Scala analysis: 182_C8
Chromatic tetrachord 20/19 * 57/55 * 11/9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 20/19 88.800698 small undevicesimal semitone 2: 12/11 150.637059 undecimal neutral second, 3/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 11/9 347.4079 undecimal neutral third 1: 20/19 88.8007 small undevicesimal semitone 2: 57/55 61.8364 3: 11/9 347.4079 undecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 57/55 61.836 cents 1: 1 20/19 88.801 cents small undevicesimal semitone 1: 1 11/9 347.408 cents undecimal neutral third 2: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 1 19/15 409.244 cents undevicesimal ditone 2: 1 220/171 436.209 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 : 88.8 150.6 498.0 88.8 : 61.8 409.2 498.0 150.6: 347.4 436.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 61.8364 .. 347.4079 cents 605/513, 285.5716 cents 57/55, 61.8364 cents 2: 150.6371 .. 436.2086 cents 605/513, 285.5716 cents 108/121,-196.7709 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 57/55, 61.8364 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 11/9, 347.4079 cents Average / Smallest step : 2.684747 Largest / Average step : 2.092630 Largest / Smallest step : 5.618182 Median interval of one step : 20/19, 88.8007 cents, amount: 1 Least squares average step : 134.58642 cents, oct.: 403.75925 cents Scale is not proper Scale has trivalence property 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 61.83636 cents Scale diversity : 0.788459 Lumma stability : 0.248316 Lumma impropriety factor : 0.395087 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 : 1100/1083, 26.9643 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 285.5716 cents: 2 -- Rational properties -- Prime limit : 19 Odd number limit : 171 (O: 57 U: 171) Highest odd numerator or denominator: 19 Scale harmonicity : 0.015147 Average absolute harmonicity : 0.093859 Specific harmonicity : 0.080783 Fundamental : 1/627, -9.2923 octaves, 0.4173 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 3.762000E+04, 15.19921 octaves Euler's gradus suavitatis : 39 Sum of Mann's harmonic distance : 34.5, average 11.50000 Mersenne's string divisions : 6279 Sum of van Prooijen's expressibility: 2.79727, average 0.93242 Sum of Tenney's harmonic distance : 5.77954, average 1.92651 Vogel's harmonic complexity : 26.66667 Wille's k value : 104 Wilson's harmonic complexity : 41 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 13.10317, average 2.18386 Lattice compactness (without 2's) : 9.79655, average 1.63276 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.33333 1 11: -1 .. 0 -0.33333 1 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 19 24 28| Scale is weakly epimorphic with val: <6 10 19 27 28| Scale is weakly epimorphic with val: <6 11 19 24 28| Scale is weakly epimorphic with val: <6 11 19 27 28| Scale is weakly epimorphic with val: <7 10 17 25 28| Scale is weakly epimorphic with val: <7 10 18 25 29| Scale is weakly epimorphic with val: <7 10 19 25 30| Scale is JI-epimorphic with val: <7 11 15 23 28| Scale is weakly epimorphic with val: <7 11 15 23 31| Scale is weakly epimorphic with val: <7 11 15 23 34| Scale is weakly epimorphic with val: <7 11 15 24 30| Scale is weakly epimorphic with val: <7 11 15 24 33| Scale is weakly epimorphic with val: <7 11 15 26 28| Scale is weakly epimorphic with val: <7 11 15 26 31| Scale is weakly epimorphic with val: <7 11 15 26 34| Scale is weakly epimorphic with val: <7 11 15 27 30| Scale is weakly epimorphic with val: <7 11 15 27 33| Scale is JI-epimorphic with val: <7 11 16 23 29| Scale is weakly epimorphic with val: <7 11 16 23 32| Scale is weakly epimorphic with val: <7 11 16 24 28| Scale is weakly epimorphic with val: <7 11 16 24 31| Scale is weakly epimorphic with val: <7 11 16 24 34| Scale is weakly epimorphic with val: <7 11 16 26 29| Scale is weakly epimorphic with val: <7 11 16 26 32| Scale is weakly epimorphic with val: <7 11 16 27 28| Scale is weakly epimorphic with val: <7 11 16 27 31| Scale is weakly epimorphic with val: <7 11 16 27 34| Scale is JI-epimorphic with val: <7 11 17 23 30| Scale is weakly epimorphic with val: <7 11 17 23 33| Scale is weakly epimorphic with val: <7 11 17 24 29| Scale is weakly epimorphic with val: <7 11 17 24 32| Scale is weakly epimorphic with val: <7 11 17 26 30| Scale is weakly epimorphic with val: <7 11 17 26 33| Scale is weakly epimorphic with val: <7 11 17 27 29| Scale is weakly epimorphic with val: <7 11 17 27 32| Scale is weakly epimorphic with val: <7 11 18 23 28| Scale is JI-epimorphic with val: <7 11 18 23 31| Scale is weakly epimorphic with val: <7 11 18 23 34| Scale is weakly epimorphic with val: <7 11 18 24 30| Scale is weakly epimorphic with val: <7 11 18 24 33| Scale is weakly epimorphic with val: <7 11 18 26 28| Scale is weakly epimorphic with val: <7 11 18 26 31| Scale is weakly epimorphic with val: <7 11 18 26 34| Scale is weakly epimorphic with val: <7 11 18 27 30| Scale is weakly epimorphic with val: <7 11 18 27 33| Scale is weakly epimorphic with val: <7 11 19 23 29| Scale is JI-epimorphic with val: <7 11 19 23 32| Scale is weakly epimorphic with val: <7 11 19 24 28| Scale is weakly epimorphic with val: <7 11 19 24 31| Scale is weakly epimorphic with val: <7 11 19 24 34| Scale is weakly epimorphic with val: <7 11 19 26 29| Scale is weakly epimorphic with val: <7 11 19 26 32| Scale is weakly epimorphic with val: <7 11 19 27 28| Scale is weakly epimorphic with val: <7 11 19 27 31| Scale is weakly epimorphic with val: <7 11 19 27 34| Scale is weakly epimorphic with val: <7 12 15 23 28| Scale is weakly epimorphic with val: <7 12 15 23 31| Scale is weakly epimorphic with val: <7 12 15 23 34| Scale is weakly epimorphic with val: <7 12 16 23 29| Scale is weakly epimorphic with val: <7 12 16 23 32| Scale is weakly epimorphic with val: <7 12 17 23 30| Scale is weakly epimorphic with val: <7 12 17 23 33| Scale is weakly epimorphic with val: <7 12 17 25 28| Scale is weakly epimorphic with val: <7 12 18 23 28| Scale is weakly epimorphic with val: <7 12 18 23 31| Scale is weakly epimorphic with val: <7 12 18 23 34| Scale is weakly epimorphic with val: <7 12 18 25 29| Scale is weakly epimorphic with val: <7 12 19 23 29| Scale is weakly epimorphic with val: <7 12 19 23 32| Scale is weakly epimorphic with val: <7 12 19 25 30| Scale is weakly epimorphic with val: <8 11 15 23 28| Scale is weakly epimorphic with val: <8 11 15 24 30| Scale is weakly epimorphic with val: <8 11 15 24 33| Scale is weakly epimorphic with val: <8 11 15 26 28| Scale is weakly epimorphic with val: <8 11 16 23 29| Scale is weakly epimorphic with val: <8 11 16 24 28| Scale is weakly epimorphic with val: <8 11 16 24 31| Scale is weakly epimorphic with val: <8 11 16 24 34| Scale is weakly epimorphic with val: <8 11 16 26 29| Scale is weakly epimorphic with val: <8 11 17 23 30| Scale is weakly epimorphic with val: <8 11 17 24 29| Scale is weakly epimorphic with val: <8 11 17 24 32| Scale is weakly epimorphic with val: <8 11 17 26 30| Scale is weakly epimorphic with val: <8 