Scala analysis: 551_M59
Miscellaneous tetrachord 120/113 * 113/106 * 53/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 120/113 104.053960 2: 60/53 214.764169 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 53/45 283.2808 1: 120/113 104.0540 2: 113/106 110.7102 3: 53/45 283.2808
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 120/113 104.054 cents 1: 1 113/106 110.710 cents 1: 1 53/45 283.281 cents 2: 1 60/53 214.764 cents 2: 1 424/339 387.335 cents 2: 1 113/90 393.991 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 104.1 214.8 498.0 104.1: 110.7 394.0 498.0 214.8: 283.3 387.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 104.0540 .. 283.2808 cents 5989/5400, 179.2269 cents 120/113, 104.0540 cents 2: 214.7642 .. 393.9910 cents 5989/5400, 179.2269 cents 2700/2809,-68.5167 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 120/113, 104.0540 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 53/45, 283.2808 cents Average / Smallest step : 1.595470 Largest / Average step : 1.706357 Largest / Smallest step : 2.722442 Median interval of one step : 113/106, 110.7102 cents, amount: 1 Least squares average step : 144.83695 cents, oct.: 434.51085 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1570-tone equal temperament with octave 4/3 degrees: 328 677 1570 Least number of segments generator : 787 of 249.657 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 903 of 286.455 cents and inv. generated superset size: 57 = 54 more = 1900.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 68.51666 cents Scale diversity : 1.121641 Lumma stability : 0.417850 Lumma impropriety factor : 0.137571 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 12769/12720, 6.6562 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 172.5706 cents: 2 -- Rational properties -- Prime limit : 113 Odd number limit : 339 (O: 113 U: 339) Highest odd numerator or denominator: 113 Scale harmonicity : 0.067873 Fundamental : 1/17967, -14.1331 octaves, 0.0146 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 2.156040E+06, 21.03995 octaves Euler's gradus suavitatis : 176 Sum of Mann's harmonic distance : 176.5, average 58.83333 Mersenne's string divisions : 184303 Sum of van Prooijen's expressibility: 4.25448, average 1.41816 Sum of Tenney's harmonic distance : 8.71387, average 2.90462 Vogel's harmonic complexity : 120.33333 Wille's k value : 2994 Wilson's harmonic complexity : 177 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.68774, average 2.28129 Lattice compactness (without 2's) : 8.30056, average 1.38343 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.66667 2 53: -1 .. 0 -0.33333 1 1 113: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <7 10 19 40 48| Scale is weakly epimorphic with val: <7 11 15 41 49| Scale is weakly epimorphic with val: <7 11 15 42 48| Scale is weakly epimorphic with val: <7 11 16 40 49| Scale is weakly epimorphic with val: <7 11 16 42 50| Scale is JI-epimorphic with val: <7 11 17 40 48| Scale is weakly epimorphic with val: <7 11 17 41 50| Scale is JI-epimorphic with val: <7 11 18 41 49| Scale is weakly epimorphic with val: <7 11 18 42 48| Scale is weakly epimorphic with val: <7 11 19 40 49| Scale is JI-epimorphic with val: <7 11 19 42 50| Scale is weakly epimorphic with val: <7 12 17 40 49| Scale is weakly epimorphic with val: <7 12 18 40 48| Scale is weakly epimorphic with val: <7 12 18 41 50| Scale is weakly epimorphic with val: <7 12 19 41 49| Scale is weakly epimorphic with val: <7 12 19 42 48| Scale is weakly epimorphic with val: <8 11 16 40 50| Scale is weakly epimorphic with val: <8 11 16 42 48| Scale is weakly epimorphic with val: <8 11 17 40 49| Scale is weakly epimorphic with val: <8 11 17 41 48| Scale is weakly epimorphic with val: <8 11 18 41 50| Scale is weakly epimorphic with val: <8 11 18 42 49| Scale is weakly epimorphic with val: <8 12 15 40 49| Scale is weakly epimorphic with val: <8 12 15 41 48| Scale is weakly epimorphic with val: <8 12 16 41 50| Scale is weakly epimorphic with val: <8 12 16 42 49| Scale is weakly epimorphic with val: <8 12 17 40 50| Scale is weakly epimorphic with val: <8 12 17 42 48|
FIT/MODE
3: 0 1 2 N G T3 SD: 66.3418 c. M: 104.0540 c. 4: 1 1 2 P M ME S SD: 23.0372 c. M:-34.2583 c. 5: 1 1 3 N M DE S SD: 9.3353 c. M: 15.5462 c. 9: 2 2 5 N M DE S SD: 5.3937 c. M:-6.6227 c. 14: 3 3 8 N M DE S SD: 1.7187 c. M:-2.6700 c. 39: 8 9 22 N T3 SD: 1.7335 c. M:-2.3324 c. 44: 9 10 25 N T3 SD: 1.2712 c. M: 2.1811 c. 53: 11 12 30 N T3 SD: 0.8839 c. M:-1.3686 c. 58: 12 13 33 N T3 SD: 0.5855 c. M: 1.0102 c. 67: 14 15 38 N T3 SD: 0.4663 c. M:-0.8075 c. 72: 15 16 41 N T3 SD: 0.2546 c. M: 0.3281 c. 139: 29 31 79 N T3 SD: 0.1519 c. M:-0.2193 c. 153: 32 34 87 N T3 SD: 0.0792 c. M:-0.1123 c. 225: 47 50 128 N T3 SD: 0.0314 c. M: 0.0514 c. 378: 79 84 215 N T3 SD: 0.0201 c. M:-0.0348 c. 603: 126 134 343 N T3 SD: 0.0138 c. M: 0.0184 c. 967: 202 215 550 N T3 SD: 0.0101 c. M: 0.0156 c. 1120: 234 249 637 N T3 SD: 0.0103 c. M:-0.0177 c. 1192: 249 265 678 N T3 SD: 0.0094 c. M: 0.0160 c. 1345: 281 299 765 N T3 SD: 0.0037 c. M:-0.0062 c. 1570: 328 349 893 N T3 SD: 0.0025 c. M: 0.0038 c. 1948: 407 433 1108 N T3 SD: 0.0023 c. M:-0.0037 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 6:7 S SD: 65.7854 cents 6 x 7:8 S SD: 26.0534 cents 7 x 8:9 S SD: 32.5321 cents 8 x 9:11 SD: 27.1837 cents 9 x 10:12 S SD: 16.1802 cents 10 x 11:13 SD: 33.1557 cents 11:12 x 15 S SD: 30.3465 cents 12:13:14:16 S SD: 20.8344 cents 13:14:15:17 SD: 17.6553 cents 14:15:16:19 SD: 12.6712 cents 15:16:17:20 SD: 2.6381 cents 66:70:75:88 SD: 2.3004 cents 78:83:88:104 SD: 2.2968 cents 81:86:92:108 SD: 1.9004 cents 84:89:95:112 SD: 1.4373 cents 99:105:112:132 SD: 0.8263 cents 114:121:129:152 SD: 0.3890 cents 129:137:146:172 SD: 0.1537 cents 582:618:659:776 SD: 0.1258 cents