Scala analysis: 157_C5
Chromatic tetrachord 20/19 * 38/37 * 37/30
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 20/19 88.800698 small undevicesimal semitone 2: 40/37 134.969675 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 37/30 363.0753 1: 20/19 88.8007 small undevicesimal semitone 2: 38/37 46.1690 3: 37/30 363.0753
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 38/37 46.169 cents 1: 1 20/19 88.801 cents small undevicesimal semitone 1: 1 37/30 363.075 cents 2: 1 40/37 134.970 cents 2: 1 19/15 409.244 cents undevicesimal ditone 2: 1 74/57 451.876 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 : 88.8 135.0 498.0 88.8 : 46.2 409.2 498.0 135.0: 363.1 451.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 46.1690 .. 363.0753 cents 1369/1140, 316.9063 cents 38/37, 46.1690 cents 2: 134.9697 .. 451.8760 cents 1369/1140, 316.9063 cents 1200/1369,-228.1056 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 38/37, 46.1690 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 37/30, 363.0753 cents Average / Smallest step : 3.595813 Largest / Average step : 2.187003 Largest / Smallest step : 7.864054 Median interval of one step : 20/19, 88.8007 cents, amount: 1 Least squares average step : 132.34822 cents, oct.: 397.04465 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1262-tone equal temperament with octave 4/3 degrees: 225 342 1262 Least number of segments generator : 633 of 249.812 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1253 of 494.493 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 : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 46.16898 cents Scale diversity : 0.644646 Lumma stability : 0.185401 Lumma impropriety factor : 0.458002 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 : 370/361, 42.6317 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 -- Rational properties -- Prime limit : 37 Odd number limit : 57 (O: 37 U: 57) Highest odd numerator or denominator: 37 Scale harmonicity : 0.021658 Fundamental : 1/2109, -11.0423 octaves, 0.1241 Hz. Guide tone : 40, 5.3219 octaves, 10465.023 Hz. Exponens Consonantiae : 8.436000E+04, 16.36427 octaves Euler's gradus suavitatis : 64 Sum of Mann's harmonic distance : 61.5, average 20.50000 Mersenne's string divisions : 3003 Sum of van Prooijen's expressibility: 3.32408, average 1.10803 Sum of Tenney's harmonic distance : 6.82923, average 2.27641 Vogel's harmonic complexity : 45.00000 Wille's k value : 351 Wilson's harmonic complexity : 64 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 12.72615, average 2.12103 Lattice compactness (without 2's) : 7.56048, average 1.26008 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 0 -0.33333 1 1 5: 0 .. 1 0.66667 2 19: -1 .. 