Scala analysis: 356_C29
Chromatic tetrachord 20/19 * 52/45 * 57/52
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: 208/171 339.104644 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 57/52 158.9404 1: 20/19 88.8007 small undevicesimal semitone 2: 52/45 250.3039 3: 57/52 158.9404
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 20/19 88.801 cents small undevicesimal semitone 1: 1 57/52 158.940 cents 1: 1 52/45 250.304 cents 2: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 208/171 339.105 cents 2: 1 19/15 409.244 cents undevicesimal ditone 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 : 88.8 339.1 498.0 88.8 : 250.3 409.2 498.0 339.1: 158.9 247.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.8007 .. 250.3039 cents 247/225, 161.5032 cents 20/19, 88.8007 cents 2: 247.7411 .. 409.2443 cents 247/225, 161.5032 cents 675/676,-2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 20/19, 88.8007 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 52/45, 250.3039 cents Average / Smallest step : 1.869524 Largest / Average step : 1.507719 Largest / Smallest step : 2.818716 Median interval of one step : 57/52, 158.9404 cents, amount: 1 Least squares average step : 161.51036 cents, oct.: 484.53107 cents Scale is not proper Scale has trivalence property Scale is a mode of a 774-tone equal temperament with octave 4/3 degrees: 138 527 774 Least number of segments generator : 389 of 250.309 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 569 of 366.134 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 : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.094571 Lumma stability : 0.356597 Lumma impropriety factor : 0.005146 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 : 676/675, 2.5629 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% -- Rational properties -- Prime limit : 19 Odd number limit : 171 (O: 57 U: 171) Highest odd numerator or denominator: 171 Scale harmonicity : 0.013890 Average absolute harmonicity : 0.084352 Specific harmonicity : 0.063303 Fundamental : 1/171, -7.4179 octaves, 1.5300 Hz. Guide tone : 1040, 10.0224 octaves, 272090.588 Hz. Exponens Consonantiae : 1.778400E+05, 17.44022 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 212.5, average 70.83333 Mersenne's string divisions : 103467 Sum of van Prooijen's expressibility: 3.98887, average 1.32962 Sum of Tenney's harmonic distance : 8.21002, average 2.73667 Vogel's harmonic complexity : 18.00000 Wille's k value : 28 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 16.91605, average 2.81934 Lattice compactness (without 2's) : 10.77729, average 1.79622 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 2.66667 8 3: -2 .. 0 -1.00000 3 1 5: 0 .. 1 0.33333 1 13: 0 .. 1 0.33333 1 19: -1 .. 0 -0.66667 2 2 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 15 28 29| Scale is weakly epimorphic with val: <6 10 16 29 30| Scale is weakly epimorphic with val: <6 10 17 27 28| Scale is weakly epimorphic with val: <6 10 17 30 31| Scale is weakly epimorphic with val: <6 10 18 28 29| Scale is weakly epimorphic with val: <6 10 19 25 28| Scale is weakly epimorphic with val: <6 10 19 28 28| Scale is weakly epimorphic with val: <6 10 19 29 30| Scale is weakly epimorphic with val: <6 11 19 25 28| Scale is weakly epimorphic with val: <6 11 19 28 28| Scale is weakly epimorphic with val: <7 10 15 25 30| Scale is weakly epimorphic with val: <7 10 15 28 33| Scale is weakly epimorphic