Scala analysis: 325_C24
Chromatic tetrachord 120/119 * 17/15 * 7/6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 120/119 14.487399 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: 120/119 14.4874 2: 17/15 216.6867 septendecimal whole tone 3: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 120/119 14.487 cents 1: 1 17/15 216.687 cents septendecimal whole tone 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 20/17 281.358 cents septendecimal augmented second 2: 1 119/90 483.558 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 : 14.5 231.2 498.0 14.5 : 216.7 483.6 498.0 231.2: 266.9 281.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 14.4874 .. 266.8709 cents 833/720, 252.3835 cents 120/119, 14.4874 cents 2: 231.1741 .. 483.5576 cents 833/720, 252.3835 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 120/119, 14.4874 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 11.459269 Largest / Average step : 1.607511 Largest / Smallest step : 18.420899 Median interval of one step : 17/15, 216.6867 cents, amount: 1 Least squares average step : 140.78361 cents, oct.: 422.35084 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1409-tone equal temperament with octave 4/3 degrees: 41 654 1409 Least number of segments generator : 705 of 249.199 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1021 of 360.897 cents and inv. generated superset size: 39 = 36 more = 1300.000% 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 14.48740 cents Scale diversity : 0.397283 Lumma stability : 0.058177 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 : 120/119, 14.4874 cents Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 483.5576 cents Number of appreciable fourths : 0 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 : 17 Odd number limit : 119 (O: 119 U: 119) Highest odd numerator or denominator: 119 Scale harmonicity : 0.018137 Average absolute harmonicity : 0.102871 Specific harmonicity : 0.090551 Fundamental : 1/357, -8.4798 octaves, 0.7328 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 4.284000E+04, 15.38667 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 130.5, average 43.50000 Mersenne's string divisions : 25095 Sum of van Prooijen's expressibility: 3.39777, average 1.13259 Sum of Tenney's harmonic distance : 6.98210, average 2.32737 Vogel's harmonic complexity : 21.00000 Wille's k value : 59 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 15.29643, average 2.54940 Lattice compactness (without 2's) : 9.79202, average 1.63200 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 -0.66667 2 1 17: -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: <7 10 15 18 29| Scale is weakly epimorphic with val: <7 10 15 18 32| Scale is weakly epimorphic with val: <7 10 16 18 27| Scale is weakly epimorphic with val: <7 10 16 18 30| Scale is weakly epimorphic with val: <7 10 16 18 33| Scale is weakly epimorphic with val: <7 10 17 18 28| Scale is weakly epimorphic with val: <7 10 17 18 31| Scale is weakly epimorphic with val: <7 10 18 18 29| Scale is weakly epimorphic with val: <7 10 18 18 32| Scale is weakly epimorphic with val: <7 10 18 19 27| Scale is weakly epimorphic with val: <7 10 19 19 28| Scale is JI-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 