Scala analysis: 340_C28
Chromatic tetrachord 76/71 * 71/66 * 22/19
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 76/71 117.816473 2: 38/33 244.240073 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 22/19 253.8049 Godzilla third 1: 76/71 117.8165 2: 71/66 126.4236 3: 22/19 253.8049 Godzilla third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 76/71 117.816 cents 1: 1 71/66 126.424 cents 1: 1 22/19 253.805 cents Godzilla third 2: 1 38/33 244.240 cents 2: 1 88/71 371.621 cents 2: 1 71/57 380.229 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 : 117.8 244.2 498.0 117.8: 126.4 380.2 498.0 244.2: 253.8 371.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 117.8165 .. 253.8049 cents 781/722, 135.9885 cents 76/71, 117.8165 cents 2: 244.2401 .. 380.2285 cents 781/722, 135.9885 cents 361/363,-9.5649 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 76/71, 117.8165 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 22/19, 253.8049 cents Average / Smallest step : 1.409098 Largest / Average step : 1.528807 Largest / Smallest step : 2.154240 Median interval of one step : 71/66, 126.4236 cents, amount: 1 Least squares average step : 150.03083 cents, oct.: 450.09249 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2029-tone equal temperament with octave 4/3 degrees: 480 995 2029 Least number of segments generator : 1015 of 249.145 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1830 of 449.198 cents and inv. generated superset size: 34 = 31 more = 1133.333% 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 9.56485 cents Scale diversity : 1.126038 Lumma stability : 0.473116 Lumma impropriety factor : 0.019205 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 : 5041/5016, 8.6071 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 127.3813 cents: 2 -- Rational properties -- Prime limit : 71 Odd number limit : 71 (O: 71 U: 71) Highest odd numerator or denominator: 71 Scale harmonicity : 0.017558 Fundamental : 1/2343, -11.1941 octaves, 0.1117 Hz. Guide tone : 76, 6.2479 octaves, 19883.543 Hz. Exponens Consonantiae : 1.780680E+05, 17.44207 octaves Euler's gradus suavitatis : 103 Sum of Mann's harmonic distance : 112.5, average 37.50000 Mersenne's string divisions : 10437 Sum of van Prooijen's expressibility: 3.84689, average 1.28230 Sum of Tenney's harmonic distance : 7.90955, average 2.63652 Vogel's harmonic complexity : 70.00000 Wille's k value : 674 Wilson's harmonic complexity : 104 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 11.35045, average 1.89174 Lattice compactness (without 2's) : 7.97469, average 1.32912 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 0 -0.66667 2 1 11: -1 .. 0 -0.33333 1 19: 0 .. 1 0.66667 2 1 71: -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 23 30 44| Scale is weakly epimorphic with val: <6 10 23 34 43| Scale is weakly epimorphic with val: <6 10 24 31 45| Scale is weakly epimorphic with val: <6 10 25 32 43| Scale is weakly epimorphic with val: <6 10 26 33 44| Scale is weakly epimorphic with val: <6 10 26 34 43| Scale is weakly epimorphic with val: <6 10 27 34 45| Scale is weakly epimorphic with val: <6 11 23 31 44| Scale is weakly epimorphic with val: <6 11 24 32 45| Scale is weakly epimorphic with val: <6 11 24 34 43| Scale is weakly epimorphic with val: <6 11 25 33 43| Scale is weakly epimorphic with val: <6 11 26 34 44| Scale is weakly epimorphic with val: <6 11 27 34 43| Scale is weakly epimorphic with val: <7 10 23 29 44| Scale is weakly epimorphic with val: <7 10 23 34 45| Scale is weakly epimorphic with val: <7 10 24 30 45| Scale is weakly epimorphic with val: <7 10 24 32 43| Scale is weakly epimorphic with val: <7 10 25 31 43| Scale is weakly epimorphic with val: <7 10 25 33 44| Scale is weakly epimorphic with val: <7 10 26 32 44| Scale is weakly epimorphic with val: <7 10 26 34 45| Scale is weakly epimorphic with val: <7 10 27 32 43| Scale is weakly epimorphic with val: <7 10 27 33 45| Scale is weakly epimorphic with val: <7 11 23 28 43| Scale is weakly epimorphic with val: <7 11 23 29 45| Scale is weakly epimorphic with val: <7 11 23 31 43| Scale is weakly epimorphic with val: <7 11 23 32 45| Scale is weakly epimorphic with val: <7 11 23 34 43| Scale is weakly epimorphic with val: <7 11 24 29 44| Scale is JI-epimorphic with val: <7 11 24 30 43| Scale is weakly epimorphic with val: <7 11 24 32 44| Scale is weakly epimorphic with val: <7 11 24 33 43| Scale is weakly epimorphic with val: <7 11 25 28 44| Scale is weakly epimorphic with val: <7 11 25 30 45| Scale is JI-epimorphic with val: <7 11 25 31 44| = patent Scale is weakly epimorphic with val: <7 11 25 33 45| Scale is weakly epimorphic with val: <7 11 25 34 44| Scale is weakly epimorphic with val: <7 11 26 28 43| Scale is weakly epimorphic with val: <7 11 26 29 45| Scale is weakly epimorphic with val: <7 11 26 31 43| Scale is JI-epimorphic with val: <7 11 26 32 45| Scale is weakly epimorphic with val: <7 11 26 34 43| Scale is weakly epimorphic with val: <7 11 27 29 44| Scale is weakly epimorphic with val: <7 11 27 30 43| Scale is weakly epimorphic with val: <7 11 27 32 44| Scale is weakly epimorphic with val: <7 11 27 33 43| Scale is weakly epimorphic with val: <7 12 23 31 44| Scale is weakly epimorphic with val: <7 12 23 32 43| Scale is weakly epimorphic with val: <7 12 24 32 45| Scale is weakly epimorphic with val: <7 12 24 33 44| Scale is weakly epimorphic with val: <7 12 25 33 43| Scale is weakly epimorphic with val: <7 12 25 34 45| Scale is weakly epimorphic with val: <7 12 26 32 43| Scale is weakly epimorphic with val: <7 12 26 34 44| Scale is weakly epimorphic with val: <7 12 27 33 44| Scale is weakly epimorphic with val: <8 11 23 29 44| Scale is weakly epimorphic with val: <8 11 23 30 43| Scale is weakly epimorphic with val: <8 11 24 30 45| Scale is weakly epimorphic with val: <8 11 24 31 44| Scale is weakly epimorphic with val: <8 11 25 31 43| Scale is weakly epimorphic with val: <8 11 25 32 45| Scale is weakly epimorphic with val: <8 11 26 30 43| Scale is weakly epimorphic with val: <8 11 26 32 44| Scale is weakly epimorphic with val: <8 11 27 31 44| Scale is weakly epimorphic with val: <8 11 27 33 45| Scale is weakly epimorphic with val: <8 12 23 30 44| Scale is weakly epimorphic with val: <8 12 23 32 45| Scale is weakly epimorphic with val: <8 12 24 30 43| Scale is weakly epimorphic with val: <8 12 24 31 45| Scale is weakly epimorphic with val: <8 12 25 31 44| Scale is weakly epimorphic with val: <8 12 25 32 43| Scale is weakly epimorphic with val: <8 12 26 32 45| Scale is weakly epimorphic with val: <8 12 26 33 44| Scale is weakly epimorphic with val: <8 12 27 30 43| Scale is weakly epimorphic with val: <8 12 27 34 45|
FIT/MODE
3: 1 1 1 SP B ME I SD: 57.8221 c. M:-87.7899 c. 4: 1 1 2 P M ME S SD: 4.7501 c. M:-6.6948 c. 21: 5 5 11 N M DE S SD: 4.1091 c. M: 7.0758 c. 22: 5 6 11 P T3 SD: 3.8409 c. M:-4.7824 c. 25: 6 6 13 N M DE S SD: 3.1494 c. M: 5.1785 c. 26: 6 7 13 P T3 SD: 3.2240 c. M:-4.7824 c. 29: 7 7 15 N M DE S SD: 2.5975 c. M: 3.8046 c. 33: 8 8 17 N M DE S SD: 2.3220 c. M:-2.9217 c. 35: 8 9 18 N T3 SD: 2.6622 c. M: 3.9776 c. 37: 9 9 19 N M DE S SD: 2.2272 c. M:-3.3296 c. 39: 9 10 20 N T3 SD: 1.9044 c. M: 2.8830 c. 43: 10 11 22 N T3 SD: 1.2892 c. M: 1.9921 c. 47: 11 12 24 N T3 SD: 0.7822 c. M: 1.2527 c. 51: 12 13 26 N T3 SD: 0.3680 c. M: 0.6294 c. 55: 13 14 28 N T3 SD: 0.1573 c. M:-0.2547 c. 216: 51 55 110 N T3 SD: 0.1620 c. M: 0.2225 c. 249: 59 63 127 N T3 SD: 0.1686 c. M: 0.2180 c. 271: 64 69 138 N T3 SD: 0.1572 c. M: 0.1970 c. 296: 70 75 151 N T3 SD: 0.1546 c. M: 0.2653 c. 300: 71 76 153 N T3 SD: 0.1185 c. M: 0.1980 c. 304: 72 77 155 N T3 SD: 0.1119 c. M:-0.1416 c. 351: 83 89 179 N T3 SD: 0.1093 c. M: 0.1838 c. 355: 84 90 181 N T3 SD: 0.0759 c. M: 0.1279 c. 359: 85 91 183 N T3 SD: 0.0739 c. M:-0.1050 c. 406: 96 103 207 N T3 SD: 0.0779 c. M: 0.1244 c. 410: 97 104 209 N T3 SD: 0.0449 c. M: 0.0765 c. 465: 110 118 237 N T3 SD: 0.0216 c. M: 0.0374 c. 520: 123 132 265 N T3 SD: 0.0067 c. M: 0.0097 c. 1564: 370 397 797 N T3 SD: 0.0055 c. M:-0.0075 c. 2029: 480 515 1034 N T3 SD: 0.0042 c. M:-0.0059 c. 2084: 493 529 1062 N T3 SD: 0.0024 c. M:-0.0032 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: 55.3011 cents 6 x 7:8 S SD: 11.3154 cents 7 x 8:9 S SD: 32.1512 cents 8 x 9:11 SD: 33.4085 cents 9 x 10:12 S SD: 30.9182 cents 11:12:13:15 SD: 22.6400 cents 12:13:14:16 S SD: 10.2360 cents 15:16:17:20 SD: 9.4058 cents 25:27:29:33 SD: 8.8323 cents 26:28:30:35 S SD: 6.6382 cents 27:29:31:36 SD: 2.5919 cents 60:64:69:80 SD: 2.1660 cents 72:77:83:96 SD: 0.8236 cents 99:106:114:132 SD: 0.1534 cents 369:395:425:492 SD: 0.1252 cents 468:501:539:624 SD: 0.1088 cents 567:607:653:756 SD: 0.1046 cents