with val: <7 10 16 26 31| Scale is weakly epimorphic with val: <7 10 16 29 34| Scale is weakly epimorphic with val: <7 10 17 25 28| Scale is weakly epimorphic with val: <7 10 17 27 32| Scale is weakly epimorphic with val: <7 10 17 28 28| Scale is weakly epimorphic with val: <7 10 18 25 30| Scale is weakly epimorphic with val: <7 10 18 26 29| Scale is weakly epimorphic with val: <7 10 18 28 33| Scale is weakly epimorphic with val: <7 10 18 29 29| Scale is weakly epimorphic with val: <7 10 19 26 31| Scale is weakly epimorphic with val: <7 10 19 27 30| Scale is weakly epimorphic with val: <7 10 19 29 34| Scale is weakly epimorphic with val: <7 10 19 30 30| Scale is weakly epimorphic with val: <7 11 15 25 30| Scale is weakly epimorphic with val: <7 11 15 25 33| Scale is weakly epimorphic with val: <7 11 15 27 28| Scale is weakly epimorphic with val: <7 11 15 27 31| Scale is weakly epimorphic with val: <7 11 15 27 34| Scale is weakly epimorphic with val: <7 11 15 28 30| Scale is weakly epimorphic with val: <7 11 15 28 33| Scale is weakly epimorphic with val: <7 11 15 30 31| Scale is weakly epimorphic with val: <7 11 15 30 34| Scale is JI-epimorphic with val: <7 11 16 25 29| Scale is weakly epimorphic with val: <7 11 16 25 32| Scale is weakly epimorphic with val: <7 11 16 26 28| Scale is weakly epimorphic with val: <7 11 16 26 31| Scale is weakly epimorphic with val: <7 11 16 26 34| Scale is weakly epimorphic with val: <7 11 16 28 29| Scale is weakly epimorphic with val: <7 11 16 28 32| Scale is weakly epimorphic with val: <7 11 16 29 31| Scale is weakly epimorphic with val: <7 11 16 29 34| Scale is JI-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 17 29 30| Scale is weakly epimorphic with val: <7 11 17 29 33| Scale is weakly epimorphic with val: <7 11 17 30 32| Scale is weakly epimorphic with val: <7 11 18 25 30| Scale is weakly epimorphic with val: <7 11 18 25 33| Scale is weakly epimorphic with val: <7 11 18 27 28| Scale is JI-epimorphic with val: <7 11 18 27 31| Scale is weakly epimorphic with val: <7 11 18 27 34| Scale is weakly epimorphic with val: <7 11 18 28 30| Scale is weakly epimorphic with val: <7 11 18 28 33| Scale is weakly epimorphic with val: <7 11 18 30 31| Scale is weakly epimorphic with val: <7 11 18 30 34| Scale is weakly epimorphic with val: <7 11 19 25 29| Scale is weakly epimorphic with val: <7 11 19 25 32| Scale is weakly epimorphic with val: <7 11 19 26 28| Scale is weakly epimorphic with val: <7 11 19 26 31| Scale is weakly epimorphic with val: <7 11 19 26 34| Scale is weakly epimorphic with val: <7 11 19 28 29| Scale is JI-epimorphic with val: <7 11 19 28 32| Scale is weakly epimorphic with val: <7 11 19 29 31| Scale is weakly epimorphic with val: <7 11 19 29 34| Scale is weakly epimorphic with val: <7 12 15 27 28| Scale is weakly epimorphic with val: <7 12 15 30 31| Scale is weakly epimorphic with val: <7 12 16 28 29| Scale is weakly epimorphic with val: <7 12 17 25 28| Scale is weakly epimorphic with val: <7 12 17 28 28| Scale is weakly epimorphic with val: <7 12 17 29 30| Scale is weakly epimorphic with val: <7 12 18 26 29| Scale is weakly epimorphic with val: <7 12 18 27 28| Scale is weakly epimorphic with val: <7 12 18 29 29| Scale is weakly epimorphic with val: <7 12 18 30 31| Scale is weakly epimorphic with val: <7 12 19 27 30| Scale is weakly epimorphic with val: <7 12 19 28 29| Scale is weakly epimorphic with val: <7 12 19 30 30| Scale is weakly epimorphic