Scala analysis: 328_C24
Chromatic tetrachord 7/6 * 1024/945 * 135/128
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 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: 7/6 266.8709 septimal minor third 2: 1024/945 138.9954 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 1024/945 138.995 cents 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 315/256 359.050 cents 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 : 266.9 405.9 498.0 266.9: 139.0 231.2 498.0 405.9: 92.2 359.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 266.8709 cents 448/405, 174.6922 cents 135/128, 92.1787 cents 2: 231.1741 .. 405.8663 cents 448/405, 174.6922 cents 48/49,-35.6968 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 : 7/6, 266.8709 cents Average / Smallest step : 1.801012 Largest / Average step : 1.607511 Largest / Smallest step : 2.895147 Median interval of one step : 1024/945, 138.9954 cents, amount: 1 Least squares average step : 183.76703 cents, oct.: 551.30110 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1702-tone equal temperament with octave 4/3 degrees: 912 1387 1702 Least number of segments generator : 853 of 249.608 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1227 of 359.049 cents and inv. generated superset size: 72 = 69 more = 2400.000% 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 35.69681 cents Scale diversity : 1.141062 Lumma stability : 0.370162 Lumma impropriety factor : 0.071674 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 : 49/48, 35.6968 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 7 Odd number limit : 945 (O: 315 U: 945) Highest odd numerator or denominator: 405 Scale harmonicity : 0.026772 Average absolute harmonicity : 0.108107 Specific harmonicity : 0.140280 Fundamental : 1/810, -9.6618 octaves, 0.3230 Hz. Guide tone : 3584, 11.8074 octaves, 937666.026 Hz. Exponens Consonantiae : 2.903040E+06, 21.46913 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 468.5, average 156.16667 Mersenne's string divisions : 11921 Sum of van Prooijen's expressibility: 3.92967, average 1.30989 Sum of Tenney's harmonic distance : 8.01916, average 2.67305 Vogel's harmonic complexity : 16.00000 Wille's k value : 472 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 35.24669, average 5.87445 Lattice compactness (without 2's) : 14.01622, average 2.33604 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 9 3.33333 12 3: -4 ..-1 -2.00000 6 1 5: -1 .. 0 -0.33333 1 1 7: 0 .. 1 0.33333 1 1 Average exponent except 2's :-6 / 3 =-2.00000 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 16 19| Scale is weakly epimorphic with val: <6 10 19 19| Scale is weakly epimorphic with val: <6 11 17 20| Scale is weakly epimorphic with val: <7 10 15 20| Scale is weakly epimorphic with val: <7 10 18 20| Scale is weakly epimorphic with val: <7 11 15 20| Scale is JI-epimorphic with val: <7 11 17 19| Scale is weakly epimorphic with val: <7 11 17 22| Scale is weakly epimorphic with val: <7 11 18 20| Scale is weakly epimorphic with val: <7 12 17 22| Scale is weakly epimorphic with val: <8 11 15 22| Scale is weakly epimorphic with val: <8 11 18 22|
FIT/MODE
3: 2 0 1 N G T3 SD: 56.8551 c. M: 73.8363 c. 4: 2 1 1 P M ME S SD: 21.3226 c. M: 32.3325 c. 5: 3 1 1 N M DE S SD: 18.9420 c. M:-31.9561 c. 6: 3 2 1 P T3 SD: 11.5856 c. M: 17.8484 c. 10: 5 3 2 P T3 SD: 11.1621 c. M: 17.8484 c. 11: 6 3 2 N T3 SD: 2.9203 c. M:-4.7900 c. 17: 9 5 3 N T3 SD: 3.0893 c. M:-4.2884 c. 26: 14 7 5 N T3 SD: 2.2108 c. M: 3.5992 c. 28: 15 8 5 N T3 SD: 1.8722 c. M:-3.2421 c. 32: 17 9 6 N T3 SD: 1.4911 c. M: 2.2845 c. 43: 23 12 8 N T3 SD: 0.3901 c. M: 0.4808 c. 54: 29 15 10 N T3 SD: 0.3464 c. M:-0.5977 c. 97: 52 27 18 N T3 SD: 0.1565 c. M: 0.2420 c. 140: 75 39 26 N T3 SD: 0.1855 c. M: 0.3154 c. 168: 90 47 31 N T3 SD: 0.1641 c. M:-0.2776 c. 211: 113 59 39 N T3 SD: 0.1100 c. M: 0.1454 c. 222: 119 62 41 N T3 SD: 0.1276 c. M:-0.1974 c. 254: 136 71 47 N T3 SD: 0.1167 c. M: 0.2011 c. 265: 142 74 49 N T3 SD: 0.0506 c. M:-0.0874 c. 308: 165 86 57 N T3 SD: 0.0356 c. M: 0.0611 c. 362: 194 101 67 N T3 SD: 0.0215 c. M:-0.0372 c. 627: 336 175 116 N T3 SD: 0.0252 c. M:-0.0364 c. 670: 359 187 124 N T3 SD: 0.0050 c. M: 0.0080 c. 1032: 553 288 191 N T3 SD: 0.0047 c. M:-0.0079 c. 1702: 912 475 315 N T3 SD: 0.0016 c. M:-0.0024 c. 2372: 1271 662 439 N T3 SD: 0.0016 c. M:-0.0026 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 5:6 x 7 S SD: 48.7680 cents 6:7 x 8 S SD: 0.0000 cents 7:8:9 x S SD: 23.0648 cents 9 x 11:12 SD: 29.2292 cents 10:12 x 13 S SD: 32.7861 cents 11:13:14:15 SD: 15.4496 cents 12:14:15:16 S SD: 6.5175 cents 18:21:23:24 SD: 6.1660 cents 30:35:38:40 SD: 1.1260 cents 42:49:53:56 SD: 1.0475 cents 72:84:91:96 SD: 0.1409 cents 174:203:220:232 SD: 0.0777 cents 246:287:311:328 SD: 0.0137 cents 564:658:713:752 SD: 0.0060 cents