Scala analysis: 572_M80
Miscellaneous tetrachord 10/9 * 63/55 * 22/21
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 14/11 417.507964 undecimal diminished fourth or major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 22/21 80.5370 undecimal minor semitone 1: 10/9 182.4037 minor whole tone 2: 63/55 235.1043 3: 22/21 80.5370 undecimal minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 10/9 182.404 cents minor whole tone 1: 1 63/55 235.104 cents 2: 1 220/189 262.941 cents 2: 1 6/5 315.641 cents minor third 2: 1 14/11 417.508 cents undecimal diminished fourth or 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 : 182.4 417.5 498.0 182.4: 235.1 315.6 498.0 417.5: 80.5 262.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 235.1043 cents 1323/1210, 154.5672 cents 22/21, 80.5370 cents 2: 262.9407 .. 417.5080 cents 1323/1210, 154.5672 cents 12100/11907, 27.8365 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 63/55, 235.1043 cents Average / Smallest step : 2.061350 Largest / Average step : 1.416163 Largest / Smallest step : 2.919207 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 179.39676 cents, oct.: 538.19028 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 841-tone equal temperament with octave 4/3 degrees: 308 705 841 Least number of segments generator : 421 of 249.319 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 705 of 417.505 cents and inv. generated superset size: 29 = 26 more = 966.667% 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 27.83650 cents Scale diversity : 1.052997 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.379304 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 : 12100/11907, 27.8365 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle 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 : 11 Odd number limit : 189 (O: 63 U: 189) Highest odd numerator or denominator: 11 Scale harmonicity : 0.023696 Average absolute harmonicity : 0.108918 Specific harmonicity : 0.123772 Fundamental : 1/99, -6.6294 octaves, 2.6427 Hz. Guide tone : 140, 7.1293 octaves, 36627.579 Hz. Exponens Consonantiae : 1.386000E+04, 13.75864 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 25.5, average 8.50000 Mersenne's string divisions : 3325 Sum of van Prooijen's expressibility: 2.47276, average 0.82425 Sum of Tenney's harmonic distance : 5.22094, average 1.74031 Vogel's harmonic complexity : 15.66667 Wille's k value : 31 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 12.79541, average 2.13257 Lattice compactness (without 2's) : 10.44230, average 1.74038 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.33333 4 3: -2 .. 0 -1.00000 3 1 5: 0 .. 1 0.33333 1 1 7: 0 .. 1 0.33333 1 11: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 15 20 23| Scale is weakly epimorphic with val: <6 10 15 21 24| Scale is weakly epimorphic with val: <6 10 15 22 25| Scale is weakly epimorphic with val: <6 10 17 18 23| Scale is weakly epimorphic with val: <6 10 17 18 26| Scale is weakly epimorphic with val: <6 10 17 19 24| Scale is weakly epimorphic with val: <6 10 17 19 27| Scale is weakly epimorphic with val: <6 10 17 20 25| Scale is weakly epimorphic with val: <6 10 17 21 23| Scale is weakly epimorphic with val: <6 10 17 21 26| Scale is weakly epimorphic with val: <6 10 17 22 24| Scale is weakly epimorphic with val: <6 10 17 22 27| Scale is weakly epimorphic with val: <6 10 18 20 23| Scale is weakly epimorphic with val: <6 10 18 21 24| Scale is weakly epimorphic with val: <6 10 18 22 25| Scale is weakly epimorphic with val: <6 11 15 20 23| Scale is weakly epimorphic with val: <6 11 15 21 24| Scale is weakly epimorphic with val: <6 11 15 22 25| Scale is weakly epimorphic with val: <6 11 18 20 23| Scale is weakly epimorphic with val: <6 11 18 21 24| Scale is weakly epimorphic with val: <6 11 18 22 25| Scale is weakly epimorphic with val: <6 11 19 19 23| Scale is weakly epimorphic with val: <6 11 19 19 26| Scale is weakly epimorphic with val: <6 11 19 20 24| Scale is weakly epimorphic with val: <6 11 19 20 27| Scale is weakly epimorphic with val: <6 11 19 21 25| Scale is weakly epimorphic with val: <6 11 19 22 23| Scale is weakly epimorphic with val: <6 11 19 22 26| Scale is weakly epimorphic with val: <7 10 15 19 23| Scale is weakly epimorphic with val: <7 10 15 20 24| Scale is weakly epimorphic with val: <7 10 15 21 25| Scale is weakly epimorphic with val: <7 10 15 22 26| Scale is weakly epimorphic with val: <7 10 16 18 23| Scale is weakly epimorphic with val: <7 10 16 18 26| Scale is weakly epimorphic with val: <7 10 16 19 24| Scale is weakly epimorphic with val: <7 10 16 19 27| Scale is weakly epimorphic with val: <7 10 16 20 25| Scale is weakly epimorphic with val: <7 10 16 21 23| Scale is weakly epimorphic with val: <7 10 16 21 26| Scale is weakly epimorphic with val: <7 10 16 22 24| Scale is weakly epimorphic with val: <7 10 16 22 27| Scale is weakly epimorphic with val: <7 10 18 19 23| Scale is weakly epimorphic with val: <7 10 18 20 24| Scale is weakly epimorphic with val: <7 10 18 21 25| Scale is weakly epimorphic with val: <7 10 18 22 26| Scale is JI-epimorphic with val: <7 11 16 18 23| Scale is weakly epimorphic with val: <7 11 16 18 26| Scale is JI-epimorphic with val: <7 11 16 19 24| Scale is weakly epimorphic with val: <7 11 16 19 27| Scale is JI-epimorphic with val: <7 11 16 20 25| Scale is weakly epimorphic with val: <7 11 16 21 23| Scale is JI-epimorphic with val: <7 11 16 21 26| Scale is weakly epimorphic with val: <7 11 16 22 24| Scale is JI-epimorphic with val: <7 11 16 22 27| Scale is weakly epimorphic with val: <7 11 17 18 24| Scale is weakly epimorphic with val: <7 11 17 18 27| Scale is weakly epimorphic with val: <7 11 17 19 25| Scale is weakly epimorphic with val: <7 11 17 20 23| Scale is weakly epimorphic with val: <7 11 17 20 26| Scale is weakly epimorphic with val: <7 11 17 21 24| Scale is weakly epimorphic with val: <7 11 17 21 27| Scale is weakly epimorphic with val: <7 11 17 22 25| Scale is weakly epimorphic with val: <7 11 19 19 24| Scale is weakly epimorphic with val: <7 11 19 19 27| Scale is weakly epimorphic with val: <7 11 19 20 25| Scale is weakly epimorphic with val: <7 11 19 21 23| Scale is weakly epimorphic with val: <7 11 19 21 26| Scale is weakly epimorphic with val: <7 11 19 22 24| Scale is weakly epimorphic with val: <7 11 19 22 27| Scale is weakly epimorphic with val: <7 12 15 19 23| Scale is weakly epimorphic with val: <7 12 15 20 24| Scale is weakly epimorphic with val: <7 12 15 21 25| Scale is weakly epimorphic with val: <7 12 15 22 26| Scale is weakly epimorphic with val: <7 12 18 19 23| Scale is weakly epimorphic with val: <7 12 18 20 24| Scale is weakly epimorphic with val: <7 12 18 21 25| Scale is weakly epimorphic with val: <7 12 18 22 26| Scale