Scala analysis: 437_D11
Diatonic tetrachord 160/153 * 9/8 * 17/15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 160/153 77.448303 2: 20/17 281.358304 septendecimal augmented second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 17/15 216.6867 septendecimal whole tone 1: 160/153 77.4483 2: 9/8 203.9100 major whole tone 3: 17/15 216.6867 septendecimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 160/153 77.448 cents 1: 1 9/8 203.910 cents major whole tone 1: 1 17/15 216.687 cents septendecimal whole tone 2: 1 20/17 281.358 cents septendecimal augmented second 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 51/40 420.597 cents septendecimal 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 : 77.4 281.4 498.0 77.4 : 203.9 420.6 498.0 281.4: 216.7 294.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 77.4483 .. 216.6867 cents 867/800, 139.2384 cents 160/153, 77.4483 cents 2: 281.3583 .. 420.5967 cents 867/800, 139.2384 cents 300/289, 64.6716 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 160/153, 77.4483 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/15, 216.6867 cents Average / Smallest step : 2.143559 Largest / Average step : 1.305224 Largest / Smallest step : 2.797824 Median interval of one step : 9/8, 203.9100 cents, amount: 1 Least squares average step : 152.44999 cents, oct.: 457.34998 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1209-tone equal temperament with octave 4/3 degrees: 188 683 1209 Least number of segments generator : 605 of 249.228 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 664 of 273.533 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 64.67161 cents Scale diversity : 0.940782 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.440860 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 : 136/135, 12.7767 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 126.4617 cents: 1 -- Rational properties -- Prime limit : 17 Odd number limit : 153 (O: 51 U: 153) Highest odd numerator or denominator: 153 Scale harmonicity : 0.021344 Average absolute harmonicity : 0.087197 Specific harmonicity : 0.089018 Fundamental : 1/153, -7.2574 octaves, 1.7100 Hz. Guide tone : 160, 7.3219 octaves, 41860.090 Hz. Exponens Consonantiae : 2.448000E+04, 14.57932 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 178.5, average 59.50000 Mersenne's string divisions : 81067 Sum of van Prooijen's expressibility: 3.89226, average 1.29742 Sum of Tenney's harmonic distance : 7.99947, average 2.66649 Vogel's harmonic complexity : 15.00000 Wille's k value : 25 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 19.05503, average 3.17584 Lattice compactness (without 2's) : 10.32780, average 1.72130 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 5 3.00000 9 3: -2 .. 0 -1.00000 3 1 5: 0 .. 1 0.66667 2 17: -1 .. 0 -0.66667 2 2 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 18 27| Scale is weakly epimorphic with val: <6 10 19 28| Scale is weakly epimorphic with val: <6 11 18 27| Scale is weakly epimorphic with val: <6 11 19 28| Scale is weakly epimorphic with val: <7 10 15 27| Scale is weakly epimorphic with val: <7 10 16 28| Scale is weakly epimorphic with val: <7 10 17 29| Scale is weakly epimorphic with val: <7 10 18 30| Scale is weakly epimorphic with val: <7 10 19 31| Scale is JI-epimorphic with val: <7 11 15 27| Scale is weakly epimorphic with val: <7 11 15 30| Scale is weakly epimorphic with val: <7 11 15 33| Scale is JI-epimorphic with val: <7 11 16 28| Scale is weakly epimorphic with val: <7 11 16 31| Scale is JI-epimorphic with val: <7 11 17 29| Scale is weakly epimorphic with val: <7 11 17 32| Scale is weakly epimorphic with val: <7 11 18 27| Scale is JI-epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 11 18 33| Scale is weakly epimorphic with val: <7 11 19 28| Scale is JI-epimorphic with val: <7 11 19 31| Scale is weakly epimorphic with val: <8 11 15 30| Scale is weakly epimorphic with val: <8 11 16 31| Scale is weakly epimorphic with val: <8 11 17 32| Scale is weakly epimorphic with val: <8 11 18 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 80.2129 c. M: 115.3433 c. 4: 0 2 2 P M DE S SD: 48.4556 c. M: 77.4483 c. 5: 1 2 2 SP M ME S SD: 16.2916 c. M:-22.1607 c. 7: 1 3 3 SP M DE S SD: 4.0893 c. M: 6.2990 c. 18: 3 7 8 SP T3 SD: 4.1906 c. M:-5.5592 c. 19: 3 8 8 SP M DE S SD: 4.0901 c. M:-6.9835 c. 25: 4 10 11 SP T3 SD: 1.9175 c. M: 2.4531 c. 32: 5 13 14 SP T3 SD: 0.7296 c. M: 1.2080 c. 39: 6 16 17 SP T3 SD: 0.5324 c. M: 0.8260 c. 71: 11 29 31 SP T3 SD: 0.4741 c. M: 0.7696 c. 83: 13 34 36 SP T3 SD: 0.5024 c. M:-0.6672 c. 90: 14 37 39 SP T3 SD: 0.5009 c. M:-0.8672 c. 110: 17 45 48 SP T3 SD: 0.4620 c. M: 0.6420 c. 115: 18 47 50 SP T3 SD: 0.3043 c. M:-0.5066 c. 122: 19 50 53 SP T3 SD: 0.1981 c. M:-0.3229 c. 154: 24 63 67 SP T3 SD: 0.0977 c. M:-0.1691 c. 161: 25 66 70 SP T3 SD: 0.1060 c. M:-0.1454 c. 193: 30 79 84 SP T3 SD: 0.0492 c. M: 0.0790 c. 315: 49 129 137 SP T3 SD: 0.0466 c. M:-0.0766 c. 347: 54 142 151 SP T3 SD: 0.0409 c. M:-0.0573 c. 508: 79 208 221 SP T3 SD: 0.0103 c. M:-0.0175 c. 701: 109 287 305 SP T3 SD: 0.0063 c. M: 0.0091 c. 1209: 188 495 526 SP T3 SD: 0.0017 c. M:-0.0021 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: 104.9554 cents 5 x 6:7 S SD: 45.5797 cents 6 x 7:8 S SD: 7.2437 cents 7 x 8:9 S SD: 40.2571 cents 8 x 9:11 SD: 47.0007 cents 9 x 11:12 SD: 33.0248 cents 11:12:13:15 SD: 27.7527 cents 12:13:14:16 S SD: 20.9393 cents 15:16:18:20 S SD: 16.1612 cents 16:17:19:21 SD: 13.9879 cents 17:18:20:23 SD: 11.0619 cents 18:19:21:24 SD: 7.2331 cents 21:22:25:28 SD: 6.9066 cents 23:24:27:31 SD: 6.4866 cents 24:25:28:32 SD: 5.3312 cents 39:41:46:52 SD: 3.3836 cents 45:47:53:60 SD: 0.9652 cents 108:113:127:144 SD: 0.4021 cents 153:160:180:204 SD: 0.0000 cents