19 33| Scale is weakly epimorphic with val: <7 11 15 20 28| Scale is weakly epimorphic with val: <7 11 15 20 31| Scale is weakly epimorphic with val: <7 11 15 22 27| Scale is weakly epimorphic with val: <7 11 15 22 30| Scale is weakly epimorphic with val: <7 11 15 22 33| Scale is JI-epimorphic with val: <7 11 16 19 28| Scale is weakly epimorphic with val: <7 11 16 19 31| Scale is weakly epimorphic with val: <7 11 16 20 29| Scale is weakly epimorphic with val: <7 11 16 20 32| Scale is weakly epimorphic with val: <7 11 16 22 28| Scale is weakly epimorphic with val: <7 11 16 22 31| Scale is JI-epimorphic with val: <7 11 17 19 29| Scale is weakly epimorphic with val: <7 11 17 19 32| Scale is weakly epimorphic with val: <7 11 17 20 27| Scale is weakly epimorphic with val: <7 11 17 20 30| = patent Scale is weakly epimorphic with val: <7 11 17 20 33| Scale is weakly epimorphic with val: <7 11 17 22 29| Scale is weakly epimorphic with val: <7 11 17 22 32| 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 19 33| Scale is weakly epimorphic with val: <7 11 18 20 28| Scale is weakly epimorphic with val: <7 11 18 20 31| 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 18 22 33| Scale is weakly epimorphic with val: <7 11 19 19 28| Scale is JI-epimorphic with val: <7 11 19 19 31| Scale is weakly epimorphic with val: <7 11 19 20 29| Scale is weakly epimorphic with val: <7 11 19 20 32| Scale is weakly epimorphic with val: <7 11 19 22 28| Scale is weakly epimorphic with val: <7 11 19 22 31| Scale is weakly epimorphic with val: <7 12 15 18 29| Scale is weakly epimorphic with val: <7 12 15 18 32| Scale is weakly epimorphic with val: <7 12 16 18 27| Scale is weakly epimorphic with val: <7 12 16 18 30| Scale is weakly epimorphic with val: <7 12 16 18 33| Scale is weakly epimorphic with val: <7 12 17 18 28| Scale is weakly epimorphic with val: <7 12 17 18 31| Scale is weakly epimorphic with val: <7 12 17 20 27| Scale is weakly epimorphic with val: <7 12 18 18 29| Scale is weakly epimorphic with val: <7 12 18 18 32| Scale is weakly epimorphic with val: <7 12 18 20 28| Scale is weakly epimorphic with val: <7 12 19 20 29| Scale is weakly epimorphic with val: <8 11 15 20 27| Scale is weakly epimorphic with val: <8 11 15 21 28| Scale is weakly epimorphic with val: <8 11 15 21 31| Scale is weakly epimorphic with val: <8 11 16 20 28| Scale is weakly epimorphic with val: <8 11 16 21 29| Scale is weakly epimorphic with val: <8 11 16 21 32| 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 17 21 30| Scale is weakly epimorphic with val: <8 11 17 21 33| Scale is weakly epimorphic with val: <8 11 18 20 30| Scale is weakly epimorphic with val: <8 11 18 21 28| Scale is weakly epimorphic with val: <8 11 18 21 31| Scale is weakly epimorphic with val: <8 11 19 20 31| Scale is weakly epimorphic with val: <8 11 19 21 29| Scale is weakly epimorphic with val: <8 11 19 21 32| Scale is weakly epimorphic with val: <8 12 15 19 29| Scale is weakly epimorphic with val: <8 12 15 21 28| Scale is weakly epimorphic with val: <8 12 15 21 31| Scale is weakly epimorphic with val: <8 12 16 19 30| Scale is weakly epimorphic with val: <8 12 16 21 29| Scale is weakly epimorphic with val: <8 12 16 21 32| Scale is weakly epimorphic