Scala analysis: 491_R15
Reduplicated tetrachord 40/39 * 40/39 * 507/400
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40/39 43.831051 tridecimal minor diesis 2: 1600/1521 87.662102 two (tridecimal minor diesis) 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 507/400 410.3829 1: 40/39 43.8311 tridecimal minor diesis 2: 40/39 43.8311 tridecimal minor diesis 3: 507/400 410.3829
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 40/39 43.831 cents tridecimal minor diesis 1: 1 507/400 410.383 cents 2: 1 1600/1521 87.662 cents two (tridecimal minor diesis) 2: 2 13/10 454.214 cents tridecimal semi-diminished fourth 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 : 43.8 87.7 498.0 43.8 : 43.8 454.2 498.0 87.7 : 410.4 454.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 410.3829 cents 19773/16000, 366.5518 cents 40/39, 43.8311 cents 2: 87.6621 .. 454.2139 cents 19773/16000, 366.5518 cents 640000/771147,-322.7208 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 507/400, 410.3829 cents Average / Smallest step : 3.787612 Largest / Average step : 2.471963 Largest / Smallest step : 9.362835 Median interval of one step : 40/39, 43.8311 cents, amount: 2 Most common interval of one step : 40/39, 43.8311 cents, amount: 2 Least squares average step : 122.37788 cents, oct.: 367.13363 cents Scale is not proper Scale has Myhill's property chromas: 19773/16000, 366.5518 cents and 771147/640000, 322.7208 cents, ratio: 1.135817 generators: 1 of 43.83105 cents and 454.21395 cents ET pair of linear temperament : 22&46 Scale is distributional even Scale is a mode of a 659-tone equal temperament with octave 4/3 degrees: 58 116 659 generators: 58 and 601 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 43.83105 cents Scale diversity : 0.337661 Lumma stability : 0.176012 Lumma impropriety factor : 0.647975 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 : 40/39, 43.8311 cents Most common intervals : 40/39, 43.8311 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 : 13 Odd number limit : 1521 (O: 507 U: 1521) Highest odd numerator or denominator: 1521 Scale harmonicity : 0.014611 Average absolute harmonicity : 0.086039 Specific harmonicity : 0.068120 Fundamental : 1/1521, -10.5708 octaves, 0.1720 Hz. Guide tone : 1600, 10.6439 octaves, 418600.904 Hz. Exponens Consonantiae : 2.433600E+06, 21.21466 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 1603.5, average 534.50000 Mersenne's string divisions : 1725913 Sum of van Prooijen's expressibility: 5.25032, average 1.75011 Sum of Tenney's harmonic distance : 10.65856, average 3.55285 Vogel's harmonic complexity : 23.66667 Wille's k value : 253 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 22.82453, average 3.80409 Lattice compactness (without 2's) : 12.34242, average 2.05707 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 6 3.66667 11 3: -2 ..-1 -1.33333 4 1 5: 0 .. 2 1.00000 3 13: -2 .. 0 -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 weakly epimorphic with val: <7 11 15 26| Scale is weakly epimorphic with val: <7 11 15 27| Scale is weakly epimorphic with val: <7 11 15 29| Scale is weakly epimorphic with val: <7 11 15 30| Scale is JI-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 16 28| Scale is weakly epimorphic with val: <7 11 16 30| Scale is weakly epimorphic with val: <7 11 17 25| Scale is JI-epimorphic with val: <7 11 17 26| Scale is weakly epimorphic with val: <7 11 17 28| Scale is weakly epimorphic with val: <7 11 17 29| Scale is weakly epimorphic with val: <7 11 18 26| Scale is JI-epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 18 29| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <7 11 19 27| Scale is JI-epimorphic with val: <7 11 19 28| Scale is weakly epimorphic with val: <7 11 19 30|
FIT/MODE
3: 0 0 3 N M DE S SD: 56.5856 c. M: 87.6621 c. 4: 0 1 3 N G T3 SD: 33.0607 c. M: 43.8311 c. 5: 0 1 4 N G T3 SD: 26.2291 c. M: 43.8311 c. 6: 0 1 5 N G T3 SD: 25.4482 c. M: 43.8311 c. 7: 0 1 6 N G T3 SD: 27.0422 c. M: 43.8311 c. 8: 1 0 7 N G T3 SD: 18.1195 c. M: 25.4065 c. 9: 1 1 7 N M DE S SD: 14.8558 c. M:-23.0146 c. 10: 1 1 8 N M DE S SD: 7.7117 c. M:-11.9469 c. 11: 1 1 9 N M DE S SD: 1.8665 c. M:-2.8915 c. 23: 2 2 19 N M DE S SD: 0.6749 c. M: 1.0456 c. 34: 3 3 28 N M DE S SD: 0.1473 c. M:-0.2282 c. 91: 8 8 75 N M DE S SD: 0.0605 c. M: 0.0938 c. 125: 11 11 103 N M DE S SD: 0.0040 c. M: 0.0062 c. 659: 58 58 543 N M DE S SD: 0.0038 c. M:-0.0059 c. 784: 69 69 646 N M DE S SD: 0.0026 c. M:-0.0040 c. 909: 80 80 749 N M DE S SD: 0.0017 c. M:-0.0026 c. 1034: 91 91 852 N M DE S SD: 0.0010 c. M:-0.0015 c. 1159: 102 102 955 N M DE S SD: 0.0004 c. M:-0.0007 c. 1284: 113 113 1058 N M DE S SD: 0.0000 c. M:-0.0000 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: 89.6044 cents 7 x 8:9 S SD: 78.3578 cents 8 x 9:11 SD: 63.9366 cents 9 x 10:12 S SD: 47.3708 cents 10 x 11:13 SD: 44.4493 cents 11 x 12:15 S SD: 37.0118 cents 12 x 13:16 SD: 25.4553 cents 13 x 14:17 SD: 26.3696 cents 14 x 15:19 SD: 22.0735 cents 15 x 16:20 S SD: 12.0346 cents 16 x 17:21 SD: 16.1430 cents 17 x 18:23 SD: 13.8410 cents 18 x 19:24 SD: 2.9705 cents 19 x 20:25 S SD: 11.4794 cents 20 x 21:27 SD: 10.8712 cents 21 x 22:28 SD: 3.5625 cents 22 x 23:29 SD: 11.2482 cents 23 x 24:31 SD: 11.6809 cents 24 x 25:32 SD: 8.4948 cents 25 x 26:33 SD: 13.1650 cents 26:27 x 35 SD: 13.5737 cents 27:28 x 36 SD: 9.5649 cents 28:29 x 37 SD: 11.4824 cents 30:31:32:40 S SD: 9.1084 cents 31:32:33:41 SD: 9.0909 cents 32:33:34:43 SD: 7.9563 cents 33:34:35:44 SD: 5.4100 cents 35:36:37:47 SD: 5.2620 cents 36:37:38:48 SD: 2.3160 cents 39:40:41:52 SD: 0.3608 cents 153:157:161:204 SD: 0.3412 cents 192:197:202:256 SD: 0.2388 cents 231:237:243:308 SD: 0.1874 cents 270:277:284:360 SD: 0.1673 cents 309:317:325:412 SD: 0.1652 cents 579:594:609:772 SD: 0.1647 cents