Scala analysis: 235_C15
Chromatic tetrachord 21/20 * 16/15 * 25/21, Perrett
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 28/25 196.198479 middle second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 25/21 301.8465 BP second, quasi-equal minor third 1: 21/20 84.4672 minor semitone 2: 16/15 111.7313 minor diatonic semitone 3: 25/21 301.8465 BP second, quasi-equal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 21/20 84.467 cents minor semitone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 25/21 301.847 cents BP second, quasi-equal minor third 2: 1 28/25 196.198 cents middle second 2: 1 5/4 386.314 cents major third 2: 1 80/63 413.578 cents wide major third 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 : 84.5 196.2 498.0 84.5 : 111.7 413.6 498.0 196.2: 301.8 386.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 301.8465 cents 500/441, 217.3793 cents 21/20, 84.4672 cents 2: 196.1985 .. 413.5778 cents 500/441, 217.3793 cents 588/625,-105.6480 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 21/20, 84.4672 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 25/21, 301.8465 cents Average / Smallest step : 1.965438 Largest / Average step : 1.818188 Largest / Smallest step : 3.573536 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Least squares average step : 140.78565 cents, oct.: 422.35696 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1881-tone equal temperament with octave 4/3 degrees: 319 741 1881 Least number of segments generator : 941 of 249.155 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1439 of 381.014 cents and inv. generated superset size: 58 = 55 more = 1933.333% 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 84.46719 cents Scale diversity : 1.066619 Lumma stability : 0.339195 Lumma impropriety factor : 0.212125 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 : 64/63, 27.2641 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 Limited inverse transpositions with margin 190.1152 cents: 2 -- Rational properties -- Prime limit : 7 Odd number limit : 63 (O: 25 U: 63) Highest odd numerator or denominator: 25 Scale harmonicity : 0.030846 Average absolute harmonicity : 0.100327 Specific harmonicity : 0.137999 Fundamental : 1/300, -8.2288 octaves, 0.8721 Hz. Guide tone : 84, 6.3923 octaves, 21976.547 Hz. Exponens Consonantiae : 2.520000E+04, 14.62114 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 50.5, average 16.83333 Mersenne's string divisions : 15211 Sum of van Prooijen's expressibility: 3.19728, average 1.06576 Sum of Tenney's harmonic distance : 6.54753, average 2.18251 Vogel's harmonic complexity : 15.33333 Wille's k value : 157 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 19.26437, average 3.21073 Lattice compactness (without 2's) : 11.28131, average 1.88022 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.66667 6 3: -1 .. 1 0.00000 2 1 5: -2 .. 0 -1.00000 3 7: 0 .. 1 0.66667 2 2 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 15 21| Scale is weakly epimorphic with val: <6 10 16 21| Scale is weakly epimorphic with val: <6 11 15 21| Scale is weakly epimorphic with val: <6 11 17 21| Scale is weakly epimorphic with val: <7 11 15 20| Scale is JI-epimorphic with val: <7 11 16 20| Scale is weakly epimorphic with val: <7 11 18 20| Scale is weakly epimorphic with val: <7 11 19 20| Scale is weakly epimorphic with val: <7 12 15 20| Scale is weakly epimorphic with val: <8 11 16 19| Scale is weakly epimorphic with val: <8 12 15 22| Scale is weakly epimorphic with val: <8 12 16 19|
FIT/MODE
3: 0 1 2 N G T3 SD: 51.7872 c. M: 84.4672 c. 5: 1 1 3 N M DE S SD: 8.9143 c. M:-15.1418 c. 11: 2 2 7 N M DE S SD: 9.3948 c. M: 15.0912 c. 12: 2 3 7 N T3 SD: 6.5899 c. M:-11.3203 c. 13: 2 3 8 N T3 SD: 5.2630 c. M: 7.8449 c. 18: 3 4 11 N T3 SD: 1.6785 c. M: 2.5143 c. 23: 4 5 14 N T3 SD: 1.4536 c. M:-2.1493 c. 41: 7 9 25 N T3 SD: 1.1110 c. M: 1.8395 c. 48: 8 11 29 N T3 SD: 1.0037 c. M: 1.4597 c. 53: 9 12 32 N T3 SD: 0.6611 c. M:-1.1401 c. 71: 12 16 43 N T3 SD: 0.2082 c. M: 0.2906 c. 94: 16 21 57 N T3 SD: 0.1994 c. M:-0.3064 c. 147: 25 33 89 N T3 SD: 0.2239 c. M:-0.3091 c. 165: 28 37 100 N T3 SD: 0.0286 c. M:-0.0495 c. 401: 68 90 243 N T3 SD: 0.0232 c. M:-0.0387 c. 566: 96 127 343 N T3 SD: 0.0165 c. M:-0.0277 c. 731: 124 164 443 N T3 SD: 0.0157 c. M:-0.0217 c. 1079: 183 242 654 N T3 SD: 0.0156 c. M: 0.0269 c. 1150: 195 258 697 N T3 SD: 0.0116 c. M: 0.0161 c. 1315: 223 295 797 N T3 SD: 0.0075 c. M: 0.0104 c. 1480: 251 332 897 N T3 SD: 0.0053 c. M: 0.0091 c. 1645: 279 369 997 N T3 SD: 0.0051 c. M: 0.0081 c. 1716: 291 385 1040 N T3 SD: 0.0050 c. M: 0.0085 c. 1810: 307 406 1097 N T3 SD: 0.0062 c. M:-0.0078 c. 1881: 319 422 1140 N T3 SD: 0.0021 c. M: 0.0034 c. 2046: 347 459 1240 N T3 SD: 0.0008 c. M:-0.0011 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: 73.1459 cents 6 x 7:8 S SD: 35.3362 cents 7 x 8:9 S SD: 36.0117 cents 8 x 9:11 SD: 26.9141 cents 9 x 10:12 S SD: 6.8974 cents 10 x 11:13 SD: 26.8991 cents 11 x 12:15 S SD: 29.9562 cents 12:13 x 16 SD: 27.0527 cents 13:14:15:17 SD: 25.1836 cents 14:15:16:19 SD: 19.3951 cents 15:16:17:20 SD: 11.3681 cents 17:18:19:23 SD: 9.7861 cents 18:19:20:24 S SD: 5.5152 cents 24:25:27:32 SD: 5.2680 cents 39:41:44:52 SD: 4.2707 cents 41:43:46:55 SD: 3.7102 cents 42:44:47:56 SD: 1.3990 cents 99:104:111:132 SD: 0.6831 cents 141:148:158:188 SD: 0.3513 cents 159:167:178:212 SD: 0.3116 cents 258:271:289:344 SD: 0.2275 cents 300:315:336:400 SD: 0.0000 cents