Scala analysis: 159_C5
Chromatic tetrachord 30/29 * 116/111 * 37/30
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 30/29 58.691521 2: 40/37 134.969675 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 37/30 363.0753 1: 30/29 58.6915 2: 116/111 76.2782 3: 37/30 363.0753
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 30/29 58.692 cents 1: 1 116/111 76.278 cents 1: 1 37/30 363.075 cents 2: 1 40/37 134.970 cents 2: 1 37/29 421.767 cents 2: 1 58/45 439.353 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 : 58.7 135.0 498.0 58.7 : 76.3 439.4 498.0 135.0: 363.1 421.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.6915 .. 363.0753 cents 1073/900, 304.3838 cents 30/29, 58.6915 cents 2: 134.9697 .. 439.3535 cents 1073/900, 304.3838 cents 1200/1369,-228.1056 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 30/29, 58.6915 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 37/30, 363.0753 cents Average / Smallest step : 2.828603 Largest / Average step : 2.187003 Largest / Smallest step : 6.186163 Median interval of one step : 116/111, 76.2782 cents, amount: 1 Least squares average step : 130.19756 cents, oct.: 390.59269 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1417-tone equal temperament with octave 4/3 degrees: 167 384 1417 Least number of segments generator : 709 of 249.198 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1369 of 481.174 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 58.69152 cents Scale diversity : 0.683153 Lumma stability : 0.235688 Lumma impropriety factor : 0.458002 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 : 1682/1665, 17.5866 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% Limited inverse transpositions with margin 286.7972 cents: 2 -- Rational properties -- Prime limit : 37 Odd number limit : 111 (O: 37 U: 111) Highest odd numerator or denominator: 37 Scale harmonicity : 0.014534 Fundamental : 1/3219, -11.6524 octaves, 0.0813 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 3.862800E+05, 18.55929 octaves Euler's gradus suavitatis : 76 Sum of Mann's harmonic distance : 71.5, average 23.83333 Mersenne's string divisions : 4543 Sum of van Prooijen's expressibility: 3.50772, average 1.16924 Sum of Tenney's harmonic distance : 7.18896, average 2.39632 Vogel's harmonic complexity : 52.33333 Wille's k value : 832 Wilson's harmonic complexity : 77 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.22564, average 2.37094 Lattice compactness (without 2's) : 9.00997, average 1.50166 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.66667 2 29: -1 .. 0 -0.33333 1 1 37: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 19 32 36| Scale is weakly epimorphic with val: <6 10 19 32 39| Scale is weakly epimorphic with val: <6 11 18 32 37| Scale is weakly epimorphic with val: <6 11 18 32 40| Scale is weakly epimorphic with val: <6 11 19 33 35| Scale is weakly epimorphic with val: <6 11 19 33 38| Scale is weakly epimorphic with val: <6 11 19 33 41| Scale is weakly epimorphic with val: <7 10 17 32 35| Scale is weakly epimorphic with val: <7 10 17 35 35| Scale is weakly epimorphic with val: <7 10 18 32 37| Scale is weakly epimorphic with val: <7 10 18 32 40| Scale is weakly epimorphic with val: <7 10 18 33 36| Scale is weakly epimorphic with val: <7 10 18 36 36| Scale is weakly epimorphic with val: <7 10 19 33 35| Scale is weakly epimorphic with val: <7 10 19 33 38| Scale is weakly epimorphic with val: <7 10 19 33 41| Scale is weakly epimorphic with val: <7 10 19 34 37| Scale is weakly epimorphic with val: <7 10 19 37 37| Scale is weakly epimorphic with val: <7 11 15 32 37| Scale is weakly epimorphic with val: <7 11 15 32 40| Scale is weakly epimorphic with val: <7 11 