Scala analysis: 191_C10
Chromatic tetrachord 69/65 * 65/63 * 28/23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 69/65 103.387972 2: 23/21 157.493440 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 28/23 340.5516 1: 69/65 103.3880 2: 65/63 54.1055 3: 28/23 340.5516
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 65/63 54.105 cents 1: 1 69/65 103.388 cents 1: 1 28/23 340.552 cents 2: 1 23/21 157.493 cents 2: 1 260/207 394.657 cents 2: 1 84/65 443.940 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 : 103.4 157.5 498.0 103.4: 54.1 394.7 498.0 157.5: 340.6 443.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.1055 .. 340.5516 cents 1764/1495, 286.4461 cents 65/63, 54.1055 cents 2: 157.4934 .. 443.9395 cents 1764/1495, 286.4461 cents 529/588,-183.0581 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 65/63, 54.1055 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 28/23, 340.5516 cents Average / Smallest step : 3.068359 Largest / Average step : 2.051330 Largest / Smallest step : 6.294217 Median interval of one step : 69/65, 103.3880 cents, amount: 1 Least squares average step : 136.60785 cents, oct.: 409.82354 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1344-tone equal temperament with octave 4/3 degrees: 279 425 1344 Least number of segments generator : 673 of 249.393 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1271 of 470.993 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 : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 54.10547 cents Scale diversity : 0.796222 Lumma stability : 0.217271 Lumma impropriety factor : 0.367553 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 : 4347/4225, 49.2825 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 23 Odd number limit : 207 (O: 69 U: 207) Highest odd numerator or denominator: 69 Scale harmonicity : 0.011330 Average absolute harmonicity : 0.082031 Specific harmonicity : 0.051690 Fundamental : 1/1365, -10.4147 octaves, 0.1917 Hz. Guide tone : 276, 8.1085 octaves, 72208.656 Hz. Exponens Consonantiae : 3.767400E+05, 18.52321 octaves Euler's gradus suavitatis : 51 Sum of Mann's harmonic distance : 92.5, average 30.83333 Mersenne's string divisions : 20636 Sum of van Prooijen's expressibility: 3.67770, average 1.22590 Sum of Tenney's harmonic distance : 7.41489, average 2.47163 Vogel's harmonic complexity : 34.66667 Wille's k value : 747 Wilson's harmonic complexity : 54 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 14.37998, average 2.39666 Lattice compactness (without 2's) : 11.43777, average 1.90629 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -1 .. 1 -0.33333 3 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 13: -1 .. 0 -0.33333 1 23: 0 .. 