Scala analysis: 253_C17
Chromatic tetrachord 21/20 * 15/14 * 32/27, 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: 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: 21/20 84.4672 minor semitone 2: 15/14 119.4428 major diatonic semitone 3: 32/27 294.1350 Pythagorean minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 21/20 84.467 cents minor semitone 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 56/45 378.602 cents septimal narrow 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 : 84.5 203.9 498.0 84.5 : 119.4 413.6 498.0 203.9: 294.1 378.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 294.1350 cents 640/567, 209.6678 cents 21/20, 84.4672 cents 2: 203.9100 .. 413.5778 cents 640/567, 209.6678 cents 243/256,-90.2250 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 : 32/27, 294.1350 cents Average / Smallest step : 1.965438 Largest / Average step : 1.771737 Largest / Smallest step : 3.482239 Median interval of one step : 15/14, 119.4428 cents, amount: 1 Least squares average step : 141.88730 cents, oct.: 425.66190 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2164-tone equal temperament with octave 4/3 degrees: 367 886 2164 Least number of segments generator : 1083 of 249.253 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1797 of 413.580 cents and inv. generated superset size: 27 = 24 more = 900.000% 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 : 1.091364 Lumma stability : 0.339195 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 : 50/49, 34.9756 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 -- Rational properties -- Prime limit : 7 Odd number limit : 63 (O: 21 U: 63) Highest odd numerator or denominator: 21 Scale harmonicity : 0.033686 Average absolute harmonicity : 0.127039 Specific harmonicity : 0.170714 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 252, 7.9773 octaves, 65929.642 Hz. Exponens Consonantiae : 3.024000E+04, 14.88417 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 32.5, average 10.83333 Mersenne's string divisions : 4879 Sum of van Prooijen's expressibility: 2.75358, average 0.91786 Sum of Tenney's harmonic distance : 5.55976, average 1.85325 Vogel's harmonic complexity : 12.66667 Wille's k value : 67 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 21.00874, average 3.50146 Lattice compactness (without 2's) : 11.91359, average 1.98560 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -1.00000 7 3: -1 .. 2 0.66667 4 2 5: -1 .. 0 -0.33333 1 7: 0 .. 1 0.33333 1 1 Average exponent except 2's : 2 / 3 = 0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 10 15 22| Scale is weakly epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 16 18| Scale is weakly epimorphic with val: <7 11 16 21| Scale is weakly epimorphic with val: <7 11 17 19| Scale is weakly epimorphic with val: <7 11 17 22| Scale is weakly epimorphic with val: <7 11 18 20| Scale is weakly epimorphic with val: <7 11 19 21| Scale is weakly epimorphic with val: <7 12 15 18| Scale is weakly epimorphic with val: <7 12 15 21| Scale is weakly epimorphic with val: <7 12 16 19| Scale is weakly epimorphic with val: <7 12 16 22| Scale is weakly epimorphic with val: <7 12 17 20| Scale is weakly epimorphic with val: <7 12 18 18| Scale is weakly epimorphic with val: <7 12 18 21| Scale is weakly epimorphic with val: <7 12 19 19| Scale is weakly epimorphic with val: <7 12 19 22|
FIT/MODE
3: 0 1 2 N G T3 SD: 53.4501 c. M: 84.4672 c. 4: 1 1 2 P M ME S SD: 34.8265 c. M:-45.1125 c. 5: 1 1 3 N M DE S SD: 9.1522 c. M:-15.1418 c. 7: 1 2 4 N T3 SD: 9.4576 c. M: 13.3179 c. 12: 2 3 7 N T3 SD: 2.2475 c. M:-3.6087 c. 17: 3 4 10 N T3 SD: 2.0881 c. M:-3.4231 c. 29: 5 7 17 N T3 SD: 1.4955 c. M:-2.1776 c. 46: 8 11 27 N T3 SD: 1.6202 c. M:-2.1493 c. 47: 8 11 28 N T3 SD: 1.4958 c. M: 2.5727 c. 54: 9 13 32 N T3 SD: 1.0225 c. M: 1.4597 c. 59: 10 14 35 N T3 SD: 0.7601 c. M: 1.3154 c. 71: 12 17 42 N T3 SD: 0.3255 c. M: 0.4832 c. 83: 14 20 49 N T3 SD: 0.2726 c. M: 0.4596 c. 88: 15 21 52 N T3 SD: 0.2641 c. M:-0.4268 c. 100: 17 24 59 N T3 SD: 0.2028 c. M:-0.2884 c. 159: 27 38 94 N T3 SD: 0.1874 c. M: 0.3067 c. 171: 29 41 101 N T3 SD: 0.0185 c. M: 0.0319 c. 613: 104 147 362 N T3 SD: 0.0208 c. M:-0.0298 c. 784: 133 188 463 N T3 SD: 0.0140 c. M:-0.0226 c. 955: 162 229 564 N T3 SD: 0.0104 c. M:-0.0179 c. 1126: 191 270 665 N T3 SD: 0.0087 c. M:-0.0147 c. 1297: 220 311 766 N T3 SD: 0.0082 c. M:-0.0123 c. 1380: 234 331 815 N T3 SD: 0.0093 c. M: 0.0161 c. 1468: 249 352 867 N T3 SD: 0.0084 c. M:-0.0105 c. 1551: 263 372 916 N T3 SD: 0.0088 c. M: 0.0147 c. 1651: 280 396 975 N T3 SD: 0.0081 c. M:-0.0139 c. 1722: 292 413 1017 N T3 SD: 0.0087 c. M: 0.0136 c. 1822: 309 437 1076 N T3 SD: 0.0057 c. M:-0.0096 c. 1993: 338 478 1177 N T3 SD: 0.0037 c. M:-0.0061 c. 2164: 367 519 1278 N T3 SD: 0.0021 c. M:-0.0031 c. 2335: 396 560 1379 N T3 SD: 0.0013 c. M: 0.0022 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: 27.6716 cents 13:14:15:17 SD: 23.5052 cents 14:15:16:19 SD: 17.9678 cents 15:16:17:20 SD: 10.0365 cents 18:19:20:24 S SD: 7.7888 cents 23:24:26:31 SD: 7.7191 cents 24:25:27:32 SD: 4.5983 cents 39:41:44:52 SD: 1.7864 cents 63:66:71:84 SD: 1.6584 cents 81:85:91:108 SD: 0.8618 cents 120:126:135:160 SD: 0.0000 cents