Scala analysis: 270_C19
Chromatic tetrachord 88/83 * 83/78 * 13/11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88/83 101.270625 2: 44/39 208.835280 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 13/11 289.2097 tridecimal minor third 1: 88/83 101.2706 2: 83/78 107.5647 3: 13/11 289.2097 tridecimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 88/83 101.271 cents 1: 1 83/78 107.565 cents 1: 1 13/11 289.210 cents tridecimal minor third 2: 1 44/39 208.835 cents 2: 1 104/83 390.480 cents 2: 1 83/66 396.774 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 : 101.3 208.8 498.0 101.3: 107.6 396.8 498.0 208.8: 289.2 390.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 101.2706 .. 289.2097 cents 1079/968, 187.9391 cents 88/83, 101.2706 cents 2: 208.8353 .. 396.7744 cents 1079/968, 187.9391 cents 484/507,-80.3744 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 88/83, 101.2706 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 13/11, 289.2097 cents Average / Smallest step : 1.639320 Largest / Average step : 1.742070 Largest / Smallest step : 2.855811 Median interval of one step : 83/78, 107.5647 cents, amount: 1 Least squares average step : 143.79116 cents, oct.: 431.37347 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1741-tone equal temperament with octave 4/3 degrees: 354 730 1741 Least number of segments generator : 871 of 249.166 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1668 of 477.162 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 80.37444 cents Scale diversity : 1.108003 Lumma stability : 0.406673 Lumma impropriety factor : 0.161380 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 : 6889/6864, 6.2940 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% Limited inverse transpositions with margin 181.6451 cents: 2 -- Rational properties -- Prime limit : 83 Odd number limit : 83 (O: 83 U: 83) Highest odd numerator or denominator: 83 Scale harmonicity : 0.021738 Fundamental : 1/3237, -11.6604 octaves, 0.0808 Hz. Guide tone : 88, 6.4594 octaves, 23023.050 Hz. Exponens Consonantiae : 2.848560E+05, 18.11987 octaves Euler's gradus suavitatis : 110 Sum of Mann's harmonic distance : 130.5, average 43.50000 Mersenne's string divisions : 99351 Sum of van Prooijen's expressibility: 3.98726, average 1.32909 Sum of Tenney's harmonic distance : 8.17726, average 2.72575 Vogel's harmonic complexity : 74.66667 Wille's k value : 539 Wilson's harmonic complexity : 110 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 12.92241, average 2.15374 Lattice compactness (without 2's) : 7.97469, average 1.32912 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 0 -0.66667 2 1 11: 0 .. 1 0.66667 2 13: -1 .. 0 -0.33333 1 1 83: -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: <7 10 24 25 46| Scale is weakly epimorphic with val: <7 10 25 26 47| Scale is weakly epimorphic with val: <7 10 26 27 45| Scale is weakly epimorphic with val: <7 10 27 28 46| Scale is weakly epimorphic with val: <7 10 27 29 45| Scale is weakly epimorphic with val: <7 11 23 25 45| Scale is weakly epimorphic with val: <7 11 23 27 46| Scale is weakly epimorphic with val: <7 11 23 28 45| Scale is weakly epimorphic with val: <7 11 23 30 46| Scale is weakly epimorphic with val: <7 11 24 25 47| Scale is weakly epimorphic with val: <7 11 24 26 46| Scale is weakly epimorphic with val: <7 11 24 28 47| Scale is weakly epimorphic