0 -0.33333 1 1 37: -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 28 36| Scale is weakly epimorphic with val: <6 10 19 28 39| Scale is weakly epimorphic with val: <6 11 19 28 35| Scale is weakly epimorphic with val: <6 11 19 28 38| Scale is weakly epimorphic with val: <6 11 19 28 41| Scale is weakly epimorphic with val: <7 10 17 28 36| Scale is weakly epimorphic with val: <7 10 17 28 39| Scale is weakly epimorphic with val: <7 10 17 29 35| Scale is weakly epimorphic with val: <7 10 17 32 35| Scale is weakly epimorphic with val: <7 10 18 29 37| Scale is weakly epimorphic with val: <7 10 18 29 40| Scale is weakly epimorphic with val: <7 10 18 30 36| Scale is weakly epimorphic with val: <7 10 18 33 36| Scale is weakly epimorphic with val: <7 10 19 28 37| Scale is weakly epimorphic with val: <7 10 19 30 35| Scale is weakly epimorphic with val: <7 10 19 30 38| Scale is weakly epimorphic with val: <7 10 19 30 41| Scale is weakly epimorphic with val: <7 10 19 31 37| Scale is weakly epimorphic with val: <7 10 19 34 37| Scale is weakly epimorphic with val: <7 11 15 28 37| Scale is weakly epimorphic with val: <7 11 15 28 40| Scale is weakly epimorphic with val: <7 11 15 30 35| Scale is weakly epimorphic with val: <7 11 15 30 38| Scale is weakly epimorphic with val: <7 11 15 30 41| Scale is weakly epimorphic with val: <7 11 15 31 37| Scale is weakly epimorphic with val: <7 11 15 31 40| Scale is weakly epimorphic with val: <7 11 15 33 35| Scale is weakly epimorphic with val: <7 11 15 33 38| Scale is weakly epimorphic with val: <7 11 15 33 41| Scale is weakly epimorphic with val: <7 11 15 34 37| Scale is weakly epimorphic with val: <7 11 15 34 40| Scale is weakly epimorphic with val: <7 11 16 28 36| Scale is weakly epimorphic with val: <7 11 16 28 39| Scale is JI-epimorphic with val: <7 11 16 29 35| Scale is weakly epimorphic with val: <7 11 16 29 38| Scale is weakly epimorphic with val: <7 11 16 29 41| Scale is weakly epimorphic with val: <7 11 16 31 36| Scale is weakly epimorphic with val: <7 11 16 31 39| Scale is weakly epimorphic with val: <7 11 16 32 35| Scale is weakly epimorphic with val: <7 11 16 32 38| Scale is weakly epimorphic with val: <7 11 16 32 41| Scale is weakly epimorphic with val: <7 11 16 34 36| Scale is weakly epimorphic with val: <7 11 16 34 39| Scale is weakly epimorphic with val: <7 11 17 29 37| Scale is weakly epimorphic with val: <7 11 17 29 40| Scale is JI-epimorphic with val: <7 11 17 30 36| Scale is weakly epimorphic with val: <7 11 17 30 39| Scale is weakly epimorphic with val: <7 11 17 32 37| Scale is weakly epimorphic with val: <7 11 17 32 40| Scale is weakly epimorphic with val: <7 11 17 33 36| Scale is weakly epimorphic with val: <7 11 17 33 39| Scale is weakly epimorphic with val: <7 11 18 28 37| Scale is weakly epimorphic with val: <7 11 18 28 40| Scale is weakly epimorphic with val: <7 11 18 30 35| Scale is weakly epimorphic with val: <7 11 18 30 38| Scale is weakly epimorphic with val: <7 11 18 30 41| Scale is JI-epimorphic with val: <7 11 18 31 37| Scale is weakly epimorphic with val: <7 11 18 31 40| Scale is weakly epimorphic with val: <7 11 18 33 35| Scale is weakly epimorphic with val: <7 11 18 33 38| Scale is weakly epimorphic with val: <7 11 18 33 41| Scale is weakly epimorphic with val: <7 11 18 34 37| Scale is weakly epimorphic with val: <7 11 18 34 