Scala analysis: 223_C14
Chromatic tetrachord 80/77 * 77/72 * 6/5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 80/77 66.169865 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: 80/77 66.1699 2: 77/72 116.2338 undecimal secor 3: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 80/77 66.170 cents 1: 1 77/72 116.234 cents undecimal secor 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 96/77 381.811 cents 2: 1 77/60 431.875 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 : 66.2 182.4 498.0 66.2 : 116.2 431.9 498.0 182.4: 315.6 381.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.1699 .. 315.6413 cents 231/200, 249.4714 cents 80/77, 66.1699 cents 2: 182.4037 .. 431.8751 cents 231/200, 249.4714 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 80/77, 66.1699 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 2.508922 Largest / Average step : 1.901282 Largest / Smallest step : 4.770167 Median interval of one step : 77/72, 116.2338 cents, amount: 1 Least squares average step : 137.50802 cents, oct.: 412.52406 cents Scale is not proper Scale has trivalence property Scale is a mode of a 557-tone equal temperament with octave 4/3 degrees: 74 204 557 Least number of segments generator : 279 of 249.470 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 427 of 381.805 cents and inv. generated superset size: 9 = 6 more = 300.000% 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 66.16987 cents Scale diversity : 0.957858 Lumma stability : 0.265718 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 : 5929/5760, 50.0640 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 11 Odd number limit : 77 (O: 77 U: 77) Highest odd numerator or denominator: 77 Scale harmonicity : 0.022624 Average absolute harmonicity : 0.106182 Specific harmonicity : 0.112147 Fundamental : 1/693, -9.4367 octaves, 0.3775 Hz. Guide tone : 80, 6.3219 octaves, 20930.045 Hz. Exponens Consonantiae : 5.544000E+04, 15.75864 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 91.5, average 30.50000 Mersenne's string divisions : 20881 Sum of van Prooijen's expressibility: 3.31785, average 1.10595 Sum of Tenney's harmonic distance : 6.82300, average 2.27433 Vogel's harmonic complexity : 20.66667 Wille's k value : 192 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 17.47792, average 2.91299 Lattice compactness (without 2's) : 10.83182, average 1.80530 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 4 2.33333 7 3: -2 .. 0 -1.00000 3 1 5: 0 .. 1 0.66667 2 1 7: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.33333 1 1 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 17 18 25| Scale is weakly epimorphic with val: <6 10 17 19 24| Scale is weakly epimorphic with val: <6 10 17 19 27| Scale is weakly epimorphic with val: <6 10 17 20 23| Scale is weakly epimorphic with val: <6 10 17 20 26| Scale is weakly epimorphic with val: <6 10 17 21 25| Scale is weakly epimorphic with val: <6 10 17 22 24| Scale is weakly epimorphic with val: <6 10 17 22 27| Scale is weakly epimorphic with val: <6 11 19 19 25| Scale is weakly epimorphic with val: <6 11 19 20 24| Scale is weakly epimorphic with val: <6 11 19 20 27| Scale is weakly epimorphic with val: <6 11 19 21 23| Scale is weakly epimorphic with val: <6 11 19 21 26| Scale is weakly epimorphic with val: <6 11 19 22 25| Scale is weakly epimorphic with val: <7 10 16 18 24| Scale is weakly epimorphic with val: <7 10 16 18 27| Scale is weakly epimorphic with val: <7 10 16 19 23| Scale is weakly epimorphic with val: <7 10 16 19 26| Scale is weakly epimorphic with val: <7 10 16 20 25| Scale is weakly epimorphic with val: <7 10 16 21 24| Scale is weakly epimorphic with val: <7 10 16 21 27| Scale is weakly epimorphic with val: <7 10 16 22 23| Scale is weakly epimorphic with val: <7 10 16 22 26| Scale is weakly epimorphic with val: <7 10 18 18 25| Scale is weakly epimorphic with val: <7 10 18 19 24| Scale is weakly epimorphic with val: <7 10 18 20 23| Scale is weakly epimorphic with val: <7 11 16 18 24| Scale is weakly epimorphic with val: <7 11 16 18 27| Scale is weakly epimorphic with val: <7 11 16 19 23| Scale is weakly epimorphic