Scala analysis: 559_M67
Miscellaneous tetrachord 68/65 * 65/56 * 56/51
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/65 78.114034 Valentine semitone 2: 17/14 336.129503 supraminor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 56/51 161.9155 1: 68/65 78.1140 Valentine semitone 2: 65/56 258.0155 3: 56/51 161.9155
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 68/65 78.114 cents Valentine semitone 1: 1 56/51 161.915 cents 1: 1 65/56 258.015 cents 2: 1 224/195 240.030 cents 2: 1 17/14 336.130 cents supraminor third 2: 1 65/51 419.931 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 : 78.1 336.1 498.0 78.1 : 258.0 419.9 498.0 336.1: 161.9 240.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 78.1140 .. 258.0155 cents 4225/3808, 179.9014 cents 68/65, 78.1140 cents 2: 240.0295 .. 419.9310 cents 4225/3808, 179.9014 cents 12544/12675,-17.9859 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 68/65, 78.1140 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 65/56, 258.0155 cents Average / Smallest step : 2.125290 Largest / Average step : 1.554170 Largest / Smallest step : 3.303062 Median interval of one step : 56/51, 161.9155 cents, amount: 1 Least squares average step : 160.32200 cents, oct.: 480.96601 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1052-tone equal temperament with octave 4/3 degrees: 165 710 1052 Least number of segments generator : 527 of 249.496 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 545 of 258.018 cents and inv. generated superset size: 20 = 17 more = 666.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 17.98594 cents Scale diversity : 1.051455 Lumma stability : 0.313683 Lumma impropriety factor : 0.036113 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 : 12675/12544, 17.9859 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 17 Odd number limit : 195 (O: 65 U: 195) Highest odd numerator or denominator: 65 Scale harmonicity : 0.013401 Average absolute harmonicity : 0.084973 Specific harmonicity : 0.062502 Fundamental : 1/2730, -11.4147 octaves, 0.0958 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 1.856400E+05, 17.50215 octaves Euler's gradus suavitatis : 44 Sum of Mann's harmonic distance : 85.5, average 28.50000 Mersenne's string divisions : 4123 Sum of van Prooijen's expressibility: 3.52048, average 1.17349 Sum of Tenney's harmonic distance : 7.10118, average 2.36706 Vogel's harmonic complexity : 32.00000 Wille's k value : 1657 Wilson's harmonic complexity : 45 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 15.54207, average 2.59035 Lattice compactness (without 2's) : 9.61037, average 1.60173 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 1.00000 5 3: -1 .. 