11 18 23 31| Scale is weakly epimorphic with val: <8 11 18 24 30| Scale is weakly epimorphic with val: <8 11 18 24 33| Scale is weakly epimorphic with val: <8 11 18 26 31| Scale is weakly epimorphic with val: <8 11 19 23 32| Scale is weakly epimorphic with val: <8 11 19 24 28| Scale is weakly epimorphic with val: <8 11 19 24 31| Scale is weakly epimorphic with val: <8 11 19 24 34| Scale is weakly epimorphic with val: <8 11 19 26 32| Scale is weakly epimorphic with val: <8 12 15 23 28| Scale is weakly epimorphic with val: <8 12 15 25 29| Scale is weakly epimorphic with val: <8 12 15 25 32| Scale is weakly epimorphic with val: <8 12 15 26 28| Scale is weakly epimorphic with val: <8 12 16 23 29| Scale is weakly epimorphic with val: <8 12 16 25 30| Scale is weakly epimorphic with val: <8 12 16 25 33| Scale is weakly epimorphic with val: <8 12 16 26 29| Scale is weakly epimorphic with val: <8 12 17 23 30| Scale is weakly epimorphic with val: <8 12 17 25 28| Scale is weakly epimorphic with val: <8 12 17 25 31| Scale is weakly epimorphic with val: <8 12 17 25 34| Scale is weakly epimorphic with val: <8 12 17 26 30| Scale is weakly epimorphic with val: <8 12 18 23 31| Scale is weakly epimorphic with val: <8 12 18 25 29| Scale is weakly epimorphic with val: <8 12 18 25 32| Scale is weakly epimorphic with val: <8 12 18 26 31| Scale is weakly epimorphic with val: <8 12 19 23 32| Scale is weakly epimorphic with val: <8 12 19 25 30| Scale is weakly epimorphic with val: <8 12 19 25 33| Scale is weakly epimorphic with val: <8 12 19 26 32|
FIT/MODE
3: 1 0 2 N G T3 SD: 45.4552 c. M:-77.2143 c. 4: 1 0 3 N G T3 SD: 25.5460 c. M:-35.7106 c. 5: 1 1 3 N M DE S SD: 28.7340 c. M:-48.5809 c. 6: 1 1 4 N M DE S SD: 9.4876 c. M:-15.3779 c. 7: 1 1 5 N M DE S SD: 11.2709 c. M: 17.6514 c. 10: 2 1 7 N T3 SD: 6.2800 c. M:-10.8083 c. 16: 3 2 11 N T3 SD: 3.9167 c. M:-5.0020 c. 17: 3 2 12 N T3 SD: 2.4548 c. M: 4.1532 c. 23: 4 3 16 N T3 SD: 1.3733 c. M: 2.1842 c. 33: 6 4 23 N T3 SD: 1.0254 c. M:-1.7529 c. 40: 7 5 28 N T3 SD: 1.1826 c. M: 1.6428 c. 50: 9 6 35 N T3 SD: 0.8593 c. M: 1.2236 c. 56: 10 7 39 N T3 SD: 0.3300 c. M:-0.5552 c. 73: 13 9 51 N T3 SD: 0.3187 c. M: 0.5413 c. 106: 19 13 74 N T3 SD: 0.3178 c. M:-0.4715 c. 129: 23 16 90 N T3 SD: 0.0377 c. M: 0.0653 c. 314: 56 39 219 N T3 SD: 0.0293 c. M:-0.0453 c. 443: 79 55 309 N T3 SD: 0.0117 c. M:-0.0155 c. 572: 102 71 399 N T3 SD: 0.0072 c. M:-0.0115 c. 1015: 181 126 708 N T3 SD: 0.0079 c. M:-0.0132 c. 1273: 227 158 888 N T3 SD: 0.0085 c. M: 0.0107 c. 1587: 283 197 1107 N T3 SD: 0.0073 c. M:-0.0126 c. 1845: 329 229 1287 N T3 SD: 0.0079 c. M:-0.0106 c. 2159: 385 268 1506 N T3 SD: 0.0071 c. M:-0.0123 c. 2311: 412 287 1612 N T3 SD: 0.0066 c. M: 0.0103 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: 92.6837 cents 6 x 7:8 S SD: 58.1169 cents 7 x 8:9 S SD: 51.1133 cents 8 x 9:11 SD: 37.6697 cents 9 x 10:12 S SD: 15.8833 cents 10 x 11:13 SD: 23.0628 cents 11 x 12:15 S SD: 19.4529 cents 12 x 13:16 SD: 6.0322 cents 13 x 14:17 SD: 20.1813 cents 14:15 x 19 SD: 21.6672 cents 15:16 x 20 S SD: 11.4653 cents 16:17 x 21 SD: 15.8454 cents 18:19:20:24 S SD: 10.7092 cents 20:21:22:27 SD: 8.7414 cents 21:22:23:28 SD: 3.5792 cents 54:57:59:72 SD: 1.8315 cents 57:60:62:76 SD: 1.6898 cents 75:79:82:100 SD: 1.3375 cents 78:82:85:104 SD: 0.9636 cents 111:117:121:148 SD: 0.8917 cents 132:139:144:176 SD: 0.2185 cents 285:300:311:380 SD: 0.1687 cents 342:360:373:456 SD: 0.1406 cents 417:439:455:556 SD: 0.1345 cents 474:499:517:632 SD: 0.1183 cents 495:521:540:660 SD: 0.0583 cents