Scala analysis: 323_C24
Chromatic tetrachord 30/29 * 116/105 * 7/6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 30/29 58.691521 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: 30/29 58.6915 2: 116/105 172.4826 3: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 30/29 58.692 cents 1: 1 116/105 172.483 cents 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 35/29 325.562 cents 2: 1 58/45 439.353 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 : 58.7 231.2 498.0 58.7 : 172.5 439.4 498.0 231.2: 266.9 325.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.6915 .. 266.8709 cents 203/180, 208.1794 cents 30/29, 58.6915 cents 2: 231.1741 .. 439.3535 cents 203/180, 208.1794 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 30/29, 58.6915 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 2.828603 Largest / Average step : 1.607511 Largest / Smallest step : 4.547010 Median interval of one step : 116/105, 172.4826 cents, amount: 1 Least squares average step : 143.94105 cents, oct.: 431.82315 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1256-tone equal temperament with octave 4/3 degrees: 148 583 1256 Least number of segments generator : 629 of 249.419 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 903 of 358.069 cents and inv. generated superset size: 37 = 34 more = 1233.333% 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 : 0.906483 Lumma stability : 0.235688 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 Best minor thirds form a closed circle Steps are strictly increasing 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 : 29 Odd number limit : 105 (O: 35 U: 105) Highest odd numerator or denominator: 29 Scale harmonicity : 0.012644 Average absolute harmonicity : 0.101715 Specific harmonicity : 0.067152 Fundamental : 1/609, -9.2503 octaves, 0.4296 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 7.308000E+04, 16.15719 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 40.5, average 13.50000 Mersenne's string divisions : 6195 Sum of van Prooijen's expressibility: 2.78462, average 0.92821 Sum of Tenney's harmonic distance : 5.76689, average 1.92230 Vogel's harmonic complexity : 30.66667 Wille's k value : 157 Wilson's harmonic complexity : 47 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.60457, average 2.43410 Lattice compactness (without 2's) : 9.59575, average 1.59929 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.33333 1 7: -1 .. 0 -0.33333 1 1 29: -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: <6 10 19 20 32| Scale is weakly epimorphic with val: <6 11 18 19 32| Scale is weakly epimorphic with val: <6 11 18 22 32| Scale is weakly epimorphic with val: <6 11 19 19 33| Scale is weakly epimorphic with val: <6 11 19 22 33| Scale is weakly epimorphic with val: <7 10 15 18 33| Scale is weakly epimorphic with val: <7 10 15 18 36| Scale is weakly epimorphic with val: <7 10 16 18 34| Scale is weakly epimorphic with val: <7 10 16 18 37| Scale is weakly epimorphic with val: <7 10 17 18 32| Scale is weakly epimorphic with val: <7 10 17 18 35| Scale is weakly epimorphic with val: <7 10 17 18 38| Scale is weakly epimorphic with val: <7 10 18 18 33| Scale is weakly epimorphic with val: <7 10 18 18 