Scala analysis: 464_D15
Diatonic tetrachord 9/8 * 19/18 * 64/57
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 19/16 297.513016 19th harmonic 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 64/57 200.5320 1: 9/8 203.9100 major whole tone 2: 19/18 93.6030 undevicesimal semitone 3: 64/57 200.5320
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 19/18 93.603 cents undevicesimal semitone 1: 1 64/57 200.532 cents 1: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 19/16 297.513 cents 19th harmonic 2: 1 24/19 404.442 cents smaller undevicesimal major third 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 : 203.9 297.5 498.0 203.9: 93.6 294.1 498.0 297.5: 200.5 404.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 93.6030 .. 203.9100 cents 81/76, 110.3070 cents 19/18, 93.6030 cents 2: 294.1350 .. 404.4420 cents 81/76, 110.3070 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 19/18, 93.6030 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.773607 Largest / Average step : 1.228263 Largest / Smallest step : 2.178456 Median interval of one step : 64/57, 200.5320 cents, amount: 1 Least squares average step : 163.79079 cents, oct.: 491.37236 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 2208-tone equal temperament with octave 4/3 degrees: 904 1319 2208 Least number of segments generator : 1105 of 249.248 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 2045 of 461.278 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 90.22500 cents Scale diversity : 1.042727 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.557040 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 : 513/512, 3.3780 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 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 : 19 Odd number limit : 57 (O: 19 U: 57) Highest odd numerator or denominator: 19 Scale harmonicity : 0.020788 Average absolute harmonicity : 0.120176 Specific harmonicity : 0.108610 Fundamental : 1/48, -5.5850 octaves, 5.4505 Hz. Guide tone : 684, 9.4179 octaves, 178951.887 Hz. Exponens Consonantiae : 3.283200E+04, 15.00282 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 29.5, average 9.83333 Mersenne's string divisions : 595 Sum of van Prooijen's expressibility: 2.71012, average 0.90337 Sum of Tenney's harmonic distance : 5.41939, average 1.80646 Vogel's harmonic complexity : 12.66667 Wille's k value : 28 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 24.40958, average 4.06826 Lattice compactness (without 2's) : 10.65028, average 1.77505 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -1.66667 9 3: -1 .. 2 0.33333 3 2 19: 0 .. 1 0.33333 1 1 Average exponent except 2's : 2 / 3 = 0.66667 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is weakly epimorphic with val: <7 10 31| Scale is JI-epimorphic with val: <7 11 30| Scale is weakly epimorphic with val: <7 11 33| Scale is weakly epimorphic with val: <7 12 29| Scale is weakly epimorphic with val: <7 12 32|
FIT/MODE
3: 1 1 1 SP B ME I SD: 29.5942 c. M: 37.8950 c. 5: 2 1 2 SP M ME I SD: 2.8131 c. M: 4.6920 c. 17: 7 3 7 SP M DE I SD: 2.7094 c. M: 4.5454 c. 22: 9 4 9 SP M DE I SD: 1.8579 c. M: 3.2137 c. 27: 11 5 11 SP M DE I SD: 1.4885 c. M: 2.3752 c. 32: 13 6 13 SP M DE I SD: 1.3820 c. M: 1.7988 c. 75: 31 14 30 SP T3 SD: 1.3569 c. M:-1.9486 c. 80: 33 15 32 SP T3 SD: 1.1660 c. M:-1.5336 c. 85: 35 16 34 SP T3 SD: 1.0148 c. M:-1.3140 c. 90: 37 17 36 SP T3 SD: 0.9010 c. M:-1.3140 c. 95: 39 18 38 SP T3 SD: 0.8225 c. M:-1.3140 c. 100: 41 19 40 SP T3 SD: 0.7767 c. M:-1.3140 c. 102: 42 19 41 SP T3 SD: 0.7016 c. M:-1.1674 c. 107: 44 20 43 SP T3 SD: 0.5613 c. M:-0.8935 c. 112: 46 21 45 SP T3 SD: 0.4455 c. M:-0.6442 c. 117: 48 22 47 SP T3 SD: 0.3593 c. M:-0.4626 c. 122: 50 23 49 SP T3 SD: 0.3111 c. M:-0.4975 c. 127: 52 24 51 SP T3 SD: 0.3059 c. M:-0.5297 c. 139: 57 26 56 SP T3 SD: 0.1995 c. M:-0.3243 c. 144: 59 27 58 SP T3 SD: 0.0955 c. M:-0.1501 c. 149: 61 28 60 SP T3 SD: 0.0151 c. M: 0.0231 c. 1458: 597 274 587 SP T3 SD: 0.0157 c. M:-0.0220 c. 1463: 599 275 589 SP T3 SD: 0.0122 c. M:-0.0204 c. 1607: 658 302 647 SP T3 SD: 0.0130 c. M:-0.0188 c. 1612: 660 303 649 SP T3 SD: 0.0097 c. M:-0.0163 c. 1756: 719 330 707 SP T3 SD: 0.0108 c. M:-0.0162 c. 1761: 721 331 709 SP T3 SD: 0.0077 c. M:-0.0130 c. 1910: 782 359 769 SP T3 SD: 0.0060 c. M:-0.0102 c. 2059: 843 387 829 SP T3 SD: 0.0045 c. M:-0.0078 c. 2208: 904 415 889 SP T3 SD: 0.0033 c. M:-0.0057 c. 2357: 965 443 949 SP T3 SD: 0.0023 c. M:-0.0039 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: 88.8007 cents 5 x 6:7 S SD: 43.1953 cents 6 x 7:8 S SD: 15.3211 cents 7:8 x 9 S SD: 34.3053 cents 9:10:11:12 H SD: 18.1108 cents 12 x 14:16 S SD: 15.3211 cents 13:15 x 17 SD: 27.6192 cents 14:16:17:19 SD: 18.7780 cents 15:17:18:20 SD: 7.3928 cents 27:30:32:36 S SD: 7.2567 cents 31:35:37:41 SD: 5.8901 cents 32:36:38:43 SD: 4.4909 cents 33:37:39:44 SD: 3.3836 cents 48:54:57:64 SD: 0.0000 cents