15 34 35| Scale is weakly epimorphic with val: <7 11 15 34 38| Scale is weakly epimorphic with val: <7 11 15 34 41| Scale is weakly epimorphic with val: <7 11 15 35 37| Scale is weakly epimorphic with val: <7 11 15 35 40| Scale is weakly epimorphic with val: <7 11 15 37 38| Scale is weakly epimorphic with val: <7 11 15 37 41| Scale is weakly epimorphic with val: <7 11 15 38 40| Scale is weakly epimorphic with val: <7 11 16 32 36| Scale is weakly epimorphic with val: <7 11 16 32 39| Scale is JI-epimorphic with val: <7 11 16 33 35| Scale is weakly epimorphic with val: <7 11 16 33 38| Scale is weakly epimorphic with val: <7 11 16 33 41| Scale is weakly epimorphic with val: <7 11 16 35 36| Scale is weakly epimorphic with val: <7 11 16 35 39| Scale is weakly epimorphic with val: <7 11 16 36 38| Scale is weakly epimorphic with val: <7 11 16 36 41| Scale is weakly epimorphic with val: <7 11 16 38 39| Scale is weakly epimorphic with val: <7 11 17 33 37| Scale is weakly epimorphic with val: <7 11 17 33 40| Scale is JI-epimorphic with val: <7 11 17 34 36| Scale is weakly epimorphic with val: <7 11 17 34 39| Scale is weakly epimorphic with val: <7 11 17 36 37| Scale is weakly epimorphic with val: <7 11 17 36 40| Scale is weakly epimorphic with val: <7 11 17 37 39| Scale is weakly epimorphic with val: <7 11 18 32 37| Scale is weakly epimorphic with val: <7 11 18 32 40| Scale is weakly epimorphic with val: <7 11 18 34 35| Scale is weakly epimorphic with val: <7 11 18 34 38| Scale is weakly epimorphic with val: <7 11 18 34 41| Scale is JI-epimorphic with val: <7 11 18 35 37| Scale is weakly epimorphic with val: <7 11 18 35 40| Scale is weakly epimorphic with val: <7 11 18 37 38| Scale is weakly epimorphic with val: <7 11 18 37 41| Scale is weakly epimorphic with val: <7 11 18 38 40| Scale is weakly epimorphic with val: <7 11 19 32 36| Scale is weakly epimorphic with val: <7 11 19 32 39| Scale is weakly epimorphic with val: <7 11 19 33 35| Scale is weakly epimorphic with val: <7 11 19 33 38| Scale is weakly epimorphic with val: <7 11 19 33 41| Scale is weakly epimorphic with val: <7 11 19 35 36| Scale is weakly epimorphic with val: <7 11 19 35 39| Scale is JI-epimorphic with val: <7 11 19 36 38| Scale is weakly epimorphic with val: <7 11 19 36 41| Scale is weakly epimorphic with val: <7 11 19 38 39| Scale is weakly epimorphic with val: <7 12 16 32 36| Scale is weakly epimorphic with val: <7 12 16 32 39| Scale is weakly epimorphic with val: <7 12 17 32 35| Scale is weakly epimorphic with val: <7 12 17 33 37| Scale is weakly epimorphic with val: <7 12 17 33 40| Scale is weakly epimorphic with val: <7 12 17 35 35| Scale is weakly epimorphic with val: <7 12 18 33 36| Scale is weakly epimorphic with val: <7 12 18 34 35| Scale is weakly epimorphic with val: <7 12 18 34 38| Scale is weakly epimorphic with val: <7 12 18 34 41| Scale is weakly epimorphic with val: <7 12 18 36 36| Scale is weakly epimorphic with val: <7 12 19 34 37| Scale is weakly epimorphic with val: <7 12 19 35 36| Scale is weakly epimorphic with val: <7 12 19 35 39| Scale is weakly epimorphic with val: <7 12 19 37 37| Scale is weakly epimorphic with val: <8 11 15 33 36| Scale is weakly epimorphic with val: <8 11 15 36 36| Scale is weakly epimorphic with val: <8 11 16 32 36| Scale is weakly epimorphic with val: <8 11 16 32 39| Scale is weakly epimorphic with val: <8 11 16 34 37| Scale is weakly epimorphic with val: <8 11 16 37 37| Scale is weakly epimorphic with val: <8 11 17 32 38| Scale is weakly epimorphic with val: <8 11 17 33 37| Scale is weakly epimorphic with val: <8 11 17 33 40| Scale is weakly epimorphic with val: <8 11 17 35 38| Scale is weakly epimorphic with val: <8 11 17 38 38| Scale is weakly