Scala analysis: 355_C29
Chromatic tetrachord 60/59 * 59/52 * 52/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 60/59 29.097055 2: 15/13 247.741053 tridecimal 5/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 52/45 250.3039 1: 60/59 29.0971 2: 59/52 218.6440 3: 52/45 250.3039
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 60/59 29.097 cents 1: 1 59/52 218.644 cents 1: 1 52/45 250.304 cents 2: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 208/177 279.401 cents 2: 1 59/45 468.948 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 : 29.1 247.7 498.0 29.1 : 218.6 468.9 498.0 247.7: 250.3 279.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 29.0971 .. 250.3039 cents 767/675, 221.2069 cents 60/59, 29.0971 cents 2: 247.7411 .. 468.9479 cents 767/675, 221.2069 cents 675/676,-2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 60/59, 29.0971 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 52/45, 250.3039 cents Average / Smallest step : 5.705560 Largest / Average step : 1.507719 Largest / Smallest step : 8.602381 Median interval of one step : 59/52, 218.6440 cents, amount: 1 Least squares average step : 144.19387 cents, oct.: 432.58161 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1164-tone equal temperament with octave 4/3 degrees: 68 579 1164 Least number of segments generator : 583 of 249.450 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 829 of 354.707 cents and inv. generated superset size: 34 = 31 more = 1133.333% 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 2.56289 cents Scale diversity : 0.500244 Lumma stability : 0.116845 Lumma impropriety factor : 0.005146 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 : 676/675, 2.5629 cents Number of recognisable fifths : 0 Number of recognisable 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% -- Rational properties -- Prime limit : 59 Odd number limit : 177 (O: 59 U: 177) Highest odd numerator or denominator: 59 Scale harmonicity : 0.027865 Fundamental : 1/2301, -11.1680 octaves, 0.1137 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 1.380600E+05, 17.07494 octaves Euler's gradus suavitatis : 81 Sum of Mann's harmonic distance : 77.0, average 25.66667 Mersenne's string divisions : 476 Sum of van Prooijen's expressibility: 3.42406, average 1.14135 Sum of Tenney's harmonic distance : 6.91822, average 2.30607 Vogel's harmonic complexity : 56.66667 Wille's k value : 1327 Wilson's harmonic complexity : 83 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.05202, average 2.34200 Lattice compactness (without 2's) : 9.83182, average 1.63864 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.33333 4 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.66667 2 13: -1 .. 0 -0.33333 1 1 59: -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 18 25 42| Scale is weakly epimorphic with val: <6 10 19 26 43| Scale is weakly epimorphic with val: <6 11 17 25 44| Scale is weakly epimorphic with val: <6 11 18 26 42| Scale is weakly epimorphic with val: <6 11 19 27 43| Scale is weakly epimorphic with val: <7 10 18 25 43| Scale is weakly epimorphic with val: <7 10 19 26 44| Scale is weakly epimorphic with val: <7 11 15 25 44| Scale is weakly epimorphic with val: <7 11 15 27 42| Scale is weakly epimorphic with val: <7 11 15 28 44| Scale is weakly epimorphic with val: <7 11 15 30 42| Scale is weakly epimorphic with val: <7 11 16 25 43| Scale is weakly epimorphic with val: <7 11 16 26 42| Scale is weakly epimorphic with val: <7 11 16 28 43| Scale is weakly epimorphic with val: <7 11 16 29 42| Scale is weakly epimorphic with val: <7 11 17 26 44| Scale is weakly epimorphic with val: <7 11 17 27 43| = patent Scale is weakly epimorphic with val: <7 11 17 29 44| Scale is weakly epimorphic with val: <7 11 17 30 43| Scale is weakly