Scala analysis: 563_M71
Miscellaneous tetrachord 81/70 * 256/243 * 35/32
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 81/70 252.680383 Al-Hwarizmi's lute middle finger 2: 128/105 342.905379 septimal neutral third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 35/32 155.1396 septimal neutral second 1: 81/70 252.6804 Al-Hwarizmi's lute middle finger 2: 256/243 90.2250 limma, Pythagorean minor second 3: 35/32 155.1396 septimal neutral second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 35/32 155.140 cents septimal neutral second 1: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 280/243 245.365 cents 2: 1 128/105 342.905 cents septimal 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 : 252.7 342.9 498.0 252.7: 90.2 245.4 498.0 342.9: 155.1 407.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 252.6804 cents 19683/17920, 162.4554 cents 256/243, 90.2250 cents 2: 245.3646 .. 407.8200 cents 19683/17920, 162.4554 cents 19600/19683,-7.3158 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 : 81/70, 252.6804 cents Average / Smallest step : 1.840011 Largest / Average step : 1.522033 Largest / Smallest step : 2.800559 Median interval of one step : 35/32, 155.1396 cents, amount: 1 Least squares average step : 173.75901 cents, oct.: 521.27703 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1496-tone equal temperament with octave 4/3 degrees: 759 1030 1496 Least number of segments generator : 749 of 249.355 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 885 of 294.632 cents and inv. generated superset size: 70 = 67 more = 2333.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LSM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 7.31577 cents Scale diversity : 1.109029 Lumma stability : 0.362317 Lumma impropriety factor : 0.014689 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 : 19683/19600, 7.3158 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 7 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 105 Scale harmonicity : 0.026303 Average absolute harmonicity : 0.095834 Specific harmonicity : 0.118160 Fundamental : 1/210, -7.7142 octaves, 1.2458 Hz. Guide tone : 10368, 13.3399 octaves, 2712533.861 Hz. Exponens Consonantiae : 2.177280E+06, 21.05410 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 195.5, average 65.16667 Mersenne's string divisions : 246281 Sum of van Prooijen's expressibility: 4.40680, average 1.46893 Sum of Tenney's harmonic distance : 8.96116, average 2.98705 Vogel's harmonic complexity : 12.66667 Wille's k value : 121 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 34.43620, average 5.73937 Lattice compactness (without 2's) : 18.58506, average 3.09751 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 7 2.66667 10 3: -1 .. 4 0.66667 6 1 5: -1 .. 0 -0.66667 2 7: -1 .. 0 -0.66667 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <6 11 15 20| Scale is weakly epimorphic with val: <6 11 16 19| Scale is weakly epimorphic with val: <6 11 17 18| Scale is weakly epimorphic with val: <7 11 15 18| Scale is JI-epimorphic with val: <7 11 15 21| Scale is JI-epimorphic with val: <7 11 16 20| Scale is JI-epimorphic with val: <7 11 17 19| Scale is weakly epimorphic with val: <7 11 17 22| Scale is JI-epimorphic with val: <7 11 18 18| Scale is weakly epimorphic with val: <7 11 18 21| Scale is weakly epimorphic with val: <7 11 19 20| Scale is weakly epimorphic with val: <7 12 15 19| Scale is weakly epimorphic with val: <7 12 16 18| Scale is weakly epimorphic with val: <8 12 19 22|
FIT/MODE
3: 1 1 1 SP B ME I SD: 50.4287 c. M: 86.6654 c. 4: 2 1 1 P M ME S SD: 17.8090 c. M:-30.6284 c. 6: 3 1 2 P T3 SD: 6.6246 c. M: 10.8754 c. 10: 5 2 3 P T3 SD: 3.9229 c. M:-5.7261 c. 16: 8 3 5 P T3 SD: 2.1315 c. M: 3.6579 c. 35: 18 6 11 N T3 SD: 2.1510 c. M:-3.4570 c. 38: 19 7 12 P T3 SD: 2.4461 c. M: 3.6579 c. 39: 20 7 12 N T3 SD: 1.9174 c. M:-2.7273 c. 45: 23 8 14 N T3 SD: 1.0888 c. M:-1.8759 c. 51: 26 9 16 N T3 SD: 0.9543 c. M:-1.2249 c. 55: 28 10 17 N T3 SD: 0.8549 c. M:-1.1984 c. 61: 31 11 19 N T3 SD: 0.2451 c. M:-0.4245 c. 77: 39 14 24 N T3 SD: 0.2508 c. M: 0.4238 c. 138: 70 25 43 N T3 SD: 0.0397 c. M: 0.0489 c. 337: 171 61 105 N T3 SD: 0.0304 c. M: 0.0376 c. 475: 241 86 148 N T3 SD: 0.0245 c. M: 0.0407 c. 613: 311 111 191 N T3 SD: 0.0245 c. M: 0.0424 c. 745: 378 135 232 N T3 SD: 0.0275 c. M:-0.0437 c. 751: 381 136 234 N T3 SD: 0.0258 c. M: 0.0435 c. 822: 417 149 256 N T3 SD: 0.0220 c. M:-0.0307 c. 883: 448 160 275 N T3 SD: 0.0176 c. M:-0.0293 c. 960: 487 174 299 N T3 SD: 0.0189 c. M: 0.0263 c. 1021: 518 185 318 N T3 SD: 0.0109 c. M:-0.0188 c. 1159: 588 210 361 N T3 SD: 0.0070 c. M:-0.0109 c. 1297: 658 235 404 N T3 SD: 0.0063 c. M: 0.0099 c. 1358: 689 246 423 N T3 SD: 0.0062 c. M:-0.0096 c. 1496: 759 271 466 N T3 SD: 0.0024 c. M:-0.0042 c. 1634: 829 296 509 N T3 SD: 0.0024 c. M: 0.0041 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: 43.4083 cents 5 x 6:7 S SD: 44.3792 cents 6:7 x 8 S SD: 7.0953 cents 7:8 x 9 S SD: 33.2663 cents 8:9:10:11 H SD: 28.0888 cents 9:10:11:12 H SD: 23.4736 cents 10 x 12:13 S SD: 25.8094 cents 11:13 x 15 SD: 26.6836 cents 12:14:15:16 S SD: 15.2230 cents 13:15:16:17 SD: 12.6006 cents 18:21:22:24 S SD: 4.9626 cents 27:31:33:36 SD: 4.7468 cents 32:37:39:43 SD: 4.5151 cents 33:38:40:44 SD: 4.3276 cents 45:52:55:60 SD: 1.6971 cents 51:59:62:68 SD: 1.5995 cents 69:80:84:92 SD: 1.3795 cents 96:111:117:128 SD: 0.4672 cents 114:132:139:152 SD: 0.3932 cents 210:243:256:280 SD: 0.0000 cents