Scala analysis: 294_C21
Chromatic tetrachord 68/61 * 61/60 * 20/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/61 188.070604 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: 68/61 188.0706 2: 61/60 28.6161 3: 20/17 281.3583 septendecimal augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 61/60 28.616 cents 1: 1 68/61 188.071 cents 1: 1 20/17 281.358 cents septendecimal augmented second 2: 1 17/15 216.687 cents septendecimal whole tone 2: 1 61/51 309.974 cents 2: 1 80/61 469.429 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 : 188.1 216.7 498.0 188.1: 28.6 310.0 498.0 216.7: 281.4 469.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 28.6161 .. 281.3583 cents 1200/1037, 252.7422 cents 61/60, 28.6161 cents 2: 216.6867 .. 469.4289 cents 1200/1037, 252.7422 cents 289/300,-64.6716 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 61/60, 28.6161 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 20/17, 281.3583 cents Average / Smallest step : 5.801456 Largest / Average step : 1.694776 Largest / Smallest step : 9.832171 Median interval of one step : 68/61, 188.0706 cents, amount: 1 Least squares average step : 151.11279 cents, oct.: 453.33836 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1340-tone equal temperament with octave 4/3 degrees: 506 583 1340 Least number of segments generator : 671 of 249.394 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1089 of 404.754 cents and inv. generated superset size: 28 = 25 more = 933.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 28.61609 cents Scale diversity : 0.612845 Lumma stability : 0.114914 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 : 61/60, 28.6161 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 61 Odd number limit : 61 (O: 61 U: 61) Highest odd numerator or denominator: 61 Scale harmonicity : 0.024281 Fundamental : 1/915, -9.8376 octaves, 0.2859 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 6.222000E+04, 15.92509 octaves Euler's gradus suavitatis : 85 Sum of Mann's harmonic distance : 84.0, average 28.00000 Mersenne's string divisions : 28896 Sum of van Prooijen's expressibility: 3.49290, average 1.16430 Sum of Tenney's harmonic distance : 7.10356, average 2.36785 Vogel's harmonic complexity : 57.66667 Wille's k value : 518 Wilson's harmonic complexity : 86 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 12.51738, average 2.08623 Lattice compactness (without 2's) : 7.97469, average 1.32912 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.33333 4 3: -1 .. 0 -0.66667 2 1 5: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 1 61: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 15 28 42| Scale is weakly epimorphic with val: <6 10 16 29 43| Scale is weakly epimorphic with val: <6 10 16 33 42| Scale is weakly epimorphic with val: <6 10 17 30 44| Scale is weakly epimorphic with val: <6 10 18 31 42| Scale is weakly epimorphic with val: <6 10 19 32 43| Scale is weakly epimorphic with val: <6 10 19 33 42| Scale is weakly epimorphic with val: <6 11 15 29 42| Scale is weakly epimorphic with val: <6 11 16 30 43| Scale is weakly epimorphic with val: <6 11 17 31 44| Scale is weakly epimorphic with val: <6 11 17 33 42| Scale is weakly epimorphic with val: <6 11 18 32 42| Scale is weakly epimorphic with val: <6 11 19 33 43| Scale is weakly epimorphic with val: <7 10 15 28 43| Scale is weakly epimorphic with val: <7 10 15 33 44| Scale is weakly epimorphic with val: <7 10 16 29 44| Scale is weakly epimorphic with val: <7 10 16 31 42| Scale is weakly epimorphic with val: <7 10 17 30 42| Scale is weakly epimorphic with val: <7 10 17 32 43| Scale is weakly epimorphic with val: <7 10 18 31 43| Scale is weakly epimorphic with val: <7 10 18 33 44| Scale is weakly epimorphic with val: <7 10 19 31 42| Scale is weakly epimorphic with val: <7 10 19 32 44| Scale is weakly epimorphic with val: <7 11 15 27 42| Scale is weakly epimorphic with val: <7 11 15 28 44| Scale is weakly epimorphic with val: <7 11 15 30 42| Scale is weakly epimorphic with val: <7 11 15 31 44| Scale is weakly epimorphic with val: <7 11 15 33 42| Scale is weakly epimorphic with val: <7 11 16 28 43| Scale is JI-epimorphic with val: <7 11 16 29 42| Scale is weakly epimorphic with val: <7 11 16 31 43| Scale is weakly epimorphic with val: <7 11 16 32 42| Scale is