Scala analysis: 560_M68
Miscellaneous tetrachord 12/11 * 297/256 * 256/243
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 12/11 150.637059 undecimal neutral second, 3/4-tone 2: 81/64 407.820003 Pythagorean major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 256/243 90.2250 limma, Pythagorean minor second 1: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 297/256 257.1829 3: 256/243 90.2250 limma, Pythagorean minor second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 297/256 257.183 cents 2: 1 1024/891 240.862 cents 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 81/64 407.820 cents Pythagorean major third 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 : 150.6 407.8 498.0 150.6: 257.2 347.4 498.0 407.8: 90.2 240.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 257.1829 cents 72171/65536, 166.9579 cents 256/243, 90.2250 cents 2: 240.8621 .. 407.8200 cents 72171/65536, 166.9579 cents 262144/264627,-16.3209 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 297/256, 257.1829 cents Average / Smallest step : 1.840011 Largest / Average step : 1.549155 Largest / Smallest step : 2.850462 Median interval of one step : 12/11, 150.6371 cents, amount: 1 Least squares average step : 175.74372 cents, oct.: 527.23116 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1220-tone equal temperament with octave 4/3 degrees: 369 999 1220 Least number of segments generator : 611 of 249.431 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1039 of 424.155 cents and inv. generated superset size: 30 = 27 more = 1000.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MLS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 16.32089 cents Scale diversity : 1.120464 Lumma stability : 0.362317 Lumma impropriety factor : 0.032770 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 : 264627/262144, 16.3209 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle 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% -- Rational properties -- Prime limit : 11 Odd number limit : 891 (O: 297 U: 891) Highest odd numerator or denominator: 81 Scale harmonicity : 0.025307 Average absolute harmonicity : 0.106017 Specific harmonicity : 0.129857 Fundamental : 1/2112, -11.0444 octaves, 0.1239 Hz. Guide tone : 324, 8.3399 octaves, 84766.683 Hz. Exponens Consonantiae : 6.842880E+05, 19.38424 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 87.5, average 29.16667 Mersenne's string divisions : 23345 Sum of van Prooijen's expressibility: 3.42700, average 1.14233 Sum of Tenney's harmonic distance : 6.91442, average 2.30481 Vogel's harmonic complexity : 19.66667 Wille's k value : 1336 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 32.16903, average 5.36151 Lattice compactness (without 2's) : 16.81256, average 2.80209 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 2 -0.66667 10 3: -1 .. 4 1.33333 6 2 11: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 3 / 3 = 1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is JI-epimorphic with val: <7 11 24| Scale is weakly epimorphic with val: <7 11 27|
FIT/MODE
3: 1 1 1 SP B ME I SD: 44.6490 c. M: 75.7900 c. 4: 1 2 1 P M ME I SD: 24.8871 c. M: 34.2863 c. 6: 2 3 1 P T3 SD: 9.8077 c. M:-15.3779 c. 10: 3 5 2 P T3 SD: 5.4637 c. M: 9.3840 c. 16: 5 8 3 P T3 SD: 3.4154 c. M:-5.0020 c. 17: 5 9 3 N T3 SD: 2.7508 c. M: 4.1532 c. 23: 7 12 4 N T3 SD: 2.1532 c. M:-3.6085 c. 27: 8 14 5 N T3 SD: 2.1163 c. M: 3.0682 c. 33: 10 17 6 N T3 SD: 0.2514 c. M: 0.3286 c. 116: 35 60 21 N T3 SD: 0.2136 c. M: 0.3649 c. 149: 45 77 27 N T3 SD: 0.1283 c. M: 0.2208 c. 182: 55 94 33 N T3 SD: 0.0876 c. M: 0.1290 c. 215: 65 111 39 N T3 SD: 0.0779 c. M: 0.1181 c. 337: 102 174 61 N T3 SD: 0.0750 c. M:-0.1065 c. 370: 112 191 67 N T3 SD: 0.0741 c. M:-0.1225 c. 397: 120 205 72 N T3 SD: 0.0797 c. M: 0.1005 c. 403: 122 208 73 N T3 SD: 0.0786 c. M:-0.1359 c. 420: 127 217 76 N T3 SD: 0.0631 c. M:-0.1026 c. 453: 137 234 82 N T3 SD: 0.0419 c. M:-0.0712 c. 486: 147 251 88 N T3 SD: 0.0257 c. M:-0.0440 c. 519: 157 268 94 N T3 SD: 0.0181 c. M:-0.0240 c. 701: 212 362 127 N T3 SD: 0.0097 c. M: 0.0157 c. 1187: 359 613 215 N T3 SD: 0.0093 c. M:-0.0147 c. 1220: 369 630 221 N T3 SD: 0.0032 c. M:-0.0054 c. 1921: 581 992 348 N T3 SD: 0.0030 c. M: 0.0050 c. 1954: 591 1009 354 N T3 SD: 0.0024 c. M: 0.0042 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: 21.5063 cents 5 x 6:7 S SD: 62.5132 cents 6:7 x 8 S SD: 58.1169 cents 7:8:9 x S SD: 42.5134 cents 8:9:10:11 H SD: 26.1163 cents 9:10:11:12 H SD: 22.7516 cents 10:11 x 13 SD: 23.0628 cents 11:12:14:15 S SD: 13.3646 cents 12:13:15:16 SD: 8.2197 cents 22:24:28:29 S SD: 7.3434 cents 23:25:29:31 SD: 6.9303 cents 30:33:38:40 SD: 4.8125 cents 33:36:42:44 S SD: 3.2293 cents 42:46:53:56 SD: 2.8477 cents 45:49:57:60 SD: 1.1703 cents 87:95:110:116 SD: 0.7963 cents 120:131:152:160 SD: 0.6212 cents 132:144:167:176 SD: 0.2159 cents 297:324:376:396 SD: 0.1679 cents 384:419:486:512 SD: 0.1252 cents 429:468:543:572 SD: 0.0498 cents 561:612:710:748 SD: 0.0127 cents