Scala analysis: 532_M40
Miscellaneous tetrachord 20/19 * 57/47 * 47/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 20/19 88.800698 small undevicesimal semitone 2: 60/47 422.762093 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 47/45 75.2829 1: 20/19 88.8007 small undevicesimal semitone 2: 57/47 333.9614 3: 47/45 75.2829
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 47/45 75.283 cents 1: 1 20/19 88.801 cents small undevicesimal semitone 1: 1 57/47 333.961 cents 2: 1 188/171 164.084 cents 2: 1 19/15 409.244 cents undevicesimal ditone 2: 1 60/47 422.762 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 : 88.8 422.8 498.0 88.8 : 334.0 409.2 498.0 422.8: 75.3 164.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 75.2829 .. 333.9614 cents 2565/2209, 258.6785 cents 47/45, 75.2829 cents 2: 164.0836 .. 422.7621 cents 2565/2209, 258.6785 cents 8836/9747,-169.8778 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 47/45, 75.2829 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 57/47, 333.9614 cents Average / Smallest step : 2.205215 Largest / Average step : 2.011634 Largest / Smallest step : 4.436085 Median interval of one step : 20/19, 88.8007 cents, amount: 1 Least squares average step : 173.46142 cents, oct.: 520.38426 cents Scale is not proper Scale has trivalence property Scale is a mode of a 258-tone equal temperament with octave 4/3 degrees: 46 219 258 Least number of segments generator : 131 of 252.883 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 205 of 395.733 cents and inv. generated superset size: 14 = 11 more = 466.667% Number of contiguous 1-step segments: 0 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 75.28291 cents Scale diversity : 0.893888 Lumma stability : 0.302314 Lumma impropriety factor : 0.341089 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 : 900/893, 13.5178 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 : 47 Odd number limit : 171 (O: 57 U: 171) Highest odd numerator or denominator: 47 Scale harmonicity : 0.020904 Fundamental : 1/2679, -11.3875 octaves, 0.0977 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 1.607400E+05, 17.29437 octaves Euler's gradus suavitatis : 75 Sum of Mann's harmonic distance : 76.5, average 25.50000 Mersenne's string divisions : 29211 Sum of van Prooijen's expressibility: 3.42797, average 1.14266 Sum of Tenney's harmonic distance : 7.10921, average 2.36974 Vogel's harmonic complexity : 52.33333 Wille's k value : 446 Wilson's harmonic complexity : 77 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 12.51738, average 2.08623 Lattice compactness (without 2's) : 9.21076, average 1.53513 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.66667 2 19: -1 .. 0 -0.33333 1 1 47: -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: <6 10 18 29 37| Scale is weakly epimorphic with val: <6 10 18 32 37| Scale is weakly epimorphic with val: <6 10 19 28 37| Scale is weakly epimorphic with val: <6 10 19 28 40| Scale is weakly epimorphic with val: <6 10 19 28 43| Scale is weakly epimorphic with val: <6 10 19 30 38| Scale is weakly epimorphic with val: <6 10 19 33 38| Scale is weakly epimorphic with val: <6 11 17 30 37| Scale is weakly epimorphic with val: <6 11 17 33 37| Scale is weakly epimorphic with val: <6 11 18 28 38| Scale is weakly epimorphic with val: <6 11 18 31 38| Scale is weakly epimorphic with val: <6 11 18 34 38| Scale is weakly epimorphic with val: <6 11 19 28 37| Scale is weakly epimorphic with val: <6 11 19 28 40| Scale is weakly epimorphic with val: <6 11 19 28 43| Scale is weakly epimorphic with val: <6 11 19 29 39| Scale is weakly epimorphic with val: <6 11 19 32 39| Scale is weakly epimorphic with val: <7 10 16 28 37| Scale is weakly epimorphic with val: <7 10 16 31 37| Scale is weakly epimorphic with val: <7 10 16 34 37| Scale is weakly epimorphic with val: <7 10 17 28 39| Scale is weakly epimorphic with val: <7 10 17 28 42| Scale is weakly epimorphic with val: <7 10 17 29 38| Scale is weakly epimorphic with val: <7 10 17 32 38| Scale is weakly epimorphic with val: <7 10 18 29 37| Scale is weakly epimorphic with val: <7 10 18 29 40| Scale