Scala analysis: 321_C24
Chromatic tetrachord 120/113 * 113/105 * 7/6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 120/113 104.053960 2: 8/7 231.174094 septimal whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 120/113 104.0540 2: 113/105 127.1201 3: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 120/113 104.054 cents 1: 1 113/105 127.120 cents 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 140/113 370.925 cents 2: 1 113/90 393.991 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 : 104.1 231.2 498.0 104.1: 127.1 394.0 498.0 231.2: 266.9 370.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 104.0540 .. 266.8709 cents 791/720, 162.8169 cents 120/113, 104.0540 cents 2: 231.1741 .. 393.9910 cents 791/720, 162.8169 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 120/113, 104.0540 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 1.595470 Largest / Average step : 1.607511 Largest / Smallest step : 2.564736 Median interval of one step : 113/105, 127.1201 cents, amount: 1 Least squares average step : 147.18122 cents, oct.: 441.54367 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1144-tone equal temperament with octave 4/3 degrees: 239 531 1144 Least number of segments generator : 573 of 249.458 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1011 of 440.143 cents and inv. generated superset size: 48 = 45 more = 1600.000% 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 35.69681 cents Scale diversity : 1.152935 Lumma stability : 0.417850 Lumma impropriety factor : 0.071674 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 : 12769/12600, 23.0662 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Limited inverse transpositions with margin 139.7508 cents: 2 -- Rational properties -- Prime limit : 113 Odd number limit : 113 (O: 113 U: 113) Highest odd numerator or denominator: 113 Scale harmonicity : 0.039970 Fundamental : 1/2373, -11.2125 octaves, 0.1103 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 2.847600E+05, 18.11939 octaves Euler's gradus suavitatis : 130 Sum of Mann's harmonic distance : 127.5, average 42.50000 Mersenne's string divisions : 24465 Sum of van Prooijen's expressibility: 3.37530, average 1.12510 Sum of Tenney's harmonic distance : 6.95963, average 2.31988 Vogel's harmonic complexity : 87.33333 Wille's k value : 395 Wilson's harmonic complexity : 131 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.62856, average 2.43809 Lattice compactness (without 2's) : 8.79655, average 1.46609 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.33333 1 7: -1 .. 0 -0.33333 1 1 113: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <7 10 15 18 50| Scale is weakly epimorphic with val: <7 10 16 18 48| Scale is weakly epimorphic with val: <7 10 17 18 49| Scale is weakly epimorphic with val: <7 10 18 18 50| Scale is weakly epimorphic with val: <7 11 15 19 49| Scale is weakly epimorphic with val: <7 11 15 20 48| Scale is weakly epimorphic with val: <7 11 15 22 49| Scale is weakly epimorphic with val: <7 11 16 19 50| Scale is weakly epimorphic with val: <7 11 16 20 49| Scale is weakly epimorphic with val: <7 11 16 22 50| Scale is JI-epimorphic with val: <7 11 17 19 48| Scale is weakly epimorphic with val: <7 11 17 20 50| Scale