epimorphic with val: <7 11 18 25 44| Scale is JI-epimorphic with val: <7 11 18 27 42| Scale is weakly epimorphic with val: <7 11 18 28 44| Scale is weakly epimorphic with val: <7 11 18 30 42| Scale is weakly epimorphic with val: <7 11 19 25 43| Scale is weakly epimorphic with val: <7 11 19 26 42| Scale is JI-epimorphic with val: <7 11 19 28 43| Scale is weakly epimorphic with val: <7 11 19 29 42| Scale is weakly epimorphic with val: <7 12 16 25 44| Scale is weakly epimorphic with val: <7 12 17 26 42| Scale is weakly epimorphic with val: <7 12 18 27 43| Scale is weakly epimorphic with val: <7 12 19 27 42| Scale is weakly epimorphic with val: <7 12 19 28 44| Scale is weakly epimorphic with val: <7 12 19 30 42| Scale is weakly epimorphic with val: <8 11 17 25 43| Scale is weakly epimorphic with val: <8 11 18 25 42| Scale is weakly epimorphic with val: <8 11 18 26 44| Scale is weakly epimorphic with val: <8 11 18 28 42| Scale is weakly epimorphic with val: <8 11 19 26 43| Scale is weakly epimorphic with val: <8 11 19 27 42| Scale is weakly epimorphic with val: <8 11 19 29 43| Scale is weakly epimorphic with val: <8 12 16 25 42| Scale is weakly epimorphic with val: <8 12 17 26 43| Scale is weakly epimorphic with val: <8 12 17 27 42| Scale is weakly epimorphic with val: <8 12 17 30 42| Scale is weakly epimorphic with val: <8 12 18 25 43| Scale is weakly epimorphic with val: <8 12 18 27 44| Scale is weakly epimorphic with val: <8 12 18 28 43| Scale is weakly epimorphic with val: <8 12 19 26 44| Scale is weakly epimorphic with val: <8 12 19 28 42| Scale is weakly epimorphic with val: <8 12 19 29 44|
FIT/MODE
3: 0 1 2 N G T3 SD: 50.0859 c. M: 81.7261 c. 4: 0 2 2 P M DE S SD: 16.8155 c. M: 29.0971 c. 10: 1 4 5 P T3 SD: 11.9783 c. M:-20.7074 c. 12: 1 5 6 P T3 SD: 7.2011 c. M:-12.4067 c. 14: 1 6 7 P T3 SD: 3.8123 c. M:-6.4776 c. 16: 1 7 8 P T3 SD: 1.3864 c. M:-2.0308 c. 18: 1 8 9 P T3 SD: 1.1077 c. M: 1.4279 c. 34: 2 15 17 P T3 SD: 0.7488 c. M:-1.2814 c. 50: 3 22 25 P T3 SD: 0.8678 c. M:-1.2814 c. 52: 3 23 26 P T3 SD: 0.7691 c. M:-1.2814 c. 84: 5 37 42 P T3 SD: 0.8048 c. M:-1.2814 c. 86: 5 38 43 P T3 SD: 0.7443 c. M:-1.2814 c. 99: 6 43 50 N T3 SD: 0.9496 c. M: 1.2339 c. 101: 6 44 51 N T3 SD: 0.7398 c. M: 1.1841 c. 103: 6 45 52 N T3 SD: 0.6578 c. M: 1.1362 c. 105: 6 46 53 N T3 SD: 0.7291 c. M: 1.0902 c. 117: 7 51 59 N T3 SD: 0.6346 c. M: 0.8470 c. 119: 7 52 60 N T3 SD: 0.4823 c. M: 0.8112 c. 121: 7 53 61 N T3 SD: 0.4775 c. M: 0.7766 c. 123: 7 54 62 N T3 SD: 0.6108 c. M: 0.7530 c. 133: 8 58 67 N T3 SD: 0.6027 c. M:-0.8605 c. 135: 8 59 68 N T3 SD: 0.4045 c. M: 0.5632 c. 137: 8 60 69 N T3 SD: 0.3097 c. M: 0.5362 c. 139: 8 61 70 N T3 SD: 0.3861 c. M: 0.5101 c. 153: 9 67 77 N T3 SD: 0.2307 c. M: 0.3462 c. 155: 9 68 78 N T3 SD: 0.2141 c. M: 0.3252 c. 171: 10 75 86 N T3 SD: 0.1023 c. M: 0.1748 c. 189: 11 83 95 N T3 SD: 0.0670 c. M: 0.1103 c. 205: 12 90 103 N T3 SD: 0.0506 c. M:-0.0667 c. 376: 22 165 189 N T3 SD: 0.0355 c. M:-0.0439 c. 394: 23 173 198 N T3 SD: 0.0168 c. M: 0.0234 c. 599: 35 263 301 N T3 SD: 0.0199 c. M:-0.0343 c. 770: 45 338 387 N T3 SD: 0.0089 c. M: 0.0122 c. 1164: 68 511 585 N T3 SD: 0.0016 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: 54.1875 cents 6 x 7:8 S SD: 9.5649 cents 7 x 8:9 S SD: 32.5520 cents 8 x 9:11 SD: 34.4934 cents 9 x 10:12 S SD: 32.6687 cents 10 x 12:13 S SD: 40.4092 cents 11 x 13:15 SD: 28.4311 cents 12 x 14:16 S SD: 9.5649 cents 32:33:37:43 SD: 9.3033 cents 33:34:38:44 SD: 7.6184 cents 38:39:44:51 SD: 6.8116 cents 39:40:45:52 SD: 4.9113 cents 45:46:52:60 SD: 3.1044 cents 51:52:59:68 SD: 2.1308 cents 57:58:66:76 SD: 2.0493 cents 60:61:69:80 SD: 1.9335 cents 66:67:76:88 SD: 1.5506 cents 105:107:121:140 SD: 1.3974 cents 111:113:128:148 SD: 0.6984 cents 117:119:135:156 SD: 0.0822 cents 591:601:682:788 SD: 0.0671 cents