Scala analysis: 138_C2
Chromatic tetrachord 24/23 * 161/156 * 26/21
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: 14/13 128.298245 2/3-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 26/21 369.7468 1: 24/23 73.6807 vicesimotertial minor semitone 2: 161/156 54.6176 3: 26/21 369.7468
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 161/156 54.618 cents 1: 1 24/23 73.681 cents vicesimotertial minor semitone 1: 1 26/21 369.747 cents 2: 1 14/13 128.298 cents 2/3-tone 2: 1 23/18 424.364 cents vicesimotertial major third 2: 1 208/161 443.427 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 : 73.7 128.3 498.0 73.7 : 54.6 424.4 498.0 128.3: 369.7 443.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.6176 .. 369.7468 cents 1352/1127, 315.1292 cents 161/156, 54.6176 cents 2: 128.2982 .. 443.4274 cents 1352/1127, 315.1292 cents 147/169,-241.4485 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 161/156, 54.6176 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 26/21, 369.7468 cents Average / Smallest step : 3.039588 Largest / Average step : 2.227189 Largest / Smallest step : 6.769737 Median interval of one step : 24/23, 73.6807 cents, amount: 1 Least squares average step : 130.31515 cents, oct.: 390.94546 cents Scale is not proper Scale has trivalence property 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 54.61759 cents Scale diversity : 0.631037 Lumma stability : 0.219328 Lumma impropriety factor : 0.484793 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 : 3744/3703, 19.0631 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% Limited inverse transpositions with margin 315.1292 cents: 2 -- Rational properties -- Prime limit : 23 Odd number limit : 161 (O: 161 U: 161) Highest odd numerator or denominator: 23 Scale harmonicity : 0.012069 Average absolute harmonicity : 0.088377 Specific harmonicity : 0.064107 Fundamental : 1/897, -9.8090 octaves, 0.2917 Hz. Guide tone : 168, 7.3923 octaves, 43953.095 Hz. Exponens Consonantiae : 1.506960E+05, 17.20128 octaves Euler's gradus suavitatis : 48 Sum of Mann's harmonic distance : 40.5, average 13.50000 Mersenne's string divisions : 8883 Sum of van Prooijen's expressibility: 2.95279, average 0.98426 Sum of Tenney's harmonic distance : 6.08119, average 2.02706 Vogel's harmonic complexity : 31.33333 Wille's k value : 241 Wilson's harmonic complexity : 49 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 14.56266, average 2.42711 Lattice compactness (without 2's) : 9.79655, average 1.63276 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 7: 0 .. 1 0.33333 1 13: -1 .. 0 -0.33333 1 1 23: -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 22 25 30| Scale is weakly epimorphic with val: <6 10 22 25 33| Scale is weakly epimorphic with val: <6 10 22 25 36| Scale is weakly epimorphic with val: <6 11 22 25 30| Scale is weakly epimorphic with val: <6 11 22 25 33| Scale is weakly epimorphic with val: <6 11 22 25 36| Scale is weakly epimorphic with val: <7 10 21 25 32| Scale is weakly epimorphic with val: <7 10 21 25 35| Scale is weakly epimorphic with val: <7 10 22 26 32| Scale is weakly epimorphic with val: <7 10 22 26 35| Scale is weakly epimorphic with val: <7 11 18 26 31| Scale is weakly epimorphic with val: <7 11 18 26 34| Scale is weakly epimorphic with val: <7 11 18 27 30| Scale is weakly epimorphic with val: <7 11 18 27 33| Scale is weakly epimorphic with val: <7 11 18 27 36| Scale is weakly