Scala analysis: 062_E5
Enharmonic tetrachord 42/41 * 41/40 * 80/63
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 42/41 41.718502 2: 21/20 84.467193 minor semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 80/63 413.5778 wide major third 1: 42/41 41.7185 2: 41/40 42.7487 3: 80/63 413.5778 wide major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 42/41 41.719 cents 1: 1 41/40 42.749 cents 1: 1 80/63 413.578 cents wide major third 2: 1 21/20 84.467 cents minor semitone 2: 1 160/123 455.296 cents 2: 1 82/63 456.326 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 : 41.7 84.5 498.0 41.7 : 42.7 456.3 498.0 84.5 : 413.6 455.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.7185 .. 413.5778 cents 1640/1323, 371.8593 cents 42/41, 41.7185 cents 2: 84.4672 .. 456.3265 cents 1640/1323, 371.8593 cents 1323/1600,-329.1106 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 42/41, 41.7185 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 80/63, 413.5778 cents Average / Smallest step : 3.979409 Largest / Average step : 2.491207 Largest / Smallest step : 9.913534 Median interval of one step : 41/40, 42.7487 cents, amount: 1 Least squares average step : 121.77056 cents, oct.: 365.31169 cents Scale is not proper Scale has trivalence property Scale is a mode of a 967-tone equal temperament with octave 4/3 degrees: 81 164 967 Least number of segments generator : 484 of 249.280 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 590 of 303.874 cents and inv. generated superset size: 32 = 29 more = 1066.667% 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 41.71850 cents Scale diversity : 0.313133 Lumma stability : 0.167529 Lumma impropriety factor : 0.660805 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 : 1681/1680, 1.0302 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 : 2 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 370.8291 cents: 2 -- Rational properties -- Prime limit : 41 Odd number limit : 123 (O: 41 U: 123) Highest odd numerator or denominator: 41 Scale harmonicity : 0.038433 Fundamental : 1/2460, -11.2644 octaves, 0.1064 Hz. Guide tone : 84, 6.3923 octaves, 21976.547 Hz. Exponens Consonantiae : 2.066400E+05, 17.65676 octaves Euler's gradus suavitatis : 59 Sum of Mann's harmonic distance : 65.5, average 21.83333 Mersenne's string divisions : 23821 Sum of van Prooijen's expressibility: 3.41212, average 1.13737 Sum of Tenney's harmonic distance : 6.93846, average 2.31282 Vogel's harmonic complexity : 41.66667 Wille's k value : 1291 Wilson's harmonic complexity : 59 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 16.91605, average 2.81934 Lattice compactness (without 2's) : 9.83182, average 1.63864 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.33333 5 3: -1 .. 1 0.33333 3 1 5: -1 .. 0 -0.33333 1 7: 0 .. 1 0.66667 2 1 41: -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: <6 10 15 20 38| Scale is weakly epimorphic with val: <6 10 15 20 41| Scale is weakly epimorphic with val: <6 10 16 21 36| Scale is weakly epimorphic with val: <6 10 16 21 39| Scale is weakly epimorphic with val: <6 10 16 21 42| Scale is weakly epimorphic with val: <6 10 17 22 37| Scale is weakly epimorphic with val: <6 10 17 22 40| Scale is weakly epimorphic with val: <6 11 15 19 37| Scale is weakly epimorphic with val: <6 11 15 19 40| Scale is weakly epimorphic with val: <6 11 16 20 38| Scale is weakly epimorphic with val: <6 11 16 20 41| Scale is weakly epimorphic with val: <6 11 16 22 36| Scale is