Scala analysis: 225_C14
Chromatic tetrachord 88/81 * 45/44 * 6/5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88/81 143.497939 2nd undecimal neutral second 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: 88/81 143.4979 2nd undecimal neutral second 2: 45/44 38.9058 1/5-tone 3: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 45/44 38.906 cents 1/5-tone 1: 1 88/81 143.498 cents 2nd undecimal neutral second 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 176/135 459.139 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 : 143.5 182.4 498.0 143.5: 38.9 354.5 498.0 182.4: 315.6 459.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.9058 .. 315.6413 cents 88/75, 276.7355 cents 45/44, 38.9058 cents 2: 182.4037 .. 459.1392 cents 88/75, 276.7355 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 45/44, 38.9058 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 4.267104 Largest / Average step : 1.901282 Largest / Smallest step : 8.112968 Median interval of one step : 88/81, 143.4979 cents, amount: 1 Least squares average step : 143.03145 cents, oct.: 429.09436 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1600-tone equal temperament with octave 4/3 degrees: 461 586 1600 Least number of segments generator : 801 of 249.334 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1093 of 340.227 cents and inv. generated superset size: 26 = 23 more = 866.667% 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 38.90577 cents Scale diversity : 0.757752 Lumma stability : 0.156234 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 : 45/44, 38.9058 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 135 (O: 45 U: 135) Highest odd numerator or denominator: 81 Scale harmonicity : 0.026145 Average absolute harmonicity : 0.108072 Specific harmonicity : 0.135121 Fundamental : 1/81, -6.3399 octaves, 3.2299 Hz. Guide tone : 440, 8.7814 octaves, 115115.249 Hz. Exponens Consonantiae : 3.564000E+04, 15.12121 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 97.5, average 32.50000 Mersenne's string divisions : 22477 Sum of van Prooijen's expressibility: 3.33985, average 1.11328 Sum of Tenney's harmonic distance : 6.88639, average 2.29546 Vogel's harmonic complexity : 12.33333 Wille's k value : 22 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 17.99553, average 2.99926 Lattice compactness (without 2's) : 14.38515, average 2.39753 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -4 ..-1 -2.33333 7 1 5: 0 .. 1 0.33333 1 1 11: 0 .. 1 0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 15 25| Scale is weakly epimorphic with val: <6 10 17 23| Scale is weakly epimorphic with val: <6 10 17 26| Scale is weakly epimorphic with val: <6 10 18 25| Scale is weakly epimorphic with val: <6 11 19 25| Scale is weakly epimorphic with val: <7 10 16 24| Scale is weakly epimorphic with val: <7 10 16 27| Scale is weakly epimorphic with val: <7 11 16 25| Scale is JI-epimorphic with val: <7 11 17 24| Scale is weakly epimorphic with val: <7 11 17 27| Scale is weakly epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <8 11 15 23| Scale is weakly epimorphic with val: <8 11 17 24| Scale is weakly epimorphic with val: <8 11 17 27| Scale is weakly epimorphic with val: <8 11 18 23| Scale is weakly epimorphic with val: <8 12 15 27| Scale is weakly epimorphic with val: <8 12 18 27| Scale is weakly epimorphic with val: <8 12 19 23| Scale is weakly epimorphic with val: <8 12 19 26|
FIT/MODE
3: 1 0 2 N G T3 SD: 16.0791 c. M:-22.5171 c. 7: 2 1 4 N T3 SD: 17.9367 c. M:-31.0441 c. 8: 2 1 5 N T3 SD: 11.2477 c. M: 18.9867 c. 10: 3 1 6 N T3 SD: 10.2910 c. M:-16.8143 c. 11: 3 1 7 N T3 SD: 4.4897 c. M: 7.6675 c. 14: 4 1 9 N T3 SD: 2.7058 c. M: 4.5305 c. 24: 7 2 15 N T3 SD: 2.7174 c. M:-4.3632 c. 25: 7 2 16 N T3 SD: 2.9451 c. M: 4.0453 c. 27: 8 2 17 N T3 SD: 2.6335 c. M:-4.0709 c. 35: 10 3 22 N T3 SD: 1.6450 c. M:-2.5844 c. 38: 11 3 24 N T3 SD: 0.7379 c. M:-1.0866 c. 52: 15 4 33 N T3 SD: 0.2644 c. M: 0.4257 c. 90: 26 7 57 N T3 SD: 0.2523 c. M:-0.3817 c. 139: 40 11 88 N T3 SD: 0.2170 c. M:-0.3322 c. 142: 41 11 90 N T3 SD: 0.1758 c. M:-0.3038 c. 153: 44 12 97 N T3 SD: 0.1686 c. M: 0.2693 c. 191: 55 15 121 N T3 SD: 0.0867 c. M:-0.1259 c. 243: 70 19 154 N T3 SD: 0.0169 c. M: 0.0282 c. 781: 225 61 495 N T3 SD: 0.0149 c. M: 0.0210 c. 1024: 295 80 649 N T3 SD: 0.0133 c. M: 0.0182 c. 1114: 321 87 706 N T3 SD: 0.0085 c. M:-0.0141 c. 1357: 391 106 860 N T3 SD: 0.0047 c. M:-0.0066 c. 1600: 461 125 1014 N T3 SD: 0.0031 c. M:-0.0053 c. 2138: 616 167 1355 N T3 SD: 0.0028 c. M: 0.0046 c. 2381: 686 186 1509 N T3 SD: 0.0031 c. M: 0.0041 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 11:12 x 15 S SD: 19.7777 cents 12:13 x 16 SD: 2.4626 cents 13:14 x 17 SD: 18.4469 cents 15:16:17:20 SD: 15.5793 cents 18 x 20:24 S SD: 0.0000 cents 19 x 21:25 SD: 12.3417 cents 20 x 22:27 SD: 13.8317 cents 21:23 x 28 SD: 6.9978 cents 22:24 x 29 SD: 10.5172 cents 24:26:27:32 SD: 7.3544 cents 27:29:30:36 SD: 6.5952 cents 29 x 32:39 SD: 9.5443 cents 30 x 33:40 SD: 8.6997 cents 31:34 x 41 SD: 10.7957 cents 32:35:36:43 SD: 9.3069 cents 33:36:37:44 SD: 5.7391 cents 34:37:38:45 SD: 5.5247 cents 35:38:39:47 SD: 4.4409 cents 36:39:40:48 S SD: 1.6418 cents 45:49:50:60 SD: 1.3101 cents 81:88:90:108 SD: 0.0000 cents