Scala analysis: 090_E10
Enharmonic tetrachord 54/53 * 53/51 * 34/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 54/53 32.360457 2: 18/17 98.954592 Arabic lute index finger 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 34/27 399.0904 septendecimal major third 1: 54/53 32.3605 2: 53/51 66.5941 3: 34/27 399.0904 septendecimal major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 54/53 32.360 cents 1: 1 53/51 66.594 cents 1: 1 34/27 399.090 cents septendecimal major third 2: 1 18/17 98.955 cents Arabic lute index finger 2: 1 68/53 431.451 cents 2: 1 106/81 465.685 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 : 32.4 99.0 498.0 32.4 : 66.6 465.7 498.0 99.0 : 399.1 431.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 32.3605 .. 399.0904 cents 901/729, 366.7299 cents 54/53, 32.3605 cents 2: 98.9546 .. 465.6845 cents 901/729, 366.7299 cents 243/289,-300.1358 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 54/53, 32.3605 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 34/27, 399.0904 cents Average / Smallest step : 5.130181 Largest / Average step : 2.403942 Largest / Smallest step : 12.332657 Median interval of one step : 53/51, 66.5941 cents, amount: 1 Least squares average step : 123.17176 cents, oct.: 369.51528 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1062-tone equal temperament with octave 4/3 degrees: 69 211 1062 Least number of segments generator : 533 of 249.960 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1039 of 487.259 cents and inv. generated superset size: 41 = 38 more = 1366.667% 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 32.36046 cents Scale diversity : 0.384221 Lumma stability : 0.129950 Lumma impropriety factor : 0.602628 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 : 54/53, 32.3605 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly 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% -- Rational properties -- Prime limit : 53 Odd number limit : 81 (O: 53 U: 81) Highest odd numerator or denominator: 53 Scale harmonicity : 0.023373 Fundamental : 1/2703, -11.4003 octaves, 0.0968 Hz. Guide tone : 108, 6.7549 octaves, 28255.561 Hz. Exponens Consonantiae : 2.919240E+05, 18.15523 octaves Euler's gradus suavitatis : 79 Sum of Mann's harmonic distance : 74.5, average 24.83333 Mersenne's string divisions : 3745 Sum of van Prooijen's expressibility: 3.43185, average 1.14395 Sum of Tenney's harmonic distance : 7.02157, average 2.34052 Vogel's harmonic complexity : 55.00000 Wille's k value : 715 Wilson's harmonic complexity : 82 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 16.70178, average 2.78363 Lattice compactness (without 2's) : 14.81256, average 2.46876 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.33333 4 3: -1 .. 3 1.33333 6 1 17: -1 .. 0 -0.33333 1 1 53: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 2 / 3 = 0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 11 27 42| Scale is weakly epimorphic with val: <7 11 28 41| Scale is weakly epimorphic with val: <7 11 30 42| Scale is weakly epimorphic with val: <7 11 31 41| Scale is weakly epimorphic with val: <7 11 33 42| Scale is weakly epimorphic with val: <7 12 27 40| Scale is weakly epimorphic with val: <7 12 28 42| Scale is weakly epimorphic with val: <7 12 30 40| Scale is weakly epimorphic with val: <7 12 33 40| Scale is weakly epimorphic with val: <8 11 27 40| Scale is weakly epimorphic with val: <8 12 27 41| Scale is weakly epimorphic with val: <8 12 29 42| Scale is weakly epimorphic with val: <8 12 30 41| Scale is weakly epimorphic with val: <8 12 33 41|