36| Scale is weakly epimorphic with val: <7 10 18 19 32| Scale is weakly epimorphic with val: <7 10 18 22 32| Scale is weakly epimorphic with val: <7 10 19 19 33| Scale is weakly epimorphic with val: <7 10 19 22 33| Scale is JI-epimorphic with val: <7 11 15 19 32| Scale is weakly epimorphic with val: <7 11 15 19 35| Scale is weakly epimorphic with val: <7 11 15 19 38| Scale is weakly epimorphic with val: <7 11 15 20 34| Scale is weakly epimorphic with val: <7 11 15 20 37| Scale is weakly epimorphic with val: <7 11 15 22 32| Scale is weakly epimorphic with val: <7 11 15 22 35| Scale is weakly epimorphic with val: <7 11 15 22 38| Scale is JI-epimorphic with val: <7 11 16 19 33| Scale is weakly epimorphic with val: <7 11 16 19 36| Scale is weakly epimorphic with val: <7 11 16 20 32| Scale is weakly epimorphic with val: <7 11 16 20 35| Scale is weakly epimorphic with val: <7 11 16 20 38| Scale is weakly epimorphic with val: <7 11 16 22 33| Scale is weakly epimorphic with val: <7 11 16 22 36| Scale is JI-epimorphic with val: <7 11 17 19 34| Scale is weakly epimorphic with val: <7 11 17 19 37| Scale is weakly epimorphic with val: <7 11 17 20 33| Scale is weakly epimorphic with val: <7 11 17 20 36| Scale is weakly epimorphic with val: <7 11 17 22 34| Scale is weakly epimorphic with val: <7 11 17 22 37| Scale is weakly epimorphic with val: <7 11 18 19 32| Scale is JI-epimorphic with val: <7 11 18 19 35| Scale is weakly epimorphic with val: <7 11 18 19 38| Scale is weakly epimorphic with val: <7 11 18 20 34| Scale is weakly epimorphic with val: <7 11 18 20 37| Scale is weakly epimorphic with val: <7 11 18 22 32| Scale is weakly epimorphic with val: <7 11 18 22 35| Scale is weakly epimorphic with val: <7 11 18 22 38| Scale is weakly epimorphic with val: <7 11 19 19 33| Scale is JI-epimorphic with val: <7 11 19 19 36| Scale is weakly epimorphic with val: <7 11 19 20 32| Scale is weakly epimorphic with val: <7 11 19 20 35| Scale is weakly epimorphic with val: <7 11 19 20 38| Scale is weakly epimorphic with val: <7 11 19 22 33| Scale is weakly epimorphic with val: <7 11 19 22 36| Scale is weakly epimorphic with val: <7 12 15 18 33| Scale is weakly epimorphic with val: <7 12 15 18 36| Scale is weakly epimorphic with val: <7 12 16 18 34| Scale is weakly epimorphic with val: <7 12 16 18 37| Scale is weakly epimorphic with val: <7 12 16 20 32| Scale is weakly epimorphic with val: <7 12 17 18 32| Scale is weakly epimorphic with val: <7 12 17 18 35| Scale is weakly epimorphic with val: <7 12 17 18 38| Scale is weakly epimorphic with val: <7 12 17 20 33| Scale is weakly epimorphic with val: <7 12 18 18 33| Scale is weakly epimorphic with val: <7 12 18 18 36| Scale is weakly epimorphic with val: <7 12 18 20 34| Scale is weakly epimorphic with val: <7 12 19 20 35| Scale is weakly epimorphic with val: <8 11 15 21 33| Scale is weakly epimorphic with val: <8 11 15 21 36| Scale is weakly epimorphic with val: <8 11 16 20 32| Scale is weakly epimorphic with val: <8 11 16 21 34| Scale is weakly epimorphic with val: <8 11 16 21 37| Scale is weakly epimorphic with val: <8 11 17 20 33| Scale is weakly epimorphic with val: <8 11 17 21 32| Scale is weakly epimorphic with val: <8 11 17 21 35| Scale is