Scala analysis: 322_C24
Chromatic tetrachord 60/59 * 118/105 * 7/6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 60/59 29.097055 2: 8/7 231.174094 septimal whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 60/59 29.0971 2: 118/105 202.0770 3: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 60/59 29.097 cents 1: 1 118/105 202.077 cents 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 70/59 295.968 cents 2: 1 59/45 468.948 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 : 29.1 231.2 498.0 29.1 : 202.1 468.9 498.0 231.2: 266.9 296.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 29.0971 .. 266.8709 cents 413/360, 237.7739 cents 60/59, 29.0971 cents 2: 231.1741 .. 468.9479 cents 413/360, 237.7739 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 60/59, 29.0971 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 5.705560 Largest / Average step : 1.607511 Largest / Smallest step : 9.171750 Median interval of one step : 118/105, 202.0770 cents, amount: 1 Least squares average step : 141.82716 cents, oct.: 425.48148 cents Scale is not proper Scale has trivalence property Scale is a mode of a 907-tone equal temperament with octave 4/3 degrees: 53 421 907 Least number of segments generator : 454 of 249.297 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 815 of 447.527 cents and inv. generated superset size: 30 = 27 more = 1000.000% 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 29.09706 cents Scale diversity : 0.571251 Lumma stability : 0.116845 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 : 60/59, 29.0971 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 : 59 Odd number limit : 105 (O: 59 U: 105) Highest odd numerator or denominator: 59 Scale harmonicity : 0.039970 Fundamental : 1/1239, -10.2750 octaves, 0.2112 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 1.486800E+05, 17.18185 octaves Euler's gradus suavitatis : 76 Sum of Mann's harmonic distance : 70.5, average 23.50000 Mersenne's string divisions : 1785 Sum of van Prooijen's expressibility: 3.09307, average 1.03102 Sum of Tenney's harmonic distance : 6.37637, average 2.12546 Vogel's harmonic complexity : 51.00000 Wille's k value : 206 Wilson's harmonic complexity : 77 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.81595, average 2.30266 Lattice compactness (without 2's) : 8.79655, average 1.46609 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.33333 1 7: -1 .. 0 -0.33333 1 1 59: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <7 10 15 18 43| Scale is weakly epimorphic with val: <7 10 16 18 44| Scale is weakly epimorphic with val: <7 10 17 18 42| Scale is weakly epimorphic with val: <7 10 18 18 43| Scale is weakly epimorphic with val: <7 11 15 19 42| Scale is weakly epimorphic with val: <7 11 15 20 44| Scale is weakly epimorphic with val: <7 11 15 22 42| Scale is weakly epimorphic with val: <7 11 16 19 43| Scale is weakly epimorphic with val: <7 11 16 20 42| Scale is weakly epimorphic with val: <7 11 16 22 43| Scale is weakly epimorphic with val: <7 11 17 19 44| Scale is weakly epimorphic with val: <7 11 17 20 43| = patent Scale is weakly epimorphic with val: <7 11 17 22 44| Scale is JI-epimorphic with val: <7 11 18 19 42| Scale is weakly epimorphic with val: <7 11 18 20 44| Scale is weakly epimorphic with val: <7 11 18 22 42| Scale is JI-epimorphic with val: <7 11 19 19 43| Scale is weakly