Scala analysis: 254_C17
Chromatic tetrachord 135/128 * 16/15 * 32/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 135/128 92.178716 major chroma, major limma 2: 9/8 203.910002 major whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 32/27 294.1350 Pythagorean minor third 1: 135/128 92.1787 major chroma, major limma 2: 16/15 111.7313 minor diatonic semitone 3: 32/27 294.1350 Pythagorean minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 135/128 92.179 cents major chroma, major limma 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 5/4 386.314 cents major third 2: 1 512/405 405.866 cents narrow 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 : 92.2 203.9 498.0 92.2 : 111.7 405.9 498.0 203.9: 294.1 386.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 294.1350 cents 4096/3645, 201.9563 cents 135/128, 92.1787 cents 2: 203.9100 .. 405.8663 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 135/128, 92.1787 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 1.801012 Largest / Average step : 1.771737 Largest / Smallest step : 3.190921 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Least squares average step : 142.43812 cents, oct.: 427.31437 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1529-tone equal temperament with octave 4/3 degrees: 283 626 1529 Least number of segments generator : 765 of 249.185 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1222 of 398.045 cents and inv. generated superset size: 32 = 29 more = 1066.667% 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 90.22500 cents Scale diversity : 1.100249 Lumma stability : 0.370162 Lumma impropriety factor : 0.181158 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 : 2048/2025, 19.5526 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Limited inverse transpositions with margin 182.4037 cents: 2 -- Rational properties -- Prime limit : 5 Odd number limit : 405 (O: 135 U: 405) Highest odd numerator or denominator: 135 Scale harmonicity : 0.038363 Average absolute harmonicity : 0.127004 Specific harmonicity : 0.184899 Fundamental : 1/384, -8.5850 octaves, 0.6813 Hz. Guide tone : 540, 9.0768 octaves, 141277.805 Hz. Exponens Consonantiae : 2.073600E+05, 17.66178 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 143.5, average 47.83333 Mersenne's string divisions : 31297 Sum of van Prooijen's expressibility: 3.56170, average 1.18723 Sum of Tenney's harmonic distance : 7.17406, average 2.39135 Vogel's harmonic complexity : 13.00000 Wille's k value : 202 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 33.49585, average 5.58264 Lattice compactness (without 2's) : 14.69960, average 2.44993 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 2 -2.66667 12 3: -1 .. 3 1.33333 6 2 5: 0 .. 1 0.33333 1 1 Average exponent except 2's : 5 / 3 = 1.66667 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <7 11 15| Scale is weakly epimorphic with val: <7 11 18| Scale is weakly epimorphic with val: <7 12 17|
FIT/MODE
3: 0 1 2 N G T3 SD: 57.5411 c. M: 92.1787 c. 4: 1 1 2 P M ME S SD: 32.0444 c. M:-45.1125 c. 5: 1 1 3 N M DE S SD: 5.0736 c. M:-7.4303 c. 17: 3 4 10 N T3 SD: 2.5660 c. M: 4.2884 c. 22: 4 5 13 N T3 SD: 0.9430 c. M: 1.6251 c. 27: 5 6 16 N T3 SD: 0.5797 c. M: 1.0028 c. 49: 9 11 29 N T3 SD: 0.5428 c. M: 0.7011 c. 76: 14 17 45 N T3 SD: 0.5052 c. M: 0.7601 c. 125: 23 28 74 N T3 SD: 0.5134 c. M: 0.7076 c. 129: 24 29 76 N T3 SD: 0.4966 c. M:-0.7131 c. 146: 27 33 86 N T3 SD: 0.4444 c. M:-0.7660 c. 151: 28 34 89 N T3 SD: 0.3525 c. M:-0.5853 c. 156: 29 35 92 N T3 SD: 0.3359 c. M:-0.4162 c. 173: 32 39 102 N T3 SD: 0.2846 c. M:-0.4900 c. 178: 33 40 105 N T3 SD: 0.2182 c. M:-0.3444 c. 200: 37 45 118 N T3 SD: 0.1682 c. M:-0.2884 c. 205: 38 46 121 N T3 SD: 0.1265 c. M:-0.1670 c. 227: 42 51 134 N T3 SD: 0.0797 c. M:-0.1349 c. 232: 43 52 137 N T3 SD: 0.0779 c. M:-0.1313 c. 254: 47 57 150 N T3 SD: 0.0144 c. M: 0.0208 c. 789: 146 177 466 N T3 SD: 0.0160 c. M: 0.0209 c. 994: 184 223 587 N T3 SD: 0.0134 c. M:-0.0179 c. 1021: 189 229 603 N T3 SD: 0.0105 c. M:-0.0157 c. 1248: 231 280 737 N T3 SD: 0.0108 c. M:-0.0171 c. 1275: 236 286 753 N T3 SD: 0.0055 c. M:-0.0084 c. 1529: 283 343 903 N T3 SD: 0.0022 c. M:-0.0036 c. 1783: 330 400 1053 N T3 SD: 0.0004 c. M:-0.0007 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: 70.0332 cents 6 x 7:8 S SD: 31.4805 cents 7 x 8:9 S SD: 34.3053 cents 8 x 9:11 SD: 26.6365 cents 9 x 10:12 S SD: 10.7531 cents 10 x 11:13 SD: 29.3037 cents 11 x 12:15 S SD: 32.9836 cents 12:13:14:16 S SD: 26.0693 cents 13:14:15:17 SD: 21.9997 cents 14:15:16:19 SD: 16.4168 cents 15:16:17:20 SD: 7.7856 cents 18:19:20:24 S SD: 7.1845 cents 24:25:27:32 SD: 7.1688 cents 32:34:36:43 SD: 6.1892 cents 33:35:37:44 SD: 3.7705 cents 39:41:44:52 SD: 2.4857 cents 54:57:61:72 SD: 2.4170 cents 57:60:64:76 SD: 1.5924 cents 72:76:81:96 SD: 0.4748 cents 183:193:206:244 SD: 0.3511 cents 201:212:226:268 SD: 0.3198 cents 240:253:270:320 SD: 0.2850 cents 255:269:287:340 SD: 0.2774 cents 273:288:307:364 SD: 0.2739 cents 312:329:351:416 SD: 0.1096 cents 384:405:432:512 SD: 0.0000 cents