Scala analysis: 324_C24
Chromatic tetrachord 88/81 * 81/77 * 7/6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88/81 143.497939 2nd undecimal neutral second 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: 88/81 143.4979 2nd undecimal neutral second 2: 81/77 87.6762 3: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 81/77 87.676 cents 1: 1 88/81 143.498 cents 2nd undecimal neutral second 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 308/243 410.369 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 : 143.5 231.2 498.0 143.5: 87.7 354.5 498.0 231.2: 266.9 410.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 87.6762 .. 266.8709 cents 539/486, 179.1948 cents 81/77, 87.6762 cents 2: 231.1741 .. 410.3688 cents 539/486, 179.1948 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 81/77, 87.6762 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 1.893502 Largest / Average step : 1.607511 Largest / Smallest step : 3.043825 Median interval of one step : 88/81, 143.4979 cents, amount: 1 Least squares average step : 149.99865 cents, oct.: 449.99596 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2079-tone equal temperament with octave 4/3 degrees: 599 965 2079 Least number of segments generator : 1040 of 249.142 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1763 of 422.344 cents and inv. generated superset size: 44 = 41 more = 1466.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.125351 Lumma stability : 0.352081 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 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 -- Rational properties -- Prime limit : 11 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.023734 Average absolute harmonicity : 0.106984 Specific harmonicity : 0.123011 Fundamental : 1/567, -9.1472 octaves, 0.4614 Hz. Guide tone : 88, 6.4594 octaves, 23023.050 Hz. Exponens Consonantiae : 4.989600E+04, 15.60664 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 95.5, average 31.83333 Mersenne's string divisions : 17745 Sum of van Prooijen's expressibility: 3.23070, average 1.07690 Sum of Tenney's harmonic distance : 6.68034, average 2.22678 Vogel's harmonic complexity : 18.00000 Wille's k value : 94 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 19.78868, average 3.29811 Lattice compactness (without 2's) : 14.94224, average 2.49037 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -4 .. 0 -1.66667 5 1 7: -1 .. 0 -0.33333 1 1 11: 0 .. 1 0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 20 25| Scale is weakly epimorphic with val: <7 10 18 24| Scale is weakly epimorphic with val: <7 10 18 27| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 19 27| Scale is weakly epimorphic with val: <7 11 20 25| = patent Scale is weakly epimorphic with val: <7 11 22 24| Scale is weakly epimorphic with val: <7 11 22 27| Scale is weakly epimorphic with val: <7 12 18 25| Scale is weakly epimorphic with val: <8 11 20 23| Scale is weakly epimorphic with val: <8 11 21 24| Scale is weakly epimorphic with val: <8 11 21 27| Scale is weakly epimorphic with val: <8 12 19 27| Scale is weakly epimorphic with val: <8 12 21 23| Scale is weakly epimorphic with val: <8 12 21 26| Scale is weakly epimorphic with val: <8 12 22 27|
FIT/MODE
3: 1 0 2 N G T3 SD: 39.8025 c. M: 65.1591 c. 4: 1 1 2 P M ME S SD: 15.0450 c. M: 18.9867 c. 6: 2 1 3 P T3 SD: 16.5890 c. M:-22.5171 c. 7: 2 1 4 N T3 SD: 10.2576 c. M: 17.7262 c. 10: 3 2 5 P T3 SD: 10.8560 c. M:-17.8484 c. 11: 3 2 6 N T3 SD: 5.2197 c. M: 7.6675 c. 17: 5 3 9 N T3 SD: 2.5269 c. M:-3.2000 c. 24: 7 4 13 N T3 SD: 1.9618 c. M: 2.9035 c. 28: 8 5 15 N T3 SD: 0.6934 c. M: 1.1994 c. 45: 13 8 24 N T3 SD: 0.7529 c. M:-1.2469 c. 69: 20 12 37 N T3 SD: 0.5110 c. M:-0.8629 c. 73: 21 13 39 N T3 SD: 0.4754 c. M:-0.7921 c. 80: 23 14 43 N T3 SD: 0.5106 c. M: 0.8283 c. 97: 28 17 52 N T3 SD: 0.1699 c. M:-0.2676 c. 125: 36 22 67 N T3 SD: 0.0586 c. M: 0.0812 c. 347: 100 61 186 N T3 SD: 0.0564 c. M: 0.0927 c. 392: 113 69 210 N T3 SD: 0.0541 c. M:-0.0712 c. 420: 121 74 225 N T3 SD: 0.0361 c. M:-0.0611 c. 517: 149 91 277 N T3 SD: 0.0274 c. M:-0.0392 c. 545: 157 96 292 N T3 SD: 0.0216 c. M:-0.0284 c. 642: 185 113 344 N T3 SD: 0.0118 c. M:-0.0197 c. 767: 221 135 411 N T3 SD: 0.0062 c. M: 0.0085 c. 1312: 378 231 703 N T3 SD: 0.0054 c. M:-0.0069 c. 1437: 414 253 770 N T3 SD: 0.0064 c. M: 0.0111 c. 1954: 563 344 1047 N T3 SD: 0.0039 c. M:-0.0065 c. 2079: 599 366 1114 N T3 SD: 0.0011 c. M: 0.0016 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 9:10 x 12 S SD: 19.4529 cents 10:11 x 13 SD: 24.4115 cents 11:12:13:15 SD: 23.4112 cents 12:13:14:16 S SD: 12.0117 cents 15:16:17:20 SD: 11.6381 cents 20:22:23:27 SD: 10.7569 cents 21:23:24:28 SD: 4.6652 cents 35:38:40:47 SD: 4.1244 cents 36:39:41:48 SD: 2.5931 cents 48:52:55:64 SD: 2.2244 cents 57:62:65:76 SD: 1.4426 cents 69:75:79:92 SD: 1.0827 cents 105:114:120:140 SD: 0.3748 cents 231:251:264:308 SD: 0.0852 cents 336:365:384:448 SD: 0.0586 cents 567:616:648:756 SD: 0.0000 cents