Scala analysis: 477_R1
Reduplicated tetrachord 11/10 * 11/10 * 400/363
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 121/100 330.008457 two (Ptolemy's second, 4/5-tone) 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 400/363 168.0365 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 11/10 165.0042 Ptolemy's second, 4/5-tone 3: 400/363 168.0365
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 400/363 168.037 cents 2: 1 121/100 330.008 cents two (Ptolemy's second, 4/5-tone) 2: 2 40/33 333.041 cents 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 : 165.0 330.0 498.0 165.0: 165.0 333.0 498.0 330.0: 168.0 333.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 165.0042 .. 168.0365 cents 4000/3993, 3.0323 cents 11/10, 165.0042 cents 2: 330.0085 .. 333.0408 cents 4000/3993, 3.0323 cents 43923/40000, 161.9719 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 11/10, 165.0042 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 400/363, 168.0365 cents Average / Smallest step : 1.006126 Largest / Average step : 1.012177 Largest / Smallest step : 1.018377 Median interval of one step : 11/10, 165.0042 cents, amount: 2 Most common interval of one step : 11/10, 165.0042 cents, amount: 2 Least squares average step : 165.65401 cents, oct.: 496.96203 cents Scale is strictly proper Scale has Myhill's property chromas: 4000/3993, 3.0323 cents and 43923/40000, 161.9719 cents, ratio: 53.415291 generators: 1 of 165.00423 cents and 333.04077 cents ET pair of linear temperament : 326&658 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 329-tone equal temperament with octave 4/3 degrees: 109 218 329 generators: 109 and 220 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAB Step pattern size order : SSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 161.97191 cents Scale diversity : 1.158885 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.987823 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 : 4000/3993, 3.0323 cents Most common intervals : 11/10, 165.0042 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Steps are 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% Scale is n-1 differentially coherent in interval class 1 Limited transpositions with margin 3.0323 cents: 1 2 Limited inverse transpositions : 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 11 Odd number limit : 363 (O: 121 U: 363) Highest odd numerator or denominator: 121 Scale harmonicity : 0.017911 Average absolute harmonicity : 0.090973 Specific harmonicity : 0.082870 Fundamental : 1/300, -8.2288 octaves, 0.8721 Hz. Guide tone : 484, 8.9189 octaves, 126626.774 Hz. Exponens Consonantiae : 1.452000E+05, 17.14768 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 124.5, average 41.50000 Mersenne's string divisions : 4641 Sum of van Prooijen's expressibility: 3.60130, average 1.20043 Sum of Tenney's harmonic distance : 7.20336, average 2.40112 Vogel's harmonic complexity : 19.66667 Wille's k value : 181 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 17.62837, average 2.93806 Lattice compactness (without 2's) : 11.38891, average 1.89815 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.33333 5 3: -1 .. 0 -0.33333 1 1 5: -2 .. 