Scala analysis: 220_C14
Chromatic tetrachord 21/20 * 200/189 * 6/5, Perrett
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 10/9 182.403712 minor whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 21/20 84.4672 minor semitone 2: 200/189 97.9365 3: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 21/20 84.467 cents minor semitone 1: 1 200/189 97.937 cents 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 63/50 400.108 cents quasi-equal major third 2: 1 80/63 413.578 cents wide major third 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 : 84.5 182.4 498.0 84.5 : 97.9 413.6 498.0 182.4: 315.6 400.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 315.6413 cents 8/7, 231.1741 cents 21/20, 84.4672 cents 2: 182.4037 .. 413.5778 cents 8/7, 231.1741 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 21/20, 84.4672 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 1.965438 Largest / Average step : 1.901282 Largest / Smallest step : 3.736851 Median interval of one step : 200/189, 97.9365 cents, amount: 1 Least squares average step : 138.81497 cents, oct.: 416.44492 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1256-tone equal temperament with octave 4/3 degrees: 213 460 1256 Least number of segments generator : 629 of 249.419 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1105 of 438.169 cents and inv. generated superset size: 44 = 41 more = 1466.667% 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 84.46719 cents Scale diversity : 1.004064 Lumma stability : 0.339195 Lumma impropriety factor : 0.267521 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 : 4000/3969, 13.4693 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% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 217.7048 cents: 2 -- Rational properties -- Prime limit : 7 Odd number limit : 189 (O: 63 U: 189) Highest odd numerator or denominator: 21 Scale harmonicity : 0.028502 Average absolute harmonicity : 0.113217 Specific harmonicity : 0.146891 Fundamental : 1/180, -7.4919 octaves, 1.4535 Hz. Guide tone : 420, 8.7142 octaves, 109882.737 Hz. Exponens Consonantiae : 7.560000E+04, 16.20610 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 33.5, average 11.16667 Mersenne's string divisions : 5453 Sum of van Prooijen's expressibility: 2.75358, average 0.91786 Sum of Tenney's harmonic distance : 5.65667, average 1.88556 Vogel's harmonic complexity : 13.66667 Wille's k value : 94 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 18.54961, average 3.09160 Lattice compactness (without 2's) : 12.57348, average 2.09558 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.33333 5 3: -2 .. 1 -0.66667 4 1 5: -1 .. 1 0.00000 2 1 7: 0 .. 1 0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 15 20| Scale is weakly epimorphic with val: <6 10 17 20| Scale is weakly epimorphic with val: <6 11 15 19| Scale is weakly epimorphic with val: <6 11 18 22| Scale is weakly epimorphic with val: <6 11 19 19| Scale is weakly epimorphic with val: <6 11 19 22| Scale is weakly epimorphic with val: <7 10 15 22| Scale is weakly epimorphic with val: <7 10 16 19| Scale is weakly epimorphic with val: <7 10 16 22| Scale is weakly epimorphic with val: <7 11 16 18| Scale is weakly epimorphic with val: <7 11 16 21| Scale is weakly epimorphic with val: <7 11 17 18| Scale is JI-epimorphic with val: <7 11 17 21| Scale is weakly epimorphic with val: <7 11 19 21| Scale is weakly epimorphic with val: <7 12 15 20| Scale is weakly epimorphic with val: <8 11 17 20| Scale is weakly epimorphic with val: <8 12 15 22| Scale is weakly epimorphic with val: <8 12 19 19| Scale is weakly epimorphic with val: <8 12 19 22|
FIT/MODE
3: 0 1 2 N G T3 SD: 49.6766 c. M: 84.4672 c. 4: 0 1 3 N G T3 SD: 59.1220 c. M: 84.4672 c. 5: 1 1 3 N M DE S SD: 13.0639 c. M:-16.8143 c. 6: 1 1 4 N M DE S SD: 9.4995 c. M: 16.3887 c. 11: 2 2 7 N M DE S SD: 3.5928 c. M:-6.0864 c. 19: 3 4 12 N T3 SD: 3.4231 c. M: 5.8285 c. 24: 4 5 15 N T3 SD: 2.6563 c. M:-4.3632 c. 30: 5 6 19 N T3 SD: 0.8517 c. M: 1.4597 c. 41: 7 8 26 N T3 SD: 0.3445 c. M:-0.5649 c. 71: 12 14 45 N T3 SD: 0.1682 c. M: 0.2906 c. 112: 19 22 71 N T3 SD: 0.0500 c. M: 0.0837 c. 295: 50 58 187 N T3 SD: 0.0500 c. M: 0.0686 c. 407: 69 80 258 N T3 SD: 0.0459 c. M: 0.0727 c. 519: 88 102 329 N T3 SD: 0.0449 c. M: 0.0751 c. 631: 107 124 400 N T3 SD: 0.0448 c. M: 0.0766 c. 666: 113 131 422 N T3 SD: 0.0420 c. M:-0.0632 c. 737: 125 145 467 N T3 SD: 0.0319 c. M:-0.0551 c. 778: 132 153 493 N T3 SD: 0.0312 c. M:-0.0421 c. 808: 137 159 512 N T3 SD: 0.0306 c. M:-0.0484 c. 849: 144 167 538 N T3 SD: 0.0216 c. M:-0.0368 c. 890: 151 175 564 N T3 SD: 0.0242 c. M:-0.0326 c. 920: 156 181 583 N T3 SD: 0.0209 c. M:-0.0323 c. 961: 163 189 609 N T3 SD: 0.0141 c. M:-0.0228 c. 1032: 175 203 654 N T3 SD: 0.0133 c. M:-0.0197 c. 1073: 182 211 680 N T3 SD: 0.0089 c. M:-0.0117 c. 1144: 194 225 725 N T3 SD: 0.0074 c. M:-0.0096 c. 1185: 201 233 751 N T3 SD: 0.0067 c. M:-0.0113 c. 1256: 213 247 796 N T3 SD: 0.0034 c. M: 0.0057 c. 1368: 232 269 867 N T3 SD: 0.0038 c. M: 0.0057 c. 2329: 395 458 1476 N T3 SD: 0.0036 c. M:-0.0061 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: 78.8780 cents 6 x 7:8 S SD: 42.2336 cents 7 x 8:9 S SD: 39.8203 cents 8 x 9:11 SD: 28.7251 cents 9 x 10:12 S SD: 0.0000 cents 10 x 11:13 SD: 23.5791 cents 11 x 12:15 S SD: 25.1136 cents 12 x 13:16 SD: 21.9155 cents 13:14 x 17 SD: 27.6192 cents 14:15:16:19 SD: 22.4618 cents 15:16:17:20 SD: 14.6008 cents 16:17:18:21 S SD: 13.4397 cents 17:18:19:23 SD: 10.2835 cents 18:19:20:24 S SD: 3.0453 cents 60:63:67:80 SD: 2.8782 cents 62:65:69:83 SD: 2.6542 cents 63:66:70:84 SD: 1.3101 cents 81:85:90:108 SD: 0.3394 cents 99:104:110:132 SD: 0.2775 cents 180:189:200:240 SD: 0.0000 cents