1 0.66667 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is JI-epimorphic with val: <7 11 16 19 26 32| Scale is weakly epimorphic with val: <7 11 16 19 26 35| Scale is weakly epimorphic with val: <7 11 16 19 27 34| Scale is JI-epimorphic with val: <7 11 16 20 27 33| Scale is weakly epimorphic with val: <7 11 16 20 28 32| Scale is weakly epimorphic with val: <7 11 16 20 28 35| Scale is weakly epimorphic with val: <7 11 16 21 26 33| Scale is JI-epimorphic with val: <7 11 16 21 28 34| Scale is weakly epimorphic with val: <7 11 17 19 26 34| Scale is weakly epimorphic with val: <7 11 17 19 28 32| Scale is weakly epimorphic with val: <7 11 17 19 28 35| Scale is JI-epimorphic with val: <7 11 17 20 26 33| Scale is weakly epimorphic with val: <7 11 17 20 27 32| Scale is weakly epimorphic with val: <7 11 17 20 27 35| Scale is JI-epimorphic with val: <7 11 17 21 27 34| Scale is weakly epimorphic with val: <7 11 17 21 28 33| Scale is weakly epimorphic with val: <7 11 18 19 27 32| Scale is weakly epimorphic with val: <7 11 18 19 27 35| Scale is weakly epimorphic with val: <7 11 18 19 28 34| Scale is weakly epimorphic with val: <7 11 18 20 26 32| Scale is weakly epimorphic with val: <7 11 18 20 26 35| Scale is weakly epimorphic with val: <7 11 18 20 28 33| Scale is JI-epimorphic with val: <7 11 18 21 26 34| Scale is weakly epimorphic with val: <7 11 18 21 27 33| Scale is weakly epimorphic with val: <7 12 16 19 26 34| Scale is weakly epimorphic with val: <7 12 16 19 28 35| Scale is weakly epimorphic with val: <7 12 16 20 26 33| Scale is weakly epimorphic with val: <7 12 16 20 27 35| Scale is weakly epimorphic with val: <7 12 16 21 27 34| Scale is weakly epimorphic with val: <7 12 17 19 27 35| Scale is weakly epimorphic with val: <7 12 17 19 28 34| Scale is weakly epimorphic with val: <7 12 17 20 26 35| Scale is weakly epimorphic with val: <7 12 17 21 26 34| Scale is weakly epimorphic with val: <7 12 18 19 26 35| Scale is weakly epimorphic with val: <7 12 18 19 27 34| Scale is weakly epimorphic with val: <7 12 18 20 28 35|
FIT/MODE
3: 1 0 2 N G T3 SD: 36.4909 c. M:-62.6270 c. 4: 1 0 3 N G T3 SD: 22.6128 c. M: 32.9822 c. 5: 1 1 3 N M DE S SD: 24.1883 c. M:-41.7246 c. 6: 1 1 4 N M DE S SD: 12.7538 c. M: 20.3805 c. 9: 2 1 6 N T3 SD: 6.4741 c. M:-8.5216 c. 10: 2 1 7 N T3 SD: 5.1500 c. M: 8.0799 c. 19: 4 2 13 N T3 SD: 0.8542 c. M:-1.4636 c. 63: 13 7 43 N T3 SD: 0.5033 c. M: 0.6168 c. 82: 17 9 56 N T3 SD: 0.2565 c. M:-0.4233 c. 101: 21 11 69 N T3 SD: 0.1995 c. M:-0.3030 c. 193: 40 21 132 N T3 SD: 0.1066 c. M: 0.1662 c. 212: 44 23 145 N T3 SD: 0.0546 c. M: 0.0924 c. 294: 61 32 201 N T3 SD: 0.0423 c. M: 0.0521 c. 313: 65 34 214 N T3 SD: 0.0307 c. M:-0.0399 c. 506: 105 55 346 N T3 SD: 0.0229 c. M: 0.0387 c. 525: 109 57 359 N T3 SD: 0.0131 c. M: 0.0164 c. 819: 170 89 560 N T3 SD: 0.0068 c. M: 0.0087 c. 1344: 279 146 919 N T3 SD: 0.0010 c. M: 0.0015 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: 89.6458 cents 6 x 7:8 S SD: 54.6887 cents 7 x 8:9 S SD: 48.4585 cents 8 x 9:11 SD: 35.3288 cents 9 x 10:12 S SD: 12.4551 cents 10 x 11:13 SD: 22.2350 cents 11 x 12:15 S SD: 19.7527 cents 12 x 13:16 SD: 9.4604 cents 13:14 x 17 SD: 20.9203 cents 14:15 x 19 SD: 17.2967 cents 15:16 x 20 S SD: 4.1717 cents 25 x 27:33 SD: 14.9256 cents 26:28 x 35 S SD: 14.9582 cents 27:29:30:36 SD: 10.7165 cents 28:30:31:37 SD: 9.7133 cents 29:31:32:39 SD: 7.7006 cents 30:32:33:40 SD: 3.7420 cents 33:35:36:44 SD: 2.3410 cents 51:54:56:68 SD: 2.0872 cents 63:67:69:84 SD: 1.0610 cents 96:102:105:128 SD: 0.9427 cents 114:121:125:152 SD: 0.6640 cents 147:156:161:196 SD: 0.1707 cents 357:379:391:476 SD: 0.0469 cents 504:535:552:672 SD: 0.0166 cents