epimorphic with val: <7 11 18 29 31| Scale is weakly epimorphic with val: <7 11 18 29 34| Scale is weakly epimorphic with val: <7 11 18 30 30| Scale is weakly epimorphic with val: <7 11 18 30 33| Scale is weakly epimorphic with val: <7 11 18 30 36| Scale is weakly epimorphic with val: <7 11 19 25 30| Scale is weakly epimorphic with val: <7 11 19 25 33| Scale is weakly epimorphic with val: <7 11 19 25 36| Scale is weakly epimorphic with val: <7 11 19 27 31| Scale is weakly epimorphic with val: <7 11 19 27 34| Scale is weakly epimorphic with val: <7 11 19 28 30| Scale is weakly epimorphic with val: <7 11 19 28 33| Scale is weakly epimorphic with val: <7 11 19 28 36| Scale is weakly epimorphic with val: <7 11 19 30 31| Scale is weakly epimorphic with val: <7 11 19 30 34| Scale is JI-epimorphic with val: <7 11 20 25 31| Scale is weakly epimorphic with val: <7 11 20 25 34| Scale is weakly epimorphic with val: <7 11 20 26 30| Scale is weakly epimorphic with val: <7 11 20 26 33| Scale is weakly epimorphic with val: <7 11 20 26 36| Scale is weakly epimorphic with val: <7 11 20 28 31| Scale is weakly epimorphic with val: <7 11 20 28 34| Scale is weakly epimorphic with val: <7 11 20 29 30| Scale is weakly epimorphic with val: <7 11 20 29 33| Scale is weakly epimorphic with val: <7 11 20 29 36| Scale is JI-epimorphic with val: <7 11 21 26 31| Scale is weakly epimorphic with val: <7 11 21 26 34| Scale is weakly epimorphic with val: <7 11 21 27 30| Scale is weakly epimorphic with val: <7 11 21 27 33| Scale is weakly epimorphic with val: <7 11 21 27 36| Scale is weakly epimorphic with val: <7 11 21 29 31| Scale is weakly epimorphic with val: <7 11 21 29 34| Scale is weakly epimorphic with val: <7 11 21 30 30| Scale is weakly epimorphic with val: <7 11 21 30 33| Scale is weakly epimorphic with val: <7 11 21 30 36| Scale is weakly epimorphic with val: <7 11 22 25 30| Scale is weakly epimorphic with val: <7 11 22 25 33| Scale is weakly epimorphic with val: <7 11 22 25 36| Scale is JI-epimorphic with val: <7 11 22 27 31| Scale is weakly epimorphic with val: <7 11 22 27 34| Scale is weakly epimorphic with val: <7 11 22 28 30| Scale is weakly epimorphic with val: <7 11 22 28 33| Scale is weakly epimorphic with val: <7 11 22 28 36| Scale is weakly epimorphic with val: <7 11 22 30 31| Scale is weakly epimorphic with val: <7 11 22 30 34| Scale is weakly epimorphic with val: <7 12 18 27 30| Scale is weakly epimorphic with val: <7 12 18 30 30| Scale is weakly epimorphic with val: <7 12 19 25 30| Scale is weakly epimorphic with val: <7 12 19 28 30| Scale is weakly epimorphic with val: <7 12 20 26 30| Scale is weakly epimorphic with val: <7 12 20 29 30| Scale is weakly epimorphic with val: <7 12 21 25 32| Scale is weakly epimorphic with val: <7 12 21 25 35| Scale is weakly epimorphic with val: <7 12 21 27 30| Scale is weakly epimorphic with val: <7 12 21 30 30| Scale is weakly epimorphic with val: <7 12 22 25 30| Scale is weakly epimorphic with val: <7 12 22 26 32| Scale is weakly epimorphic with val: <7 12 22 26 35| Scale is weakly epimorphic with val: <7 12 22 28 30| Scale is weakly epimorphic with val: <8 11 18 25 32| Scale is weakly epimorphic with val: <8 11 18 28 32| Scale is weakly epimorphic with val: <8 11 19 26 32| Scale is weakly epimorphic with val: <8 11 19 29 32| Scale is weakly epimorphic with val: <8 11 20 25 31| Scale is weakly epimorphic with val: <8 11 20 25 34| Scale is weakly epimorphic