with val: <7 11 16 19 26| Scale is weakly epimorphic with val: <7 11 16 20 25| Scale is weakly epimorphic with val: <7 11 16 21 24| Scale is weakly epimorphic with val: <7 11 16 21 27| Scale is weakly epimorphic with val: <7 11 16 22 23| Scale is weakly epimorphic with val: <7 11 16 22 26| Scale is weakly epimorphic with val: <7 11 17 18 23| Scale is JI-epimorphic with val: <7 11 17 18 26| Scale is JI-epimorphic with val: <7 11 17 19 25| Scale is JI-epimorphic with val: <7 11 17 20 24| Scale is weakly epimorphic with val: <7 11 17 20 27| Scale is JI-epimorphic with val: <7 11 17 21 23| Scale is weakly epimorphic with val: <7 11 17 21 26| Scale is weakly epimorphic with val: <7 11 17 22 25| Scale is weakly epimorphic with val: <7 11 19 19 23| Scale is weakly epimorphic with val: <7 11 19 19 26| Scale is weakly epimorphic with val: <7 11 19 20 25| Scale is weakly epimorphic with val: <7 11 19 21 24| Scale is weakly epimorphic with val: <7 11 19 21 27| Scale is weakly epimorphic with val: <7 11 19 22 23| Scale is weakly epimorphic with val: <7 11 19 22 26| Scale is weakly epimorphic with val: <7 12 18 18 25| Scale is weakly epimorphic with val: <7 12 18 19 24| Scale is weakly epimorphic with val: <7 12 18 20 23| Scale is weakly epimorphic with val: <8 11 15 18 26| Scale is weakly epimorphic with val: <8 11 15 19 25| Scale is weakly epimorphic with val: <8 11 15 20 24| Scale is weakly epimorphic with val: <8 11 15 21 23| Scale is weakly epimorphic with val: <8 11 17 18 24| Scale is weakly epimorphic with val: <8 11 17 18 27| Scale is weakly epimorphic with val: <8 11 17 19 23| Scale is weakly epimorphic with val: <8 11 17 19 26| Scale is weakly epimorphic with val: <8 11 17 20 25| Scale is weakly epimorphic with val: <8 11 17 21 24| Scale is weakly epimorphic with val: <8 11 17 21 27| Scale is weakly epimorphic with val: <8 11 17 22 23| Scale is weakly epimorphic with val: <8 11 17 22 26| Scale is weakly epimorphic with val: <8 11 18 20 27| Scale is weakly epimorphic with val: <8 11 18 21 26| Scale is weakly epimorphic with val: <8 11 18 22 25| Scale is weakly epimorphic with val: <8 12 15 18 26| Scale is weakly epimorphic with val: <8 12 15 19 25| Scale is weakly epimorphic with val: <8 12 15 20 24| Scale is weakly epimorphic with val: <8 12 15 21 23| Scale is weakly epimorphic with val: <8 12 18 20 27| Scale is weakly epimorphic with val: <8 12 18 21 26| Scale is weakly epimorphic with val: <8 12 18 22 25| Scale is weakly epimorphic with val: <8 12 19 19 24| Scale is weakly epimorphic with val: <8 12 19 19 27| Scale is weakly epimorphic with val: <8 12 19 20 23| Scale is weakly epimorphic with val: <8 12 19 20 26| Scale is weakly epimorphic with val: <8 12 19 21 25| Scale is weakly epimorphic with val: <8 12 19 22 24| Scale is weakly epimorphic with val: <8 12 19 22 27|
FIT/MODE
3: 0 1 2 N G T3 SD: 39.3575 c. M: 66.1699 c. 5: 1 1 3 N M DE S SD: 21.6094 c. M:-33.4391 c. 6: 1 1 4 N M DE S SD: 13.5658 c. M:-16.8376 c. 8: 1 2 5 N T3 SD: 3.3842 c. M:-4.3632 c. 22: 3 5 14 N T3 SD: 1.2553 c. M:-1.7454 c. 30: 4 7 19 N T3 SD: 0.1835 c. M:-0.2361 c. 287: 38 67 182 N T3 SD: 0.1715 c. M: 0.2266 c. 309: 41 72 196 N T3 SD: 0.1641 c. M: 0.2708 c. 317: 42 74 201 N T3 SD: 0.1379 c. M: 0.1828 c. 339: 45 79 215 N T3 SD: 0.1358 c. M: 0.2280 c. 347: 46 81 220 N T3 SD: 0.1102 c. M: 0.1466 c. 377: 50 88 239 N T3 SD: 0.0868 c. M: 0.1162 c. 407: 54 95 258 N T3 SD: 0.0669 c. M: 0.0902 c. 437: 58 102 277 N T3 SD: 0.0497 c. M: 0.0678 c. 467: 62 109 296 N T3 SD: 0.0348 c. M: 0.0483 c. 497: 66 116 315 N T3 SD: 0.0217 c. M: 0.0311 c. 527: 70 123 334 N T3 SD: 0.0102 c. M: 0.0159 c. 557: 74 130 353 N T3 SD: 0.0027 c. M:-0.0042 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 x 14:17 SD: 31.8493 cents 14:15:16:19 SD: 26.1523 cents 15:16:17:20 SD: 19.0063 cents 16:17:18:21 S SD: 17.3531 cents 17:18:19:23 SD: 14.2076 cents 18:19:20:24 S SD: 9.1444 cents 24:25:27:32 SD: 7.3242 cents 26:27:29:35 SD: 5.9565 cents 27:28:30:36 S SD: 1.0697 cents 99:103:110:132 SD: 0.8009 cents 126:131:140:168 SD: 0.4006 cents 153:159:170:204 SD: 0.1414 cents 180:187:200:240 SD: 0.0401 cents 513:533:570:684 SD: 0.0141 cents