weakly epimorphic with val: <6 11 17 21 36| Scale is weakly epimorphic with val: <6 11 17 21 39| Scale is weakly epimorphic with val: <6 11 17 21 42| Scale is weakly epimorphic with val: <6 11 18 22 37| Scale is weakly epimorphic with val: <6 11 18 22 40| Scale is weakly epimorphic with val: <6 11 19 22 36| Scale is weakly epimorphic with val: <7 10 15 22 37| Scale is weakly epimorphic with val: <7 10 15 22 40| Scale is weakly epimorphic with val: <7 10 16 22 36| Scale is weakly epimorphic with val: <7 10 19 22 36| Scale is weakly epimorphic with val: <7 11 15 19 38| Scale is weakly epimorphic with val: <7 11 15 19 41| Scale is JI-epimorphic with val: <7 11 15 20 37| Scale is weakly epimorphic with val: <7 11 15 20 40| Scale is weakly epimorphic with val: <7 11 15 22 38| Scale is weakly epimorphic with val: <7 11 15 22 41| Scale is weakly epimorphic with val: <7 11 16 18 38| Scale is weakly epimorphic with val: <7 11 16 18 41| Scale is weakly epimorphic with val: <7 11 16 20 36| Scale is weakly epimorphic with val: <7 11 16 20 39| Scale is weakly epimorphic with val: <7 11 16 20 42| Scale is JI-epimorphic with val: <7 11 16 21 38| Scale is weakly epimorphic with val: <7 11 16 21 41| Scale is weakly epimorphic with val: <7 11 17 18 37| Scale is weakly epimorphic with val: <7 11 17 18 40| Scale is weakly epimorphic with val: <7 11 17 19 36| Scale is weakly epimorphic with val: <7 11 17 19 39| Scale is weakly epimorphic with val: <7 11 17 19 42| Scale is weakly epimorphic with val: <7 11 17 21 37| Scale is weakly epimorphic with val: <7 11 17 21 40| Scale is weakly epimorphic with val: <7 11 17 22 36| Scale is JI-epimorphic with val: <7 11 17 22 39| Scale is weakly epimorphic with val: <7 11 17 22 42| Scale is weakly epimorphic with val: <7 11 18 19 38| Scale is weakly epimorphic with val: <7 11 18 19 41| Scale is weakly epimorphic with val: <7 11 18 20 37| Scale is weakly epimorphic with val: <7 11 18 20 40| Scale is weakly epimorphic with val: <7 11 18 22 38| Scale is weakly epimorphic with val: <7 11 18 22 41| Scale is weakly epimorphic with val: <7 11 19 20 36| Scale is weakly epimorphic with val: <7 11 19 20 39| Scale is weakly epimorphic with val: <7 11 19 20 42| Scale is weakly epimorphic with val: <7 11 19 21 38| Scale is weakly epimorphic with val: <7 11 19 21 41| Scale is weakly epimorphic with val: <7 12 15 20 38| Scale is weakly epimorphic with val: <7 12 15 20 41| Scale is weakly epimorphic with val: <7 12 15 21 37| Scale is weakly epimorphic with val: <7 12 16 21 36| Scale is weakly epimorphic with val: <7 12 16 21 39| Scale is weakly epimorphic with val: <7 12 16 21 42| Scale is weakly epimorphic with val: <7 12 16 22 38| Scale is weakly epimorphic with val: <7 12 17 20 36| Scale is weakly epimorphic with val: <7 12 17 22 37| Scale is weakly epimorphic with val: <7 12 17 22 40| Scale is weakly epimorphic with val: <7 12 18 21 37| Scale is weakly epimorphic with val: <7 12 19 22 38| Scale is weakly epimorphic with val: <8 11 15 21 37| Scale is weakly epimorphic with val: <8 11 16 22 38| Scale is weakly epimorphic with val: <8 11 17 20 36| Scale is weakly epimorphic with val: <8 11 18 21 37| Scale is weakly epimorphic with val: <8 11 19 22 38| Scale is weakly epimorphic with val: <8 12 15 21 38| Scale is weakly epimorphic with val: <8 12 15 22 37| Scale is weakly epimorphic with val: <8 12 15 22 40| Scale is weakly epimorphic with val: <8 12 16 19 36| Scale is weakly epimorphic with val: <8 12 16 22 39| Scale is weakly epimorphic with val: <8 12 17 20 37| Scale is weakly epimorphic with val: <8 12 18 21 38| Scale is weakly epimorphic with val: <8 12 19 19 36| Scale is weakly epimorphic with val: <8 12 19 22 39|