weakly epimorphic with val: <7 11 17 27 43| Scale is weakly epimorphic with val: <7 11 17 29 44| Scale is JI-epimorphic with val: <7 11 17 30 43| = patent Scale is weakly epimorphic with val: <7 11 17 32 44| Scale is weakly epimorphic with val: <7 11 17 33 43| Scale is weakly epimorphic with val: <7 11 18 27 42| Scale is weakly epimorphic with val: <7 11 18 28 44| Scale is weakly epimorphic with val: <7 11 18 30 42| Scale is JI-epimorphic with val: <7 11 18 31 44| Scale is weakly epimorphic with val: <7 11 18 33 42| Scale is weakly epimorphic with val: <7 11 19 28 43| Scale is weakly epimorphic with val: <7 11 19 29 42| Scale is weakly epimorphic with val: <7 11 19 31 43| Scale is weakly epimorphic with val: <7 11 19 32 42| Scale is weakly epimorphic with val: <7 12 15 30 43| Scale is weakly epimorphic with val: <7 12 15 31 42| Scale is weakly epimorphic with val: <7 12 16 31 44| Scale is weakly epimorphic with val: <7 12 16 32 43| Scale is weakly epimorphic with val: <7 12 17 32 42| Scale is weakly epimorphic with val: <7 12 17 33 44| Scale is weakly epimorphic with val: <7 12 18 31 42| Scale is weakly epimorphic with val: <7 12 18 33 43| Scale is weakly epimorphic with val: <7 12 19 32 43| Scale is weakly epimorphic with val: <8 11 15 29 44| Scale is weakly epimorphic with val: <8 11 15 30 43| Scale is weakly epimorphic with val: <8 11 16 30 42| Scale is weakly epimorphic with val: <8 11 16 31 44| Scale is weakly epimorphic with val: <8 11 17 29 42| Scale is weakly epimorphic with val: <8 11 17 31 43| Scale is weakly epimorphic with val: <8 11 18 30 43| Scale is weakly epimorphic with val: <8 11 18 32 44| Scale is weakly epimorphic with val: <8 11 19 31 44| Scale is weakly epimorphic with val: <8 11 19 33 42| Scale is weakly epimorphic with val: <8 12 15 29 42| Scale is weakly epimorphic with val: <8 12 15 30 44| Scale is weakly epimorphic with val: <8 12 16 30 43| Scale is weakly epimorphic with val: <8 12 16 31 42| Scale is weakly epimorphic with val: <8 12 17 31 44| Scale is weakly epimorphic with val: <8 12 17 32 43| Scale is weakly epimorphic with val: <8 12 18 29 42| Scale is weakly epimorphic with val: <8 12 18 33 44| Scale is weakly epimorphic with val: <8 12 19 30 43|
FIT/MODE
3: 1 0 2 N G T3 SD: 31.9065 c. M: 50.6717 c. 5: 2 0 3 N G T3 SD: 11.9641 c. M: 17.4687 c. 9: 3 1 5 N T3 SD: 13.0157 c. M: 22.0556 c. 10: 4 0 6 N G T3 SD: 11.9641 c. M: 17.4687 c. 11: 4 1 6 N T3 SD: 6.8927 c. M:-9.6974 c. 13: 5 1 7 N T3 SD: 7.8711 c. M:-13.1802 c. 14: 5 1 8 N T3 SD: 6.1773 c. M: 10.1974 c. 16: 6 1 9 N T3 SD: 1.0262 c. M: 1.3037 c. 37: 14 2 21 N T3 SD: 0.7906 c. M: 1.3159 c. 53: 20 3 30 N T3 SD: 0.3284 c. M: 0.5540 c. 69: 26 4 39 N T3 SD: 0.2465 c. M: 0.4015 c. 122: 46 7 69 N T3 SD: 0.2479 c. M: 0.3229 c. 191: 72 11 108 N T3 SD: 0.2403 c. M: 0.3259 c. 193: 73 11 109 N T3 SD: 0.1842 c. M:-0.3091 c. 209: 79 12 118 N T3 SD: 0.1436 c. M:-0.1856 c. 246: 93 14 139 N T3 SD: 0.1283 c. M:-0.2147 c. 262: 99 15 148 N T3 SD: 0.0714 c. M:-0.1220 c. 278: 105 16 157 N T3 SD: 0.0559 c. M:-0.0883 c. 315: 119 18 178 N T3 SD: 0.0639 c. M:-0.0797 c. 331: 125 19 187 N T3 SD: 0.0112 c. M: 0.0146 c. 1009: 381 58 570 N T3 SD: 0.0054 c. M: 0.0080 c. 1340: 506 77 757 N T3 SD: 0.0017 c. M: 0.0029 c. 1671: 631 96 944 N T3 SD: 0.0016 c. M: 0.0028 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 9:10 x 12 S SD: 2.8334 cents 10:11 x 13 SD: 24.7650 cents 11:12 x 15 S SD: 26.9950 cents 12:13:14:16 S SD: 23.4959 cents 13 x 15:17 SD: 22.8828 cents 14 x 16:19 SD: 16.9472 cents 15 x 17:20 SD: 0.0000 cents 16 x 18:21 S SD: 15.0547 cents 17:19 x 23 SD: 12.8346 cents 18:20 x 24 S SD: 2.8334 cents 22 x 25:29 SD: 10.1593 cents 23 x 26:31 SD: 9.6171 cents 24 x 27:32 SD: 6.3883 cents 25:28 x 33 SD: 9.6021 cents 26:29 x 35 SD: 8.2979 cents 27:30:31:36 SD: 7.7290 cents 30:33:34:40 SD: 7.6888 cents 31 x 35:41 SD: 7.7434 cents 32 x 36:43 SD: 9.2838 cents 33:37 x 44 SD: 5.0002 cents 36:40:41:48 SD: 3.3958 cents 40 x 45:53 SD: 8.3824 cents 41:46 x 55 SD: 7.6630 cents 42:47:48:56 SD: 5.3143 cents 43:48:49:57 SD: 4.6757 cents 44:49:50:59 SD: 3.6606 cents 45:50:51:60 SD: 1.8890 cents 48 x 54:64 SD: 6.3883 cents 50:56:57:67 SD: 5.2038 cents 51:57:58:68 SD: 2.4921 cents 60:67:68:80 SD: 0.9892 cents 105:117:119:140 SD: 0.2425 cents 165:184:187:220 SD: 0.2057 cents 270:301:306:360 SD: 0.0314 cents