Scala analysis: 288_C21
Chromatic tetrachord 51/50 * 10/9 * 20/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 51/50 34.282983 17th-partial chroma 2: 17/15 216.686695 septendecimal whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 20/17 281.3583 septendecimal augmented second 1: 51/50 34.2830 17th-partial chroma 2: 10/9 182.4037 minor whole tone 3: 20/17 281.3583 septendecimal augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 51/50 34.283 cents 17th-partial chroma 1: 1 10/9 182.404 cents minor whole tone 1: 1 20/17 281.358 cents septendecimal augmented second 2: 1 17/15 216.687 cents septendecimal whole tone 2: 1 6/5 315.641 cents minor third 2: 1 200/153 463.762 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 : 34.3 216.7 498.0 34.3 : 182.4 463.8 498.0 216.7: 281.4 315.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.2830 .. 281.3583 cents 1000/867, 247.0753 cents 51/50, 34.2830 cents 2: 216.6867 .. 463.7620 cents 1000/867, 247.0753 cents 289/300,-64.6716 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 51/50, 34.2830 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 20/17, 281.3583 cents Average / Smallest step : 4.842490 Largest / Average step : 1.694776 Largest / Smallest step : 8.206938 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 140.12795 cents, oct.: 420.38386 cents Scale is not proper Scale has trivalence property Scale is a mode of a 770-tone equal temperament with octave 4/3 degrees: 53 335 770 Least number of segments generator : 387 of 250.316 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 529 of 342.163 cents and inv. generated superset size: 19 = 16 more = 633.333% 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 34.28298 cents Scale diversity : 0.678842 Lumma stability : 0.137670 Lumma impropriety factor : 0.129851 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 : 51/50, 34.2830 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing 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 : 153 (O: 51 U: 153) Highest odd numerator or denominator: 51 Scale harmonicity : 0.019512 Average absolute harmonicity : 0.087090 Specific harmonicity : 0.082928 Fundamental : 1/150, -7.2288 octaves, 1.7442 Hz. Guide tone : 204, 7.6724 octaves, 53371.615 Hz. Exponens Consonantiae : 3.060000E+04, 14.90124 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 70.0, average 23.33333 Mersenne's string divisions : 22624 Sum of van Prooijen's expressibility: 3.41514, average 1.13838 Sum of Tenney's harmonic distance : 6.89226, average 2.29742 Vogel's harmonic complexity : 19.66667 Wille's k value : 76 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 15.75549, average 2.62592 Lattice compactness (without 2's) : 11.83182, average 1.97197 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -1 .. 1 -0.33333 3 1 5: -2 .. 0 -1.00000 3 17: 0 .. 1 0.66667 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 15 29| Scale is weakly epimorphic with val: <6 10 16 29| Scale is weakly epimorphic with val: <6 10 19 32| Scale is weakly epimorphic with val: <6 11 15 28| Scale is weakly epimorphic with val: <6 11 17 31| Scale is weakly epimorphic with val: <7 10 15 30| Scale is weakly epimorphic with val: <7 10 17 30| Scale is JI-epimorphic with val: <7 11 16 29| Scale is weakly epimorphic with val: <7 11 16 32| Scale is weakly 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 19 29| Scale is weakly epimorphic with val: <7 11 19 32| Scale is weakly epimorphic with val: <7 12 15 28| Scale is weakly epimorphic with val: <7 12 16 31| Scale is weakly epimorphic with val: <8 11 15 30| Scale is weakly epimorphic with val: <8 11 16 30| Scale is weakly epimorphic with val: <8 11 19 33| Scale is weakly epimorphic with val: <8 12 15 29| Scale is weakly epimorphic with val: <8 12 17 32|
FIT/MODE
3: 0 1 2 N G T3 SD: 35.3221 c. M: 50.6717 c. 4: 0 2 2 P M DE S SD: 27.2086 c. M: 34.2830 c. 5: 0 2 3 N G T3 SD: 22.2147 c. M: 34.2830 c. 7: 0 3 4 N G T3 SD: 19.8814 c. M: 34.2830 c. 9: 1 3 5 N T3 SD: 12.4513 c. M:-21.0554 c. 10: 1 3 6 N T3 SD: 13.4916 c. M: 17.4687 c. 11: 1 4 6 N T3 SD: 8.4637 c. M:-10.9938 c. 12: 1 4 7 N T3 SD: 6.7377 c. M: 9.1679 c. 14: 1 5 8 N T3 SD: 2.0132 c. M: 3.2388 c. 16: 1 6 9 N T3 SD: 1.9506 c. M: 3.1552 c. 30: 2 11 17 N T3 SD: 0.7997 c. M: 1.0800 c. 71: 5 26 40 N T3 SD: 0.6370 c. M:-0.7906 c. 85: 6 31 48 N T3 SD: 0.5080 c. M:-0.8731 c. 87: 6 32 49 N T3 SD: 0.4923 c. M:-0.8502 c. 101: 7 37 57 N T3 SD: 0.2126 c. M:-0.2834 c. 131: 9 48 74 N T3 SD: 0.0399 c. M: 0.0662 c. 377: 26 138 213 N T3 SD: 0.0414 c. M:-0.0649 c. 494: 34 181 279 N T3 SD: 0.0427 c. M:-0.0738 c. 508: 35 186 287 N T3 SD: 0.0206 c. M:-0.0311 c. 639: 44 234 361 N T3 SD: 0.0086 c. M:-0.0112 c. 770: 53 282 435 N T3 SD: 0.0030 c. M: 0.0048 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 x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 65.0514 cents 6 x 7:8 S SD: 25.0921 cents 7 x 8:9 S SD: 32.3031 cents 8 x 9:11 SD: 27.3918 cents 9 x 10:12 S SD: 17.1415 cents 10 x 11:13 SD: 33.8830 cents 11 x 12:15 S SD: 38.3282 cents 12 x 14:16 S SD: 25.0921 cents 13 x 15:17 SD: 22.8828 cents 18:19:20:24 S SD: 22.8381 cents 20:21:23:27 SD: 20.0548 cents 21:22:24:28 S SD: 16.1566 cents 22:23:25:29 SD: 15.7546 cents 23:24:26:31 SD: 14.6140 cents 24:25:27:32 SD: 12.8558 cents 27:28:31:36 SD: 12.1470 cents 28:29:32:37 SD: 11.3114 cents 29:30:33:39 SD: 9.8078 cents 30:31:34:40 SD: 7.4946 cents 36:37:41:48 SD: 5.2134 cents 39:40:44:52 SD: 4.1205 cents 44:45:50:59 SD: 3.9293 cents 45:46:51:60 SD: 1.2559 cents 96:98:109:128 SD: 1.1599 cents 99:101:112:132 SD: 1.0359 cents 105:107:119:140 SD: 0.5391 cents 150:153:170:200 SD: 0.0000 cents