Scala analysis: 538_M46
Miscellaneous tetrachord 28/27 * 16/15 * 135/112
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 448/405 174.692189 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 135/112 323.3528 septimal wide minor third 1: 28/27 62.9609 Archytas' 1/3-tone 2: 16/15 111.7313 minor diatonic semitone 3: 135/112 323.3528 septimal wide minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 135/112 323.353 cents septimal wide minor third 2: 1 448/405 174.692 cents 2: 1 5/4 386.314 cents major third 2: 1 9/7 435.084 cents septimal major third, BP 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 : 63.0 174.7 498.0 63.0 : 111.7 435.1 498.0 174.7: 323.4 386.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 323.3528 cents 3645/3136, 260.3919 cents 28/27, 62.9609 cents 2: 174.6922 .. 435.0841 cents 3645/3136, 260.3919 cents 50176/54675,-148.6606 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 135/112, 323.3528 cents Average / Smallest step : 2.636795 Largest / Average step : 1.947732 Largest / Smallest step : 5.135771 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Least squares average step : 136.17716 cents, oct.: 408.53149 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1052-tone equal temperament with octave 4/3 degrees: 133 369 1052 Least number of segments generator : 527 of 249.496 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 683 of 323.351 cents and inv. generated superset size: 33 = 30 more = 1100.000% 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 62.96090 cents Scale diversity : 0.913705 Lumma stability : 0.252832 Lumma impropriety factor : 0.298488 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 : 36/35, 48.7704 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 : 405 (O: 135 U: 405) Highest odd numerator or denominator: 405 Scale harmonicity : 0.029983 Average absolute harmonicity : 0.097854 Specific harmonicity : 0.138317 Fundamental : 1/405, -8.6618 octaves, 0.6460 Hz. Guide tone : 448, 8.8074 octaves, 117208.253 Hz. Exponens Consonantiae : 1.814400E+05, 17.46913 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 457.5, average 152.50000 Mersenne's string divisions : 328405 Sum of van Prooijen's expressibility: 4.51594, average 1.50531 Sum of Tenney's harmonic distance : 9.21644, average 3.07215 Vogel's harmonic complexity : 15.33333 Wille's k value : 67 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 25.00106, average 4.16684 Lattice compactness (without 2's) : 15.37182, average 2.56197 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 6 3.33333 10 3: -4 ..-1 -2.66667 8 1 5: -1 .. 0 -0.33333 1 7: 0 .. 1 0.66667 2 2 Average exponent except 2's :-7 / 3 =-2.33333 Average absolute exponent except 2's: 11 / 3 = 3.66667 Scale is weakly epimorphic with val: <6 10 15 22| Scale is weakly epimorphic with val: <6 10 16 21| Scale is weakly epimorphic with val: <6 10 19 21| Scale is weakly epimorphic with val: <7 10 16 19| Scale is weakly epimorphic with val: <7 10 17 18| Scale is weakly epimorphic with val: <7 10 19 19| Scale is weakly epimorphic with val: <7 11 15 18| Scale is weakly epimorphic with val: <7 11 15 21| Scale is JI-epimorphic with val: <7 11 16 20| Scale is weakly epimorphic with val: <7 11 18 18| Scale is weakly epimorphic with val: <7 11 18 21| Scale is weakly epimorphic with val: <7 11 19 20| Scale is weakly epimorphic with val: <8 11 17 20| Scale is weakly epimorphic with val: <8 12 16 19| Scale is weakly epimorphic with val: <8 12 19 22|
FIT/MODE
3: 0 1 2 N G T3 SD: 36.6941 c. M: 62.9609 c. 5: 1 1 3 N M DE S SD: 25.4598 c. M:-36.6481 c. 6: 1 1 4 N M DE S SD: 12.6116 c. M:-20.0466 c. 8: 1 2 5 N T3 SD: 6.9832 c. M:-12.0747 c. 9: 1 2 6 N T3 SD: 6.6683 c. M: 8.6772 c. 14: 2 3 9 N T3 SD: 5.0718 c. M:-8.1884 c. 17: 2 4 11 N T3 SD: 2.5986 c. M: 4.3674 c. 23: 3 5 15 N T3 SD: 1.4300 c. M:-2.0015 c. 31: 4 7 20 N T3 SD: 1.3944 c. M:-2.0335 c. 40: 5 9 26 N T3 SD: 0.4616 c. M: 0.7053 c. 71: 9 16 46 N T3 SD: 0.4025 c. M:-0.6758 c. 94: 12 21 61 N T3 SD: 0.3684 c. M:-0.6193 c. 103: 13 23 67 N T3 SD: 0.3616 c. M: 0.6182 c. 111: 14 25 72 N T3 SD: 0.1905 c. M:-0.2966 c. 134: 17 30 87 N T3 SD: 0.1293 c. M:-0.2239 c. 174: 22 39 113 N T3 SD: 0.0524 c. M: 0.0902 c. 285: 36 64 185 N T3 SD: 0.0453 c. M:-0.0604 c. 419: 53 94 272 N T3 SD: 0.0315 c. M:-0.0396 c. 459: 58 103 298 N T3 SD: 0.0158 c. M: 0.0271 c. 593: 75 133 385 N T3 SD: 0.0171 c. M:-0.0296 c. 633: 80 142 411 N T3 SD: 0.0162 c. M: 0.0224 c. 878: 111 197 570 N T3 SD: 0.0121 c. M:-0.0206 c. 1052: 133 236 683 N T3 SD: 0.0031 c. M:-0.0049 c. 1511: 191 339 981 N T3 SD: 0.0032 c. M: 0.0049 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: 82.1604 cents 6 x 7:8 S SD: 46.0894 cents 7 x 8:9 S SD: 42.2915 cents 8 x 9:11 SD: 30.3796 cents 9 x 10:12 S SD: 3.8558 cents 10 x 11:13 SD: 22.4445 cents 11 x 12:15 S SD: 22.8709 cents 12 x 13:16 SD: 18.0598 cents 13 x 14:17 SD: 28.6466 cents 14 x 15:19 SD: 31.5889 cents 15:16:17:20 SD: 21.4530 cents 16:17:18:21 S SD: 19.3234 cents 17:18:19:23 SD: 15.8236 cents 18:19:20:24 S SD: 10.5325 cents 21:22:23:28 SD: 8.1970 cents 26:27:29:35 SD: 7.3503 cents 27:28:30:36 S SD: 2.5705 cents 57:59:63:76 SD: 1.1850 cents 84:87:93:112 SD: 0.8935 cents 132:137:146:176 SD: 0.4719 cents 189:196:209:252 SD: 0.1840 cents 216:224:239:288 SD: 0.1610 cents 405:420:448:540 SD: 0.0000 cents