with val: <8 12 16 22 27| Scale is weakly epimorphic with val: <8 12 17 19 31| Scale is weakly epimorphic with val: <8 12 17 21 27| Scale is weakly epimorphic with val: <8 12 17 21 30| Scale is weakly epimorphic with val: <8 12 17 21 33| Scale is weakly epimorphic with val: <8 12 17 22 28| Scale is weakly epimorphic with val: <8 12 18 19 32| Scale is weakly epimorphic with val: <8 12 18 21 28| Scale is weakly epimorphic with val: <8 12 18 21 31| Scale is weakly epimorphic with val: <8 12 18 22 29| Scale is weakly epimorphic with val: <8 12 19 19 33| Scale is weakly epimorphic with val: <8 12 19 21 29| Scale is weakly epimorphic with val: <8 12 19 21 32| Scale is weakly epimorphic with val: <8 12 19 22 30|
FIT/MODE
3: 0 1 2 N G T3 SD: 38.5383 c. M: 65.1591 c. 4: 0 2 2 P M DE S SD: 13.2722 c. M:-17.8484 c. 7: 0 3 4 N G T3 SD: 13.2175 c. M: 17.7262 c. 9: 0 4 5 N G T3 SD: 10.1050 c. M: 14.4874 c. 11: 0 5 6 N G T3 SD: 8.8096 c. M: 14.4874 c. 13: 0 6 7 N G T3 SD: 8.3983 c. M: 14.4874 c. 15: 0 7 8 N G T3 SD: 8.3952 c. M: 14.4874 c. 19: 1 8 10 N T3 SD: 7.3024 c. M:-11.7255 c. 21: 1 9 11 N T3 SD: 6.3524 c. M:-9.2290 c. 22: 1 9 12 N T3 SD: 5.4584 c. M:-8.1510 c. 23: 1 10 12 N T3 SD: 5.7926 c. M:-7.1667 c. 24: 1 10 13 N T3 SD: 3.9864 c. M:-6.2645 c. 26: 1 11 14 N T3 SD: 2.7988 c. M:-4.6682 c. 28: 1 12 15 N T3 SD: 1.9055 c. M:-3.2999 c. 30: 1 13 16 N T3 SD: 1.4171 c. M:-2.1141 c. 39: 1 17 21 N T3 SD: 1.2459 c. M: 1.7170 c. 65: 2 28 35 N T3 SD: 0.8962 c. M: 1.3072 c. 67: 2 29 36 N T3 SD: 0.4778 c. M: 0.7354 c. 69: 2 30 37 N T3 SD: 0.1174 c. M: 0.1967 c. 209: 6 91 112 N T3 SD: 0.1103 c. M: 0.1895 c. 239: 7 104 128 N T3 SD: 0.0971 c. M:-0.1355 c. 308: 9 134 165 N T3 SD: 0.0519 c. M:-0.0659 c. 377: 11 164 202 N T3 SD: 0.0269 c. M:-0.0444 c. 446: 13 194 239 N T3 SD: 0.0202 c. M:-0.0296 c. 586: 17 255 314 N T3 SD: 0.0225 c. M: 0.0390 c. 655: 19 285 351 N T3 SD: 0.0261 c. M: 0.0403 c. 823: 24 358 441 N T3 SD: 0.0211 c. M:-0.0364 c. 894: 26 389 479 N T3 SD: 0.0124 c. M:-0.0213 c. 963: 28 419 516 N T3 SD: 0.0049 c. M: 0.0063 c. 1409: 41 613 755 N T3 SD: 0.0031 c. M:-0.0050 c. 2372: 69 1032 1271 N T3 SD: 0.0007 c. M:-0.0011 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 x 14:16 S SD: 17.8484 cents 13 x 15:17 SD: 18.7389 cents 26:27:30:35 S SD: 18.6626 cents 27:28:31:36 SD: 16.3762 cents 28:29:32:37 SD: 16.2666 cents 29:30:33:39 SD: 15.7437 cents 30:31:34:40 SD: 14.8976 cents 33:34:38:44 SD: 13.1411 cents 34:35:39:45 SD: 12.8144 cents 35:36:40:47 SD: 12.1434 cents 36:37:41:48 SD: 11.1641 cents 40:41:46:53 SD: 10.7127 cents 41:42:47:55 SD: 9.8886 cents 42:43:48:56 SD: 8.7498 cents 47:48:54:63 S SD: 8.5048 cents 48:49:55:64 SD: 7.2274 cents 51:52:58:68 SD: 6.9787 cents 54:55:62:72 SD: 6.3466 cents 55:56:63:73 SD: 6.2961 cents 56:57:64:75 SD: 5.9670 cents 57:58:65:76 SD: 5.3592 cents 62:63:71:83 SD: 5.1129 cents 63:64:72:84 S SD: 4.2589 cents 69:70:79:92 SD: 3.6279 cents 75:76:86:100 SD: 3.4072 cents 77:78:88:103 SD: 3.2169 cents 78:79:89:104 SD: 2.6867 cents 84:85:96:112 SD: 2.0003 cents 90:91:103:120 SD: 1.7425 cents 99:100:113:132 SD: 1.2140 cents 105:106:120:140 SD: 0.6408 cents 120:121:137:160 SD: 0.6028 cents 126:127:144:168 SD: 0.2672 cents 231:233:264:308 SD: 0.1457 cents 357:360:408:476 SD: 0.0000 cents