Scala analysis: 217_C14
Chromatic tetrachord 55/54 * 12/11 * 6/5, Barbour
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 55/54 31.766654 telepathma 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: 55/54 31.7667 telepathma 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 55/54 31.767 cents telepathma 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 72/55 466.278 cents undecimal semi-diminished fourth 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 : 31.8 182.4 498.0 31.8 : 150.6 466.3 498.0 182.4: 315.6 347.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.7667 .. 315.6413 cents 324/275, 283.8746 cents 55/54, 31.7667 cents 2: 182.4037 .. 466.2783 cents 324/275, 283.8746 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 55/54, 31.7667 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 5.226078 Largest / Average step : 1.901282 Largest / Smallest step : 9.936246 Median interval of one step : 12/11, 150.6371 cents, amount: 1 Least squares average step : 135.05065 cents, oct.: 405.15194 cents Scale is not proper Scale has trivalence property 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 31.76665 cents Scale diversity : 0.688547 Lumma stability : 0.127565 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 : 55/54, 31.7667 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 All steps are superparticular (epimoric) 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 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 55 (O: 55 U: 55) Highest odd numerator or denominator: 55 Scale harmonicity : 0.028104 Average absolute harmonicity : 0.107532 Specific harmonicity : 0.136972 Fundamental : 1/54, -5.7549 octaves, 4.8449 Hz. Guide tone : 220, 7.7814 octaves, 57557.624 Hz. Exponens Consonantiae : 1.188000E+04, 13.53625 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 67.5, average 22.50000 Mersenne's string divisions : 14497 Sum of van Prooijen's expressibility: 3.17173, average 1.05724 Sum of Tenney's harmonic distance : 6.50618, average 2.16873 Vogel's harmonic complexity : 11.66667 Wille's k value : 27 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 16.20418, average 2.70070 Lattice compactness (without 2's) : 11.83061, average 1.97177 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -3 ..-1 -2.00000 6 1 5: 0 .. 1 0.66667 2 1 11: 0 .. 1 0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 15 24| 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 11 15 27| Scale is weakly epimorphic with val: <6 11 18 24| Scale is weakly epimorphic with val: <6 11 19 25| Scale is weakly epimorphic with val: <7 10 15 25| Scale is weakly epimorphic with val: <7 10 16 23| Scale is weakly epimorphic with val: <7 10 16 26| Scale is weakly epimorphic with val: <7 11 16 23| Scale is weakly epimorphic with val: <7 11 16 26| 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 23| Scale is weakly epimorphic with val: <7 11 19 26| Scale is weakly epimorphic with val: <8 11 17 25| Scale is weakly epimorphic with val: <8 11 18 26| Scale is weakly epimorphic with val: <8 12 19 24| Scale is weakly epimorphic with val: <8 12 19 27|
FIT/MODE
3: 0 1 2 N G T3 SD: 20.6374 c. M: 31.7667 c. 8: 1 2 5 N T3 SD: 17.7821 c. M:-30.4890 c. 10: 1 3 6 N T3 SD: 14.2371 c. M:-18.0378 c. 11: 1 3 7 N T3 SD: 7.8359 c. M:-13.5102 c. 13: 1 4 8 N T3 SD: 6.4959 c. M:-9.1521 c. 14: 1 4 9 N T3 SD: 3.4169 c. M: 4.5305 c. 16: 1 5 10 N T3 SD: 2.5459 c. M:-4.3632 c. 30: 2 9 19 N T3 SD: 0.8383 c. M:-1.4363 c. 49: 3 15 31 N T3 SD: 0.8016 c. M: 1.2741 c. 63: 4 19 40 N T3 SD: 0.3439 c. M: 0.5778 c. 79: 5 24 50 N T3 SD: 0.2821 c. M:-0.4229 c. 93: 6 28 59 N T3 SD: 0.2814 c. M:-0.3653 c. 109: 7 33 69 N T3 SD: 0.2455 c. M:-0.3651 c. 142: 9 43 90 N T3 SD: 0.1163 c. M: 0.2004 c. 172: 11 52 109 N T3 SD: 0.0504 c. M:-0.0851 c. 314: 20 95 199 N T3 SD: 0.0254 c. M: 0.0440 c. 486: 31 147 308 N T3 SD: 0.0046 c. M:-0.0078 c. 1772: 113 536 1123 N T3 SD: 0.0054 c. M:-0.0067 c. 2179: 139 659 1381 N T3 SD: 0.0052 c. M: 0.0082 c. 2258: 144 683 1431 N T3 SD: 0.0048 c. M:-0.0069 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: 14.8181 cents 25:26:28:33 SD: 14.1369 cents 26:27:29:35 SD: 12.6738 cents 27:28:30:36 S SD: 10.3981 cents 30:31:33:40 SD: 10.1530 cents 33:34:37:44 SD: 8.4466 cents 34:35:38:45 SD: 8.2027 cents 35:36:39:47 SD: 7.1907 cents 36:37:40:48 SD: 5.2225 cents 42:43:47:56 SD: 5.0804 cents 43:44:48:57 SD: 5.0660 cents 44:45:49:59 SD: 4.2508 cents 45:46:50:60 SD: 2.0947 cents 54:55:60:72 S SD: 0.0000 cents