Scala analysis: 141_C3
Chromatic tetrachord 204/199 * 199/189 * 21/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 204/199 42.960866 2: 68/63 132.219501 supraminor second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 21/17 365.8255 submajor third 1: 204/199 42.9609 2: 199/189 89.2586 3: 21/17 365.8255 submajor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 204/199 42.961 cents 1: 1 199/189 89.259 cents 1: 1 21/17 365.825 cents submajor third 2: 1 68/63 132.220 cents supraminor second 2: 1 252/199 408.786 cents 2: 1 199/153 455.084 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 : 43.0 132.2 498.0 43.0 : 89.3 455.1 498.0 132.2: 365.8 408.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 42.9609 .. 365.8255 cents 1393/1156, 322.8646 cents 204/199, 42.9609 cents 2: 132.2195 .. 455.0841 cents 1393/1156, 322.8646 cents 1156/1323,-233.6060 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 204/199, 42.9609 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 21/17, 365.8255 cents Average / Smallest step : 3.864331 Largest / Average step : 2.203569 Largest / Smallest step : 8.515320 Median interval of one step : 199/189, 89.2586 cents, amount: 1 Least squares average step : 128.68106 cents, oct.: 386.04319 cents Scale is not proper Scale has trivalence property 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 42.96087 cents Scale diversity : 0.615919 Lumma stability : 0.172518 Lumma impropriety factor : 0.469046 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 : 204/199, 42.9609 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 199 Odd number limit : 199 (O: 199 U: 199) Highest odd numerator or denominator: 199 Scale harmonicity : 0.019840 Fundamental : 1/12537, -13.6139 octaves, 0.0209 Hz. Guide tone : 204, 7.6724 octaves, 53371.615 Hz. Exponens Consonantiae : 2.557548E+06, 21.28633 octaves Euler's gradus suavitatis : 229 Sum of Mann's harmonic distance : 270.5, average 90.16667 Mersenne's string divisions : 369551 Sum of van Prooijen's expressibility: 4.57531, average 1.52510 Sum of Tenney's harmonic distance : 9.31951, average 3.10650 Vogel's harmonic complexity : 154.66667 Wille's k value : 2089 Wilson's harmonic complexity : 232 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 14.97823, average 2.49637 Lattice compactness (without 2's) : 11.99410, average 1.99902 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -2 .. 1 -0.66667 4 1 7: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 1 199: -1 .. 0 -0.33333 1 1 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 18 29 56| Scale is weakly epimorphic with val: <6 10 19 30 54| Scale is weakly epimorphic with val: <6 10 20 31 55| Scale is weakly epimorphic with val: <6 10 21 32 56| Scale is weakly epimorphic with val: <6 10 22 33 54| Scale is weakly epimorphic with val: <6 11 18 31 55| Scale is weakly epimorphic with val: <6 11 19 32 56| Scale is weakly epimorphic with val: <6 11 20 33 54| Scale is weakly epimorphic with val: <7 10 18 27 55| Scale is weakly epimorphic with val: <7 10 19 28 56| Scale is weakly epimorphic with val: <7 10 19 33 54| Scale is weakly epimorphic with val: <7 10 20 29 54| Scale is weakly epimorphic with val: <7 10 21 30 55| Scale is weakly epimorphic with val: <7 10 22 31 56| Scale is weakly epimorphic with val: <7 10 22 33 54| Scale is weakly epimorphic with val: <7 11 18 27 56| Scale is weakly epimorphic with val: <7 11 18 28 55| Scale is weakly epimorphic with val: <7 11 18 30 56| Scale is weakly epimorphic with val: <7 11 18 31 55| Scale is weakly epimorphic with val: <7 11 18 33 56| Scale is weakly epimorphic with val: <7 11 19 28 54| Scale is weakly epimorphic with val: <7 11 19 29 56| Scale is weakly epimorphic with val: <7 11 19 31 54| Scale is weakly epimorphic with val: <7 11 19 32 56| Scale is weakly epimorphic with val: <7 11 20 27 54| Scale is weakly epimorphic with val: <7 11 20 29 55| Scale is JI-epimorphic with val: <7 11 20 30 54| Scale is weakly epimorphic with val: <7 11 20 32 55| Scale