Scala analysis: 470_D15
Diatonic tetrachord 9/8 * 4096/3645 * 135/128
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: 512/405 405.866283 narrow diminished fourth 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 135/128 92.1787 major chroma, major limma 1: 9/8 203.9100 major whole tone 2: 4096/3645 201.9563 narrow diminished third 3: 135/128 92.1787 major chroma, major limma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 135/128 92.179 cents major chroma, major limma 1: 1 4096/3645 201.956 cents narrow diminished third 1: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 1215/1024 296.089 cents wide augmented second 2: 1 512/405 405.866 cents narrow 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 : 203.9 405.9 498.0 203.9: 202.0 294.1 498.0 405.9: 92.2 296.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 203.9100 cents 16/15, 111.7313 cents 135/128, 92.1787 cents 2: 294.1350 .. 405.8663 cents 16/15, 111.7313 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 135/128, 92.1787 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.801012 Largest / Average step : 1.228263 Largest / Smallest step : 2.212116 Median interval of one step : 4096/3645, 201.9563 cents, amount: 1 Least squares average step : 179.26983 cents, oct.: 537.80948 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1529-tone equal temperament with octave 4/3 degrees: 626 1246 1529 Least number of segments generator : 765 of 249.185 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1222 of 398.045 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 : LMS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.025355 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.551321 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 : 32805/32768, 1.9537 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 decreasing 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% Limited inverse transpositions with margin 109.7776 cents: 2 -- Rational properties -- Prime limit : 5 Odd number limit : 3645 (O: 1215 U: 3645) Highest odd numerator or denominator: 405 Scale harmonicity : 0.029070 Average absolute harmonicity : 0.124216 Specific harmonicity : 0.148331 Fundamental : 1/3240, -11.6618 octaves, 0.0807 Hz. Guide tone : 4608, 12.1699 octaves, 1205570.605 Hz. Exponens Consonantiae : 1.492992E+07, 23.83170 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 470.5, average 156.83333 Mersenne's string divisions : 15589 Sum of van Prooijen's expressibility: 4.03882, average 1.34627 Sum of Tenney's harmonic distance : 8.25324, average 2.75108 Vogel's harmonic complexity : 18.00000 Wille's k value : 1822 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 7 Lattice compactness : 42.70684, average 7.11781 Lattice compactness (without 2's) : 19.36815, average 3.22802 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 9 2.66667 14 3: -4 .. 2 -1.00000 7 2 5: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is JI-epimorphic with val: <7 11 17| = patent Scale is weakly epimorphic with val: <7 12 17|
FIT/MODE
3: 1 1 1 SP B ME I SD: 47.9160 c. M: 73.8363 c. 4: 2 1 1 P M ME S SD: 32.0444 c. M:-45.1125 c. 5: 2 2 1 SP M ME S SD: 5.0736 c. M: 7.4303 c. 17: 7 7 3 SP M DE S SD: 2.5660 c. M:-4.2884 c. 22: 9 9 4 SP M DE S SD: 0.9430 c. M:-1.6251 c. 27: 11 11 5 SP M DE S SD: 0.5797 c. M: 1.0028 c. 49: 20 20 9 SP M DE S SD: 0.5428 c. M:-0.7011 c. 76: 31 31 14 SP M DE S SD: 0.5052 c. M: 0.7601 c. 129: 53 52 24 SP T3 SD: 0.4966 c. M:-0.7131 c. 141: 58 57 26 SP T3 SD: 0.5879 c. M:-0.9596 c. 146: 60 59 27 SP T3 SD: 0.4444 c. M:-0.7660 c. 151: 62 61 28 SP T3 SD: 0.3525 c. M:-0.5853 c. 156: 64 63 29 SP T3 SD: 0.3359 c. M:-0.4162 c. 173: 71 70 32 SP T3 SD: 0.2846 c. M:-0.4900 c. 178: 73 72 33 SP T3 SD: 0.2182 c. M:-0.3444 c. 200: 82 81 37 SP T3 SD: 0.1682 c. M:-0.2884 c. 205: 84 83 38 SP T3 SD: 0.1265 c. M:-0.1670 c. 227: 93 92 42 SP T3 SD: 0.0797 c. M:-0.1349 c. 232: 95 94 43 SP T3 SD: 0.0779 c. M: 0.1313 c. 254: 104 103 47 SP T3 SD: 0.0144 c. M:-0.0208 c. 994: 407 403 184 SP T3 SD: 0.0134 c. M:-0.0179 c. 1021: 418 414 189 SP T3 SD: 0.0105 c. M: 0.0157 c. 1275: 522 517 236 SP T3 SD: 0.0055 c. M: 0.0084 c. 1529: 626 620 283 SP T3 SD: 0.0022 c. M: 0.0036 c. 1783: 730 723 330 SP T3 SD: 0.0004 c. M:-0.0007 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: 19.5526 cents 5 x 6:7 S SD: 61.7966 cents 6:7 x 8 S SD: 31.4805 cents 7:8:9 x S SD: 19.9813 cents 8:9:10:11 H SD: 18.9159 cents 10:11 x 13 SD: 29.3037 cents 11:12:14:15 S SD: 22.3288 cents 12:14:15:16 S SD: 21.9757 cents 14:16:18:19 S SD: 16.7861 cents 15:17:19:20 SD: 4.4052 cents 33:37:42:44 SD: 4.3413 cents 39:44:49:52 SD: 3.9255 cents 42:47:53:56 SD: 3.2357 cents 48:54:61:64 SD: 3.0212 cents 57:64:72:76 SD: 1.2220 cents 72:81:91:96 SD: 0.1409 cents 552:621:698:736 SD: 0.1347 cents