Scala analysis: 485_R9
Reduplicated tetrachord 256/243 * 256/243 * 19683/16384
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 256/243 90.224996 limma, Pythagorean minor second 2: 65536/59049 180.449991 Pythagorean diminished third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 19683/16384 317.5950 Pythagorean augmented second 1: 256/243 90.2250 limma, Pythagorean minor second 2: 256/243 90.2250 limma, Pythagorean minor second 3: 19683/16384 317.5950 Pythagorean augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 256/243 90.225 cents limma, Pythagorean minor second 1: 1 19683/16384 317.595 cents Pythagorean augmented second 2: 1 65536/59049 180.450 cents Pythagorean diminished third 2: 2 81/64 407.820 cents Pythagorean major third Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 90.2 180.4 498.0 90.2 : 90.2 407.8 498.0 180.4: 317.6 407.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 317.5950 cents 4782969/4194304, 227.3700 cents 256/243, 90.2250 cents 2: 180.4500 .. 407.8200 cents 4782969/4194304, 227.3700 cents 1073741824/1162261467,-137.1450 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 19683/16384, 317.5950 cents Average / Smallest step : 1.840011 Largest / Average step : 1.913050 Largest / Smallest step : 3.520034 Median interval of one step : 256/243, 90.2250 cents, amount: 2 Most common interval of one step : 256/243, 90.2250 cents, amount: 2 Least squares average step : 138.94714 cents, oct.: 416.84142 cents Scale is not proper Scale has Myhill's property chromas: 4782969/4194304, 227.3700 cents and 1162261467/1073741824, 137.1450 cents, ratio: 1.657880 generators: 1 of 90.22500 cents and 407.82000 cents ET pair of linear temperament : 22&254 Scale is distributional even Scale is a mode of a 138-tone equal temperament with octave 4/3 degrees: 25 50 138 generators: 25 and 113 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAB Step pattern size order : SSL Interval vector is [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 0.989125 Lumma stability : 0.362317 Lumma impropriety factor : 0.275367 Rothenberg efficiency : 0.888889 redundancy: 0.111111 Efficiency x scale size : 2.666667 Number of different interval sizes : 4 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 256/243, 90.2250 cents Most common intervals : 256/243, 90.2250 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 3 Odd number limit : 59049 (O: 19683 U: 59049) Highest odd numerator or denominator: 59049 Scale harmonicity : 0.023438 Average absolute harmonicity : 0.094866 Specific harmonicity : 0.110599 Fundamental : 1/59049, -15.8496 octaves, 0.0044 Hz. Guide tone : 65536, 16.0000 octaves, 17145893.048 Hz. Exponens Consonantiae : 3.869835E+09, 31.84963 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 62545.5, average 20848.50000 Mersenne's string divisions : 435175405 Sum of van Prooijen's expressibility: 7.63394, average 2.54465 Sum of Tenney's harmonic distance : 15.46072, average 5.15357 Vogel's harmonic complexity : 22.66667 Wille's k value : 9841 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 10 Triangular lattice diameter : 9 Lattice compactness : 63.82641, average 10.63774 Lattice compactness (without 2's) : 34.00000, average 5.66667 Number of different primes : 2 Prime exponents' range, average, count, tones@limit: 2: 2 .. 16 8.66667 26 3: -10 ..-1 -5.33333 16 3 Average exponent except 2's :-16 / 3 =-5.33333 Average absolute exponent except 2's: 16 / 3 = 5.33333 Scale is JI-epimorphic with val: <7 11| = patent
FIT/MODE
3: 0 1 2 N G T3 SD: 52.7539 c. M: 90.2250 c. 4: 1 0 3 N G T3 SD: 37.8800 c. M: 55.9387 c. 5: 1 1 3 N M DE S SD: 12.1147 c. M:-18.7680 c. 6: 1 1 4 N M DE S SD: 9.3177 c. M: 14.4350 c. 11: 2 2 7 N M DE S SD: 0.4243 c. M:-0.6573 c. 72: 13 13 46 N M DE S SD: 0.3876 c. M: 0.6004 c. 83: 15 15 53 N M DE S SD: 0.2800 c. M: 0.4337 c. 94: 17 17 60 N M DE S SD: 0.1976 c. M: 0.3061 c. 105: 19 19 67 N M DE S SD: 0.1324 c. M: 0.2051 c. 116: 21 21 74 N M DE S SD: 0.0796 c. M: 0.1234 c. 127: 23 23 81 N M DE S SD: 0.0360 c. M: 0.0557 c. 138: 25 25 88 N M DE S SD: 0.0007 c. M:-0.0011 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: 79.7048 cents 6 x 7:8 S SD: 43.2105 cents 7 x 8:9 S SD: 40.4259 cents 8 x 9:11 SD: 29.1049 cents 9 x 10:12 S SD: 0.9769 cents 10 x 11:13 SD: 23.2365 cents 11 x 12:15 S SD: 24.5075 cents 12 x 13:16 SD: 20.9387 cents 13:14 x 17 SD: 25.3953 cents 14:15:16:19 SD: 22.0241 cents 15:16:17:20 SD: 14.0460 cents 16:17:18:21 S SD: 12.9559 cents 17:18:19:23 SD: 9.7842 cents 18:19:20:24 S SD: 1.3008 cents 93:98:103:124 SD: 1.2220 cents 111:117:123:148 SD: 0.9601 cents 129:136:143:172 SD: 0.8094 cents 147:155:163:196 SD: 0.7310 cents 165:174:183:220 SD: 0.6986 cents 183:193:203:244 SD: 0.6940 cents 207:218:230:276 SD: 0.6801 cents 210:221:233:280 SD: 0.6364 cents 228:240:253:304 SD: 0.4870 cents 246:259:273:328 SD: 0.3614 cents 264:278:293:352 SD: 0.2563 cents 282:297:313:376 SD: 0.1719 cents 300:316:333:400 SD: 0.1166 cents 318:335:353:424 SD: 0.1087 cents