is weakly epimorphic with val: <8 11 15 18 23| Scale is weakly epimorphic with val: <8 11 15 19 24| Scale is weakly epimorphic with val: <8 11 15 20 25| Scale is weakly epimorphic with val: <8 11 15 21 26| Scale is weakly epimorphic with val: <8 11 15 22 27| Scale is weakly epimorphic with val: <8 11 17 18 25| Scale is weakly epimorphic with val: <8 11 17 19 23| Scale is weakly epimorphic with val: <8 11 17 19 26| Scale is weakly epimorphic with val: <8 11 17 20 24| Scale is weakly epimorphic with val: <8 11 17 20 27| Scale is weakly epimorphic with val: <8 11 17 21 25| Scale is weakly epimorphic with val: <8 11 17 22 23| Scale is weakly epimorphic with val: <8 11 17 22 26| Scale is weakly epimorphic with val: <8 11 18 18 23| Scale is weakly epimorphic with val: <8 11 18 19 24| Scale is weakly epimorphic with val: <8 11 18 20 25| Scale is weakly epimorphic with val: <8 11 18 21 26| Scale is weakly epimorphic with val: <8 11 18 22 27| Scale is weakly epimorphic with val: <8 12 15 18 23| Scale is weakly epimorphic with val: <8 12 15 19 24| Scale is weakly epimorphic with val: <8 12 15 20 25| Scale is weakly epimorphic with val: <8 12 15 21 26| Scale is weakly epimorphic with val: <8 12 15 22 27| Scale is weakly epimorphic with val: <8 12 18 18 23| Scale is weakly epimorphic with val: <8 12 18 19 24| Scale is weakly epimorphic with val: <8 12 18 20 25| Scale is weakly epimorphic with val: <8 12 18 21 26| Scale is weakly epimorphic with val: <8 12 18 22 27| Scale is weakly epimorphic with val: <8 12 19 19 25| Scale is weakly epimorphic with val: <8 12 19 20 23| Scale is weakly epimorphic with val: <8 12 19 20 26| Scale is weakly epimorphic with val: <8 12 19 21 24| Scale is weakly epimorphic with val: <8 12 19 21 27| Scale is weakly epimorphic with val: <8 12 19 22 25|
FIT/MODE
3: 1 1 1 SP B ME I SD: 50.2496 c. M: 85.4780 c. 4: 1 2 1 P M ME I SD: 41.9733 c. M: 57.8925 c. 5: 2 2 1 SP M ME S SD: 14.6795 c. M: 19.0720 c. 6: 2 3 1 P T3 SD: 9.5689 c. M: 16.3887 c. 11: 4 5 2 SP T3 SD: 5.8313 c. M: 10.0166 c. 13: 5 6 2 SP T3 SD: 5.7470 c. M:-9.1521 c. 17: 6 8 3 SP T3 SD: 5.7136 c. M: 7.3533 c. 19: 7 9 3 SP T3 SD: 1.2628 c. M:-1.8984 c. 44: 16 21 7 SP T3 SD: 1.0611 c. M:-1.3026 c. 49: 18 23 8 SP T3 SD: 0.5499 c. M: 0.7764 c. 68: 25 32 11 SP T3 SD: 0.4051 c. M:-0.7011 c. 74: 27 35 12 SP T3 SD: 0.4164 c. M: 0.6846 c. 93: 34 44 15 SP T3 SD: 0.2214 c. M: 0.3227 c. 142: 52 67 23 SP T3 SD: 0.0773 c. M: 0.1322 c. 161: 59 76 26 SP T3 SD: 0.0886 c. M:-0.1097 c. 235: 86 111 38 SP T3 SD: 0.0811 c. M: 0.1404 c. 303: 111 143 49 SP T3 SD: 0.0281 c. M:-0.0484 c. 396: 145 187 64 SP T3 SD: 0.0342 c. M:-0.0449 c. 445: 163 210 72 SP T3 SD: 0.0303 c. M: 0.0455 c. 538: 197 254 87 SP T3 SD: 0.0197 c. M: 0.0341 c. 680: 249 321 110 SP T3 SD: 0.0247 c. M: 0.0314 c. 699: 256 330 113 SP T3 SD: 0.0135 c. M:-0.0233 c. 841: 308 397 136 SP T3 SD: 0.0030 c. M: 0.0044 c. 1985: 727 937 321 SP T3 SD: 0.0028 c. M:-0.0037 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: 31.1943 cents 5 x 6:7 S SD: 66.1656 cents 6:7 x 8 S SD: 42.2336 cents 7:8:9 x S SD: 25.9204 cents 8:9:10:11 H SD: 21.7909 cents 10:11:13 x SD: 20.3105 cents 11:12:14:15 S SD: 16.7424 cents 13:14 x 17 SD: 31.8493 cents 14:16:18:19 S SD: 20.0732 cents 15:17:19:20 SD: 11.7550 cents 18:20:23:24 SD: 2.2855 cents 63:70:80:84 S SD: 1.3101 cents 81:90:103:108 SD: 0.5091 cents 99:110:126:132 SD: 0.0000 cents