Scala analysis: 586_M94
Miscellaneous tetrachord 240/221 * 221/202 * 101/90
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 240/221 142.785643 2: 120/101 298.414935 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 101/90 199.6301 1: 240/221 142.7856 2: 221/202 155.6293 3: 101/90 199.6301
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 240/221 142.786 cents 1: 1 221/202 155.629 cents 1: 1 101/90 199.630 cents 2: 1 120/101 298.415 cents 2: 1 808/663 342.416 cents 2: 1 221/180 355.259 cents 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 : 142.8 298.4 498.0 142.8: 155.6 355.3 498.0 298.4: 199.6 342.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 142.7856 .. 199.6301 cents 22321/21600, 56.8444 cents 240/221, 142.7856 cents 2: 298.4149 .. 355.2594 cents 22321/21600, 56.8444 cents 10800/10201, 98.7849 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 240/221, 142.7856 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 101/90, 199.6301 cents Average / Smallest step : 1.162687 Largest / Average step : 1.202482 Largest / Smallest step : 1.398110 Median interval of one step : 221/202, 155.6293 cents, amount: 1 Least squares average step : 159.55361 cents, oct.: 478.66082 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 2173-tone equal temperament with octave 4/3 degrees: 623 1302 2173 Least number of segments generator : 1087 of 249.137 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 2111 of 483.835 cents and inv. generated superset size: 47 = 44 more = 1566.667% 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 98.78487 cents Scale diversity : 1.347949 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.771730 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 : 48841/48480, 12.8436 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 44.0008 cents: 2 -- Rational properties -- Prime limit : 101 Odd number limit : 663 (O: 221 U: 663) Highest odd numerator or denominator: 221 Scale harmonicity : 0.014705 Fundamental : 1/66963, -16.0311 octaves, 0.0039 Hz. Guide tone : 240, 7.9069 octaves, 62790.136 Hz. Exponens Consonantiae : 1.607112E+07, 23.93797 octaves Euler's gradus suavitatis : 141 Sum of Mann's harmonic distance : 344.5, average 114.83333 Mersenne's string divisions : 713167 Sum of van Prooijen's expressibility: 4.82583, average 1.60861 Sum of Tenney's harmonic distance : 9.88729, average 3.29576 Vogel's harmonic complexity : 97.66667 Wille's k value : 11160 Wilson's harmonic complexity : 142 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 17.52299, average 2.92050 Lattice compactness (without 2's) : 10.71025, average 1.78504 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.66667 2 13: -1 .. 0 -0.33333 1 17: -1 .. 0 -0.33333 1 1 101: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 11 16 26 30 47| Scale is weakly epimorphic with val: <7 11 16 26 31 49| Scale is weakly epimorphic with val: <7 11 16 27 29 47| Scale is weakly epimorphic with val: <7 11 16 27 30 49| Scale is weakly epimorphic with val: <7 11 16 28 29 49| Scale is weakly epimorphic with val: <7 11 16 28 31 47| Scale is JI-epimorphic with val: <7 11 17 26 29 47| Scale is weakly epimorphic with val: <7 11 17 26 31 48| Scale is weakly epimorphic with val: <7 11 17 27 30 48| = patent Scale is weakly epimorphic with val: <7 11 17 27 31 47| Scale is weakly epimorphic with val: <7 11 17 28 29 48| Scale is weakly epimorphic with val: <7 11 17 28 30 47| Scale is weakly epimorphic with val: <7 11 18 26 29 49| Scale is JI-epimorphic with val: <7 11 18 26 30 48| Scale is JI-epimorphic with val: <7 11 18 27 29 48| Scale is weakly epimorphic with val: <7 11 18 27 31 49| Scale is weakly epimorphic with val: <7 11 18 28 30 49| Scale is weakly epimorphic with val: <7 11 18 28 31 48| Scale is weakly epimorphic with val: <7 12 17 26 30 47| Scale is weakly epimorphic with val: <7 12 17 27 29 47| Scale is weakly epimorphic with val: <7 12 17 28 31 47| Scale is weakly epimorphic with val: <7 12 18 26 29 47| Scale is weakly epimorphic with val: <7 12 18 26 31 48| Scale is weakly epimorphic with val: <7 12 18 27 30 48| Scale is weakly epimorphic with val: <7 12 18 28 29 48|
FIT/MODE
3: 1 1 1 SP B ME I SD: 23.5908 c. M:-33.6151 c. 7: 2 2 3 SP M ME S SD: 7.9827 c. M: 13.8178 c. 10: 3 3 4 SP M ME S SD: 3.8340 c. M:-6.6279 c. 17: 5 5 7 SP M DE S SD: 3.8013 c. M: 5.4473 c. 25: 7 8 10 SP T3 SD: 1.9390 c. M: 3.3330 c. 32: 9 10 13 SP T3 SD: 2.2091 c. M: 2.7105 c. 35: 10 11 14 SP T3 SD: 0.3683 c. M: 0.4871 c. 80: 23 25 32 SP T3 SD: 0.3325 c. M:-0.4121 c. 115: 33 36 46 SP T3 SD: 0.2497 c. M:-0.4121 c. 122: 35 38 49 SP T3 SD: 0.2400 c. M: 0.4044 c. 150: 43 47 60 SP T3 SD: 0.2380 c. M:-0.4121 c. 157: 45 49 63 SP T3 SD: 0.1299 c. M: 0.2224 c. 192: 55 60 77 SP T3 SD: 0.0912 c. M: 0.1165 c. 237: 68 74 95 SP T3 SD: 0.0656 c. M:-0.1133 c. 272: 78 85 109 SP T3 SD: 0.0337 c. M:-0.0459 c. 429: 123 134 172 SP T3 SD: 0.0308 c. M: 0.0523 c. 464: 133 145 186 SP T3 SD: 0.0185 c. M: 0.0271 c. 701: 201 219 281 SP T3 SD: 0.0144 c. M:-0.0204 c. 736: 211 230 295 SP T3 SD: 0.0041 c. M:-0.0060 c. 1901: 545 594 762 SP T3 SD: 0.0041 c. M: 0.0071 c. 2173: 623 679 871 SP T3 SD: 0.0024 c. M:-0.0041 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: 87.8988 cents 5 x 6:7 S SD: 43.1029 cents 6 x 7:8 S SD: 15.7720 cents 7 x 8:9 S SD: 46.0581 cents 8:9:10:11 H SD: 39.8614 cents 9:10:11:12 H SD: 21.0024 cents 10:11:12:13 H SD: 17.3576 cents 11:12:13:15 SD: 13.5812 cents 12:13:14:16 S SD: 10.6080 cents 21:23:25:28 SD: 5.0343 cents 33:36:39:44 SD: 4.0329 cents 36:39:43:48 SD: 3.3707 cents 48:52:57:64 SD: 1.4361 cents 69:75:82:92 SD: 0.5407 cents 117:127:139:156 SD: 0.2704 cents 186:202:221:248 SD: 0.0366 cents