40| Scale is weakly epimorphic with val: <7 11 19 28 36| Scale is weakly epimorphic with val: <7 11 19 28 39| Scale is weakly epimorphic with val: <7 11 19 29 35| Scale is weakly epimorphic with val: <7 11 19 29 38| Scale is weakly epimorphic with val: <7 11 19 29 41| Scale is weakly epimorphic with val: <7 11 19 31 36| Scale is weakly epimorphic with val: <7 11 19 31 39| Scale is weakly epimorphic with val: <7 11 19 32 35| Scale is JI-epimorphic with val: <7 11 19 32 38| Scale is weakly epimorphic with val: <7 11 19 32 41| Scale is weakly epimorphic with val: <7 11 19 34 36| Scale is weakly epimorphic with val: <7 11 19 34 39| Scale is weakly epimorphic with val: <7 12 17 28 37| Scale is weakly epimorphic with val: <7 12 17 28 40| Scale is weakly epimorphic with val: <7 12 17 30 35| Scale is weakly epimorphic with val: <7 12 17 33 35| Scale is weakly epimorphic with val: <7 12 18 28 36| Scale is weakly epimorphic with val: <7 12 18 29 35| Scale is weakly epimorphic with val: <7 12 18 29 38| Scale is weakly epimorphic with val: <7 12 18 29 41| Scale is weakly epimorphic with val: <7 12 18 31 36| Scale is weakly epimorphic with val: <7 12 18 34 36| Scale is weakly epimorphic with val: <7 12 19 29 37| Scale is weakly epimorphic with val: <7 12 19 30 36| Scale is weakly epimorphic with val: <7 12 19 30 39| Scale is weakly epimorphic with val: <7 12 19 32 37| Scale is weakly epimorphic with val: <8 11 15 28 35| Scale is weakly epimorphic with val: <8 11 15 28 38| Scale is weakly epimorphic with val: <8 11 15 28 41| Scale is weakly epimorphic with val: <8 11 15 30 36| Scale is weakly epimorphic with val: <8 11 15 33 36| Scale is weakly epimorphic with val: <8 11 16 28 37| Scale is weakly epimorphic with val: <8 11 16 29 36| Scale is weakly epimorphic with val: <8 11 16 29 39| Scale is weakly epimorphic with val: <8 11 16 31 37| Scale is weakly epimorphic with val: <8 11 16 34 37| Scale is weakly epimorphic with val: <8 11 17 29 38| Scale is weakly epimorphic with val: <8 11 17 30 37| Scale is weakly epimorphic with val: <8 11 17 30 40| Scale is weakly epimorphic with val: <8 11 17 32 38| Scale is weakly epimorphic with val: <8 11 18 30 39| Scale is weakly epimorphic with val: <8 11 18 31 35| Scale is weakly epimorphic with val: <8 11 18 31 38| Scale is weakly epimorphic with val: <8 11 18 31 41| Scale is weakly epimorphic with val: <8 11 18 33 39| Scale is weakly epimorphic with val: <8 11 19 28 40| Scale is weakly epimorphic with val: <8 11 19 31 40| Scale is weakly epimorphic with val: <8 11 19 32 36| Scale is weakly epimorphic with val: <8 11 19 32 39| Scale is weakly epimorphic with val: <8 11 19 34 40| Scale is weakly epimorphic with val: <8 12 15 28 37| Scale is weakly epimorphic with val: <8 12 15 28 40| Scale is weakly epimorphic with val: <8 12 15 29 36| Scale is weakly epimorphic with val: <8 12 15 32 36| Scale is weakly epimorphic with val: <8 12 16 29 35| Scale is weakly epimorphic with val: <8 12 16 29 38| Scale is weakly epimorphic with val: <8 12 16 29 41| Scale is weakly epimorphic