epimorphic with val: <8 11 18 33 39| Scale is weakly epimorphic with val: <8 11 18 34 35| Scale is weakly epimorphic with val: <8 11 18 34 38| Scale is weakly epimorphic with val: <8 11 18 34 41| Scale is weakly epimorphic with val: <8 11 18 36 39| Scale is weakly epimorphic with val: <8 11 19 34 40| Scale is weakly epimorphic with val: <8 11 19 35 36| Scale is weakly epimorphic with val: <8 11 19 35 39| Scale is weakly epimorphic with val: <8 11 19 37 40| Scale is weakly epimorphic with val: <8 12 15 32 37| Scale is weakly epimorphic with val: <8 12 15 32 40| Scale is weakly epimorphic with val: <8 12 15 33 36| Scale is weakly epimorphic with val: <8 12 15 36 36| Scale is weakly epimorphic with val: <8 12 16 33 35| Scale is weakly epimorphic with val: <8 12 16 33 38| Scale is weakly epimorphic with val: <8 12 16 33 41| Scale is weakly epimorphic with val: <8 12 16 34 37| Scale is weakly epimorphic with val: <8 12 16 37 37| Scale is weakly epimorphic with val: <8 12 17 32 38| Scale is weakly epimorphic with val: <8 12 17 34 36| Scale is weakly epimorphic with val: <8 12 17 34 39| Scale is weakly epimorphic with val: <8 12 17 35 38| Scale is weakly epimorphic with val: <8 12 17 38 38| Scale is weakly epimorphic with val: <8 12 18 33 39| Scale is weakly epimorphic with val: <8 12 18 35 37| Scale is weakly epimorphic with val: <8 12 18 35 40| Scale is weakly epimorphic with val: <8 12 18 36 39| Scale is weakly epimorphic with val: <8 12 19 34 40| Scale is weakly epimorphic with val: <8 12 19 36 38| Scale is weakly epimorphic with val: <8 12 19 36 41| Scale is weakly epimorphic with val: <8 12 19 37 40|
FIT/MODE
3: 0 1 2 N G T3 SD: 38.3341 c. M: 58.6915 c. 4: 0 1 3 N G T3 SD: 34.4193 c. M: 58.6915 c. 5: 0 1 4 N G T3 SD: 39.5604 c. M: 58.6915 c. 6: 1 1 4 N M DE S SD: 22.7675 c. M:-31.0453 c. 7: 1 1 5 N M DE S SD: 8.3448 c. M:-12.4578 c. 8: 1 1 6 N M DE S SD: 6.3792 c. M: 10.4584 c. 15: 2 2 11 N M DE S SD: 4.6249 c. M:-7.7145 c. 18: 2 3 13 N T3 SD: 2.7473 c. M:-3.3762 c. 25: 3 4 18 N T3 SD: 2.6614 c. M:-4.4829 c. 26: 3 4 19 N T3 SD: 0.8709 c. M: 1.2248 c. 59: 7 9 43 N T3 SD: 0.2363 c. M:-0.3986 c. 85: 10 13 62 N T3 SD: 0.1310 c. M: 0.2046 c. 144: 17 22 105 N T3 SD: 0.0773 c. M:-0.1055 c. 229: 27 35 167 N T3 SD: 0.0758 c. M: 0.1278 c. 365: 43 56 266 N T3 SD: 0.0680 c. M:-0.1165 c. 391: 46 60 285 N T3 SD: 0.0636 c. M: 0.0980 c. 424: 50 65 309 N T3 SD: 0.0694 c. M:-0.1133 c. 450: 53 69 328 N T3 SD: 0.0374 c. M:-0.0559 c. 509: 60 78 371 N T3 SD: 0.0361 c. M:-0.0602 c. 535: 63 82 390 N T3 SD: 0.0263 c. M: 0.0432 c. 594: 70 91 433 N T3 SD: 0.0129 c. M:-0.0223 c. 679: 80 104 495 N T3 SD: 0.0076 c. M: 0.0117 c. 1273: 150 195 928 N T3 SD: 0.0054 c. M:-0.0072 c. 1417: 167 217 1033 N T3 SD: 0.0033 c. M:-0.0054 c. 2011: 237 308 1466 N T3 SD: 0.0038 c. M:-0.0052 c. 2096: 247 321 1528 N T3 SD: 0.0019 c. M: 0.0033 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: 99.7208 cents 6 x 7:8 S SD: 65.9506 cents 7 x 8:9 S SD: 57.4877 cents 8 x 9:11 SD: 43.5625 cents 9 x 10:12 S SD: 23.7170 cents 10 x 11:13 SD: 26.5671 cents 11 x 12:15 S SD: 20.9710 cents 12 x 13:16 SD: 1.8015 cents 13 x 14:17 SD: 17.1364 cents 14 x 15:19 SD: 17.1757 cents 15 x 16:20 S SD: 11.6192 cents 16 x 17:21 SD: 20.2743 cents 17 x 18:23 SD: 21.9992 cents 18:19 x 24 SD: 17.4557 cents 20:21:22:27 SD: 15.0147 cents 21:22:23:28 SD: 10.4592 cents 22:23:24:29 SD: 10.3845 cents 23:24:25:31 SD: 8.5831 cents 24:25:26:32 SD: 4.1703 cents 27:28:29:36 SD: 4.0133 cents 36:37:39:48 SD: 3.9400 cents 51:53:55:68 SD: 2.9907 cents 60:62:65:80 SD: 1.3616 cents 87:90:94:116 SD: 0.3317 cents 234:242:253:312 SD: 0.1756 cents 321:332:347:428 SD: 0.1280 cents 492:509:532:656 SD: 0.1236 cents 579:599:626:772 SD: 0.0599 cents