epimorphic with val: <7 11 19 20 42| Scale is weakly epimorphic with val: <7 11 19 22 43| Scale is weakly epimorphic with val: <7 12 15 18 43| Scale is weakly epimorphic with val: <7 12 16 18 44| Scale is weakly epimorphic with val: <7 12 17 18 42| Scale is weakly epimorphic with val: <7 12 18 18 43| Scale is weakly epimorphic with val: <7 12 19 20 42| Scale is weakly epimorphic with val: <8 11 15 21 44| Scale is weakly epimorphic with val: <8 11 16 21 42| Scale is weakly epimorphic with val: <8 11 17 21 43| Scale is weakly epimorphic with val: <8 11 18 20 42| Scale is weakly epimorphic with val: <8 11 18 21 44| Scale is weakly epimorphic with val: <8 11 19 20 43| Scale is weakly epimorphic with val: <8 11 19 21 42| Scale is weakly epimorphic with val: <8 12 15 21 44| Scale is weakly epimorphic with val: <8 12 16 21 42| Scale is weakly epimorphic with val: <8 12 17 19 42| Scale is weakly epimorphic with val: <8 12 17 21 43| Scale is weakly epimorphic with val: <8 12 17 22 42| Scale is weakly epimorphic with val: <8 12 18 19 43| Scale is weakly epimorphic with val: <8 12 18 21 44| Scale is weakly epimorphic with val: <8 12 18 22 43| Scale is weakly epimorphic with val: <8 12 19 19 44| Scale is weakly epimorphic with val: <8 12 19 21 42| Scale is weakly epimorphic with val: <8 12 19 22 44|
FIT/MODE
3: 0 1 2 N G T3 SD: 41.2001 c. M: 65.1591 c. 4: 0 2 2 P M DE S SD: 19.7079 c. M: 29.0971 c. 7: 0 3 4 N G T3 SD: 19.6711 c. M: 29.0971 c. 9: 0 4 5 N G T3 SD: 17.7303 c. M: 29.0971 c. 11: 1 4 6 N T3 SD: 9.7422 c. M:-16.1798 c. 13: 1 5 7 N T3 SD: 5.3730 c. M:-9.2141 c. 15: 1 6 8 N T3 SD: 2.4775 c. M:-4.1059 c. 17: 1 7 9 N T3 SD: 1.8511 c. M:-3.2000 c. 32: 2 13 17 N T3 SD: 1.7647 c. M:-2.2845 c. 49: 3 20 26 N T3 SD: 1.7047 c. M:-2.6021 c. 50: 3 20 27 N T3 SD: 1.2801 c. M: 2.0734 c. 52: 3 21 28 N T3 SD: 0.7834 c. M: 1.3072 c. 67: 4 27 36 N T3 SD: 0.5617 c. M: 0.7354 c. 69: 4 28 37 N T3 SD: 0.1725 c. M: 0.2249 c. 153: 9 62 82 N T3 SD: 0.1196 c. M:-0.1997 c. 155: 9 63 83 N T3 SD: 0.1446 c. M: 0.1783 c. 222: 13 90 119 N T3 SD: 0.0693 c. M: 0.0992 c. 308: 18 125 165 N T3 SD: 0.0357 c. M:-0.0611 c. 377: 22 153 202 N T3 SD: 0.0209 c. M: 0.0334 c. 530: 31 215 284 N T3 SD: 0.0199 c. M:-0.0339 c. 599: 35 243 321 N T3 SD: 0.0163 c. M: 0.0280 c. 838: 49 340 449 N T3 SD: 0.0180 c. M:-0.0249 c. 907: 53 368 486 N T3 SD: 0.0036 c. M:-0.0059 c. 1284: 75 521 688 N T3 SD: 0.0046 c. M:-0.0057 c. 1883: 110 764 1009 N T3 SD: 0.0033 c. M: 0.0050 c. 2191: 128 889 1174 N T3 SD: 0.0025 c. M:-0.0043 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: 59.7273 cents 6 x 7:8 S SD: 17.8484 cents 7 x 8:9 S SD: 31.4805 cents 8 x 9:11 SD: 29.9221 cents 9 x 10:12 S SD: 24.3852 cents 10 x 11:13 SD: 39.6850 cents 11 x 13:15 SD: 34.9349 cents 12 x 14:16 S SD: 17.8484 cents 21:22:24:28 S SD: 17.1467 cents 24:25:27:32 SD: 16.5725 cents 26:27:30:35 S SD: 14.3847 cents 27:28:31:36 SD: 11.5984 cents 29:30:33:39 SD: 11.3166 cents 30:31:34:40 SD: 10.4110 cents 33:34:38:44 SD: 8.6975 cents 34:35:39:45 SD: 8.4871 cents 35:36:40:47 SD: 7.7379 cents 36:37:41:48 SD: 6.4335 cents 41:42:47:55 SD: 5.7526 cents 42:43:48:56 SD: 3.8799 cents 48:49:55:64 SD: 2.6631 cents 56:57:64:75 SD: 2.6216 cents 57:58:65:76 SD: 1.3111 cents 63:64:72:84 S SD: 0.6110 cents 168:171:192:224 SD: 0.5150 cents 174:177:199:232 SD: 0.4464 cents 231:235:264:308 SD: 0.2081 cents 294:299:336:392 SD: 0.0327 cents