Scala analysis: 227_C14
Chromatic tetrachord 52/51 * 85/78 * 6/5, Wilson
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 52/51 33.617251 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: 52/51 33.6173 2: 85/78 148.7865 3: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 52/51 33.617 cents 1: 1 85/78 148.786 cents 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 104/85 349.259 cents 2: 1 17/13 464.428 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 : 33.6 182.4 498.0 33.6 : 148.8 464.4 498.0 182.4: 315.6 349.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.6173 .. 315.6413 cents 153/130, 282.0240 cents 52/51, 33.6173 cents 2: 182.4037 .. 464.4277 cents 153/130, 282.0240 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 52/51, 33.6173 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 4.938387 Largest / Average step : 1.901282 Largest / Smallest step : 9.389265 Median interval of one step : 85/78, 148.7865 cents, amount: 1 Least squares average step : 135.18283 cents, oct.: 405.54850 cents Scale is not proper Scale has trivalence property Scale is a mode of a 800-tone equal temperament with octave 4/3 degrees: 54 293 800 Least number of segments generator : 401 of 249.645 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 749 of 466.295 cents and inv. generated superset size: 58 = 55 more = 1933.333% 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 33.61725 cents Scale diversity : 0.706924 Lumma stability : 0.134997 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 : 52/51, 33.6173 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 -- Rational properties -- Prime limit : 17 Odd number limit : 85 (O: 85 U: 85) Highest odd numerator or denominator: 51 Scale harmonicity : 0.015150 Average absolute harmonicity : 0.103460 Specific harmonicity : 0.080396 Fundamental : 1/153, -7.2574 octaves, 1.7100 Hz. Guide tone : 260, 8.0224 octaves, 68022.647 Hz. Exponens Consonantiae : 3.978000E+04, 15.27976 octaves Euler's gradus suavitatis : 39 Sum of Mann's harmonic distance : 64.5, average 21.50000 Mersenne's string divisions : 13699 Sum of van Prooijen's expressibility: 3.13893, average 1.04631 Sum of Tenney's harmonic distance : 6.45700, average 2.15233 Vogel's harmonic complexity : 21.00000 Wille's k value : 42 Wilson's harmonic complexity : 41 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 12.71364, average 2.11894 Lattice compactness (without 2's) : 9.79655, average 1.63276 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -2 ..-1 -1.33333 4 1 5: 0 .. 1 0.33333 1 1 13: 0 .. 1 0.33333 1 17: -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 25 29| Scale is weakly epimorphic with val: <6 10 17 25 32| Scale is weakly epimorphic with val: <6 10 17 26 27| Scale is weakly epimorphic with val: <6 10 17 26 30| Scale is weakly epimorphic with val: <6 10 17 26 33| Scale is weakly epimorphic with val: <6 10 17 27 28| Scale is weakly epimorphic with val: <6 10 17 27 31| Scale is weakly epimorphic with val: <6 10 17 28 29| Scale is weakly epimorphic with val: <6 10 17 28 32| Scale is weakly epimorphic with val: <6 10 17 29 30| Scale is weakly epimorphic with val: <6 10 17 29 33| Scale is weakly epimorphic with val: <6 10 17 30 31| Scale is weakly epimorphic with val: <6 11 19 25 27| Scale is weakly epimorphic with val: <6 11 19 25 30| Scale is weakly epimorphic with val: <6 11 19 25 33| Scale is weakly epimorphic with val: <6 