is weakly epimorphic with val: <7 10 18 29 43| Scale is weakly epimorphic with val: <7 10 18 30 39| Scale is weakly epimorphic with val: <7 10 18 33 39| Scale is weakly epimorphic with val: <7 10 19 28 40| Scale is weakly epimorphic with val: <7 10 19 30 38| Scale is weakly epimorphic with val: <7 10 19 30 41| Scale is weakly epimorphic with val: <7 10 19 31 40| Scale is weakly epimorphic with val: <7 10 19 34 40| Scale is JI-epimorphic with val: <7 11 15 28 38| Scale is weakly epimorphic with val: <7 11 15 28 41| Scale is weakly epimorphic with val: <7 11 15 30 39| Scale is weakly epimorphic with val: <7 11 15 30 42| Scale is weakly epimorphic with val: <7 11 15 31 38| Scale is weakly epimorphic with val: <7 11 15 31 41| Scale is weakly epimorphic with val: <7 11 15 33 39| Scale is weakly epimorphic with val: <7 11 15 33 42| Scale is weakly epimorphic with val: <7 11 15 34 38| Scale is weakly epimorphic with val: <7 11 15 34 41| Scale is weakly epimorphic with val: <7 11 16 28 37| Scale is weakly epimorphic with val: <7 11 16 28 40| Scale is weakly epimorphic with val: <7 11 16 28 43| Scale is JI-epimorphic with val: <7 11 16 29 39| Scale is weakly epimorphic with val: <7 11 16 29 42| Scale is weakly epimorphic with val: <7 11 16 31 37| Scale is weakly epimorphic with val: <7 11 16 31 40| Scale is weakly epimorphic with val: <7 11 16 31 43| Scale is weakly epimorphic with val: <7 11 16 32 39| Scale is weakly epimorphic with val: <7 11 16 32 42| Scale is weakly epimorphic with val: <7 11 16 34 37| Scale is weakly epimorphic with val: <7 11 16 34 40| Scale is weakly epimorphic with val: <7 11 16 34 43| Scale is weakly epimorphic with val: <7 11 17 29 38| Scale is weakly epimorphic with val: <7 11 17 29 41| Scale is weakly epimorphic with val: <7 11 17 30 37| Scale is JI-epimorphic with val: <7 11 17 30 40| Scale is weakly epimorphic with val: <7 11 17 30 43| Scale is weakly epimorphic with val: <7 11 17 32 38| Scale is weakly epimorphic with val: <7 11 17 32 41| Scale is weakly epimorphic with val: <7 11 17 33 37| Scale is weakly epimorphic with val: <7 11 17 33 40| Scale is weakly epimorphic with val: <7 11 17 33 43| Scale is weakly epimorphic with val: <7 11 18 28 38| Scale is weakly epimorphic with val: <7 11 18 28 41| Scale is weakly epimorphic with val: <7 11 18 30 39| Scale is weakly epimorphic with val: <7 11 18 30 42| Scale is weakly epimorphic with val: <7 11 18 31 38| Scale is JI-epimorphic with val: <7 11 18 31 41| Scale is weakly epimorphic with val: <7 11 18 33 39| Scale is weakly epimorphic with val: <7 11 18 33 42| Scale is weakly epimorphic with val: <7 11 18 34 38| Scale is weakly epimorphic with val: <7 11 18 34 41| Scale is weakly epimorphic with val: <7 11 19 28 37| Scale is weakly epimorphic with val: <7 11 19 28 40| Scale is weakly epimorphic with val: <7 11 19 28 43| Scale is weakly epimorphic with val: <7 11 19 29 39| Scale is weakly epimorphic with val: <7 11 19 29 42| Scale is weakly epimorphic with val: <7 11 19 31 37| Scale is weakly epimorphic with val: <7 11 19 31 40| Scale is weakly epimorphic with val: <7 11 19 31 43| Scale is weakly epimorphic with val: <7 11 19 32 39| Scale is JI-epimorphic with val: <7 11 19 32 42| Scale is weakly epimorphic with val: <7 11 19 34 37| Scale is weakly epimorphic with val: <7 11 19 34 40| Scale is weakly epimorphic with val: <7 11 19 34 43| Scale is weakly epimorphic with val: <7 12 15 28 38| Scale is weakly epimorphic with val: <7 12 15 31 38| Scale is weakly epimorphic with val: <7 12 15 34 38| Scale is weakly epimorphic with val: <7 12 16 29 39| Scale is weakly epimorphic with val: <7 12 16 32 39| Scale is weakly epimorphic with val: <7 12 17 28 39| Scale is weakly epimorphic with val: <7 12 17 28 42| Scale is weakly epimorphic with val: <7 12 17 30 40| Scale is weakly epimorphic with val: <7 12 17 33 40| Scale is weakly epimorphic with val: <7 12 18 28 41| Scale is weakly epimorphic with val: <7 12 18 29 37| Scale is weakly epimorphic with val: <7 12 18 29 40| Scale is weakly epimorphic with val: <7 12 18 29 43| Scale is weakly epimorphic with val: <7 12 18 31 41| Scale is weakly epimorphic