Scala analysis: 534_M42
Miscellaneous tetrachord 24/23 * 115/109 * 109/90
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 24/23 73.680654 vicesimotertial minor semitone 2: 120/109 166.447525 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 109/90 331.5975 1: 24/23 73.6807 vicesimotertial minor semitone 2: 115/109 92.7669 3: 109/90 331.5975
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 24/23 73.681 cents vicesimotertial minor semitone 1: 1 115/109 92.767 cents 1: 1 109/90 331.597 cents 2: 1 120/109 166.448 cents 2: 1 436/345 405.278 cents 2: 1 23/18 424.364 cents vicesimotertial 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 : 73.7 166.4 498.0 73.7 : 92.8 424.4 498.0 166.4: 331.6 405.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.6807 .. 331.5975 cents 2507/2160, 257.9168 cents 24/23, 73.6807 cents 2: 166.4475 .. 424.3643 cents 2507/2160, 257.9168 cents 10800/11881,-165.1499 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 24/23, 73.6807 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 109/90, 331.5975 cents Average / Smallest step : 2.253169 Largest / Average step : 1.997395 Largest / Smallest step : 4.500469 Median interval of one step : 115/109, 92.7669 cents, amount: 1 Least squares average step : 135.76505 cents, oct.: 407.29515 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 73.68065 cents Scale diversity : 0.906138 Lumma stability : 0.295880 Lumma impropriety factor : 0.331596 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 : 2645/2616, 19.0862 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% Limited inverse transpositions with margin 238.8306 cents: 2 -- Rational properties -- Prime limit : 109 Odd number limit : 345 (O: 115 U: 345) Highest odd numerator or denominator: 109 Scale harmonicity : 0.017599 Fundamental : 1/7521, -12.8767 octaves, 0.0348 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 9.025200E+05, 19.78360 octaves Euler's gradus suavitatis : 142 Sum of Mann's harmonic distance : 141.5, average 47.16667 Mersenne's string divisions : 75341 Sum of van Prooijen's expressibility: 3.87628, average 1.29209 Sum of Tenney's harmonic distance : 7.93773, average 2.64591 Vogel's harmonic complexity : 96.33333 Wille's k value : 1253 Wilson's harmonic complexity : 143 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 15.18251, average 2.53042 Lattice compactness (without 2's) : 9.71478, average 1.61913 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.33333 1 23: -1 .. 0 -0.33333 1 1 109: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 11 15 30 49| Scale is weakly epimorphic with val: <7 11 15 31 48| Scale is weakly epimorphic with val: <7 11 15 33 49| Scale is weakly epimorphic with val: <7 11 15 34 48| Scale is weakly epimorphic with val: <7 11 15 36 49| Scale is weakly epimorphic with val: <7 11 16 30 50| Scale is weakly epimorphic with val: <7 11 16 31 49| Scale is weakly epimorphic with val: <7 11 16 33 50| Scale is weakly epimorphic with val: <7 11 16 34 49| Scale is weakly epimorphic with val: <7 11 16 36 50| Scale is weakly epimorphic with val: <7 11 17 30 48| Scale is weakly epimorphic with val: <7 11 17 31 50| Scale is weakly epimorphic with val: <7 11 17 33 48| Scale is weakly epimorphic with val: <7 11 17 34 50| Scale is weakly epimorphic with val: <7 11 17 36 48| Scale is weakly epimorphic with val: <7 11 18 30 49| Scale is JI-epimorphic with val: <7 11 18 31 48| Scale is weakly epimorphic with val: <7 11 18 33 49| Scale is weakly epimorphic with val: <7 11 18 34 48| Scale is weakly epimorphic with val: <7 11 18 36 49| Scale is weakly epimorphic with val: <7 11 19 30 50| Scale is JI-epimorphic with val: <7 11 19 31 49| Scale is weakly epimorphic with val: <7 11 19 33 50| Scale is weakly