Scala analysis: 215_C14
Chromatic tetrachord 16/15 * 25/24 * 6/5, Didymos
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 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: 16/15 111.7313 minor diatonic semitone 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 5/4 386.314 cents major third 2: 1 32/25 427.373 cents classic 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 : 111.7 182.4 498.0 111.7: 70.7 386.3 498.0 182.4: 315.6 427.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 315.6413 cents 144/125, 244.9689 cents 25/24, 70.6724 cents 2: 182.4037 .. 427.3726 cents 144/125, 244.9689 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 2.349077 Largest / Average step : 1.901282 Largest / Smallest step : 4.466258 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Least squares average step : 140.76241 cents, oct.: 422.28722 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1783-tone equal temperament with octave 4/3 degrees: 400 653 1783 Least number of segments generator : 892 of 249.162 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1477 of 412.570 cents and inv. generated superset size: 28 = 25 more = 933.333% 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 70.67243 cents Scale diversity : 0.976978 Lumma stability : 0.283799 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 : 128/125, 41.0589 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 All steps are superparticular (epimoric) 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 Scale is n-1 differentially coherent in interval class 2 -- Rational properties -- Prime limit : 5 Odd number limit : 25 (O: 25 U: 25) Highest odd numerator or denominator: 15 Scale harmonicity : 0.045181 Average absolute harmonicity : 0.123116 Specific harmonicity : 0.237388 Fundamental : 1/45, -5.4919 octaves, 5.8139 Hz. Guide tone : 80, 6.3219 octaves, 20930.045 Hz. Exponens Consonantiae : 3.600000E+03, 11.81378 octaves Euler's gradus suavitatis : 17 Sum of Mann's harmonic distance : 28.5, average 9.50000 Mersenne's string divisions : 4123 Sum of van Prooijen's expressibility: 2.60746, average 0.86915 Sum of Tenney's harmonic distance : 5.41363, average 1.80454 Vogel's harmonic complexity : 9.33333 Wille's k value : 12 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 16.63797, average 2.77300 Lattice compactness (without 2's) : 9.30056, average 1.55009 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 4 2.33333 7 3: -2 ..-1 -1.33333 4 1 5: -1 .. 1 0.00000 2 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 10 15| Scale is weakly epimorphic with val: <7 10 16| Scale is weakly epimorphic with val: <8 11 17| Scale is weakly epimorphic with val: <8 11 18|
FIT/MODE
3: 1 0 2 N G T3 SD: 32.7379 c. M:-54.2837 c. 5: 1 1 3 N M DE S SD: 11.9676 c. M:-16.8143 c. 8: 2 1 5 N T3 SD: 7.7967 c. M:-12.7800 c. 13: 3 2 8 N T3 SD: 5.5980 c. M:-9.1521 c. 14: 3 2 9 N T3 SD: 3.8987 c. M: 5.0074 c. 22: 5 3 14 N T3 SD: 1.1276 c. M:-1.4608 c. 49: 11 7 31 N T3 SD: 0.3214 c. M:-0.5516 c. 71: 16 10 45 N T3 SD: 0.2914 c. M:-0.5042 c. 120: 27 17 76 N T3 SD: 0.2261 c. M:-0.3288 c. 134: 30 19 85 N T3 SD: 0.2100 c. M: 0.2828 c. 183: 41 26 116 N T3 SD: 0.0918 c. M: 0.1474 c. 232: 52 33 147 N T3 SD: 0.0706 c. M: 0.1005 c. 254: 57 36 161 N T3 SD: 0.0345 c. M: 0.0487 c. 303: 68 43 192 N T3 SD: 0.0367 c. M:-0.0484 c. 486: 109 69 308 N T3 SD: 0.0178 c. M: 0.0298 c. 740: 166 105 469 N T3 SD: 0.0080 c. M: 0.0116 c. 1043: 234 148 661 N T3 SD: 0.0051 c. M:-0.0065 c. 1529: 343 217 969 N T3 SD: 0.0047 c. M:-0.0065 c. 1783: 400 253 1130 N T3 SD: 0.0009 c. M: 0.0014 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 12:13 x 16 SD: 13.4207 cents 13:14 x 17 SD: 18.7389 cents 15:16:17:20 SD: 11.4277 cents 17:18:19:23 SD: 10.0284 cents 18:19:20:24 S SD: 6.0428 cents 27:29:30:36 SD: 3.9936 cents 44:47:49:59 SD: 3.6163 cents 45:48:50:60 S SD: 0.0000 cents