Scala analysis: 206_C12
Chromatic tetrachord 55/54 * 27/25 * 40/33
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: 11/10 165.004228 Ptolemy's second, 4/5-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 40/33 333.0408 1: 55/54 31.7667 telepathma 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 40/33 333.0408
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 55/54 31.767 cents telepathma 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 1 40/33 333.041 cents 2: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 1 100/81 364.807 cents grave major 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 : 31.8 165.0 498.0 31.8 : 133.2 466.3 498.0 165.0: 333.0 364.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.7667 .. 333.0408 cents 144/121, 301.2741 cents 55/54, 31.7667 cents 2: 165.0042 .. 466.2783 cents 144/121, 301.2741 cents 363/400,-168.0365 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 : 40/33, 333.0408 cents Average / Smallest step : 5.226078 Largest / Average step : 2.006088 Largest / Smallest step : 10.483974 Median interval of one step : 27/25, 133.2376 cents, amount: 1 Least squares average step : 132.56501 cents, oct.: 397.69502 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 : 0.666789 Lumma stability : 0.127565 Lumma impropriety factor : 0.337392 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 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% -- Rational properties -- Prime limit : 11 Odd number limit : 81 (O: 55 U: 81) Highest odd numerator or denominator: 55 Scale harmonicity : 0.023820 Average absolute harmonicity : 0.094384 Specific harmonicity : 0.108258 Fundamental : 1/270, -8.0768 octaves, 0.9690 Hz. Guide tone : 220, 7.7814 octaves, 57557.624 Hz. Exponens Consonantiae : 5.940000E+04, 15.85818 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 68.5, average 22.83333 Mersenne's string divisions : 2289 Sum of van Prooijen's expressibility: 3.25888, average 1.08629 Sum of Tenney's harmonic distance : 6.59333, average 2.19778 Vogel's harmonic complexity : 18.33333 Wille's k value : 148 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 18.37486, average 3.06248 Lattice compactness (without 2's) : 13.51793, average 2.25299 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.00000 4 3: -3 .. 0 -1.33333 4 1 5: -1 .. 1 0.00000 2 11: 0 .. 1 0.66667 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 16 23| Scale is weakly epimorphic with val: <6 10 17 26| Scale is weakly epimorphic with val: <6 11 16 25| Scale is weakly epimorphic with val: <6 11 17 25| Scale is weakly epimorphic with val: <7 10 16 26| Scale is weakly epimorphic with val: <7 10 17 23| Scale is JI-epimorphic with val: <7 11 16 25| Scale is weakly epimorphic with val: <7 11 17 25| = patent Scale is weakly epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <7 12 17 27| Scale is weakly epimorphic with val: <7 12 19 27| Scale is weakly epimorphic with val: <8 11 19 25| Scale is weakly epimorphic with val: <8 12 16 27|
FIT/MODE
3: 0 1 2 N G T3 SD: 18.3498 c. M: 31.7667 c. 6: 0 2 4 N G T3 SD: 18.3498 c. M: 31.7667 c. 9: 1 2 6 N T3 SD: 13.6216 c. M:-23.5717 c. 11: 1 3 7 N T3 SD: 12.1358 c. M:-16.1030 c. 12: 1 3 8 N T3 SD: 5.6519 c. M:-9.7371 c. 15: 1 4 10 N T3 SD: 1.0140 c. M:-1.4363 c. 48: 3 13 32 N T3 SD: 0.6904 c. M:-1.0108 c. 63: 4 17 42 N T3 SD: 0.5895 c. M:-1.0108 c. 78: 5 21 52 N T3 SD: 0.5908 c. M:-1.0108 c. 93: 6 25 62 N T3 SD: 0.6205 c. M:-1.0108 c. 94: 6 25 63 N T3 SD: 0.4363 c. M: 0.7553 c. 109: 7 29 73 N T3 SD: 0.3214 c. M: 0.5123 c. 124: 8 33 83 N T3 SD: 0.2835 c. M:-0.3653 c. 127: 8 34 85 N T3 SD: 0.2845 c. M: 0.3937 c. 142: 9 38 95 N T3 SD: 0.1475 c. M: 0.2004 c. 157: 10 42 105 N T3 SD: 0.0370 c. M: 0.0466 c. 329: 21 88 220 N T3 SD: 0.0136 c. M:-0.0235 c. 486: 31 130 325 N T3 SD: 0.0081 c. M: 0.0140 c. 815: 52 218 545 N T3 SD: 0.0075 c. M:-0.0105 c. 1301: 83 348 870 N T3 SD: 0.0071 c. M: 0.0101 c. 1787: 114 478 1195 N T3 SD: 0.0072 c. M: 0.0111 c. 2116: 135 566 1415 N T3 SD: 0.0072 c. M: 0.0092 c. 2273: 145 608 1520 N T3 SD: 0.0073 c. M: 0.0118 c. 2321: 148 621 1552 N T3 SD: 0.0073 c. M:-0.0094 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: 86.3514 cents 6 x 7:8 S SD: 50.9333 cents 7 x 8:9 S SD: 45.6687 cents 8 x 9:11 SD: 32.9836 cents 9 x 10:12 S SD: 8.6997 cents 10 x 11:13 SD: 21.9155 cents 11 x 12:15 S SD: 20.7369 cents 12 x 13:16 SD: 13.2158 cents 13 x 14:17 SD: 24.8870 cents 14 x 15:19 SD: 27.4535 cents 15 x 17:20 SD: 25.8412 cents 16 x 18:21 S SD: 23.7539 cents 17 x 19:23 SD: 18.6947 cents 21:22:23:28 SD: 16.4484 cents 24:25:26:32 SD: 15.6783 cents 26:27:29:35 SD: 14.8310 cents 27:28:30:36 S SD: 11.9062 cents 28:29:31:37 SD: 11.5795 cents 29:30:32:39 SD: 10.4091 cents 30:31:33:40 SD: 8.3334 cents 33:34:36:44 SD: 8.1857 cents 36:37:40:48 SD: 7.8046 cents 37:38:41:49 SD: 7.5044 cents 38:39:42:51 SD: 6.4246 cents 39:40:43:52 SD: 4.2400 cents 42:43:46:56 SD: 3.8998 cents 48:49:53:64 SD: 2.5449 cents 51:52:56:68 SD: 1.2002 cents 60:61:66:80 SD: 1.0502 cents 108:110:119:144 SD: 0.9707 cents 111:113:122:148 SD: 0.5514 cents 159:162:175:212 SD: 0.3847 cents 210:214:231:280 SD: 0.2997 cents 219:223:241:292 SD: 0.2793 cents 270:275:297:360 SD: 0.0000 cents