11 19 26 28| Scale is weakly epimorphic with val: <6 11 19 26 31| Scale is weakly epimorphic with val: <6 11 19 27 29| Scale is weakly epimorphic with val: <6 11 19 27 32| Scale is weakly epimorphic with val: <6 11 19 28 30| Scale is weakly epimorphic with val: <6 11 19 28 33| Scale is weakly epimorphic with val: <6 11 19 29 31| Scale is weakly epimorphic with val: <6 11 19 30 32| Scale is weakly epimorphic with val: <7 10 15 26 27| Scale is weakly epimorphic with val: <7 10 15 27 28| Scale is weakly epimorphic with val: <7 10 15 28 29| Scale is weakly epimorphic with val: <7 10 15 29 30| Scale is weakly epimorphic with val: <7 10 15 30 31| Scale is weakly epimorphic with val: <7 10 16 25 27| Scale is weakly epimorphic with val: <7 10 16 25 30| Scale is weakly epimorphic with val: <7 10 16 25 33| Scale is weakly epimorphic with val: <7 10 16 26 28| Scale is weakly epimorphic with val: <7 10 16 26 31| Scale is weakly epimorphic with val: <7 10 16 27 29| Scale is weakly epimorphic with val: <7 10 16 27 32| Scale is weakly epimorphic with val: <7 10 16 28 30| Scale is weakly epimorphic with val: <7 10 16 28 33| Scale is weakly epimorphic with val: <7 10 16 29 31| Scale is weakly epimorphic with val: <7 10 16 30 32| Scale is weakly epimorphic with val: <7 10 18 26 27| Scale is weakly epimorphic with val: <7 10 18 27 28| Scale is weakly epimorphic with val: <7 10 18 28 29| Scale is weakly epimorphic with val: <7 10 18 29 30| Scale is weakly epimorphic with val: <7 10 18 30 31| Scale is weakly 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 27| Scale is weakly epimorphic with val: <7 11 16 26 30| Scale is weakly epimorphic with val: <7 11 16 26 33| 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 28 29| Scale is weakly epimorphic with val: <7 11 16 28 32| Scale is weakly epimorphic with val: <7 11 16 29 30| Scale is weakly epimorphic with val: <7 11 16 29 33| Scale is weakly epimorphic with val: <7 11 16 30 31| Scale is JI-epimorphic with val: <7 11 17 25 27| Scale is weakly epimorphic with val: <7 11 17 25 30| Scale is weakly epimorphic with val: <7 11 17 25 33| Scale is JI-epimorphic with val: <7 11 17 26 28| Scale is weakly epimorphic with val: <7 11 17 26 31| Scale is JI-epimorphic with val: <7 11 17 27 29| Scale is weakly epimorphic with val: <7 11 17 27 32| Scale is JI-epimorphic with val: <7 11 17 28 30| Scale is weakly epimorphic with val: <7 11 17 28 33| Scale is JI-epimorphic with val: <7 11 17 29 31| Scale is JI-epimorphic with val: <7 11 17 30 32| 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 27| Scale is weakly epimorphic with val: <7 11 19 26 30| Scale is weakly epimorphic with val: <7 11 19 26 33| 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 28 29| Scale is weakly epimorphic with val: <7 11 19 28 32| Scale is weakly epimorphic with val: <7 11 19 29 30| Scale is weakly epimorphic with val: <7 11 19 29 33| Scale is weakly epimorphic with val: <7 11 19 30 31| Scale is weakly epimorphic with val: <8 11 15 25 27| Scale is weakly epimorphic with val: <8 11 15 26 28| Scale is weakly epimorphic with val: <8 11 15 27 29| Scale is weakly epimorphic with val: <8 11 15 28 30| Scale is weakly epimorphic with val: <8 11 15 29 31| Scale is weakly epimorphic with val: <8 11 15 30 32| Scale is weakly epimorphic with val: <8 11 17 25 29| Scale is weakly epimorphic with val: <8 11 17 25 32| Scale is weakly epimorphic with val: <8 11 17 26 27| Scale is