with val: <7 11 24 29 46| Scale is JI-epimorphic with val: <7 11 25 26 45| Scale is weakly epimorphic with val: <7 11 25 27 47| Scale is weakly epimorphic with val: <7 11 25 29 45| Scale is weakly epimorphic with val: <7 11 25 30 47| Scale is JI-epimorphic with val: <7 11 26 27 46| Scale is weakly epimorphic with val: <7 11 26 28 45| Scale is weakly epimorphic with val: <7 11 26 30 46| Scale is JI-epimorphic with val: <7 11 27 28 47| Scale is weakly epimorphic with val: <7 11 27 29 46| Scale is weakly epimorphic with val: <7 12 27 28 45| Scale is weakly epimorphic with val: <8 11 23 25 46| Scale is weakly epimorphic with val: <8 11 24 25 45| Scale is weakly epimorphic with val: <8 11 24 26 47| Scale is weakly epimorphic with val: <8 11 24 28 45| Scale is weakly epimorphic with val: <8 11 25 26 46| Scale is weakly epimorphic with val: <8 11 25 27 45| Scale is weakly epimorphic with val: <8 11 25 29 46| Scale is weakly epimorphic with val: <8 11 26 27 47| Scale is weakly epimorphic with val: <8 11 26 28 46| Scale is weakly epimorphic with val: <8 11 26 30 47| Scale is weakly epimorphic with val: <8 11 27 29 47| Scale is weakly epimorphic with val: <8 12 24 25 46| Scale is weakly epimorphic with val: <8 12 24 26 45| Scale is weakly epimorphic with val: <8 12 24 29 45| Scale is weakly epimorphic with val: <8 12 25 26 47| Scale is weakly epimorphic with val: <8 12 25 27 46| Scale is weakly epimorphic with val: <8 12 25 30 46| Scale is weakly epimorphic with val: <8 12 26 27 45| Scale is weakly epimorphic with val: <8 12 26 28 47| Scale is weakly epimorphic with val: <8 12 27 28 46|
FIT/MODE
3: 0 1 2 N G T3 SD: 63.4805 c. M: 101.2706 c. 4: 1 1 2 P M ME S SD: 26.8026 c. M:-40.1872 c. 5: 1 1 3 N M DE S SD: 5.6348 c. M: 9.6173 c. 14: 3 3 8 N M DE S SD: 4.1237 c. M:-5.4533 c. 19: 4 4 11 N M DE S SD: 2.1273 c. M:-3.5810 c. 24: 5 5 14 N M DE S SD: 1.6255 c. M:-2.4888 c. 43: 9 9 25 N M DE S SD: 1.7275 c. M:-2.9714 c. 45: 9 10 26 N T3 SD: 1.2734 c. M: 1.6616 c. 50: 10 11 29 N T3 SD: 0.9796 c. M: 1.6616 c. 55: 11 12 32 N T3 SD: 1.0127 c. M: 1.6616 c. 64: 13 14 37 N T3 SD: 0.7400 c. M:-1.2775 c. 69: 14 15 40 N T3 SD: 0.3086 c. M:-0.4880 c. 74: 15 16 43 N T3 SD: 0.2141 c. M: 0.3156 c. 143: 29 31 83 N T3 SD: 0.1734 c. M: 0.2685 c. 162: 33 35 94 N T3 SD: 0.1655 c. M:-0.2206 c. 167: 34 36 97 N T3 SD: 0.0852 c. M:-0.1278 c. 236: 48 51 137 N T3 SD: 0.0544 c. M:-0.0904 c. 310: 63 67 180 N T3 SD: 0.0343 c. M: 0.0550 c. 477: 97 103 277 N T3 SD: 0.0084 c. M: 0.0114 c. 787: 160 170 457 N T3 SD: 0.0094 c. M: 0.0162 c. 1190: 242 257 691 N T3 SD: 0.0088 c. M:-0.0125 c. 1264: 257 273 734 N T3 SD: 0.0043 c. M: 0.0067 c. 1741: 354 376 1011 N T3 SD: 0.0034 c. M: 0.0054 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: 68.0849 cents 6 x 7:8 S SD: 29.0178 cents 7 x 8:9 S SD: 33.4032 cents 8 x 9:11 SD: 26.7501 cents 9 x 10:12 S SD: 13.2158 cents 10 x 11:13 SD: 30.9932 cents 11:12 x 15 S SD: 31.4273 cents 12:13:14:16 S SD: 22.9966 cents 13:14:15:17 SD: 19.3628 cents 14:15:16:19 SD: 14.0166 cents 15:16:17:20 SD: 4.3598 cents 33:35:37:44 SD: 3.5936 cents 48:51:54:64 SD: 2.0504 cents 63:67:71:84 SD: 1.8741 cents 69:73:78:92 SD: 1.6816 cents 84:89:95:112 SD: 1.4568 cents 102:108:115:136 SD: 0.8631 cents 117:124:132:156 SD: 0.2242 cents 249:264:281:332 SD: 0.1580 cents 366:388:413:488 SD: 0.1292 cents 414:439:467:552 SD: 0.1237 cents 531:563:599:708 SD: 0.0751 cents