weakly epimorphic with val: <8 11 17 21 38| Scale is weakly epimorphic with val: <8 11 18 20 34| Scale is weakly epimorphic with val: <8 11 18 21 33| Scale is weakly epimorphic with val: <8 11 18 21 36| Scale is weakly epimorphic with val: <8 11 19 20 35| Scale is weakly epimorphic with val: <8 11 19 21 34| Scale is weakly epimorphic with val: <8 11 19 21 37| Scale is weakly epimorphic with val: <8 12 15 19 32| Scale is weakly epimorphic with val: <8 12 15 21 33| Scale is weakly epimorphic with val: <8 12 15 21 36| Scale is weakly epimorphic with val: <8 12 15 22 32| Scale is weakly epimorphic with val: <8 12 16 19 33| Scale is weakly epimorphic with val: <8 12 16 21 34| Scale is weakly epimorphic with val: <8 12 16 21 37| Scale is weakly epimorphic with val: <8 12 16 22 33| Scale is weakly epimorphic with val: <8 12 17 19 34| Scale is weakly epimorphic with val: <8 12 17 21 32| Scale is weakly epimorphic with val: <8 12 17 21 35| Scale is weakly epimorphic with val: <8 12 17 21 38| Scale is weakly epimorphic with val: <8 12 17 22 34| Scale is weakly epimorphic with val: <8 12 18 19 35| Scale is weakly epimorphic with val: <8 12 18 21 33| Scale is weakly epimorphic with val: <8 12 18 21 36| Scale is weakly epimorphic with val: <8 12 18 22 35| Scale is weakly epimorphic with val: <8 12 19 19 36| Scale is weakly epimorphic with val: <8 12 19 21 34| Scale is weakly epimorphic with val: <8 12 19 21 37| Scale is weakly epimorphic with val: <8 12 19 22 36|
FIT/MODE
3: 0 1 2 N G T3 SD: 50.6307 c. M: 65.1591 c. 4: 0 2 2 P M DE S SD: 35.4178 c. M: 58.6915 c. 5: 0 2 3 N G T3 SD: 38.5828 c. M: 58.6915 c. 6: 1 2 3 P T3 SD: 17.4149 c. M:-24.3160 c. 7: 1 2 4 N T3 SD: 12.5089 c. M: 17.7262 c. 8: 1 3 4 P T3 SD: 10.5082 c. M:-17.8484 c. 9: 1 3 5 N T3 SD: 5.9914 c. M: 9.8208 c. 15: 2 5 8 N T3 SD: 4.5118 c. M:-7.7145 c. 17: 2 6 9 N T3 SD: 1.8484 c. M:-3.2000 c. 26: 3 9 14 N T3 SD: 1.0342 c. M: 1.3072 c. 43: 5 15 23 N T3 SD: 0.5268 c. M: 0.7793 c. 67: 8 23 36 N T3 SD: 0.6175 c. M:-0.7765 c. 69: 8 24 37 N T3 SD: 0.5585 c. M: 0.9472 c. 84: 10 29 45 N T3 SD: 0.3479 c. M:-0.5996 c. 101: 12 35 54 N T3 SD: 0.4397 c. M:-0.5894 c. 110: 13 38 59 N T3 SD: 0.1800 c. M: 0.2623 c. 127: 15 44 68 N T3 SD: 0.1391 c. M:-0.2011 c. 153: 18 53 82 N T3 SD: 0.0649 c. M: 0.0980 c. 280: 33 97 150 N T3 SD: 0.0355 c. M:-0.0611 c. 390: 46 135 209 N T3 SD: 0.0348 c. M:-0.0522 c. 433: 51 150 232 N T3 SD: 0.0210 c. M: 0.0303 c. 543: 64 188 291 N T3 SD: 0.0222 c. M: 0.0372 c. 670: 79 232 359 N T3 SD: 0.0197 c. M:-0.0332 c. 823: 97 285 441 N T3 SD: 0.0055 c. M:-0.0088 c. 1256: 148 435 673 N T3 SD: 0.0037 c. M: 0.0047 c. 2079: 245 720 1114 N T3 SD: 0.0008 c. M:-0.0012 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 x 11:13 SD: 39.6850 cents 11 x 13:15 SD: 34.9349 cents 12:13:14:16 S SD: 29.1648 cents 13:14:15:17 SD: 26.3516 cents 14:15:16:19 SD: 22.6805 cents 15:16:17:20 SD: 18.3276 cents 18:19:21:24 SD: 16.6436 cents 19:20:22:25 SD: 14.6989 cents 20:21:23:27 SD: 11.7533 cents 21:22:24:28 S SD: 7.2818 cents 27:28:31:36 SD: 3.0216 cents 56:58:64:75 SD: 2.6606 cents 57:59:65:76 SD: 1.3111 cents 84:87:96:112 SD: 0.6866 cents 147:152:168:196 SD: 0.2618 cents 231:239:264:308 SD: 0.0833 cents 378:391:432:504 SD: 0.0509 cents