Scala analysis: 530_M38
Miscellaneous tetrachord 28/27 * 128/105 * 135/128
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: 512/405 405.866283 narrow diminished fourth 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 135/128 92.1787 major chroma, major limma 1: 28/27 62.9609 Archytas' 1/3-tone 2: 128/105 342.9054 septimal neutral third 3: 135/128 92.1787 major chroma, major limma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 135/128 92.179 cents major chroma, major limma 1: 1 128/105 342.905 cents septimal neutral third 2: 1 35/32 155.140 cents septimal neutral second 2: 1 512/405 405.866 cents narrow diminished fourth 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 : 63.0 405.9 498.0 63.0 : 342.9 435.1 498.0 405.9: 92.2 155.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 342.9054 cents 288/245, 279.9445 cents 28/27, 62.9609 cents 2: 155.1396 .. 435.0841 cents 288/245, 279.9445 cents 3675/4096,-187.7658 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 : 128/105, 342.9054 cents Average / Smallest step : 2.636795 Largest / Average step : 2.065508 Largest / Smallest step : 5.446322 Median interval of one step : 135/128, 92.1787 cents, amount: 1 Least squares average step : 169.20203 cents, oct.: 507.60610 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1313-tone equal temperament with octave 4/3 degrees: 166 1070 1313 Least number of segments generator : 657 of 249.212 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1067 of 404.733 cents and inv. generated superset size: 18 = 15 more = 600.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 62.96090 cents Scale diversity : 0.817751 Lumma stability : 0.252832 Lumma impropriety factor : 0.377006 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 : 3645/3584, 29.2178 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% -- Rational properties -- Prime limit : 7 Odd number limit : 405 (O: 135 U: 405) Highest odd numerator or denominator: 405 Scale harmonicity : 0.027509 Average absolute harmonicity : 0.100648 Specific harmonicity : 0.139871 Fundamental : 1/405, -8.6618 octaves, 0.6460 Hz. Guide tone : 3584, 11.8074 octaves, 937666.026 Hz. Exponens Consonantiae : 1.451520E+06, 20.46913 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 489.5, average 163.16667 Mersenne's string divisions : 50435 Sum of van Prooijen's expressibility: 4.51594, average 1.50531 Sum of Tenney's harmonic distance : 9.27443, average 3.09148 Vogel's harmonic complexity : 14.00000 Wille's k value : 67 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 33.00554, average 5.50092 Lattice compactness (without 2's) : 15.41578, average 2.56930 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 9 4.33333 13 3: -4 ..-1 -2.66667 8 1 5: -1 .. 0 -0.33333 1 1 7: 0 .. 1 0.33333 1 1 Average exponent except 2's :-8 / 3 =-2.66667 Average absolute exponent except 2's: 10 / 3 = 3.33333 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 15 19| Scale is weakly epimorphic with val: <7 10 18 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 17 20| = patent 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: <8 11 15 20| Scale is weakly epimorphic with val: <8 11 18 20|
FIT/MODE
3: 0 2 1 N G T3 SD: 56.0234 c. M: 73.8363 c. 4: 0 3 1 N G T3 SD: 40.8635 c. M: 62.9609 c. 5: 1 3 1 N M DE I SD: 21.5893 c. M:-36.6481 c. 6: 1 4 1 N M DE I SD: 12.7276 c. M:-20.0466 c. 9: 1 6 2 N T3 SD: 11.5510 c. M: 18.4980 c. 10: 1 7 2 N T3 SD: 8.7235 c. M: 13.1564 c. 15: 2 10 3 N T3 SD: 4.7286 c. M: 7.4303 c. 16: 2 11 3 N T3 SD: 0.8060 c. M: 1.2047 c. 70: 9 48 13 N T3 SD: 0.6459 c. M:-1.0735 c. 71: 9 49 13 N T3 SD: 0.5786 c. M:-0.9874 c. 86: 11 59 16 N T3 SD: 0.5107 c. M:-0.7425 c. 87: 11 60 16 N T3 SD: 0.3374 c. M:-0.5842 c. 103: 13 71 19 N T3 SD: 0.1862 c. M:-0.3063 c. 119: 15 82 22 N T3 SD: 0.1208 c. M: 0.1821 c. 135: 17 93 25 N T3 SD: 0.1441 c. M: 0.2441 c. 222: 28 153 41 N T3 SD: 0.1412 c. M:-0.1974 c. 254: 32 175 47 N T3 SD: 0.1248 c. M: 0.2151 c. 276: 35 190 51 N T3 SD: 0.1425 c. M:-0.1970 c. 292: 37 201 54 N T3 SD: 0.0954 c. M:-0.1475 c. 308: 39 212 57 N T3 SD: 0.0598 c. M:-0.1032 c. 324: 41 223 60 N T3 SD: 0.0472 c. M:-0.0633 c. 411: 52 283 76 N T3 SD: 0.0565 c. M:-0.0828 c. 427: 54 294 79 N T3 SD: 0.0242 c. M:-0.0346 c. 443: 56 305 82 N T3 SD: 0.0061 c. M: 0.0102 c. 1313: 166 904 243 N T3 SD: 0.0043 c. M:-0.0059 c. 1756: 222 1209 325 N T3 SD: 0.0022 c. M:-0.0038 c. 2199: 278 1514 407 N T3 SD: 0.0017 c. M:-0.0025 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: 19.5526 cents 5 x 6:7 S SD: 61.7966 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 85.3659 cents 8:9:10:11 H SD: 50.6480 cents 9:10:11:12 H SD: 44.3270 cents 10:11 x 13 SD: 55.5293 cents 11:12:14:15 S SD: 32.2082 cents 12:13:15:16 SD: 26.0330 cents 14:15:18:19 S SD: 23.5297 cents 15:16:19:20 SD: 16.2957 cents 18:19:23:24 SD: 11.9309 cents 19:20:24:25 S SD: 11.5255 cents 21:22:27:28 SD: 11.3656 cents 22:23:28:29 SD: 8.9621 cents 23:24:29:31 SD: 7.3487 cents 24:25:30:32 S SD: 7.0061 cents 26:27:33:35 SD: 6.0317 cents 27:28:34:36 SD: 2.2586 cents 57:59:72:76 SD: 1.1850 cents 129:134:163:172 SD: 1.0003 cents 132:137:167:176 SD: 0.6393 cents 159:165:201:212 SD: 0.3893 cents 189:196:239:252 SD: 0.1610 cents 216:224:273:288 SD: 0.1409 cents 405:420:512:540 SD: 0.0000 cents