FIT/MODE
3: 0 0 3 N M DE S SD: 54.3910 c. M: 84.4672 c. 4: 0 1 3 N G T3 SD: 33.3864 c. M: 41.7185 c. 5: 0 1 4 N G T3 SD: 25.6236 c. M: 41.7185 c. 6: 0 1 5 N G T3 SD: 24.1009 c. M: 41.7185 c. 7: 0 1 6 N G T3 SD: 25.2837 c. M: 41.7185 c. 8: 1 0 7 N G T3 SD: 17.4655 c. M: 22.2116 c. 9: 1 1 7 N M DE S SD: 17.0532 c. M:-26.2095 c. 10: 1 1 8 N M DE S SD: 9.9106 c. M:-15.1418 c. 11: 1 1 9 N M DE S SD: 4.0705 c. M:-6.0864 c. 12: 1 1 10 N M DE S SD: 0.8518 c. M: 1.4597 c. 35: 3 3 29 N M DE S SD: 0.7691 c. M:-0.9711 c. 47: 4 4 39 N M DE S SD: 0.4245 c. M:-0.6683 c. 59: 5 5 49 N M DE S SD: 0.2838 c. M:-0.4887 c. 71: 6 6 59 N M DE S SD: 0.2715 c. M:-0.3698 c. 130: 11 11 108 N M DE S SD: 0.2664 c. M:-0.4238 c. 165: 14 14 137 N M DE S SD: 0.3130 c. M:-0.5399 c. 189: 16 16 157 N M DE S SD: 0.2692 c. M:-0.4440 c. 201: 17 17 167 N M DE S SD: 0.2662 c. M:-0.4047 c. 224: 19 19 186 N M DE S SD: 0.3042 c. M:-0.5264 c. 225: 19 19 187 N M DE S SD: 0.2824 c. M: 0.3529 c. 241: 20 21 200 N T3 SD: 0.2700 c. M: 0.3870 c. 253: 21 22 210 N T3 SD: 0.2423 c. M: 0.3788 c. 265: 22 23 220 N T3 SD: 0.2231 c. M: 0.3714 c. 276: 23 24 229 N T3 SD: 0.2345 c. M:-0.3448 c. 277: 23 24 230 N T3 SD: 0.2117 c. M: 0.3646 c. 288: 24 25 239 N T3 SD: 0.1990 c. M:-0.2696 c. 289: 24 25 240 N T3 SD: 0.2073 c. M: 0.3584 c. 300: 25 26 249 N T3 SD: 0.1696 c. M: 0.2148 c. 312: 26 27 259 N T3 SD: 0.1469 c. M: 0.2148 c. 324: 27 28 269 N T3 SD: 0.1318 c. M: 0.2148 c. 336: 28 29 279 N T3 SD: 0.1247 c. M: 0.2148 c. 348: 29 30 289 N T3 SD: 0.1251 c. M: 0.2148 c. 359: 30 31 298 N T3 SD: 0.1081 c. M:-0.1588 c. 371: 31 32 308 N T3 SD: 0.0855 c. M:-0.1065 c. 383: 32 33 318 N T3 SD: 0.0698 c. M: 0.1064 c. 395: 33 34 328 N T3 SD: 0.0637 c. M: 0.1097 c. 407: 34 35 338 N T3 SD: 0.0677 c. M: 0.1128 c. 430: 36 37 357 N T3 SD: 0.0504 c. M:-0.0846 c. 442: 37 38 367 N T3 SD: 0.0292 c. M:-0.0427 c. 454: 38 39 377 N T3 SD: 0.0185 c. M: 0.0319 c. 513: 43 44 426 N T3 SD: 0.0163 c. M:-0.0280 c. 955: 80 82 793 N T3 SD: 0.0105 c. M:-0.0179 c. 967: 81 83 803 N T3 SD: 0.0003 c. M: 0.0004 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: 91.2019 cents 7 x 8:9 S SD: 79.8232 cents 8 x 9:11 SD: 65.3923 cents 9 x 10:12 S SD: 48.9683 cents 10 x 11:13 SD: 45.8459 cents 11 x 12:15 S SD: 38.3800 cents 12 x 13:16 SD: 27.0527 cents 13 x 14:17 SD: 27.6192 cents 14 x 15:19 SD: 23.2499 cents 15 x 16:20 S SD: 13.6320 cents 16 x 17:21 SD: 17.0521 cents 17 x 18:23 SD: 14.5659 cents 18 x 19:24 SD: 4.5679 cents 19 x 20:25 S SD: 11.6682 cents 20 x 21:27 SD: 10.7531 cents 21 x 22:28 SD: 1.9651 cents 22 x 23:29 SD: 10.5817 cents 23 x 24:31 SD: 10.8010 cents 24 x 25:32 SD: 6.8974 cents 25 x 26:33 SD: 12.0126 cents 26 x 27:35 SD: 12.6532 cents 27:28 x 36 SD: 10.6212 cents 28:29 x 37 SD: 12.2814 cents 29:30 x 39 SD: 11.2796 cents 30:31:32:40 S SD: 10.3805 cents 31:32:33:41 SD: 10.2034 cents 32:33:34:43 SD: 9.0356 cents 33:34:35:44 SD: 6.6835 cents 35:36:37:47 SD: 6.1402 cents 36:37:38:48 SD: 3.5921 cents 39:40:41:52 SD: 0.9959 cents 81:83:85:108 SD: 0.3794 cents 120:123:126:160 SD: 0.3434 cents 201:206:211:268 SD: 0.3057 cents 417:427:438:556 SD: 0.3038 cents 456:467:479:608 SD: 0.2842 cents 459:470:482:612 SD: 0.2469 cents 498:510:523:664 SD: 0.1990 cents 537:550:564:716 SD: 0.1845 cents 540:553:567:720 SD: 0.1781 cents 579:593:608:772 SD: 0.1278 cents