Scala analysis: 327_C24
Chromatic tetrachord 26/25 * 7/6 * 100/91
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 26/25 67.900234 tridecimal 1/3-tone 2: 91/75 334.771140 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 100/91 163.2739 1: 26/25 67.9002 tridecimal 1/3-tone 2: 7/6 266.8709 septimal minor third 3: 100/91 163.2739
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 26/25 67.900 cents tridecimal 1/3-tone 1: 1 100/91 163.274 cents 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 91/75 334.771 cents 2: 1 50/39 430.145 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 : 67.9 334.8 498.0 67.9 : 266.9 430.1 498.0 334.8: 163.3 231.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 67.9002 .. 266.8709 cents 175/156, 198.9707 cents 26/25, 67.9002 cents 2: 231.1741 .. 430.1448 cents 175/156, 198.9707 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 26/25, 67.9002 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 2.444984 Largest / Average step : 1.607511 Largest / Smallest step : 3.930339 Median interval of one step : 100/91, 163.2739 cents, amount: 1 Least squares average step : 159.39839 cents, oct.: 478.19518 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1577-tone equal temperament with octave 4/3 degrees: 215 1060 1577 Least number of segments generator : 789 of 249.180 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1249 of 394.457 cents and inv. generated superset size: 34 = 31 more = 1133.333% 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 35.69681 cents Scale diversity : 0.994084 Lumma stability : 0.272667 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 : 49/48, 35.6968 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 13 Odd number limit : 91 (O: 91 U: 91) Highest odd numerator or denominator: 91 Scale harmonicity : 0.020038 Average absolute harmonicity : 0.087657 Specific harmonicity : 0.084953 Fundamental : 1/75, -6.2288 octaves, 3.4883 Hz. Guide tone : 364, 8.5078 octaves, 95231.706 Hz. Exponens Consonantiae : 2.730000E+04, 14.73661 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 112.0, average 37.33333 Mersenne's string divisions : 59262 Sum of van Prooijen's expressibility: 3.83410, average 1.27803 Sum of Tenney's harmonic distance : 7.72620, average 2.57540 Vogel's harmonic complexity : 16.33333 Wille's k value : 45 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 14.87139, average 2.47856 Lattice compactness (without 2's) : 12.19501, average 2.03250 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.00000 3 3: -1 .. 0 -0.66667 2 1 5: -2 .. 0 -1.33333 4 7: 0 .. 1 0.33333 1 13: 0 .. 1 0.66667 2 2 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 15 18 25| Scale is weakly epimorphic with val: <6 10 15 20 27| Scale is weakly epimorphic with val: <6 10 16 18 27| Scale is weakly epimorphic with val: <6 10 16 20 29| Scale is weakly epimorphic with val: <6 10 17 18 29| Scale is weakly epimorphic with val: <6 10 17 21 26| Scale is weakly epimorphic with val: <6 10 18 21 28| Scale is weakly epimorphic with val: <6 10 19 21 30| Scale is weakly epimorphic with val: <6 11 15 18 26| Scale is weakly epimorphic with val: <6 11 15 19 27| Scale is weakly epimorphic with val: <6 11 15 22 27| Scale is weakly epimorphic with val: <6 11 16 18 28| Scale is weakly epimorphic with val: <6 11 16 19 29| Scale is weakly epimorphic with val: <6 11 16 21 25| Scale is weakly epimorphic with val: <6 11 16 22 29| Scale is weakly epimorphic with val: <6 11 17 18 30| Scale is weakly epimorphic with val: <6 11 17 21 27| Scale is weakly epimorphic with val: <6 11 18 21 29| Scale is weakly epimorphic with val: <7 10 15 18 25| Scale is weakly epimorphic with val: <7 10 15 19 26| Scale is weakly epimorphic with val: <7 10 15 22 26| Scale is weakly epimorphic with val: <7 10 16 18 27| Scale is weakly epimorphic with val: <7 10 16 19 28| Scale is weakly epimorphic with val: <7 10 16 22 28| Scale is weakly epimorphic with val: <7 10 17 18 29| Scale is weakly epimorphic with val: <7 10 17 19 30| Scale is weakly epimorphic with val: <7 10 17 21 26| Scale is weakly epimorphic with val: <7 10 17 22 30| Scale is weakly epimorphic with val: <7 10 18 21 28| Scale is weakly epimorphic with val: <7 10 19 21 30| Scale is weakly epimorphic with val: <7 11 15 19 27| Scale is weakly epimorphic with val: <7 11 15 19 30| Scale is weakly epimorphic with val: <7 11 15 20 25| Scale is weakly epimorphic with val: <7 11 15 20 