Scala analysis: 492_R16
Reduplicated tetrachord 46/45 * 46/45 * 675/529
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 46/45 38.050632 23rd-partial chroma 2: 2116/2025 76.101263 two (23rd-partial chroma) 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 675/529 421.9437 1: 46/45 38.0506 23rd-partial chroma 2: 46/45 38.0506 23rd-partial chroma 3: 675/529 421.9437
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 46/45 38.051 cents 23rd-partial chroma 1: 1 675/529 421.944 cents 2: 1 2116/2025 76.101 cents two (23rd-partial chroma) 2: 2 30/23 459.994 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 : 38.1 76.1 498.0 38.1 : 38.1 460.0 498.0 76.1 : 421.9 460.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.0506 .. 421.9437 cents 30375/24334, 383.8931 cents 46/45, 38.0506 cents 2: 76.1013 .. 459.9944 cents 30375/24334, 383.8931 cents 1119364/1366875,-345.8425 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 46/45, 38.0506 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 675/529, 421.9437 cents Average / Smallest step : 4.363002 Largest / Average step : 2.541600 Largest / Smallest step : 11.089007 Median interval of one step : 46/45, 38.0506 cents, amount: 2 Most common interval of one step : 46/45, 38.0506 cents, amount: 2 Least squares average step : 120.31344 cents, oct.: 360.94032 cents Scale is not proper Scale has Myhill's property chromas: 30375/24334, 383.8931 cents and 1366875/1119364, 345.8425 cents, ratio: 1.110023 generators: 1 of 38.05063 cents and 459.99437 cents ET pair of linear temperament : 26&288 Scale is distributional even Scale is a mode of a 445-tone equal temperament with octave 4/3 degrees: 34 68 445 generators: 34 and 411 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 38.05063 cents Scale diversity : 0.251796 Lumma stability : 0.152800 Lumma impropriety factor : 0.694400 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 : 46/45, 38.0506 cents Most common intervals : 46/45, 38.0506 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 : 23 Odd number limit : 2025 (O: 675 U: 2025) Highest odd numerator or denominator: 2025 Scale harmonicity : 0.009121 Average absolute harmonicity : 0.080549 Specific harmonicity : 0.041986 Fundamental : 1/2025, -10.9837 octaves, 0.1292 Hz. Guide tone : 2116, 11.0471 octaves, 553599.696 Hz. Exponens Consonantiae : 4.284900E+06, 22.03083 octaves Euler's gradus suavitatis : 63 Sum of Mann's harmonic distance : 2119.5, average 706.50000 Mersenne's string divisions : 376831 Sum of van Prooijen's expressibility: 5.43676, average 1.81225 Sum of Tenney's harmonic distance : 11.02709, average 3.67570 Vogel's harmonic complexity : 34.66667 Wille's k value : 517 Wilson's harmonic complexity : 68 Rectangular lattice diameter : 8 Triangular lattice diameter : 5 Lattice compactness : 18.94218, average 3.15703 Lattice compactness (without 2's) : 16.65312, average 2.77552 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -4 ..-1 -2.33333 7 1 5: -2 .. 0 -1.00000 3 23: 0 .. 