with val: <8 11 20 27 32| Scale is weakly epimorphic with val: <8 11 20 30 32| Scale is weakly epimorphic with val: <8 11 21 25 32| Scale is weakly epimorphic with val: <8 11 21 26 31| Scale is weakly epimorphic with val: <8 11 21 26 34| Scale is weakly epimorphic with val: <8 11 21 28 32| Scale is weakly epimorphic with val: <8 11 22 26 32| Scale is weakly epimorphic with val: <8 11 22 27 31| Scale is weakly epimorphic with val: <8 11 22 27 34| Scale is weakly epimorphic with val: <8 11 22 29 32| Scale is weakly epimorphic with val: <8 12 18 27 33| Scale is weakly epimorphic with val: <8 12 18 30 33| Scale is weakly epimorphic with val: <8 12 19 25 33| Scale is weakly epimorphic with val: <8 12 19 28 33| Scale is weakly epimorphic with val: <8 12 20 25 31| Scale is weakly epimorphic with val: <8 12 20 25 34| Scale is weakly epimorphic with val: <8 12 20 26 33| Scale is weakly epimorphic with val: <8 12 20 29 33| Scale is weakly epimorphic with val: <8 12 21 26 31| Scale is weakly epimorphic with val: <8 12 21 26 34| Scale is weakly epimorphic with val: <8 12 21 27 33| Scale is weakly epimorphic with val: <8 12 21 30 33| Scale is weakly epimorphic with val: <8 12 22 25 33| Scale is weakly epimorphic with val: <8 12 22 27 31| Scale is weakly epimorphic with val: <8 12 22 27 34| Scale is weakly epimorphic with val: <8 12 22 28 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 47.7891 c. M: 73.6807 c. 4: 1 0 3 N G T3 SD: 29.4284 c. M:-50.8306 c. 5: 1 0 4 N G T3 SD: 22.3260 c. M: 28.6892 c. 6: 1 1 4 N M DE S SD: 22.4317 c. M:-37.7168 c. 7: 1 1 5 N M DE S SD: 8.2142 c. M:-14.0003 c. 8: 1 1 6 N M DE S SD: 6.9492 c. M: 11.4250 c. 12: 2 1 9 N T3 SD: 5.8118 c. M:-9.3268 c. 15: 2 2 11 N M DE S SD: 4.9428 c. M: 7.2747 c. 19: 3 2 14 N T3 SD: 3.2779 c. M:-4.9580 c. 20: 3 2 15 N T3 SD: 2.2653 c. M: 3.7870 c. 27: 4 3 20 N T3 SD: 0.4798 c. M:-0.8245 c. 74: 11 8 55 N T3 SD: 0.3176 c. M: 0.4218 c. 101: 15 11 75 N T3 SD: 0.1731 c. M:-0.2864 c. 128: 19 14 95 N T3 SD: 0.1552 c. M:-0.2479 c. 155: 23 17 115 N T3 SD: 0.1847 c. M:-0.2295 c. 190: 28 21 141 N T3 SD: 0.1844 c. M: 0.2845 c. 210: 31 23 156 N T3 SD: 0.1614 c. M: 0.2295 c. 229: 34 25 170 N T3 SD: 0.1533 c. M:-0.2649 c. 237: 35 26 176 N T3 SD: 0.0980 c. M: 0.1297 c. 264: 39 29 196 N T3 SD: 0.0616 c. M: 0.1058 c. 291: 43 32 216 N T3 SD: 0.0620 c. M: 0.0864 c. 338: 50 37 251 N T3 SD: 0.0597 c. M: 0.1032 c. 365: 54 40 271 N T3 SD: 0.0200 c. M: 0.0346 c. 392: 58 43 291 N T3 SD: 0.0152 c. M:-0.0246 c. 757: 112 83 562 N T3 SD: 0.0043 c. M:-0.0063 c. 1906: 282 209 1415 N T3 SD: 0.0042 c. M:-0.0070 c. 2170: 321 238 1611 N T3 SD: 0.0039 c. M: 0.0067 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: 69.2863 cents 7 x 8:9 S SD: 60.3065 cents 8 x 9:11 SD: 46.2470 cents 9 x 10:12 S SD: 27.0527 cents 10 x 11:13 SD: 28.5854 cents 11 x 12:15 S SD: 22.4315 cents 12 x 13:16 SD: 5.1372 cents 13 x 14:17 SD: 16.8086 cents 14 x 15:19 SD: 15.9480 cents 15 x 16:20 S SD: 8.2835 cents 16 x 17:21 SD: 17.9459 cents 17:18 x 23 SD: 17.8714 cents 18:19 x 24 SD: 9.9612 cents 19:20 x 25 S SD: 13.7334 cents 21:22:23:28 SD: 9.9965 cents 23:24:25:31 SD: 8.2196 cents 24:25:26:32 SD: 3.5686 cents 51:53:55:68 SD: 2.4964 cents 66:69:71:88 SD: 1.2581 cents 90:94:97:120 SD: 0.7035 cents 117:122:126:156 SD: 0.4112 cents 183:191:197:244 SD: 0.2608 cents 207:216:223:276 SD: 0.1991 cents 300:313:323:400 SD: 0.1591 cents 390:407:420:520 SD: 0.0617 cents 507:529:546:676 SD: 0.0474 cents