with val: <7 12 18 34 41| Scale is weakly epimorphic with val: <7 12 19 29 42| Scale is weakly epimorphic with val: <7 12 19 30 38| Scale is weakly epimorphic with val: <7 12 19 30 41| Scale is weakly epimorphic with val: <7 12 19 32 42| Scale is weakly epimorphic with val: <8 11 15 28 38| Scale is weakly epimorphic with val: <8 11 15 28 41| Scale is weakly epimorphic with val: <8 11 15 30 39| Scale is weakly epimorphic with val: <8 11 15 33 39| Scale is weakly epimorphic with val: <8 11 16 28 40| Scale is weakly epimorphic with val: <8 11 16 29 39| Scale is weakly epimorphic with val: <8 11 16 29 42| Scale is weakly epimorphic with val: <8 11 16 31 40| Scale is weakly epimorphic with val: <8 11 16 34 40| Scale is weakly epimorphic with val: <8 11 17 29 41| Scale is weakly epimorphic with val: <8 11 17 30 37| Scale is weakly epimorphic with val: <8 11 17 30 40| Scale is weakly epimorphic with val: <8 11 17 30 43| Scale is weakly epimorphic with val: <8 11 17 32 41| Scale is weakly epimorphic with val: <8 11 18 30 42| Scale is weakly epimorphic with val: <8 11 18 31 38| Scale is weakly epimorphic with val: <8 11 18 31 41| Scale is weakly epimorphic with val: <8 11 18 33 42| Scale is weakly epimorphic with val: <8 11 19 28 43| Scale is weakly epimorphic with val: <8 11 19 31 43| Scale is weakly epimorphic with val: <8 11 19 32 39| Scale is weakly epimorphic with val: <8 11 19 32 42| Scale is weakly epimorphic with val: <8 11 19 34 43| Scale is weakly epimorphic with val: <8 12 15 28 38| Scale is weakly epimorphic with val: <8 12 15 28 41| Scale is weakly epimorphic with val: <8 12 15 29 40| Scale is weakly epimorphic with val: <8 12 15 32 40| Scale is weakly epimorphic with val: <8 12 16 29 39| Scale is weakly epimorphic with val: <8 12 16 29 42| Scale is weakly epimorphic with val: <8 12 16 30 41| Scale is weakly epimorphic with val: <8 12 16 33 41| Scale is weakly epimorphic with val: <8 12 17 28 42| Scale is weakly epimorphic with val: <8 12 17 30 37| Scale is weakly epimorphic with val: <8 12 17 30 40| Scale is weakly epimorphic with val: <8 12 17 30 43| Scale is weakly epimorphic with val: <8 12 17 31 42| Scale is weakly epimorphic with val: <8 12 17 34 42| Scale is weakly epimorphic with val: <8 12 18 29 43| Scale is weakly epimorphic with val: <8 12 18 31 38| Scale is weakly epimorphic with val: <8 12 18 31 41| Scale is weakly epimorphic with val: <8 12 18 32 43| Scale is weakly epimorphic with val: <8 12 19 32 39| Scale is weakly epimorphic with val: <8 12 19 32 42|
FIT/MODE
3: 0 2 1 N G T3 SD: 73.2982 c. M: 90.7321 c. 4: 1 2 1 P M ME I SD: 35.1125 c. M: 49.2283 c. 5: 1 3 1 N M DE I SD: 15.3686 c. M: 24.3261 c. 6: 1 4 1 N M DE I SD: 5.5747 c. M: 7.7246 c. 21: 4 14 3 N T3 SD: 4.2376 c. M:-6.0650 c. 26: 5 17 4 N T3 SD: 4.1018 c. M:-6.9772 c. 27: 5 18 4 N T3 SD: 2.1610 c. M:-3.4299 c. 33: 6 22 5 N T3 SD: 1.0173 c. M:-1.7529 c. 39: 7 26 6 N T3 SD: 0.8455 c. M: 1.3394 c. 67: 12 45 10 N T3 SD: 0.5943 c. M:-0.9478 c. 73: 13 49 11 N T3 SD: 0.1493 c. M:-0.2350 c. 179: 32 120 27 N T3 SD: 0.1639 c. M:-0.2353 c. 185: 33 124 28 N T3 SD: 0.0605 c. M: 0.0969 c. 258: 46 173 39 N T3 SD: 0.0021 c. M: 0.0030 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: 36.4484 cents 5 x 6:7 S SD: 68.2085 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 71.4528 cents 8:9:10:11 H SD: 43.9907 cents 9:10 x 12 S SD: 46.8015 cents 10:11:13 x SD: 41.2195 cents 11:12:14:15 S SD: 24.4154 cents 12:13:15:16 SD: 20.5635 cents 13:14 x 17 SD: 25.9335 cents 14:15:18:19 S SD: 15.0174 cents 15:16:19:20 SD: 8.8728 cents 18:19:23:24 SD: 1.6875 cents 75:79:96:100 SD: 1.5842 cents 93:98:119:124 SD: 1.4792 cents 111:117:142:148 SD: 1.4408 cents 112:118:143:149 SD: 1.3913 cents 116:122:148:155 SD: 1.3789 cents 130:137:166:173 SD: 1.3033 cents 134:141:171:179 SD: 1.1179 cents 152:160:194:203 SD: 0.9568 cents 156:164:199:208 SD: 0.8570 cents 171:180:218:228 SD: 0.7880 cents 174:183:222:232 SD: 0.5981 cents 192:202:245:256 SD: 0.3913 cents 210:221:268:280 SD: 0.2290 cents 228:240:291:304 SD: 0.1266 cents 474:499:605:632 SD: 0.1183 cents 495:521:632:660 SD: 0.0971 cents 513:540:655:684 SD: 0.0937 cents