Scala analysis: 469_D15
Diatonic tetrachord 121/108 * 9/8 * 128/121, Partch
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 121/108 196.770882 2: 121/96 400.680884 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 128/121 97.3641 undecimal semitone 1: 121/108 196.7709 2: 9/8 203.9100 major whole tone 3: 128/121 97.3641 undecimal semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 128/121 97.364 cents undecimal semitone 1: 1 121/108 196.771 cents 1: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 2: 1 121/96 400.681 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 : 196.8 400.7 498.0 196.8: 203.9 301.3 498.0 400.7: 97.4 294.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 97.3641 .. 203.9100 cents 1089/1024, 106.5459 cents 128/121, 97.3641 cents 2: 294.1350 .. 400.6809 cents 1089/1024, 106.5459 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 128/121, 97.3641 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.705094 Largest / Average step : 1.228263 Largest / Smallest step : 2.094303 Median interval of one step : 121/108, 196.7709 cents, amount: 1 Least squares average step : 178.01912 cents, oct.: 534.05735 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 977-tone equal temperament with octave 4/3 degrees: 386 786 977 Least number of segments generator : 489 of 249.277 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 782 of 398.640 cents and inv. generated superset size: 24 = 21 more = 800.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MLS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.087420 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.572144 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 : 243/242, 7.1391 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 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 106.5459 cents: 2 -- Rational properties -- Prime limit : 11 Odd number limit : 121 (O: 121 U: 121) Highest odd numerator or denominator: 121 Scale harmonicity : 0.019469 Average absolute harmonicity : 0.086188 Specific harmonicity : 0.083136 Fundamental : 1/864, -9.7549 octaves, 0.3028 Hz. Guide tone : 484, 8.9189 octaves, 126626.774 Hz. Exponens Consonantiae : 4.181760E+05, 18.67375 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 226.5, average 75.50000 Mersenne's string divisions : 49693 Sum of van Prooijen's expressibility: 4.64269, average 1.54756 Sum of Tenney's harmonic distance : 9.26045, average 3.08682 Vogel's harmonic complexity : 22.00000 Wille's k value : 544 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 27.62104, average 4.60351 Lattice compactness (without 2's) : 13.67005, average 2.27834 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.66667 9 3: -3 ..-1 -1.66667 5 1 11: 0 .. 2 1.33333 4 2 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is JI-epimorphic with val: <7 11 24| Scale is weakly epimorphic with val: <7 11 27| Scale is weakly epimorphic with val: <8 11 26|
FIT/MODE
3: 1 1 1 SP B ME I SD: 43.4314 c. M: 68.6509 c. 5: 2 2 1 SP M ME S SD: 1.9173 c. M:-2.4471 c. 36: 14 15 7 SP T3 SD: 1.8074 c. M: 3.0867 c. 41: 16 17 8 SP T3 SD: 1.3966 c. M: 2.4119 c. 46: 18 19 9 SP T3 SD: 1.0885 c. M: 1.8837 c. 51: 20 21 10 SP T3 SD: 0.8591 c. M: 1.4591 c. 56: 22 23 11 SP T3 SD: 0.6953 c. M: 1.1103 c. 61: 24 25 12 SP T3 SD: 0.5902 c. M: 0.8188 c. 66: 26 27 13 SP T3 SD: 0.5378 c. M: 0.7357 c. 71: 28 29 14 SP T3 SD: 0.5284 c. M: 0.8419 c. 127: 50 52 25 SP T3 SD: 0.5579 c. M: 0.6902 c. 129: 51 53 25 SP T3 SD: 0.4930 c. M:-0.8438 c. 134: 53 55 26 SP T3 SD: 0.4389 c. M:-0.7285 c. 139: 55 57 27 SP T3 SD: 0.3978 c. M:-0.6216 c. 144: 57 59 28 SP T3 SD: 0.3701 c. M:-0.5220 c. 149: 59 61 29 SP T3 SD: 0.3555 c. M:-0.4416 c. 154: 61 63 30 SP T3 SD: 0.3531 c. M:-0.5067 c. 185: 73 76 36 SP T3 SD: 0.2944 c. M:-0.4473 c. 190: 75 78 37 SP T3 SD: 0.2395 c. M:-0.3764 c. 195: 77 80 38 SP T3 SD: 0.1889 c. M:-0.3092 c. 200: 79 82 39 SP T3 SD: 0.1438 c. M:-0.2453 c. 205: 81 84 40 SP T3 SD: 0.1071 c. M:-0.1846 c. 210: 83 86 41 SP T3 SD: 0.0852 c. M:-0.1268 c. 271: 107 111 53 SP T3 SD: 0.0761 c. M: 0.1258 c. 276: 109 113 54 SP T3 SD: 0.0648 c. M: 0.0795 c. 476: 188 195 93 SP T3 SD: 0.0495 c. M: 0.0640 c. 481: 190 197 94 SP T3 SD: 0.0291 c. M: 0.0379 c. 486: 192 199 95 SP T3 SD: 0.0091 c. M: 0.0124 c. 977: 386 400 191 SP T3 SD: 0.0011 c. M: 0.0019 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: 14.3672 cents 5 x 6:7 S SD: 59.9300 cents 6:7 x 8 S SD: 35.0500 cents 7:8:9 x S SD: 24.3267 cents 8:9:10:11 H SD: 18.5454 cents 9:10:11:12 H SD: 18.3921 cents 10:11 x 13 SD: 27.0660 cents 11:12:14:15 S SD: 20.8836 cents 12:13:15:16 SD: 19.9818 cents 14:16:18:19 S SD: 19.1662 cents 15:17:19:20 SD: 7.2263 cents 24:27:30:32 S SD: 5.3477 cents 27:30:34:36 SD: 4.8183 cents 39:44:49:52 SD: 4.4213 cents 42:47:53:56 SD: 0.9635 cents 108:121:136:144 SD: 0.5302 cents 150:168:189:200 SD: 0.2698 cents 315:353:397:420 SD: 0.1436 cents 357:400:450:476 SD: 0.0567 cents 507:568:639:676 SD: 0.0399 cents