Scala analysis: 309_C24
Chromatic tetrachord 24/23 * 23/21 * 7/6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 24/23 73.680654 vicesimotertial minor semitone 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: 24/23 73.6807 vicesimotertial minor semitone 2: 23/21 157.4934 3: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 24/23 73.681 cents vicesimotertial minor semitone 1: 1 23/21 157.493 cents 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 28/23 340.552 cents 2: 1 23/18 424.364 cents vicesimotertial major third 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 : 73.7 231.2 498.0 73.7 : 157.5 424.4 498.0 231.2: 266.9 340.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.6807 .. 266.8709 cents 161/144, 193.1903 cents 24/23, 73.6807 cents 2: 231.1741 .. 424.3643 cents 161/144, 193.1903 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 24/23, 73.6807 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 2.253169 Largest / Average step : 1.607511 Largest / Smallest step : 3.621994 Median interval of one step : 23/21, 157.4934 cents, amount: 1 Least squares average step : 145.01170 cents, oct.: 435.03511 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1521-tone equal temperament with octave 4/3 degrees: 225 706 1521 Least number of segments generator : 761 of 249.186 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1327 of 434.521 cents and inv. generated superset size: 36 = 33 more = 1200.000% 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 : 1.041654 Lumma stability : 0.295880 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 : 23 Odd number limit : 23 (O: 23 U: 23) Highest odd numerator or denominator: 23 Scale harmonicity : 0.016473 Average absolute harmonicity : 0.103498 Specific harmonicity : 0.087375 Fundamental : 1/483, -8.9159 octaves, 0.5417 Hz. Guide tone : 24, 4.5850 octaves, 6279.014 Hz. Exponens Consonantiae : 1.159200E+04, 13.50084 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 34.5, average 11.50000 Mersenne's string divisions : 4935 Sum of van Prooijen's expressibility: 2.68395, average 0.89465 Sum of Tenney's harmonic distance : 5.56931, average 1.85644 Vogel's harmonic complexity : 25.66667 Wille's k value : 80 Wilson's harmonic complexity : 36 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 14.62856, average 2.43809 Lattice compactness (without 2's) : 8.79655, average 1.46609 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -1 .. 1 0.00000 2 1 7: -1 .. 0 -0.33333 1 1 23: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is weakly epimorphic with val: <7 10 18 32| Scale is weakly epimorphic with val: <7 10 18 35| Scale is JI-epimorphic with val: <7 11 19 31| Scale is weakly epimorphic with val: <7 11 19 34| Scale is weakly epimorphic with val: <7 11 20 30| Scale is weakly epimorphic with val: <7 11 20 33| = patent Scale is weakly epimorphic with val: <7 11 20 36| Scale is weakly epimorphic with val: <7 11 22 31| Scale is weakly epimorphic with val: <7 11 22 34| Scale is weakly epimorphic with val: <7 12 18 32| Scale is weakly epimorphic with val: <7 12 18 35| Scale is weakly epimorphic with val: <7 12 20 30| Scale is weakly epimorphic with val: <8 11 20 32| Scale is weakly epimorphic with val: <8 11 21 31| Scale is weakly epimorphic with val: <8 11 21 34| Scale is weakly epimorphic with val: <8 12 19 33| Scale is weakly epimorphic with val: <8 12 21 31| Scale is weakly epimorphic with val: <8 12 21 34| Scale is weakly epimorphic with val: <8 12 22 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 56.7878 c. M: 73.6807 c. 4: 1 1 2 P M ME S SD: 31.1037 c. M:-50.8306 c. 5: 1 1 3 N M DE S SD: 23.7590 c. M: 31.9561 c. 6: 1 2 3 P T3 SD: 11.6269 c. M:-17.8484 c. 7: 1 2 4 N T3 SD: 10.3381 c. M: 17.7262 c. 11: 2 3 6 N T3 SD: 10.1266 c. M:-16.8730 c. 13: 2 4 7 N T3 SD: 1.8585 c. M:-2.9417 c. 28: 4 9 15 N T3 SD: 1.4619 c. M: 2.5314 c. 41: 6 13 22 N T3 SD: 0.5075 c. M: 0.7960 c. 54: 8 17 29 N T3 SD: 0.3502 c. M: 0.5977 c. 95: 14 30 51 N T3 SD: 0.3325 c. M: 0.5006 c. 129: 19 41 69 N T3 SD: 0.3322 c. M:-0.4747 c. 136: 20 43 73 N T3 SD: 0.3679 c. M: 0.4621 c. 142: 21 45 76 N T3 SD: 0.1805 c. M:-0.3116 c. 155: 23 49 83 N T3 SD: 0.1639 c. M:-0.2228 c. 183: 27 58 98 N T3 SD: 0.1466 c. M: 0.1986 c. 196: 29 62 105 N T3 SD: 0.0357 c. M:-0.0611 c. 446: 66 141 239 N T3 SD: 0.0163 c. M:-0.0211 c. 642: 95 203 344 N T3 SD: 0.0107 c. M:-0.0176 c. 1075: 159 340 576 N T3 SD: 0.0115 c. M: 0.0163 c. 1088: 161 344 583 N T3 SD: 0.0113 c. M:-0.0190 c. 1129: 167 357 605 N T3 SD: 0.0119 c. M: 0.0177 c. 1325: 196 419 710 N T3 SD: 0.0056 c. M: 0.0076 c. 1521: 225 481 815 N T3 SD: 0.0034 c. M: 0.0054 c. 1967: 291 622 1054 N T3 SD: 0.0013 c. M: 0.0022 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 11:12:13:15 SD: 34.6476 cents 12:13:14:16 S SD: 24.6875 cents 13:14:15:17 SD: 22.0798 cents 14:15:16:19 SD: 18.3579 cents 15:16:17:20 SD: 13.5718 cents 19:20:22:25 SD: 11.8630 cents 20:21:23:27 SD: 8.7890 cents 21:22:24:28 S SD: 2.2855 cents 48:50:55:64 SD: 1.8050 cents 69:72:79:92 SD: 1.0445 cents 90:94:103:120 SD: 0.9627 cents 141:147:161:188 SD: 0.7238 cents 162:169:185:216 SD: 0.4695 cents 183:191:209:244 SD: 0.4156 cents 210:219:240:280 SD: 0.3436 cents 231:241:264:308 SD: 0.1041 cents 252:263:288:336 SD: 0.0954 cents 483:504:552:644 SD: 0.0000 cents