Scala analysis: 222_C14
Chromatic tetrachord 60/59 * 59/54 * 6/5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 60/59 29.097055 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: 60/59 29.0971 2: 59/54 153.3067 3: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 60/59 29.097 cents 1: 1 59/54 153.307 cents 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 72/59 344.738 cents Ibn Sina's neutral third 2: 1 59/45 468.948 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 : 29.1 182.4 498.0 29.1 : 153.3 468.9 498.0 182.4: 315.6 344.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 29.0971 .. 315.6413 cents 59/50, 286.5442 cents 60/59, 29.0971 cents 2: 182.4037 .. 468.9479 cents 59/50, 286.5442 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 60/59, 29.0971 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 5.705560 Largest / Average step : 1.901282 Largest / Smallest step : 10.847877 Median interval of one step : 59/54, 153.3067 cents, amount: 1 Least squares average step : 134.85996 cents, oct.: 404.57989 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1712-tone equal temperament with octave 4/3 degrees: 100 627 1712 Least number of segments generator : 857 of 249.313 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1435 of 417.462 cents and inv. generated superset size: 42 = 39 more = 1400.000% 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 29.09706 cents Scale diversity : 0.661575 Lumma stability : 0.116845 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 : 60/59, 29.0971 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 : 59 Odd number limit : 59 (O: 59 U: 59) Highest odd numerator or denominator: 59 Scale harmonicity : 0.060976 Fundamental : 1/531, -9.0526 octaves, 0.4927 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 3.186000E+04, 14.95946 octaves Euler's gradus suavitatis : 71 Sum of Mann's harmonic distance : 72.5, average 24.16667 Mersenne's string divisions : 2261 Sum of van Prooijen's expressibility: 3.20222, average 1.06741 Sum of Tenney's harmonic distance : 6.58243, average 2.19414 Vogel's harmonic complexity : 48.33333 Wille's k value : 147 Wilson's harmonic complexity : 73 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.26544, average 2.37757 Lattice compactness (without 2's) : 11.30056, average 1.88343 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -2 .. 1 -0.66667 4 1 5: 0 .. 1 0.66667 2 1 59: -1 .. 0 -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 17 44| Scale is weakly epimorphic with val: <6 11 19 43| Scale is weakly epimorphic with val: <7 10 16 44| Scale is weakly epimorphic with val: <7 11 16 42| Scale is weakly epimorphic with val: <7 11 17 44| Scale is weakly epimorphic with val: <7 11 19 42| Scale is weakly epimorphic with val: <8 11 17 43| Scale is weakly epimorphic with val: <8 11 18 42| Scale is weakly epimorphic with val: <8 12 18 43| Scale is weakly epimorphic with val: <8 12 19 42|
FIT/MODE
3: 0 1 2 N G T3 SD: 19.2806 c. M: 29.0971 c. 8: 0 3 5 N G T3 SD: 16.9870 c. M: 29.0971 c. 11: 1 3 7 N T3 SD: 9.3713 c. M:-16.1798 c. 13: 1 4 8 N T3 SD: 7.4980 c. M:-9.2141 c. 14: 1 4 9 N T3 SD: 4.5638 c. M:-6.4776 c. 16: 1 5 10 N T3 SD: 2.7786 c. M:-4.3632 c. 19: 1 6 12 N T3 SD: 1.7794 c. M: 2.8842 c. 33: 2 10 21 N T3 SD: 0.9770 c. M: 1.2964 c. 49: 3 15 31 N T3 SD: 0.8663 c. M:-1.3955 c. 52: 3 16 33 N T3 SD: 0.3233 c. M: 0.4257 c. 101: 6 31 64 N T3 SD: 0.2842 c. M:-0.4898 c. 120: 7 37 76 N T3 SD: 0.1255 c. M:-0.2128 c. 153: 9 47 97 N T3 SD: 0.1324 c. M:-0.1997 c. 172: 10 53 109 N T3 SD: 0.0822 c. M: 0.1410 c. 273: 16 84 173 N T3 SD: 0.0561 c. M:-0.0924 c. 325: 19 100 206 N T3 SD: 0.0270 c. M: 0.0426 c. 445: 26 137 282 N T3 SD: 0.0152 c. M:-0.0263 c. 770: 45 237 488 N T3 SD: 0.0057 c. M:-0.0095 c. 1215: 71 374 770 N T3 SD: 0.0060 c. M:-0.0078 c. 1712: 100 527 1085 N T3 SD: 0.0033 c. M: 0.0056 c. 2157: 126 664 1367 N T3 SD: 0.0037 c. M:-0.0050 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: 15.6028 cents 25:26:28:33 SD: 14.9024 cents 26:27:29:35 SD: 13.4660 cents 27:28:30:36 S SD: 11.2879 cents 30:31:33:40 SD: 10.8953 cents 33:34:37:44 SD: 9.1625 cents 34:35:38:45 SD: 8.8883 cents 35:36:39:47 SD: 7.9111 cents 36:37:40:48 SD: 6.1123 cents 42:43:47:56 SD: 5.6501 cents 43:44:48:57 SD: 5.5877 cents 44:45:49:59 SD: 4.8059 cents 45:46:50:60 SD: 2.9845 cents 54:55:60:72 S SD: 0.8899 cents 63:64:70:84 SD: 0.6110 cents 117:119:130:156 SD: 0.0822 cents 297:302:330:396 SD: 0.0648 cents 414:421:460:552 SD: 0.0232 cents 531:540:590:708 SD: 0.0000 cents