2 1.00000 3 2 Average exponent except 2's :-7 / 3 =-2.33333 Average absolute exponent except 2's: 13 / 3 = 4.33333 Scale is JI-epimorphic with val: <7 11 15 31| Scale is weakly epimorphic with val: <7 11 15 32| Scale is weakly epimorphic with val: <7 11 15 34| Scale is weakly epimorphic with val: <7 11 15 35| Scale is weakly epimorphic with val: <7 11 16 30| Scale is JI-epimorphic with val: <7 11 16 32| Scale is weakly epimorphic with val: <7 11 16 33| Scale is weakly epimorphic with val: <7 11 16 35| Scale is weakly epimorphic with val: <7 11 16 36| Scale is weakly epimorphic with val: <7 11 17 30| Scale is weakly epimorphic with val: <7 11 17 31| Scale is JI-epimorphic with val: <7 11 17 33| = patent Scale is weakly epimorphic with val: <7 11 17 34| Scale is weakly epimorphic with val: <7 11 17 36| Scale is weakly epimorphic with val: <7 11 18 31| Scale is weakly epimorphic with val: <7 11 18 32| Scale is JI-epimorphic with val: <7 11 18 34| Scale is weakly epimorphic with val: <7 11 18 35| Scale is weakly epimorphic with val: <7 11 19 30| Scale is weakly epimorphic with val: <7 11 19 32| Scale is weakly epimorphic with val: <7 11 19 33| Scale is JI-epimorphic with val: <7 11 19 35| Scale is weakly epimorphic with val: <7 11 19 36|
FIT/MODE
3: 0 0 3 N M DE S SD: 49.1232 c. M: 76.1013 c. 5: 0 1 4 N G T3 SD: 25.8229 c. M: 38.0506 c. 6: 0 1 5 N G T3 SD: 22.3275 c. M: 38.0506 c. 7: 0 1 6 N G T3 SD: 22.1538 c. M: 38.0506 c. 8: 0 1 7 N G T3 SD: 23.3777 c. M: 38.0506 c. 9: 0 1 8 N G T3 SD: 25.0263 c. M: 38.0506 c. 10: 1 1 8 N M DE S SD: 15.1742 c. M:-23.5077 c. 11: 1 1 9 N M DE S SD: 9.3290 c. M:-14.4524 c. 12: 1 1 10 N M DE S SD: 4.4580 c. M:-6.9062 c. 13: 1 1 11 N M DE S SD: 0.3363 c. M:-0.5210 c. 79: 6 6 67 N M DE S SD: 0.2897 c. M: 0.4489 c. 92: 7 7 78 N M DE S SD: 0.2013 c. M: 0.3118 c. 105: 8 8 89 N M DE S SD: 0.1347 c. M: 0.2087 c. 118: 9 9 100 N M DE S SD: 0.0828 c. M: 0.1283 c. 131: 10 10 111 N M DE S SD: 0.0412 c. M: 0.0639 c. 144: 11 11 122 N M DE S SD: 0.0071 c. M: 0.0111 c. 445: 34 34 377 N M DE S SD: 0.0029 c. M:-0.0045 c. 589: 45 45 499 N M DE S SD: 0.0004 c. M:-0.0007 c. 1322: 101 101 1120 N M DE S SD: 0.0004 c. M: 0.0006 c. 1911: 146 146 1619 N M DE S SD: 0.0001 c. M: 0.0002 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: 95.3848 cents 7 x 8:9 S SD: 83.6834 cents 8 x 9:11 SD: 69.2334 cents 9 x 10:12 S SD: 53.1512 cents 10 x 11:13 SD: 49.5603 cents 11 x 12:15 S SD: 42.0394 cents 12 x 13:16 SD: 31.2357 cents 13 x 14:17 SD: 31.0429 cents 14 x 15:19 SD: 26.5397 cents 15 x 16:20 S SD: 17.8150 cents 16 x 17:21 SD: 19.8488 cents 17 x 18:23 SD: 17.0371 cents 18 x 19:24 SD: 8.7509 cents 19 x 20:25 S SD: 13.1062 cents 20 x 21:27 SD: 11.5381 cents 21 x 22:28 SD: 2.2179 cents 22 x 23:29 SD: 9.9021 cents 23 x 24:31 SD: 9.4361 cents 24 x 25:32 SD: 2.7144 cents 25 x 26:33 SD: 9.6177 cents 26 x 27:35 SD: 9.8783 cents 27 x 28:36 SD: 6.5702 cents 28 x 29:37 SD: 10.9168 cents 29 x 30:39 SD: 11.4448 cents 30:31 x 40 SD: 9.3581 cents 31:32 x 41 SD: 10.9839 cents 32:33 x 43 SD: 10.1641 cents 33:34 x 44 SD: 6.8159 cents 36:37:38:48 SD: 6.6195 cents 38:39:40:51 SD: 6.1285 cents 39:40:41:52 SD: 3.9890 cents 42:43:44:56 SD: 1.7286 cents 45:46:47:60 SD: 0.2728 cents 177:181:185:236 SD: 0.2564 cents 222:227:232:296 SD: 0.1795 cents 267:273:279:356 SD: 0.1410 cents 312:319:326:416 SD: 0.1261 cents 357:365:373:476 SD: 0.1246 cents