Scala analysis: 556_M64
Miscellaneous tetrachord 10/9 * 117/100 * 40/39
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 13/10 454.213948 tridecimal semi-diminished fourth 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 40/39 43.8311 tridecimal minor diesis 1: 10/9 182.4037 minor whole tone 2: 117/100 271.8102 3: 40/39 43.8311 tridecimal minor diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 10/9 182.404 cents minor whole tone 1: 1 117/100 271.810 cents 2: 1 400/351 226.235 cents 2: 1 6/5 315.641 cents minor third 2: 1 13/10 454.214 cents tridecimal 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 : 182.4 454.2 498.0 182.4: 271.8 315.6 498.0 454.2: 43.8 226.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 271.8102 cents 4563/4000, 227.9792 cents 40/39, 43.8311 cents 2: 226.2348 .. 454.2139 cents 4563/4000, 227.9792 cents 40000/41067,-45.5755 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 117/100, 271.8102 cents Average / Smallest step : 3.787612 Largest / Average step : 1.637263 Largest / Smallest step : 6.201317 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 184.64047 cents, oct.: 553.92142 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABC Step pattern size order : MLS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 43.83105 cents Scale diversity : 0.761041 Lumma stability : 0.176012 Lumma impropriety factor : 0.091509 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 : 40/39, 43.8311 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 : 13 Odd number limit : 351 (O: 117 U: 351) Highest odd numerator or denominator: 13 Scale harmonicity : 0.023102 Average absolute harmonicity : 0.108885 Specific harmonicity : 0.119824 Fundamental : 1/90, -6.4919 octaves, 2.9070 Hz. Guide tone : 260, 8.0224 octaves, 68022.647 Hz. Exponens Consonantiae : 2.340000E+04, 14.51422 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 24.5, average 8.16667 Mersenne's string divisions : 3059 Sum of van Prooijen's expressibility: 2.54531, average 0.84844 Sum of Tenney's harmonic distance : 5.14737, average 1.71579 Vogel's harmonic complexity : 14.00000 Wille's k value : 58 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 15.21931, average 2.53655 Lattice compactness (without 2's) : 10.79655, average 1.79942 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -2 .. 0 -1.00000 3 1 5: -1 .. 1 0.00000 2 1 13: 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: <6 10 17 27| Scale is weakly epimorphic with val: <6 10 17 30| Scale is weakly epimorphic with val: <6 10 18 27| Scale is weakly epimorphic with val: <6 11 18 27| Scale is weakly epimorphic with val: <6 11 19 27| Scale is weakly epimorphic with val: <6 11 19 30| Scale is weakly epimorphic with val: <7 10 15 25| Scale is weakly epimorphic with val: <7 10 16 25| Scale is weakly epimorphic with val: <7 10 16 28| Scale is weakly epimorphic with val: <7 10 18 28| Scale is JI-epimorphic with val: <7 11 16 25| Scale is weakly epimorphic with val: <7 11 16 28| Scale is weakly epimorphic with val: <7 11 17 25| Scale is weakly epimorphic with val: <7 11 17 28| Scale is weakly epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <7 11 19 28| Scale is weakly epimorphic with val: <7 12 15 25| Scale is weakly epimorphic with val: <7 12 18 28| Scale is weakly epimorphic with val: <8 11 15 26| Scale is weakly epimorphic with val: <8 11 17 26| Scale is weakly epimorphic with val: <8 11 17 29| Scale is weakly epimorphic with val: <8 11 18 29| Scale is weakly epimorphic with val: <8 12 15 26| Scale is weakly epimorphic with val: <8 12 18 29| Scale is weakly epimorphic with val: <8 12 19 26| Scale is weakly epimorphic with val: <8 12 19 29|
FIT/MODE
3: 1 2 0 N G T3 SD: 27.0170 c. M:-43.8311 c. 5: 2 3 0 N G T3 SD: 27.1040 c. M:-43.8311 c. 6: 2 3 1 P T3 SD: 24.5179 c. M: 39.1764 c. 8: 3 4 1 P T3 SD: 10.9316 c. M: 18.4246 c. 9: 3 5 1 N T3 SD: 11.5615 c. M: 16.3887 c. 10: 4 5 1 P T3 SD: 10.3021 c. M:-16.8143 c. 11: 4 6 1 N T3 SD: 1.1212 c. M: 1.4458 c. 46: 17 25 4 N T3 SD: 1.0028 c. M:-1.6564 c. 57: 21 31 5 N T3 SD: 0.6327 c. M:-1.0866 c. 68: 25 37 6 N T3 SD: 0.4101 c. M:-0.7011 c. 79: 29 43 7 N T3 SD: 0.2992 c. M:-0.4229 c. 90: 33 49 8 N T3 SD: 0.2820 c. M: 0.4396 c. 101: 37 55 9 N T3 SD: 0.3183 c. M: 0.5492 c. 161: 59 88 14 N T3 SD: 0.3084 c. M:-0.5228 c. 169: 62 92 15 N T3 SD: 0.2809 c. M: 0.3741 c. 172: 63 94 15 N T3 SD: 0.2294 c. M:-0.3969 c. 183: 67 100 16 N T3 SD: 0.1687 c. M:-0.2861 c. 194: 71 106 17 N T3 SD: 0.1318 c. M:-0.1879 c. 205: 75 112 18 N T3 SD: 0.1251 c. M: 0.1921 c. 251: 92 137 22 N T3 SD: 0.1330 c. M:-0.1777 c. 262: 96 143 23 N T3 SD: 0.0804 c. M:-0.1095 c. 273: 100 149 24 N T3 SD: 0.0322 c. M:-0.0469 c. 284: 104 155 25 N T3 SD: 0.0137 c. M: 0.0210 c. 557: 204 304 49 N T3 SD: 0.0103 c. M:-0.0174 c. 841: 308 459 74 N T3 SD: 0.0052 c. M:-0.0078 c. 1125: 412 614 99 N T3 SD: 0.0053 c. M: 0.0086 c. 1966: 720 1073 173 N T3 SD: 0.0049 c. M: 0.0068 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 5 x S SD: 67.9002 cents 5:6 x 7 S SD: 78.8780 cents 6:7 x 8 S SD: 42.2336 cents 7:8:9 x S SD: 26.1940 cents 9:10 x 12 S SD: 0.0000 cents 10:11:13 x SD: 8.6997 cents 12:13 x 16 SD: 21.9155 cents 13:14:17 x SD: 27.5305 cents 14:16:18:19 S SD: 20.2305 cents 15:17 x 20 SD: 17.1415 cents 16:18:21 x S SD: 13.5737 cents 17:19:22:23 SD: 9.4488 cents 19:21:25 x SD: 11.4050 cents 20:22:26:27 SD: 9.2211 cents 22:24 x 29 SD: 18.7123 cents 23:26:30:31 SD: 11.9010 cents 24:27:31:32 SD: 8.0724 cents 25:28 x 33 SD: 11.1022 cents 26:29:34:35 SD: 6.8553 cents 27:30:35:36 S SD: 1.6464 cents 63:70:82:84 SD: 0.7042 cents 90:100:117:120 SD: 0.0000 cents