epimorphic with val: <7 11 19 34 49| Scale is weakly epimorphic with val: <7 11 19 36 50| Scale is weakly epimorphic with val: <7 12 15 30 50| Scale is weakly epimorphic with val: <7 12 16 30 48| Scale is weakly epimorphic with val: <7 12 17 30 49| Scale is weakly epimorphic with val: <7 12 18 30 50| Scale is weakly epimorphic with val: <7 12 18 32 48| Scale is weakly epimorphic with val: <7 12 18 35 48| Scale is weakly epimorphic with val: <7 12 19 30 48| Scale is weakly epimorphic with val: <7 12 19 32 49| Scale is weakly epimorphic with val: <7 12 19 35 49| Scale is weakly epimorphic with val: <8 11 15 32 49| Scale is weakly epimorphic with val: <8 11 16 31 48| Scale is weakly epimorphic with val: <8 11 16 32 50| Scale is weakly epimorphic with val: <8 11 16 34 48| Scale is weakly epimorphic with val: <8 11 17 31 49| Scale is weakly epimorphic with val: <8 11 17 32 48| Scale is weakly epimorphic with val: <8 11 17 34 49| Scale is weakly epimorphic with val: <8 11 18 31 50| Scale is weakly epimorphic with val: <8 11 18 32 49| Scale is weakly epimorphic with val: <8 11 18 34 50| Scale is weakly epimorphic with val: <8 11 19 32 50| Scale is weakly epimorphic with val: <8 12 15 31 48| Scale is weakly epimorphic with val: <8 12 15 33 49| Scale is weakly epimorphic with val: <8 12 15 34 48| Scale is weakly epimorphic with val: <8 12 16 31 49| Scale is weakly epimorphic with val: <8 12 16 33 50| Scale is weakly epimorphic with val: <8 12 16 34 49| Scale is weakly epimorphic with val: <8 12 17 31 50| Scale is weakly epimorphic with val: <8 12 17 33 48| Scale is weakly epimorphic with val: <8 12 17 34 50| Scale is weakly epimorphic with val: <8 12 18 33 49| Scale is weakly epimorphic with val: <8 12 19 33 50|
FIT/MODE
3: 0 1 2 N G T3 SD: 42.5403 c. M: 73.6807 c. 4: 0 1 3 N G T3 SD: 48.9472 c. M: 73.6807 c. 5: 1 1 3 N M DE S SD: 24.1259 c. M:-32.7705 c. 6: 1 1 4 N M DE S SD: 5.3906 c. M:-9.3268 c. 15: 2 3 10 N T3 SD: 4.2074 c. M: 7.2747 c. 21: 3 4 14 N T3 SD: 1.4827 c. M: 2.5314 c. 27: 4 5 18 N T3 SD: 0.2568 c. M: 0.4325 c. 129: 19 24 86 N T3 SD: 0.3124 c. M: 0.4325 c. 156: 23 29 104 N T3 SD: 0.2887 c. M: 0.4325 c. 183: 27 34 122 N T3 SD: 0.2748 c. M: 0.4325 c. 197: 29 37 131 N T3 SD: 0.3168 c. M:-0.4102 c. 203: 30 38 135 N T3 SD: 0.2269 c. M:-0.3853 c. 209: 31 39 139 N T3 SD: 0.2365 c. M:-0.3618 c. 224: 33 42 149 N T3 SD: 0.2517 c. M:-0.3086 c. 230: 34 43 153 N T3 SD: 0.1702 c. M:-0.2893 c. 236: 35 44 157 N T3 SD: 0.1884 c. M:-0.2709 c. 251: 37 47 167 N T3 SD: 0.2016 c. M: 0.2637 c. 257: 38 48 171 N T3 SD: 0.1254 c. M:-0.2134 c. 263: 39 49 175 N T3 SD: 0.1525 c. M:-0.1987 c. 284: 42 53 189 N T3 SD: 0.0891 c. M:-0.1520 c. 311: 46 58 207 N T3 SD: 0.0591 c. M:-0.1013 c. 338: 50 63 225 N T3 SD: 0.0340 c. M:-0.0586 c. 365: 54 68 243 N T3 SD: 0.0130 c. M:-0.0223 c. 392: 58 73 261 N T3 SD: 0.0076 c. M:-0.0097 c. 757: 112 141 504 N T3 SD: 0.0051 c. M:-0.0063 c. 1149: 170 214 765 N T3 SD: 0.0043 c. M:-0.0075 c. 1906: 282 355 1269 N T3 SD: 0.0044 c. M:-0.0070 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: 85.7226 cents 6 x 7:8 S SD: 50.2117 cents 7 x 8:9 S SD: 45.1487 cents 8 x 9:11 SD: 32.5632 cents 9 x 10:12 S SD: 7.9781 cents 10 x 11:13 SD: 21.9274 cents 11 x 12:15 S SD: 20.9978 cents 12 x 13:16 SD: 13.9374 cents 13 x 14:17 SD: 25.4238 cents 14:15 x 19 SD: 27.5369 cents 15:16:17:20 SD: 21.0075 cents 16:17:18:21 S SD: 18.6335 cents 17:18:19:23 SD: 14.7546 cents 18:19:20:24 S SD: 8.5082 cents 20:21:22:27 SD: 8.0343 cents 21:22:23:28 SD: 3.7592 cents 48:50:53:64 SD: 1.9743 cents 69:72:76:92 SD: 0.2787 cents 228:238:251:304 SD: 0.2119 cents 297:310:327:396 SD: 0.1690 cents 366:382:403:488 SD: 0.1604 cents 486:507:535:648 SD: 0.1565 cents 555:579:611:740 SD: 0.1303 cents 576:601:634:768 SD: 0.1241 cents