Scala analysis: 462_D15
Diatonic tetrachord 9/8 * 17/16 * 512/459
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: 153/128 308.865411 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 512/459 189.1796 1: 9/8 203.9100 major whole tone 2: 17/16 104.9554 17th harmonic 3: 512/459 189.1796
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 17/16 104.955 cents 17th harmonic 1: 1 512/459 189.180 cents 1: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 153/128 308.865 cents 2: 1 64/51 393.090 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 : 203.9 308.9 498.0 203.9: 105.0 294.1 498.0 308.9: 189.2 393.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 104.9554 .. 203.9100 cents 18/17, 98.9546 cents 17/16, 104.9554 cents 2: 294.1350 .. 393.0896 cents 18/17, 98.9546 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 17/16, 104.9554 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.581767 Largest / Average step : 1.228263 Largest / Smallest step : 1.942825 Median interval of one step : 512/459, 189.1796 cents, amount: 1 Least squares average step : 165.41256 cents, oct.: 496.23768 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1082-tone equal temperament with octave 4/3 degrees: 443 671 1082 Least number of segments generator : 543 of 249.943 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1021 of 469.967 cents and inv. generated superset size: 26 = 23 more = 866.667% 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 : 1.171077 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.602628 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 : 4131/4096, 14.7304 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 : 17 Odd number limit : 459 (O: 153 U: 459) Highest odd numerator or denominator: 153 Scale harmonicity : 0.021223 Average absolute harmonicity : 0.119280 Specific harmonicity : 0.106890 Fundamental : 1/384, -8.5850 octaves, 0.6813 Hz. Guide tone : 612, 9.2574 octaves, 160114.846 Hz. Exponens Consonantiae : 2.350080E+05, 17.84235 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 152.5, average 50.83333 Mersenne's string divisions : 33439 Sum of van Prooijen's expressibility: 3.61606, average 1.20535 Sum of Tenney's harmonic distance : 7.22842, average 2.40947 Vogel's harmonic complexity : 16.00000 Wille's k value : 229 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 32.68354, average 5.44726 Lattice compactness (without 2's) : 12.39835, average 2.06639 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 2 -2.66667 12 3: -1 .. 2 1.00000 5 2 17: 0 .. 1 0.33333 1 1 Average exponent except 2's : 4 / 3 = 1.33333 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 10 32| Scale is JI-epimorphic with val: <7 11 29| Scale is weakly epimorphic with val: <7 11 32| 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: 25.6426 c. M: 37.8950 c. 5: 2 1 2 SP M ME I SD: 6.3975 c. M: 10.0384 c. 19: 8 4 7 SP T3 SD: 4.6879 c. M:-5.7932 c. 22: 9 5 8 SP T3 SD: 4.6615 c. M:-8.0723 c. 24: 10 5 9 SP T3 SD: 2.5063 c. M:-3.6087 c. 29: 12 6 11 SP T3 SD: 1.2666 c. M:-2.1776 c. 34: 14 7 13 SP T3 SD: 0.9872 c. M: 1.2494 c. 61: 25 13 23 SP T3 SD: 0.8126 c. M:-1.3921 c. 66: 27 14 25 SP T3 SD: 0.3183 c. M:-0.5262 c. 71: 29 15 27 SP T3 SD: 0.3060 c. M: 0.4832 c. 100: 41 21 38 SP T3 SD: 0.1724 c. M:-0.2884 c. 166: 68 35 63 SP T3 SD: 0.1128 c. M:-0.1625 c. 171: 70 36 65 SP T3 SD: 0.0805 c. M: 0.1358 c. 237: 97 50 90 SP T3 SD: 0.0486 c. M: 0.0688 c. 337: 138 71 128 SP T3 SD: 0.0224 c. M:-0.0372 c. 574: 235 121 218 SP T3 SD: 0.0158 c. M:-0.0266 c. 745: 305 157 283 SP T3 SD: 0.0094 c. M: 0.0124 c. 1082: 443 228 411 SP T3 SD: 0.0028 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: 77.4483 cents 5 x 6:7 S SD: 42.3693 cents 6 x 7:8 S SD: 20.9973 cents 7:8 x 9 S SD: 34.3053 cents 8:9:10:11 H SD: 31.3338 cents 9:10:11:12 H SD: 14.7122 cents 12 x 14:16 S SD: 20.9973 cents 14:16:17:19 SD: 16.4168 cents 15:17:18:20 SD: 4.8207 cents 40:45:48:53 SD: 4.2652 cents 41:46:49:55 SD: 3.8429 cents 47:53:56:63 SD: 3.8271 cents 48:54:57:64 SD: 3.7841 cents 55:62:66:73 SD: 3.6565 cents 56:63:67:75 SD: 2.6263 cents 57:64:68:76 SD: 1.5924 cents 72:81:86:96 SD: 0.4192 cents 225:253:269:300 SD: 0.3083 cents 240:270:287:320 SD: 0.2514 cents 297:334:355:396 SD: 0.2163 cents 312:351:373:416 SD: 0.0967 cents 384:432:459:512 SD: 0.0000 cents