0 -1.00000 3 11: 0 .. 2 1.00000 3 2 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is JI-epimorphic with val: <7 11 15 23| Scale is weakly epimorphic with val: <7 11 15 24| Scale is weakly epimorphic with val: <7 11 15 26| Scale is weakly epimorphic with val: <7 11 15 27| Scale is JI-epimorphic with val: <7 11 16 24| Scale is weakly epimorphic with val: <7 11 16 25| Scale is weakly epimorphic with val: <7 11 16 27| Scale is weakly epimorphic with val: <7 11 17 23| Scale is JI-epimorphic with val: <7 11 17 25| = patent Scale is weakly epimorphic with val: <7 11 17 26| Scale is weakly epimorphic with val: <7 11 18 23| Scale is weakly epimorphic with val: <7 11 18 24| Scale is JI-epimorphic with val: <7 11 18 26| Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 19 25| Scale is JI-epimorphic with val: <7 11 19 27|
FIT/MODE
3: 1 1 1 SP B ME I SD: 1.3049 c. M:-2.0215 c. 85: 28 28 29 SP M ME S SD: 1.2166 c. M: 1.8847 c. 88: 29 29 30 SP M ME S SD: 1.1306 c. M: 1.7515 c. 91: 30 30 31 SP M ME S SD: 1.0503 c. M: 1.6271 c. 94: 31 31 32 SP M ME S SD: 0.9751 c. M: 1.5107 c. 97: 32 32 33 SP M ME S SD: 0.9046 c. M: 1.4014 c. 100: 33 33 34 SP M ME S SD: 0.8383 c. M: 1.2988 c. 103: 34 34 35 SP M ME S SD: 0.7759 c. M: 1.2020 c. 106: 35 35 36 SP M ME S SD: 0.7170 c. M: 1.1108 c. 109: 36 36 37 SP M ME S SD: 0.6614 c. M: 1.0246 c. 112: 37 37 38 SP M ME S SD: 0.6087 c. M: 0.9430 c. 115: 38 38 39 SP M ME S SD: 0.5588 c. M: 0.8657 c. 118: 39 39 40 SP M ME S SD: 0.5114 c. M: 0.7923 c. 121: 40 40 41 SP M ME S SD: 0.4664 c. M: 0.7225 c. 124: 41 41 42 SP M ME S SD: 0.4235 c. M: 0.6561 c. 127: 42 42 43 SP M ME S SD: 0.3827 c. M: 0.5929 c. 130: 43 43 44 SP M ME S SD: 0.3437 c. M: 0.5325 c. 133: 44 44 45 SP M ME S SD: 0.3066 c. M: 0.4749 c. 136: 45 45 46 SP M ME S SD: 0.2710 c. M: 0.4199 c. 139: 46 46 47 SP M ME S SD: 0.2370 c. M: 0.3672 c. 142: 47 47 48 SP M ME S SD: 0.2044 c. M: 0.3167 c. 145: 48 48 49 SP M ME S SD: 0.1732 c. M: 0.2683 c. 148: 49 49 50 SP M ME S SD: 0.1432 c. M: 0.2219 c. 151: 50 50 51 SP M ME S SD: 0.1145 c. M: 0.1773 c. 154: 51 51 52 SP M ME S SD: 0.0868 c. M: 0.1345 c. 157: 52 52 53 SP M ME S SD: 0.0602 c. M: 0.0933 c. 160: 53 53 54 SP M ME S SD: 0.0346 c. M: 0.0536 c. 163: 54 54 55 SP M ME S SD: 0.0100 c. M: 0.0155 c. 329: 109 109 111 SP M DE S SD: 0.0020 c. M:-0.0031 c. 492: 163 163 166 SP M DE S SD: 0.0020 c. M: 0.0030 c. 821: 272 272 277 SP M DE S SD: 0.0004 c. M: 0.0006 c. 1150: 381 381 388 SP M DE S SD: 0.0003 c. M:-0.0005 c. 1971: 653 653 665 SP M DE S SD: 0.0000 c. M:-0.0001 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 5 x S SD: 56.3053 cents 5 x 6:7 S SD: 42.8402 cents 6 x 7:8 S SD: 31.5688 cents 7:8 x 9 S SD: 45.6687 cents 8:9:10:11 H SD: 28.9097 cents 9:10:11:12 H SD: 8.2022 cents 19:21:23:25 SD: 8.1286 cents 28:31:34:37 SD: 6.7009 cents 29:32:35:39 SD: 5.4768 cents 30:33:36:40 S SD: 4.7891 cents 38:42:46:51 SD: 4.6872 cents 39:43:47:52 SD: 2.6881 cents 48:53:58:64 SD: 2.3222 cents 71:78:86:95 SD: 2.2419 cents 72:79:87:96 SD: 1.6618 cents 81:89:98:108 SD: 0.6507 cents 90:99:109:120 SD: 0.5297 cents 129:142:156:172 SD: 0.5254 cents 171:188:207:228 SD: 0.3964 cents 210:231:254:280 SD: 0.2272 cents 300:330:363:400 SD: 0.0000 cents