Scala analysis: 124_E15
Enharmonic tetrachord 25/24 * 36/35 * 56/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 15/14 119.442808 major diatonic semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 56/45 378.6022 septimal narrow major third 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 56/45 378.6022 septimal narrow major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 56/45 378.602 cents septimal narrow major third 2: 1 15/14 119.443 cents major diatonic semitone 2: 1 32/25 427.373 cents classic diminished fourth 2: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 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 : 70.7 119.4 498.0 70.7 : 48.8 427.4 498.0 119.4: 378.6 449.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 378.6022 cents 98/81, 329.8318 cents 36/35, 48.7704 cents 2: 119.4428 .. 449.2746 cents 98/81, 329.8318 cents 675/784,-259.1594 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 56/45, 378.6022 cents Average / Smallest step : 3.404013 Largest / Average step : 2.280530 Largest / Smallest step : 7.762953 Median interval of one step : 25/24, 70.6724 cents, amount: 1 Least squares average step : 128.83522 cents, oct.: 386.50565 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1205-tone equal temperament with octave 4/3 degrees: 171 289 1205 Least number of segments generator : 603 of 249.229 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 631 of 260.802 cents and inv. generated superset size: 18 = 15 more = 600.000% 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 48.77038 cents Scale diversity : 0.559850 Lumma stability : 0.195847 Lumma impropriety factor : 0.520353 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 : 875/864, 21.9020 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 Limited inverse transpositions with margin 329.8318 cents: 2 -- Rational properties -- Prime limit : 7 Odd number limit : 45 (O: 35 U: 45) Highest odd numerator or denominator: 25 Scale harmonicity : 0.029923 Average absolute harmonicity : 0.105857 Specific harmonicity : 0.145027 Fundamental : 1/168, -7.3923 octaves, 1.5573 Hz. Guide tone : 300, 8.2288 octaves, 78487.670 Hz. Exponens Consonantiae : 5.040000E+04, 15.62114 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 42.5, average 14.16667 Mersenne's string divisions : 1421 Sum of van Prooijen's expressibility: 3.05115, average 1.01705 Sum of Tenney's harmonic distance : 6.17955, average 2.05985 Vogel's harmonic complexity : 14.00000 Wille's k value : 87 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 20.39815, average 3.39969 Lattice compactness (without 2's) : 11.86710, average 1.97785 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.66667 6 3: -1 .. 1 -0.33333 3 1 5: 0 .. 2 1.00000 3 1 7: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 19 20| Scale is weakly epimorphic with val: <6 11 16 19| Scale is weakly epimorphic with val: <6 11 16 22| Scale is weakly epimorphic with val: <6 11 17 19| Scale is weakly epimorphic with val: <7 10 17 18| Scale is weakly epimorphic with val: <7 10 17 21| Scale is weakly epimorphic with val: <7 10 18 18| Scale is weakly epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 17 20| = patent Scale is weakly epimorphic with val: <7 11 18 20| Scale is weakly epimorphic with val: <7 12 17 19| Scale is weakly epimorphic with val: <7 12 18 19| Scale is weakly epimorphic with val: <7 12 18 22| Scale is weakly epimorphic with val: <8 11 18 18| Scale is weakly epimorphic with val: <8 11 19 21| Scale is weakly epimorphic with val: <8 12 19 20|
FIT/MODE
3: 0 1 2 N G T3 SD: 48.8657 c. M: 70.6724 c. 4: 1 0 3 N G T3 SD: 31.2213 c. M:-53.8388 c. 5: 1 0 4 N G T3 SD: 20.2543 c. M:-28.9366 c. 7: 1 1 5 N M DE S SD: 13.1987 c. M:-22.8558 c. 8: 1 1 6 N M DE S SD: 5.6725 c. M: 8.4168 c. 13: 2 1 10 N T3 SD: 4.3103 c. M:-5.9499 c. 20: 3 2 15 N T3 SD: 3.7401 c. M:-5.0684 c. 21: 3 2 16 N T3 SD: 0.5681 c. M: 0.8607 c. 50: 7 5 38 N T3 SD: 0.5486 c. M: 0.9461 c. 71: 10 7 54 N T3 SD: 0.3230 c. M: 0.5252 c. 92: 13 9 70 N T3 SD: 0.2627 c. M: 0.3451 c. 183: 26 18 139 N T3 SD: 0.1837 c. M:-0.3057 c. 204: 29 20 155 N T3 SD: 0.1302 c. M:-0.1856 c. 225: 32 22 171 N T3 SD: 0.1057 c. M:-0.1606 c. 275: 39 27 209 N T3 SD: 0.0559 c. M:-0.0880 c. 296: 42 29 225 N T3 SD: 0.0122 c. M:-0.0207 c. 613: 87 60 466 N T3 SD: 0.0091 c. M:-0.0126 c. 909: 129 89 691 N T3 SD: 0.0042 c. M:-0.0072 c. 1205: 171 118 916 N T3 SD: 0.0040 c. M:-0.0053 c. 2114: 300 207 1607 N T3 SD: 0.0038 c. M:-0.0057 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 x 7 SD: 84.4672 cents 6 x 7:8 S SD: 73.7140 cents 7 x 8:9 S SD: 64.1248 cents 8 x 9:11 SD: 49.9317 cents 9 x 10:12 S SD: 31.4805 cents 10 x 11:13 SD: 31.6109 cents 11 x 12:15 S SD: 24.9336 cents 12 x 13:16 SD: 9.5649 cents 13 x 14:17 SD: 17.3820 cents 14 x 15:19 SD: 15.3211 cents 15 x 16:20 S SD: 3.8558 cents 16 x 17:21 SD: 15.4371 cents 17 x 18:23 SD: 16.2676 cents 18:19 x 24 SD: 11.4653 cents 19:20 x 25 S SD: 14.6155 cents 20:21 x 27 SD: 12.7751 cents 22:23:24:29 SD: 12.4902 cents 23:24:25:31 SD: 10.4343 cents 24:25:26:32 SD: 6.3766 cents 27:28:29:36 SD: 2.9382 cents 68:71:73:91 SD: 2.7572 cents 69:72:74:92 SD: 1.1472 cents 72:75:77:96 SD: 1.0697 cents 96:100:103:128 SD: 0.8009 cents 99:103:106:132 SD: 0.8006 cents 141:147:151:188 SD: 0.5617 cents 168:175:180:224 SD: 0.0000 cents