weakly epimorphic with val: <8 11 17 26 30| Scale is weakly epimorphic with val: <8 11 17 26 33| Scale is weakly epimorphic with val: <8 11 17 27 28| Scale is weakly epimorphic with val: <8 11 17 27 31| Scale is weakly epimorphic with val: <8 11 17 28 29| Scale is weakly epimorphic with val: <8 11 17 28 32| Scale is weakly epimorphic with val: <8 11 17 29 30| Scale is weakly epimorphic with val: <8 11 17 29 33| Scale is weakly epimorphic with val: <8 11 17 30 31| Scale is weakly epimorphic with val: <8 11 18 25 27| Scale is weakly epimorphic with val: <8 11 18 26 28| Scale is weakly epimorphic with val: <8 11 18 27 29| Scale is weakly epimorphic with val: <8 11 18 28 30| Scale is weakly epimorphic with val: <8 11 18 29 31| Scale is weakly epimorphic with val: <8 11 18 30 32| Scale is weakly epimorphic with val: <8 12 15 26 27| Scale is weakly epimorphic with val: <8 12 15 27 28| Scale is weakly epimorphic with val: <8 12 15 28 29| Scale is weakly epimorphic with val: <8 12 15 29 30| Scale is weakly epimorphic with val: <8 12 15 30 31| Scale is weakly epimorphic with val: <8 12 18 26 27| Scale is weakly epimorphic with val: <8 12 18 27 28| Scale is weakly epimorphic with val: <8 12 18 28 29| Scale is weakly epimorphic with val: <8 12 18 29 30| Scale is weakly epimorphic with val: <8 12 18 30 31| Scale is weakly epimorphic with val: <8 12 19 25 27| 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 28| Scale is weakly epimorphic with val: <8 12 19 26 31| Scale is weakly epimorphic with val: <8 12 19 27 29| Scale is weakly epimorphic with val: <8 12 19 27 32| Scale is weakly epimorphic with val: <8 12 19 28 30| Scale is weakly epimorphic with val: <8 12 19 28 33| Scale is weakly epimorphic with val: <8 12 19 29 31| Scale is weakly epimorphic with val: <8 12 19 30 32|
FIT/MODE
3: 0 1 2 N G T3 SD: 21.5925 c. M: 33.6173 c. 8: 1 2 5 N T3 SD: 16.7252 c. M:-28.6384 c. 10: 1 3 6 N T3 SD: 13.4753 c. M:-16.8143 c. 11: 1 3 7 N T3 SD: 6.7731 c. M:-11.6596 c. 13: 1 4 8 N T3 SD: 5.9384 c. M:-9.1521 c. 14: 1 4 9 N T3 SD: 2.8494 c. M: 4.5305 c. 16: 1 5 10 N T3 SD: 2.9003 c. M:-4.3632 c. 27: 2 8 17 N T3 SD: 2.2330 c. M:-3.2750 c. 30: 2 9 19 N T3 SD: 0.2689 c. M: 0.4143 c. 104: 7 31 66 N T3 SD: 0.2518 c. M: 0.4257 c. 134: 9 40 85 N T3 SD: 0.1895 c. M: 0.2828 c. 164: 11 49 104 N T3 SD: 0.1651 c. M: 0.2118 c. 194: 13 58 123 N T3 SD: 0.1590 c. M: 0.2431 c. 221: 15 66 140 N T3 SD: 0.1339 c. M:-0.1867 c. 251: 17 75 159 N T3 SD: 0.1076 c. M:-0.1466 c. 281: 19 84 178 N T3 SD: 0.0949 c. M:-0.1537 c. 295: 20 88 187 N T3 SD: 0.0944 c. M:-0.1485 c. 311: 21 93 197 N T3 SD: 0.0923 c. M:-0.1594 c. 325: 22 97 206 N T3 SD: 0.0609 c. M:-0.0966 c. 355: 24 106 225 N T3 SD: 0.0331 c. M:-0.0534 c. 385: 26 115 244 N T3 SD: 0.0099 c. M:-0.0170 c. 415: 28 124 263 N T3 SD: 0.0110 c. M: 0.0142 c. 800: 54 239 507 N T3 SD: 0.0031 c. M:-0.0053 c. 1985: 134 593 1258 N T3 SD: 0.0031 c. M:-0.0039 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 x 16:19 SD: 28.7988 cents 15 x 17:20 SD: 17.1415 cents 24:25:27:32 SD: 14.2813 cents 25:26:28:33 SD: 13.6152 cents 26:27:29:35 SD: 12.1326 cents 27:28:30:36 S SD: 9.7812 cents 30:31:33:40 SD: 9.6531 cents 33:34:37:44 SD: 7.9709 cents 34:35:38:45 SD: 7.7518 cents 35:36:39:47 SD: 6.7152 cents 36:37:40:48 SD: 4.6056 cents 44:45:49:59 SD: 3.9388 cents 45:46:50:60 SD: 1.4778 cents 54:55:60:72 S SD: 0.6169 cents 99:101:110:132 SD: 0.3362 cents 153:156:170:204 SD: 0.0000 cents