FIT/MODE
3: 0 0 3 N M DE S SD: 60.1088 c. M: 98.9546 c. 4: 0 1 3 N G T3 SD: 23.8072 c. M: 32.3605 c. 5: 0 1 4 N G T3 SD: 18.6871 c. M: 32.3605 c. 6: 0 1 5 N G T3 SD: 20.8287 c. M: 32.3605 c. 9: 1 1 7 N M DE S SD: 14.8928 c. M:-22.9779 c. 10: 1 1 8 N M DE S SD: 10.0784 c. M:-17.4440 c. 11: 1 1 9 N M DE S SD: 8.8959 c. M:-12.9164 c. 13: 1 2 10 N T3 SD: 9.8444 c. M:-15.9789 c. 14: 1 2 11 N T3 SD: 4.8543 c. M:-7.7693 c. 15: 1 2 12 N T3 SD: 0.6159 c. M:-0.8425 c. 61: 4 8 49 N T3 SD: 0.5906 c. M: 0.9785 c. 76: 5 10 61 N T3 SD: 0.4454 c. M: 0.6562 c. 91: 6 12 73 N T3 SD: 0.3750 c. M:-0.4777 c. 106: 7 14 85 N T3 SD: 0.3472 c. M:-0.5293 c. 121: 8 16 97 N T3 SD: 0.3422 c. M:-0.5681 c. 136: 9 18 109 N T3 SD: 0.3484 c. M:-0.5984 c. 141: 9 19 113 N T3 SD: 0.3307 c. M: 0.5704 c. 156: 10 21 125 N T3 SD: 0.2510 c. M: 0.4345 c. 171: 11 23 137 N T3 SD: 0.1908 c. M: 0.3225 c. 186: 12 25 149 N T3 SD: 0.1487 c. M: 0.2285 c. 201: 13 27 161 N T3 SD: 0.1256 c. M:-0.1588 c. 216: 14 29 173 N T3 SD: 0.1207 c. M:-0.1933 c. 231: 15 31 185 N T3 SD: 0.1294 c. M:-0.2232 c. 232: 15 31 186 N T3 SD: 0.1496 c. M: 0.2043 c. 246: 16 33 197 N T3 SD: 0.1453 c. M:-0.2495 c. 247: 16 33 198 N T3 SD: 0.1046 c. M: 0.1521 c. 262: 17 35 210 N T3 SD: 0.0664 c. M: 0.1060 c. 277: 18 37 222 N T3 SD: 0.0375 c. M: 0.0648 c. 292: 19 39 234 N T3 SD: 0.0313 c. M:-0.0466 c. 569: 37 76 456 N T3 SD: 0.0303 c. M: 0.0458 c. 740: 48 99 593 N T3 SD: 0.0334 c. M: 0.0548 c. 755: 49 101 605 N T3 SD: 0.0216 c. M: 0.0370 c. 770: 50 103 617 N T3 SD: 0.0123 c. M: 0.0199 c. 785: 51 105 629 N T3 SD: 0.0117 c. M:-0.0200 c. 1047: 68 140 839 N T3 SD: 0.0103 c. M: 0.0137 c. 1062: 69 142 851 N T3 SD: 0.0015 c. M: 0.0021 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: 83.9582 cents 7 x 8:9 S SD: 73.2224 cents 8 x 9:11 SD: 58.8508 cents 9 x 10:12 S SD: 41.7246 cents 10 x 11:13 SD: 39.6349 cents 11 x 12:15 S SD: 32.3448 cents 12 x 13:16 SD: 19.8090 cents 13 x 14:17 SD: 22.3113 cents 14 x 15:19 SD: 18.4303 cents 15 x 16:20 S SD: 6.3883 cents 16 x 17:21 SD: 13.9583 cents 17 x 18:23 SD: 12.6370 cents 18 x 19:24 SD: 2.6758 cents 19 x 20:25 S SD: 12.5391 cents 20 x 21:27 SD: 12.9654 cents 21 x 22:28 SD: 9.2088 cents 22 x 23:29 SD: 14.7935 cents 23 x 24:31 SD: 15.7247 cents 24 x 25:32 SD: 14.1411 cents 25 x 26:33 SD: 17.7983 cents 26:27:28:35 S SD: 15.7162 cents 27:28:29:36 SD: 13.1205 cents 28:29:30:37 SD: 12.7667 cents 29:30:31:39 SD: 11.4820 cents 30:31:32:40 S SD: 9.1828 cents 32:33:34:43 SD: 8.5300 cents 33:34:35:44 SD: 6.5134 cents 36:37:38:48 SD: 5.3318 cents 45:46:48:60 S SD: 4.6622 cents 47:48:50:63 SD: 4.3173 cents 48:49:51:64 SD: 2.2886 cents 51:52:54:68 SD: 0.4189 cents 270:275:286:360 SD: 0.3091 cents 321:327:340:428 SD: 0.2233 cents 324:330:343:432 SD: 0.2213 cents 372:379:394:496 SD: 0.1747 cents 375:382:397:500 SD: 0.1425 cents 426:434:451:568 SD: 0.0905 cents 477:486:505:636 SD: 0.0672 cents