0 -0.33333 1 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 13: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 11 16 19 26 30| Scale is weakly epimorphic with val: <7 11 16 19 28 31| Scale is JI-epimorphic with val: <7 11 16 20 26 29| Scale is weakly epimorphic with val: <7 11 16 20 27 31| Scale is JI-epimorphic with val: <7 11 16 21 27 30| Scale is weakly epimorphic with val: <7 11 16 21 28 29| Scale is weakly epimorphic with val: <7 11 17 19 27 31| Scale is weakly epimorphic with val: <7 11 17 19 28 30| Scale is weakly epimorphic with val: <7 11 17 20 26 31| Scale is weakly epimorphic with val: <7 11 17 20 28 29| Scale is JI-epimorphic with val: <7 11 17 21 26 30| Scale is weakly epimorphic with val: <7 11 17 21 27 29| Scale is weakly epimorphic with val: <7 11 18 19 26 31| Scale is weakly epimorphic with val: <7 11 18 19 27 30| Scale is weakly epimorphic with val: <7 11 18 20 27 29| Scale is weakly epimorphic with val: <7 11 18 20 28 31| Scale is weakly epimorphic with val: <7 11 18 21 26 29| Scale is weakly epimorphic with val: <7 11 18 21 28 30| Scale is weakly epimorphic with val: <7 12 16 19 26 29| Scale is weakly epimorphic with val: <7 12 16 20 26 31| Scale is weakly epimorphic with val: <7 12 16 20 27 30| Scale is weakly epimorphic with val: <7 12 16 21 28 31| Scale is weakly epimorphic with val: <7 12 17 19 28 29| Scale is weakly epimorphic with val: <7 12 17 20 26 30| Scale is weakly epimorphic with val: <7 12 17 21 27 31| Scale is weakly epimorphic with val: <7 12 18 19 27 29| Scale is weakly epimorphic with val: <7 12 18 20 28 30| Scale is weakly epimorphic with val: <7 12 18 21 26 31|
FIT/MODE
3: 0 2 1 N G T3 SD: 45.1612 c. M: 78.1140 c. 4: 1 2 1 P M ME I SD: 34.4082 c. M:-46.3972 c. 5: 1 2 2 SP M ME S SD: 24.8563 c. M: 37.3025 c. 6: 1 3 2 P T3 SD: 3.6856 c. M:-4.8935 c. 19: 3 10 6 N T3 SD: 2.6949 c. M:-4.6381 c. 25: 4 13 8 N T3 SD: 1.7255 c. M:-2.5411 c. 31: 5 16 10 N T3 SD: 1.4705 c. M:-2.2158 c. 46: 7 24 15 N T3 SD: 1.3716 c. M: 2.3246 c. 52: 8 27 17 N T3 SD: 1.0079 c. M: 1.4917 c. 58: 9 30 19 N T3 SD: 0.8605 c. M: 1.2372 c. 71: 11 37 23 N T3 SD: 0.6428 c. M: 0.9521 c. 77: 12 40 25 N T3 SD: 0.3119 c. M: 0.4966 c. 83: 13 43 27 N T3 SD: 0.0842 c. M: 0.1070 c. 357: 56 185 116 N T3 SD: 0.0499 c. M:-0.0857 c. 440: 69 228 143 N T3 SD: 0.0301 c. M:-0.0509 c. 446: 70 231 145 N T3 SD: 0.0316 c. M:-0.0545 c. 523: 82 271 170 N T3 SD: 0.0219 c. M:-0.0271 c. 529: 83 274 172 N T3 SD: 0.0203 c. M:-0.0291 c. 612: 96 317 199 N T3 SD: 0.0187 c. M: 0.0305 c. 886: 139 459 288 N T3 SD: 0.0182 c. M:-0.0228 c. 969: 152 502 315 N T3 SD: 0.0094 c. M:-0.0123 c. 1052: 165 545 342 N T3 SD: 0.0022 c. M:-0.0035 c. 2187: 343 1133 711 N T3 SD: 0.0016 c. M: 0.0027 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 5 x S SD: 50.1842 cents 5 x 6:7 S SD: 43.4582 cents 6 x 7:8 S SD: 34.6293 cents 7 x x 9 SD: 62.9609 cents 8:9:10:11 H SD: 48.5124 cents 9:10:11:12 H SD: 34.9659 cents 10:11:12:13 H SD: 33.1509 cents 11:12:13:15 SD: 31.5783 cents 12:13:15:16 SD: 26.1910 cents 13:14:16:17 S SD: 21.5856 cents 14:15:17:19 SD: 17.1497 cents 15:16:18:20 S SD: 13.1229 cents 18:19:22:24 SD: 6.3867 cents 24:25:29:32 SD: 3.7676 cents 42:44:51:56 SD: 0.8077 cents 108:113:131:144 SD: 0.6339 cents 150:157:182:200 SD: 0.5339 cents 192:201:233:256 SD: 0.5322 cents 195:204:237:260 SD: 0.5220 cents 219:229:266:292 SD: 0.3125 cents 261:273:317:348 SD: 0.1626 cents 303:317:368:404 SD: 0.1155 cents 369:386:448:492 SD: 0.1029 cents 411:430:499:548 SD: 0.0923 cents