Scala analysis: 266_C18
Chromatic tetrachord 228/211 * 422/405 * 45/38
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 228/211 134.148991 2: 152/135 205.334300 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 45/38 292.7107 1: 228/211 134.1490 2: 422/405 71.1853 3: 45/38 292.7107
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 422/405 71.185 cents 1: 1 228/211 134.149 cents 1: 1 45/38 292.711 cents 2: 1 152/135 205.334 cents 2: 1 211/171 363.896 cents 2: 1 270/211 426.860 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 : 134.1 205.3 498.0 134.1: 71.2 363.9 498.0 205.3: 292.7 426.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 71.1853 .. 292.7107 cents 18225/16036, 221.5254 cents 422/405, 71.1853 cents 2: 205.3343 .. 426.8597 cents 18225/16036, 221.5254 cents 5776/6075,-87.3764 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 422/405, 71.1853 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 45/38, 292.7107 cents Average / Smallest step : 2.332153 Largest / Average step : 1.763158 Largest / Smallest step : 4.111954 Median interval of one step : 228/211, 134.1490 cents, amount: 1 Least squares average step : 145.63947 cents, oct.: 436.91841 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1693-tone equal temperament with octave 4/3 degrees: 456 698 1693 Least number of segments generator : 847 of 249.170 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1154 of 339.483 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 : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 71.18531 cents Scale diversity : 1.038800 Lumma stability : 0.285859 Lumma impropriety factor : 0.175439 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 : 46170/44521, 62.9637 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 211 Odd number limit : 405 (O: 211 U: 405) Highest odd numerator or denominator: 211 Scale harmonicity : 0.018460 Fundamental : 1/28485, -14.7979 octaves, 0.0092 Hz. Guide tone : 456, 8.8329 octaves, 119301.258 Hz. Exponens Consonantiae : 1.298916E+07, 23.63080 octaves Euler's gradus suavitatis : 244 Sum of Mann's harmonic distance : 366.5, average 122.16667 Mersenne's string divisions : 125993 Sum of van Prooijen's expressibility: 4.93174, average 1.64391 Sum of Tenney's harmonic distance : 10.07358, average 3.35786 Vogel's harmonic complexity : 165.00000 Wille's k value : 4747 Wilson's harmonic complexity : 247 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 18.28215, average 3.04703 Lattice compactness (without 2's) : 14.53950, average 2.42325 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -3 .. 1 -1.00000 5 1 5: -1 .. 0 -0.33333 1 19: 0 .. 1 0.66667 2 1 211: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 15 30 57| Scale is weakly epimorphic with val: <6 10 16 31 55| Scale is weakly epimorphic with val: <6 10 17 32 56| Scale is weakly epimorphic with val: <6 10 18 33 57| Scale is weakly epimorphic with val: <6 10 19 34 55| Scale is weakly epimorphic with val: <6 11 15 33 57| Scale is weakly epimorphic with val: <6 11 16 34 55| Scale is weakly epimorphic with val: <7 10 16 28 56| Scale is weakly epimorphic with val: <7 10 17 29 57| Scale is weakly epimorphic with val: <7 10 17 34 55| Scale is weakly epimorphic with val: <7 10 18 30 55| Scale is weakly epimorphic with val: <7 10 19 31 56| Scale is weakly epimorphic with val: <7 11 15 28 57| Scale is weakly epimorphic with val: <7 11 15 29 56| Scale is weakly epimorphic with val: <7 11 15 31 57| Scale is weakly epimorphic with val: <7 11 15 32 56| Scale is weakly epimorphic with val: <7 11 15 34 57| Scale is weakly epimorphic with val: <7 11 16 29 55| Scale is weakly epimorphic with val: <7 11 16 30 57| Scale is weakly epimorphic with val: <7 11 16 32 55| Scale is weakly epimorphic with val: <7 11 16 33 57| Scale is weakly epimorphic with val: <7 11 17 28 55| Scale is weakly epimorphic with val: <7 11 17 30 56| Scale is JI-epimorphic with val: <7 11 17 31 55| Scale is weakly epimorphic with val: <7 11 17 33 56| Scale is weakly epimorphic with val: <7 11 17 34 55| Scale is weakly epimorphic with val: <7 11 18 28 57| Scale is weakly epimorphic with val: <7 11 18 29 56| Scale is weakly epimorphic with val: <7 11 18 31 57| Scale is JI-epimorphic with val: <7 11 18 32 56| Scale is weakly epimorphic with val: <7 11 18 34 57| Scale is weakly epimorphic with val: <7 11 19 29 55| Scale is weakly epimorphic with val: <7 11 19 30 57| Scale is weakly epimorphic with val: <7 11 19 32 55| Scale is JI-epimorphic with val: <7 11 19 33 57| Scale is weakly epimorphic with val: <7 12 15 33 55| Scale is weakly epimorphic with val: <7 12 15 34 57| Scale is weakly epimorphic with val: <7 12 16 32 55| Scale is weakly epimorphic with val: <7 12 16 34 56| Scale is weakly epimorphic with val: <7 12 17 33 56| Scale is weakly epimorphic with val: <7 12 18 34 57| Scale is weakly epimorphic with val: <7 12 19 32 55| Scale is weakly epimorphic with val: <8 11 15 31 55| Scale is weakly epimorphic with val: <8 11 16 28 57| Scale is weakly epimorphic with val: <8 11 16 32 56| Scale is weakly epimorphic with val: <8 11 17 29 55| Scale is weakly epimorphic with val: <8 11 17 33 57| Scale is weakly epimorphic with val: <8 11 18 30 56| Scale is weakly epimorphic with val: <8 11 18 31 55| Scale is weakly epimorphic with val: <8 11 19 31 57| Scale is weakly epimorphic with val: <8 11 19 32 56| Scale is weakly epimorphic with val: <8 12 15 30 56| Scale is weakly epimorphic with val: <8 12 15 32 57| Scale is weakly epimorphic with val: <8 12 16 30 55| Scale is weakly epimorphic with val: <8 12 16 31 57| Scale is weakly epimorphic with val: <8 12 17 31 56| Scale is weakly epimorphic with val: <8 12 17 32 55| Scale is weakly epimorphic with val: <8 12 18 32 57| Scale is weakly epimorphic with val: <8 12 18 33 56| Scale is weakly epimorphic with val: <8 12 19 30 55| Scale is weakly epimorphic with val: <8 12 19 34 57|
FIT/MODE
3: 1 0 2 N G T3 SD: 29.2201 c. M: 39.3193 c. 4: 1 1 2 P M ME S SD: 25.8299 c. M:-43.6882 c. 5: 1 1 3 N M DE S SD: 20.2519 c. M: 34.5400 c. 7: 2 1 4 N T3 SD: 6.6394 c. M:-8.1496 c. 12: 3 2 7 N T3 SD: 5.7055 c. M: 9.6377 c. Vietnamese tritonic 15: 4 2 9 N T3 SD: 3.6146 c. M: 6.1163 c. 19: 5 3 11 N T3 SD: 3.0877 c. M:-4.3689 c. 22: 6 3 13 N T3 SD: 1.3355 c. M:-1.6815 c. 34: 9 5 20 N T3 SD: 1.3439 c. M: 2.3135 c. 41: 11 6 24 N T3 SD: 0.7420 c. M:-1.1722 c. 56: 15 8 33 N T3 SD: 0.6224 c. M: 0.7801 c. 63: 17 9 37 N T3 SD: 0.1852 c. M:-0.2441 c. 160: 43 23 94 N T3 SD: 0.1840 c. M: 0.2994 c. 182: 49 26 107 N T3 SD: 0.0653 c. M: 0.0960 c. 245: 66 35 144 N T3 SD: 0.0147 c. M:-0.0182 c. 1140: 307 163 670 N T3 SD: 0.0152 c. M: 0.0263 c. 1203: 324 172 707 N T3 SD: 0.0095 c. M: 0.0122 c. 1385: 373 198 814 N T3 SD: 0.0108 c. M: 0.0185 c. 1448: 390 207 851 N T3 SD: 0.0054 c. M: 0.0070 c. 1693: 456 242 995 N T3 SD: 0.0025 c. M: 0.0034 c. 1938: 522 277 1139 N T3 SD: 0.0004 c. M: 0.0006 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: 69.4664 cents 6 x 7:8 S SD: 30.7683 cents 7 x 8:9 S SD: 34.0286 cents 8 x 9:11 SD: 26.6460 cents 9 x 10:12 S SD: 11.4653 cents 10:11 x 13 SD: 26.8012 cents 11:12 x 15 S SD: 21.1277 cents 12:13:14:16 S SD: 20.5651 cents 13:14:15:17 SD: 18.1435 cents 14:15:16:19 SD: 14.2318 cents 15:16:17:20 SD: 8.3761 cents 19 x 21:25 SD: 19.7108 cents 20:22:23:27 SD: 17.4994 cents 21:23:24:28 SD: 11.6077 cents 22:24:25:29 SD: 10.1025 cents 23:25:26:31 SD: 7.4706 cents 24:26:27:32 SD: 1.5491 cents 63:68:71:84 SD: 0.8412 cents 87:94:98:116 SD: 0.2682 cents 198:214:223:264 SD: 0.2147 cents 285:308:321:380 SD: 0.2120 cents 483:522:544:644 SD: 0.2109 cents 573:619:645:764 SD: 0.2080 cents 597:645:672:796 SD: 0.1767 cents