with val: <8 12 16 30 37| Scale is weakly epimorphic with val: <8 12 16 33 37| Scale is weakly epimorphic with val: <8 12 17 28 38| Scale is weakly epimorphic with val: <8 12 17 30 36| Scale is weakly epimorphic with val: <8 12 17 30 39| Scale is weakly epimorphic with val: <8 12 17 31 38| Scale is weakly epimorphic with val: <8 12 17 34 38| Scale is weakly epimorphic with val: <8 12 18 29 39| Scale is weakly epimorphic with val: <8 12 18 31 37| Scale is weakly epimorphic with val: <8 12 18 31 40| Scale is weakly epimorphic with val: <8 12 18 32 39| Scale is weakly epimorphic with val: <8 12 19 30 40| Scale is weakly epimorphic with val: <8 12 19 32 35| Scale is weakly epimorphic with val: <8 12 19 32 38| Scale is weakly epimorphic with val: <8 12 19 32 41| Scale is weakly epimorphic with val: <8 12 19 33 40|
FIT/MODE
3: 1 0 2 N G T3 SD: 48.0481 c. M:-77.2143 c. 4: 1 0 3 N G T3 SD: 21.4835 c. M:-35.7106 c. 5: 1 0 4 N G T3 SD: 21.3479 c. M: 35.3607 c. 6: 1 1 4 N M DE S SD: 18.2334 c. M:-31.0453 c. 7: 1 1 5 N M DE S SD: 11.0346 c. M: 17.6514 c. 10: 2 1 7 N T3 SD: 10.4154 c. M:-14.4438 c. 11: 2 1 8 N T3 SD: 1.1275 c. M:-1.7529 c. 51: 9 5 37 N T3 SD: 1.1382 c. M:-1.7486 c. 56: 10 5 41 N T3 SD: 0.9068 c. M: 1.5648 c. 67: 12 6 49 N T3 SD: 0.7123 c. M: 1.1665 c. 74: 13 7 54 N T3 SD: 0.7828 c. M: 1.3063 c. 78: 14 7 57 N T3 SD: 0.6126 c. M: 0.8806 c. 85: 15 8 62 N T3 SD: 0.5387 c. M: 0.9104 c. 89: 16 8 65 N T3 SD: 0.5726 c. M:-0.7355 c. 96: 17 9 70 N T3 SD: 0.3527 c. M: 0.6052 c. 107: 19 10 78 N T3 SD: 0.2096 c. M: 0.3628 c. 118: 21 11 86 N T3 SD: 0.1097 c. M: 0.1656 c. 129: 23 12 94 N T3 SD: 0.0917 c. M:-0.1588 c. 247: 44 23 180 N T3 SD: 0.0870 c. M:-0.1276 c. 314: 56 29 229 N T3 SD: 0.0868 c. M: 0.1486 c. 325: 58 30 237 N T3 SD: 0.0810 c. M: 0.1144 c. 421: 75 39 307 N T3 SD: 0.0756 c. M: 0.1071 c. 432: 77 40 315 N T3 SD: 0.0504 c. M: 0.0825 c. 443: 79 41 323 N T3 SD: 0.0352 c. M: 0.0591 c. 454: 81 42 331 N T3 SD: 0.0394 c. M:-0.0576 c. 550: 98 51 401 N T3 SD: 0.0424 c. M: 0.0581 c. 561: 100 52 409 N T3 SD: 0.0203 c. M: 0.0270 c. 572: 102 53 417 N T3 SD: 0.0088 c. M:-0.0115 c. 1262: 225 117 920 N T3 SD: 0.0029 c. M: 0.0050 c. 1834: 327 170 1337 N T3 SD: 0.0019 c. M: 0.0033 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: 99.7208 cents 6 x 7:8 S SD: 65.9506 cents 7 x 8:9 S SD: 57.4877 cents 8 x 9:11 SD: 43.5625 cents 9 x 10:12 S SD: 23.7170 cents 10 x 11:13 SD: 26.5671 cents 11 x 12:15 S SD: 20.9710 cents 12 x 13:16 SD: 1.8015 cents 13 x 14:17 SD: 17.1364 cents 14 x 15:19 SD: 17.1757 cents 15:16 x 20 S SD: 11.4653 cents 16:17 x 21 SD: 15.8454 cents 17:18 x 23 SD: 13.6187 cents 18:19 x 24 SD: 2.4012 cents 29 x 31:39 SD: 12.2630 cents 30:32 x 40 S SD: 11.4653 cents 32:34:35:43 SD: 9.7143 cents 33:35:36:44 SD: 6.8002 cents 34:36:37:45 SD: 6.6394 cents 35:37:38:47 SD: 5.3899 cents 36:38:39:48 SD: 2.0012 cents 60:63:65:80 SD: 1.8786 cents 75:79:81:100 SD: 0.6937 cents 135:142:146:180 SD: 0.4780 cents 171:180:185:228 SD: 0.4217 cents 210:221:227:280 SD: 0.1536 cents 456:480:493:608 SD: 0.0316 cents