is weakly epimorphic with val: <7 11 20 33 54| Scale is weakly epimorphic with val: <7 11 21 27 56| Scale is weakly epimorphic with val: <7 11 21 28 55| Scale is weakly epimorphic with val: <7 11 21 30 56| Scale is JI-epimorphic with val: <7 11 21 31 55| Scale is weakly epimorphic with val: <7 11 21 33 56| Scale is weakly epimorphic with val: <7 11 22 28 54| Scale is weakly epimorphic with val: <7 11 22 29 56| Scale is weakly epimorphic with val: <7 11 22 31 54| Scale is JI-epimorphic with val: <7 11 22 32 56| Scale is weakly epimorphic with val: <7 12 18 31 56| Scale is weakly epimorphic with val: <7 12 18 32 55| Scale is weakly epimorphic with val: <7 12 19 32 54| Scale is weakly epimorphic with val: <7 12 19 33 56| Scale is weakly epimorphic with val: <7 12 20 31 54| Scale is weakly epimorphic with val: <7 12 20 33 55| Scale is weakly epimorphic with val: <7 12 21 32 55| Scale is weakly epimorphic with val: <7 12 22 33 56| Scale is weakly epimorphic with val: <8 11 18 27 56| Scale is weakly epimorphic with val: <8 11 18 31 55| Scale is weakly epimorphic with val: <8 11 19 28 54| Scale is weakly epimorphic with val: <8 11 19 32 56| Scale is weakly epimorphic with val: <8 11 20 29 55| Scale is weakly epimorphic with val: <8 11 20 30 54| Scale is weakly epimorphic with val: <8 11 21 30 56| Scale is weakly epimorphic with val: <8 11 21 31 55| Scale is weakly epimorphic with val: <8 11 22 31 54| Scale is weakly epimorphic with val: <8 11 22 32 56| Scale is weakly epimorphic with val: <8 12 18 29 55| Scale is weakly epimorphic with val: <8 12 18 31 56| Scale is weakly epimorphic with val: <8 12 19 29 54| Scale is weakly epimorphic with val: <8 12 19 30 56| Scale is weakly epimorphic with val: <8 12 20 30 55| Scale is weakly epimorphic with val: <8 12 20 31 54| Scale is weakly epimorphic with val: <8 12 21 31 56| Scale is weakly epimorphic with val: <8 12 21 32 55| Scale is weakly epimorphic with val: <8 12 22 29 54| Scale is weakly epimorphic with val: <8 12 22 33 56|
FIT/MODE
3: 0 1 2 N G T3 SD: 31.5583 c. M: 42.9609 c. 4: 0 1 3 N G T3 SD: 25.1996 c. M: 42.9609 c. 7: 1 1 5 N M DE S SD: 17.2837 c. M:-28.1884 c. 8: 1 1 6 N M DE S SD: 11.9959 c. M:-19.2948 c. 10: 1 2 7 N T3 SD: 10.6844 c. M:-17.1940 c. 11: 1 2 8 N T3 SD: 2.4767 c. M:-3.6110 c. 23: 2 4 17 N T3 SD: 1.3400 c. M: 2.2947 c. 34: 3 6 25 N T3 SD: 0.6100 c. M:-0.9843 c. 79: 7 14 58 N T3 SD: 0.6826 c. M:-1.1697 c. 83: 7 15 61 N T3 SD: 0.5654 c. M: 0.9571 c. 91: 8 16 67 N T3 SD: 0.6903 c. M: 0.8670 c. 94: 8 17 69 N T3 SD: 0.3591 c. M: 0.5741 c. 117: 10 21 86 N T3 SD: 0.2717 c. M: 0.3929 c. 128: 11 23 94 N T3 SD: 0.1018 c. M: 0.1601 c. 162: 14 29 119 N T3 SD: 0.0480 c. M:-0.0801 c. 290: 25 52 213 N T3 SD: 0.0189 c. M: 0.0260 c. 452: 39 81 332 N T3 SD: 0.0075 c. M:-0.0120 c. 742: 64 133 545 N T3 SD: 0.0064 c. M:-0.0108 c. 1194: 103 214 877 N T3 SD: 0.0052 c. M:-0.0085 c. 1646: 142 295 1209 N T3 SD: 0.0053 c. M:-0.0075 c. 2098: 181 376 1541 N T3 SD: 0.0056 c. M:-0.0069 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 x 7 SD: 84.4672 cents 6 x 7:8 S SD: 67.3257 cents 7 x 8:9 S SD: 58.6432 cents 8 x 9:11 SD: 44.6585 cents 9 x 10:12 S SD: 25.0921 cents 10 x 11:13 SD: 27.3679 cents 11 x 12:15 S SD: 21.5225 cents 12 x 13:16 SD: 3.1766 cents 13 x 14:17 SD: 16.9226 cents 14 x 15:19 SD: 16.5996 cents 15 x 16:20 S SD: 10.2441 cents 16 x 17:21 SD: 19.2786 cents 17 x 18:23 SD: 20.8886 cents 18 x 19:24 SD: 19.3082 cents 19 x 21:25 SD: 23.5095 cents 20:21:22:27 SD: 19.0325 cents 21:22:23:28 SD: 15.0950 cents 22:23:24:29 SD: 14.4775 cents 23:24:25:31 SD: 12.6545 cents 24:25:26:32 SD: 9.4768 cents 26:27:28:35 S SD: 9.3722 cents 27:28:29:36 SD: 7.2447 cents 33:34:36:44 SD: 6.7927 cents 35:36:38:47 SD: 5.6636 cents 36:37:39:48 SD: 2.5900 cents 39:40:42:52 SD: 1.3389 cents 75:77:81:100 SD: 0.9309 cents 114:117:123:152 SD: 0.7059 cents 162:166:175:216 SD: 0.5309 cents 201:206:217:268 SD: 0.1893 cents 240:246:259:320 SD: 0.1275 cents 441:452:476:588 SD: 0.1026 cents 516:529:557:688 SD: 0.0625 cents