is weakly epimorphic with val: <7 11 17 22 48| Scale is JI-epimorphic with val: <7 11 18 19 49| Scale is weakly epimorphic with val: <7 11 18 20 48| Scale is weakly epimorphic with val: <7 11 18 22 49| Scale is JI-epimorphic with val: <7 11 19 19 50| Scale is weakly epimorphic with val: <7 11 19 20 49| Scale is weakly epimorphic with val: <7 11 19 22 50| Scale is weakly epimorphic with val: <7 12 15 18 50| Scale is weakly epimorphic with val: <7 12 16 18 48| Scale is weakly epimorphic with val: <7 12 17 18 49| Scale is weakly epimorphic with val: <7 12 18 18 50| Scale is weakly epimorphic with val: <7 12 18 20 48| Scale is weakly epimorphic with val: <7 12 19 20 49| Scale is weakly epimorphic with val: <8 11 15 21 49| Scale is weakly epimorphic with val: <8 11 16 20 48| Scale is weakly epimorphic with val: <8 11 16 21 50| Scale is weakly epimorphic with val: <8 11 17 20 49| Scale is weakly epimorphic with val: <8 11 17 21 48| Scale is weakly epimorphic with val: <8 11 18 20 50| Scale is weakly epimorphic with val: <8 11 18 21 49| Scale is weakly epimorphic with val: <8 11 19 21 50| Scale is weakly epimorphic with val: <8 12 15 19 48| Scale is weakly epimorphic with val: <8 12 15 21 49| Scale is weakly epimorphic with val: <8 12 15 22 48| Scale is weakly epimorphic with val: <8 12 16 19 49| Scale is weakly epimorphic with val: <8 12 16 21 50| Scale is weakly epimorphic with val: <8 12 16 22 49| Scale is weakly epimorphic with val: <8 12 17 19 50| Scale is weakly epimorphic with val: <8 12 17 21 48| Scale is weakly epimorphic with val: <8 12 17 22 50| Scale is weakly epimorphic with val: <8 12 18 21 49| Scale is weakly epimorphic with val: <8 12 19 21 50|
FIT/MODE
3: 1 0 2 N G T3 SD: 51.9130 c. M: 65.1591 c. 4: 1 1 2 P M ME S SD: 15.6745 c. M:-20.4573 c. 9: 2 2 5 N M DE S SD: 6.8388 c. M: 9.8208 c. 13: 3 3 7 N M DE S SD: 6.3265 c. M:-10.8795 c. 15: 3 4 8 N T3 SD: 2.6654 c. M: 4.4450 c. 19: 4 5 10 N T3 SD: 2.7762 c. M:-4.7420 c. 24: 5 6 13 N T3 SD: 1.6849 c. M: 2.9035 c. 28: 6 7 15 N T3 SD: 1.5419 c. M:-2.6700 c. 39: 8 10 21 N T3 SD: 1.3272 c. M: 1.8909 c. 43: 9 11 23 N T3 SD: 0.2948 c. M:-0.4747 c. 110: 23 28 59 N T3 SD: 0.1588 c. M: 0.2623 c. 153: 32 39 82 N T3 SD: 0.0722 c. M:-0.1123 c. 196: 41 50 105 N T3 SD: 0.0824 c. M:-0.1289 c. 321: 67 82 172 N T3 SD: 0.0582 c. M: 0.1006 c. 364: 76 93 195 N T3 SD: 0.0522 c. M: 0.0665 c. 431: 90 110 231 N T3 SD: 0.0477 c. M: 0.0627 c. 474: 99 121 254 N T3 SD: 0.0201 c. M: 0.0319 c. 517: 108 132 277 N T3 SD: 0.0173 c. M:-0.0267 c. 627: 131 160 336 N T3 SD: 0.0140 c. M: 0.0240 c. 670: 140 171 359 N T3 SD: 0.0099 c. M:-0.0151 c. 1144: 239 292 613 N T3 SD: 0.0026 c. M: 0.0043 c. 1814: 379 463 972 N T3 SD: 0.0021 c. M:-0.0029 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: 59.7273 cents 6 x 7:8 S SD: 17.8484 cents 7 x 8:9 S SD: 31.4805 cents 8 x 9:11 SD: 29.9221 cents 9 x 10:12 S SD: 24.3852 cents 10:11 x 13 SD: 37.5370 cents 11:12:13:15 SD: 27.9916 cents 12:13:14:16 S SD: 16.5523 cents 13:14:15:17 SD: 14.8787 cents 14:15:16:19 SD: 11.4298 cents 15:16:17:20 SD: 5.4653 cents 33:35:38:44 SD: 4.4159 cents 36:38:41:48 SD: 4.0205 cents 48:51:55:64 SD: 1.5306 cents 63:67:72:84 SD: 0.8391 cents 147:156:168:196 SD: 0.3927 cents 210:223:240:280 SD: 0.0229 cents