Scala analysis: 490_R14
Reduplicated tetrachord 36/35 * 36/35 * 1225/972
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 2: 1296/1225 97.540763 two (septimal diesis, 1/4-tone) 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 1225/972 400.5042 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 1225/972 400.5042
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 1225/972 400.504 cents 2: 1 1296/1225 97.541 cents two (septimal diesis, 1/4-tone) 2: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 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 : 48.8 97.5 498.0 48.8 : 48.8 449.3 498.0 97.5 : 400.5 449.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 400.5042 cents 42875/34992, 351.7339 cents 36/35, 48.7704 cents 2: 97.5408 .. 449.2746 cents 42875/34992, 351.7339 cents 1259712/1500625,-302.9635 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 1225/972, 400.5042 cents Average / Smallest step : 3.404013 Largest / Average step : 2.412458 Largest / Smallest step : 8.212038 Median interval of one step : 36/35, 48.7704 cents, amount: 2 Most common interval of one step : 36/35, 48.7704 cents, amount: 2 Least squares average step : 124.14192 cents, oct.: 372.42577 cents Scale is not proper Scale has Myhill's property chromas: 42875/34992, 351.7339 cents and 1500625/1259712, 302.9635 cents, ratio: 1.160978 generators: 1 of 48.77038 cents and 449.27462 cents ET pair of linear temperament : 20&82 Scale is distributional even Scale is a mode of a 337-tone equal temperament with octave 4/3 degrees: 33 66 337 generators: 33 and 304 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 48.77038 cents Scale diversity : 0.411921 Lumma stability : 0.195847 Lumma impropriety factor : 0.608305 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 : 36/35, 48.7704 cents Most common intervals : 36/35, 48.7704 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 : 7 Odd number limit : 1225 (O: 1225 U: 1225) Highest odd numerator or denominator: 1225 Scale harmonicity : 0.019722 Average absolute harmonicity : 0.092245 Specific harmonicity : 0.091883 Fundamental : 1/3675, -11.8435 octaves, 0.0712 Hz. Guide tone : 1296, 10.3399 octaves, 339066.733 Hz. Exponens Consonantiae : 4.762800E+06, 22.18338 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 1299.5, average 433.16667 Mersenne's string divisions : 1252937 Sum of van Prooijen's expressibility: 5.10933, average 1.70311 Sum of Tenney's harmonic distance : 10.38029, average 3.46010 Vogel's harmonic complexity : 22.66667 Wille's k value : 612 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 9 Triangular lattice diameter : 5 Lattice compactness : 24.28457, average 4.04743 Lattice compactness (without 2's) : 19.85915, average 3.30986 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 2.66667 8 3: -1 .. 4 1.66667 7 1 5: -2 .. 0 -1.00000 3 7: -2 .. 0 -1.00000 3 2 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 13 / 3 = 4.33333 Scale is weakly epimorphic with val: <7 11 15 19| Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 15 22| Scale is weakly epimorphic with val: <7 11 16 18| Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 11 16 21| Scale is weakly epimorphic with val: <7 11 16 22| Scale is JI-epimorphic with val: <7 11 17 18| Scale is weakly epimorphic with val: <7 11 17 20| = patent Scale is weakly epimorphic with val: <7 11 17 21| Scale is weakly epimorphic with val: <7 11 18 19| Scale is weakly epimorphic with val: <7 11 18 20| Scale is weakly epimorphic with val: <7 11 18 22| Scale is weakly epimorphic with val: <7 11 19 19| Scale is weakly epimorphic with val: <7 11 19 21| Scale is weakly epimorphic with val: <7 11 19 22|
FIT/MODE
3: 0 0 3 N M DE S SD: 62.9623 c. M: 97.5408 c. 4: 0 1 3 N G T3 SD: 32.1764 c. M: 48.7704 c. 5: 0 1 4 N G T3 SD: 28.1829 c. M: 48.7704 c. 6: 0 1 5 N G T3 SD: 29.3812 c. M: 48.7704 c. 7: 0 1 6 N G T3 SD: 32.0159 c. M: 48.7704 c. 8: 1 1 6 N M DE S SD: 17.4094 c. M:-26.9705 c. 9: 1 1 7 N M DE S SD: 8.4792 c. M:-13.1359 c. 10: 1 1 8 N M DE S SD: 1.3350 c. M:-2.0682 c. 31: 3 3 25 N M DE S SD: 0.7391 c. M: 1.1450 c. 41: 4 4 33 N M DE S SD: 0.2332 c. M: 0.3613 c. 51: 5 5 41 N M DE S SD: 0.0743 c. M:-0.1151 c. 92: 9 9 74 N M DE S SD: 0.0627 c. M: 0.0972 c. 143: 14 14 115 N M DE S SD: 0.0139 c. M: 0.0215 c. 194: 19 19 156 N M DE S SD: 0.0093 c. M:-0.0144 c. 337: 33 33 271 N M DE S SD: 0.0005 c. M: 0.0008 c. 1879: 184 184 1511 N M DE S SD: 0.0005 c. M:-0.0008 c. 2216: 217 217 1782 N M DE S SD: 0.0003 c. M:-0.0005 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: 84.6651 cents 7 x 8:9 S SD: 73.8613 cents 8 x 9:11 SD: 59.4820 cents 9 x 10:12 S SD: 42.4315 cents 10 x 11:13 SD: 40.2259 cents 11 x 12:15 S SD: 32.9123 cents 12 x 13:16 SD: 20.5159 cents 13 x 14:17 SD: 22.7824 cents 14 x 15:19 SD: 18.8324 cents 15 x 16:20 S SD: 7.0953 cents 16 x 17:21 SD: 14.1272 cents 17 x 18:23 SD: 12.6567 cents 18 x 19:24 SD: 1.9689 cents 19 x 20:25 S SD: 12.2699 cents 20 x 21:27 SD: 12.5841 cents 21 x 22:28 SD: 8.5019 cents 22 x 23:29 SD: 14.2758 cents 23 x 24:31 SD: 15.1625 cents 24:25 x 32 SD: 10.9510 cents 25:26 x 33 SD: 12.9296 cents 26:27:28:35 S SD: 12.8882 cents 27:28:29:36 SD: 9.9237 cents 28:29:30:37 SD: 9.7998 cents 29:30:31:39 SD: 8.4347 cents 30:31:32:40 S SD: 5.4295 cents 32:33:34:43 SD: 5.3413 cents 33:34:35:44 SD: 1.7383 cents 36:37:38:48 SD: 1.3861 cents 69:71:73:92 SD: 0.2324 cents 243:250:257:324 SD: 0.2303 cents 312:321:330:416 SD: 0.2120 cents 381:392:403:508 SD: 0.2055 cents 450:463:476:600 SD: 0.2037 cents