with val: <8 11 15 25 28| Scale is weakly epimorphic with val: <8 11 15 26 33| Scale is weakly epimorphic with val: <8 11 15 28 28| Scale is weakly epimorphic with val: <8 11 16 26 29| Scale is weakly epimorphic with val: <8 11 16 27 34| Scale is weakly epimorphic with val: <8 11 16 29 29| Scale is weakly epimorphic with val: <8 11 17 25 32| Scale is weakly epimorphic with val: <8 11 17 27 30| Scale is weakly epimorphic with val: <8 11 17 30 30| Scale is weakly epimorphic with val: <8 11 18 25 31| Scale is weakly epimorphic with val: <8 11 18 26 33| Scale is weakly epimorphic with val: <8 11 18 28 31| Scale is weakly epimorphic with val: <8 11 19 26 32| Scale is weakly epimorphic with val: <8 11 19 27 34| Scale is weakly epimorphic with val: <8 11 19 29 32| Scale is weakly epimorphic with val: <8 12 15 25 28| Scale is weakly epimorphic with val: <8 12 15 27 32| Scale is weakly epimorphic with val: <8 12 15 28 28| Scale is weakly epimorphic with val: <8 12 16 25 30| Scale is weakly epimorphic with val: <8 12 16 26 29| Scale is weakly epimorphic with val: <8 12 16 28 33| Scale is weakly epimorphic with val: <8 12 16 29 29| Scale is weakly epimorphic with val: <8 12 17 26 31| Scale is weakly epimorphic with val: <8 12 17 27 30| Scale is weakly epimorphic with val: <8 12 17 29 34| Scale is weakly epimorphic with val: <8 12 17 30 30| Scale is weakly epimorphic with val: <8 12 18 25 31| Scale is weakly epimorphic with val: <8 12 18 27 32| Scale is weakly epimorphic with val: <8 12 18 28 31| Scale is weakly epimorphic with val: <8 12 19 25 30| Scale is weakly epimorphic with val: <8 12 19 26 32| Scale is weakly epimorphic with val: <8 12 19 28 33| Scale is weakly epimorphic with val: <8 12 19 29 32|
FIT/MODE
3: 0 2 1 N G T3 SD: 51.4316 c. M: 88.8007 c. 4: 1 2 1 P M ME I SD: 28.6392 c. M:-35.7106 c. 5: 1 2 2 SP M ME S SD: 24.0770 c. M: 40.2776 c. 6: 1 3 2 P T3 SD: 5.2793 c. M: 7.0746 c. 16: 3 8 5 P T3 SD: 3.2609 c. M:-4.5827 c. 22: 4 11 7 P T3 SD: 1.0480 c. M:-1.7529 c. 28: 5 14 9 P T3 SD: 0.6660 c. M: 1.1455 c. 50: 9 25 16 P T3 SD: 0.5497 c. M:-0.8474 c. 78: 14 39 25 P T3 SD: 0.5247 c. M: 0.6895 c. 107: 19 54 34 N T3 SD: 0.4465 c. M:-0.6831 c. 113: 20 57 36 N T3 SD: 0.4072 c. M: 0.6511 c. 129: 23 65 41 N T3 SD: 0.3735 c. M:-0.6470 c. 135: 24 68 43 N T3 SD: 0.2306 c. M:-0.3038 c. 157: 28 79 50 N T3 SD: 0.1894 c. M:-0.3273 c. 163: 29 82 52 N T3 SD: 0.1150 c. M: 0.1915 c. 185: 33 93 59 N T3 SD: 0.0645 c. M:-0.1044 c. 213: 38 107 68 N T3 SD: 0.0460 c. M: 0.0599 c. 376: 67 189 120 N T3 SD: 0.0313 c. M: 0.0533 c. 398: 71 200 127 N T3 SD: 0.0285 c. M:-0.0465 c. 561: 100 282 179 N T3 SD: 0.0206 c. M:-0.0276 c. 589: 105 296 188 N T3 SD: 0.0184 c. M: 0.0282 c. 774: 138 389 247 N T3 SD: 0.0023 c. M:-0.0035 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 5 x S SD: 47.2091 cents 5 x 6:7 S SD: 43.8327 cents 6 x 7:8 S SD: 36.1169 cents 7 x x 9 SD: 62.9609 cents 8:9:10:11 H SD: 45.1133 cents 9:10:11:12 H SD: 31.3235 cents 10:11:12:13 H SD: 30.3291 cents 11:12:13:15 SD: 29.4899 cents 12:13:15:16 SD: 22.8666 cents 13:14:16:17 S SD: 18.5742 cents 14:15:17:19 SD: 14.4788 cents 15:16:18:20 S SD: 10.9359 cents 18:19:22:24 SD: 3.1973 cents 42:44:51:56 SD: 2.9276 cents 56:59:68:75 SD: 2.8029 cents 57:60:69:76 SD: 2.7811 cents 60:63:73:80 SD: 1.4511 cents 78:82:95:104 SD: 1.0513 cents 93:98:113:124 SD: 0.8818 cents 111:117:135:148 SD: 0.7829 cents 153:161:186:204 SD: 0.3771 cents 171:180:208:228 SD: 0.0000 cents