Scala analysis: 489_R13
Reduplicated tetrachord 34/33 * 34/33 * 363/289
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 34/33 51.682466 2: 1156/1089 103.364933 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 363/289 394.6801 1: 34/33 51.6825 2: 34/33 51.6825 3: 363/289 394.6801
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 34/33 51.682 cents 1: 1 363/289 394.680 cents 2: 1 1156/1089 103.365 cents 2: 2 22/17 446.363 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 : 51.7 103.4 498.0 51.7 : 51.7 446.4 498.0 103.4: 394.7 446.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.6825 .. 394.6801 cents 11979/9826, 342.9976 cents 34/33, 51.6825 cents 2: 103.3649 .. 446.3625 cents 11979/9826, 342.9976 cents 334084/395307,-291.3151 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 34/33, 51.6825 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 363/289, 394.6801 cents Average / Smallest step : 3.212211 Largest / Average step : 2.377376 Largest / Smallest step : 7.636634 Median interval of one step : 34/33, 51.6825 cents, amount: 2 Most common interval of one step : 34/33, 51.6825 cents, amount: 2 Least squares average step : 125.18195 cents, oct.: 375.54586 cents Scale is not proper Scale has Myhill's property chromas: 11979/9826, 342.9976 cents and 395307/334084, 291.3151 cents, ratio: 1.177411 generators: 1 of 51.68247 cents and 446.36253 cents ET pair of linear temperament : 20&38 Scale is distributional even Scale is a mode of a 106-tone equal temperament with octave 4/3 degrees: 11 22 106 generators: 11 and 95 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 2 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 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 51.68247 cents Scale diversity : 0.455948 Lumma stability : 0.207541 Lumma impropriety factor : 0.584917 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 : 34/33, 51.6825 cents Most common intervals : 34/33, 51.6825 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 inverse transpositions : 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 17 Odd number limit : 1089 (O: 363 U: 1089) Highest odd numerator or denominator: 1089 Scale harmonicity : 0.009622 Average absolute harmonicity : 0.081050 Specific harmonicity : 0.044309 Fundamental : 1/1089, -10.0888 octaves, 0.2402 Hz. Guide tone : 1156, 10.1749 octaves, 302439.153 Hz. Exponens Consonantiae : 1.258884E+06, 20.26371 octaves Euler's gradus suavitatis : 59 Sum of Mann's harmonic distance : 1159.5, average 386.50000 Mersenne's string divisions : 1052905 Sum of van Prooijen's expressibility: 5.03266, average 1.67755 Sum of Tenney's harmonic distance : 10.22916, average 3.40972 Vogel's harmonic complexity : 31.66667 Wille's k value : 280 Wilson's harmonic complexity : 62 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 14.96812, average 2.49469 Lattice compactness (without 2's) : 12.34242, average 2.05707 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -2 ..-1 -1.33333 4 1 11: -2 .. 0 -1.00000 3 17: 0 .. 2 1.00000 3 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is JI-epimorphic with val: <7 11 23 28| Scale is weakly epimorphic with val: <7 11 23 29| Scale is weakly epimorphic with val: <7 11 23 31| Scale is weakly epimorphic with val: <7 11 23 32| Scale is weakly epimorphic with val: <7 11 24 27| Scale is JI-epimorphic with val: <7 11 24 29| Scale is weakly epimorphic with val: <7 11 24 30| Scale is weakly epimorphic with val: <7 11 24 32| Scale is weakly epimorphic with val: <7 11 24 33| Scale is weakly epimorphic with val: <7 11 25 27| Scale is weakly epimorphic with val: <7 11 25 28| Scale is JI-epimorphic with val: <7 11 25 30| = patent Scale is weakly epimorphic with val: <7 11 25 31| Scale is weakly epimorphic with val: <7 11 25 33| Scale is weakly epimorphic with val: <7 11 26 28| Scale is weakly epimorphic with val: <7 11 26 29| Scale is JI-epimorphic with val: <7 11 26 31| Scale is weakly epimorphic with val: <7 11 26 32| Scale is weakly epimorphic with val: <7 11 27 27| Scale is weakly epimorphic with val: <7 11 27 29| Scale is weakly epimorphic with val: <7 11 27 30| Scale is JI-epimorphic with val: <7 11 27 32| Scale is weakly epimorphic with val: <7 11 27 33|
FIT/MODE
3: 0 0 3 N M DE S SD: 66.7218 c. M: 103.3649 c. 4: 0 1 3 N G T3 SD: 32.2400 c. M: 51.6825 c. 5: 0 1 4 N G T3 SD: 29.9176 c. M: 51.6825 c. 6: 0 1 5 N G T3 SD: 32.0702 c. M: 51.6825 c. 7: 1 0 6 N G T3 SD: 21.7317 c. M: 32.2156 c. 8: 1 1 6 N M DE S SD: 13.6499 c. M:-21.1463 c. 9: 1 1 7 N M DE S SD: 4.7197 c. M:-7.3117 c. 10: 1 1 8 N M DE S SD: 2.4244 c. M: 3.7559 c. 19: 2 2 15 N M DE S SD: 0.9596 c. M:-1.4866 c. 29: 3 3 23 N M DE S SD: 0.2073 c. M: 0.3211 c. 77: 8 8 61 N M DE S SD: 0.0806 c. M:-0.1249 c. 106: 11 11 84 N M DE S SD: 0.0019 c. M:-0.0029 c. 1725: 179 179 1367 N M DE S SD: 0.0016 c. M: 0.0026 c. 1831: 190 190 1451 N M DE S SD: 0.0014 c. M: 0.0022 c. 1937: 201 201 1535 N M DE S SD: 0.0013 c. M: 0.0020 c. 2043: 212 212 1619 N M DE S SD: 0.0011 c. M: 0.0017 c. 2149: 223 223 1703 N M DE S SD: 0.0010 c. M: 0.0015 c. 2255: 234 234 1787 N M DE S SD: 0.0008 c. M: 0.0013 c. 2361: 245 245 1871 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 x 7 SD: 84.4672 cents 6 x 7:8 S SD: 81.7530 cents 7 x 8:9 S SD: 71.2377 cents 8 x 9:11 SD: 56.8931 cents 9 x 10:12 S SD: 39.5194 cents 10 x 11:13 SD: 37.8172 cents 11 x 12:15 S SD: 30.6117 cents 12 x 13:16 SD: 17.6039 cents 13 x 14:17 SD: 20.9272 cents 14 x 15:19 SD: 17.3020 cents 15 x 16:20 S SD: 4.1832 cents 16 x 17:21 SD: 13.6552 cents 17 x 18:23 SD: 12.8279 cents 18 x 19:24 SD: 4.8810 cents 19 x 20:25 S SD: 13.5824 cents 20 x 21:27 SD: 14.3147 cents 21 x 22:28 SD: 11.4139 cents 22:23 x 29 SD: 16.0487 cents 23:24 x 31 SD: 14.4414 cents 24:25 x 32 SD: 9.4950 cents 27:28:29:36 SD: 7.7547 cents 29:30:31:39 SD: 6.8004 cents 30:31:32:40 S SD: 3.2634 cents 33:34:35:44 SD: 0.4994 cents 129:133:137:172 SD: 0.4764 cents 162:167:172:216 SD: 0.3332 cents 195:201:207:260 SD: 0.2612 cents 228:235:242:304 SD: 0.2327 cents 261:269:277:348 SD: 0.2293 cents 489:504:519:652 SD: 0.2288 cents 567:584:602:756 SD: 0.2111 cents 600:618:637:800 SD: 0.1866 cents