28| Scale is weakly epimorphic with val: <7 11 15 22 27| Scale is weakly epimorphic with val: <7 11 15 22 30| Scale is JI-epimorphic with val: <7 11 16 19 26| Scale is weakly epimorphic with val: <7 11 16 19 29| Scale is weakly epimorphic with val: <7 11 16 20 27| Scale is weakly epimorphic with val: <7 11 16 20 30| Scale is weakly epimorphic with val: <7 11 16 22 26| Scale is weakly epimorphic with val: <7 11 16 22 29| Scale is weakly epimorphic with val: <7 11 17 19 25| Scale is JI-epimorphic with val: <7 11 17 19 28| Scale is weakly epimorphic with val: <7 11 17 20 26| Scale is weakly epimorphic with val: <7 11 17 20 29| Scale is weakly epimorphic with val: <7 11 17 22 25| Scale is weakly epimorphic with val: <7 11 17 22 28| Scale is weakly epimorphic with val: <7 11 18 19 27| Scale is JI-epimorphic with val: <7 11 18 19 30| Scale is weakly epimorphic with val: <7 11 18 20 25| Scale is weakly epimorphic with val: <7 11 18 20 28| Scale is weakly epimorphic with val: <7 11 18 22 27| Scale is weakly epimorphic with val: <7 11 18 22 30| Scale is weakly epimorphic with val: <7 11 19 19 26| Scale is weakly epimorphic with val: <7 11 19 19 29| Scale is weakly epimorphic with val: <7 11 19 20 27| Scale is weakly epimorphic with val: <7 11 19 20 30| Scale is weakly epimorphic with val: <7 11 19 22 26| Scale is weakly epimorphic with val: <7 11 19 22 29| Scale is weakly epimorphic with val: <7 12 15 18 27| Scale is weakly epimorphic with val: <7 12 15 20 26| Scale is weakly epimorphic with val: <7 12 16 18 29| Scale is weakly epimorphic with val: <7 12 16 20 28| Scale is weakly epimorphic with val: <7 12 16 21 26| Scale is weakly epimorphic with val: <7 12 17 20 30| Scale is weakly epimorphic with val: <7 12 17 21 28| Scale is weakly epimorphic with val: <7 12 18 21 30| Scale is weakly epimorphic with val: <8 11 15 18 26| Scale is weakly epimorphic with val: <8 11 15 20 25| Scale is weakly epimorphic with val: <8 11 16 18 28| Scale is weakly epimorphic with val: <8 11 16 20 27| Scale is weakly epimorphic with val: <8 11 16 21 25| Scale is weakly epimorphic with val: <8 11 17 18 30| Scale is weakly epimorphic with val: <8 11 17 20 29| Scale is weakly epimorphic with val: <8 11 17 21 27| Scale is weakly epimorphic with val: <8 11 18 21 29| Scale is weakly epimorphic with val: <8 12 15 18 27| Scale is weakly epimorphic with val: <8 12 15 19 25| Scale is weakly epimorphic with val: <8 12 15 22 25| Scale is weakly epimorphic with val: <8 12 16 18 29| Scale is weakly epimorphic with val: <8 12 16 19 27| Scale is weakly epimorphic with val: <8 12 16 21 26| Scale is weakly epimorphic with val: <8 12 16 22 27| Scale is weakly epimorphic with val: <8 12 17 19 29| Scale is weakly epimorphic with val: <8 12 17 21 28| Scale is weakly epimorphic with val: <8 12 17 22 29| Scale is weakly epimorphic with val: <8 12 18 21 30|
FIT/MODE
3: 0 2 1 N G T3 SD: 39.2342 c. M: 67.9002 c. 5: 1 2 2 SP M ME S SD: 27.6733 c. M: 35.9441 c. 6: 1 3 2 P T3 SD: 8.8646 c. M:-15.1073 c. 9: 1 5 3 N T3 SD: 7.4233 c. M: 12.5619 c. 13: 2 7 4 N T3 SD: 7.6738 c. M:-10.0292 c. 15: 2 8 5 N T3 SD: 1.8025 c. M: 2.7411 c. 36: 5 19 12 N T3 SD: 1.7449 c. M: 2.7411 c. 37: 5 20 12 N T3 SD: 1.0652 c. M:-1.7458 c. 43: 6 23 14 N T3 SD: 1.1248 c. M:-1.5944 c. 52: 7 28 17 N T3 SD: 0.5586 c. M: 0.8557 c. 58: 8 31 19 N T3 SD: 0.4647 c. M:-0.7956 c. 73: 10 39 24 N T3 SD: 0.3285 c. M: 0.4670 c. 110: 15 59 36 N T3 SD: 0.1603 c. M:-0.2773 c. 125: 17 67 41 N T3 SD: 0.1077 c. M: 0.1661 c. 183: 25 98 60 N T3 SD: 0.0809 c. M:-0.1387 c. 235: 32 126 77 N T3 SD: 0.0678 c. M:-0.0846 c. 293: 40 157 96 N T3 SD: 0.0752 c. M:-0.0923 c. 308: 42 165 101 N T3 SD: 0.0280 c. M: 0.0461 c. 418: 57 224 137 N T3 SD: 0.0241 c. M:-0.0390 c. 543: 74 291 178 N T3 SD: 0.0166 c. M: 0.0267 c. 726: 99 389 238 N T3 SD: 0.0088 c. M:-0.0150 c. 851: 116 456 279 N T3 SD: 0.0088 c. M: 0.0116 c. 1269: 173 680 416 N T3 SD: 0.0039 c. M:-0.0062 c. 1577: 215 845 517 N 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: 51.5426 cents 5 x 6:7 S SD: 43.3032 cents 6 x 7:8 S SD: 33.9501 cents 7 x x 9 SD: 62.9609 cents 8 x 10:11 S SD: 37.0629 cents 10:11:12:13 H SD: 36.0806 cents 11:12:13:15 SD: 34.0504 cents 12:13:15:16 SD: 29.1571 cents 13:14:16:17 S SD: 24.4681 cents 14:15:17:19 SD: 19.9928 cents 15:16:18:20 S SD: 15.9413 cents 18:19:22:24 SD: 9.5471 cents 23:24:28:31 SD: 6.8079 cents 24:25:29:32 SD: 2.5559 cents 51:53:62:68 SD: 1.1998 cents 75:78:91:100 SD: 0.0000 cents