M: 0.1498 c. 225: 76 41 108 SP T3 SD: 0.0635 c. M:-0.1090 c. 302: 102 55 145 SP T3 SD: 0.0248 c. M:-0.0430 c. 379: 128 69 182 SP T3 SD: 0.0051 c. M: 0.0080 c. 1593: 538 290 765 SP T3 SD: 0.0060 c. M: 0.0097 c. 1972: 666 359 947 SP T3 SD: 0.0055 c. M: 0.0094 c. 2351: 794 428 1129 SP T3 SD: 0.0053 c. M: 0.0091 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 8:9 x 11 SD: 32.0635 cents 9:10 x 12 S SD: 7.0953 cents 15 x 17:20 SD: 21.0939 cents 16:18:19:21 SD: 19.7499 cents 17:19:20:23 SD: 13.8922 cents 18:20:21:24 S SD: 5.4295 cents 30:33:35:40 SD: 2.8721 cents 57:63:66:76 SD: 2.3863 cents 68:75:79:91 SD: 2.1823 cents 69:76:80:92 SD: 0.9803 cents 87:96:101:116 SD: 0.7592 cents 99:109:115:132 SD: 0.5637 cents 168:185:195:224 SD: 0.5295 cents 186:205:216:248 SD: 0.0575 cents