Scala analysis: 077_E8
Enharmonic tetrachord 768/755 * 755/729 * 81/64
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 768/755 29.555600 2: 256/243 90.224996 limma, Pythagorean minor second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 81/64 407.8200 Pythagorean major third 1: 768/755 29.5556 2: 755/729 60.6694 3: 81/64 407.8200 Pythagorean major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 768/755 29.556 cents 1: 1 755/729 60.669 cents 1: 1 81/64 407.820 cents Pythagorean major third 2: 1 256/243 90.225 cents limma, Pythagorean minor second 2: 1 972/755 437.376 cents 2: 1 755/576 468.489 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 : 29.6 90.2 498.0 29.6 : 60.7 468.5 498.0 90.2 : 407.8 437.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 29.5556 .. 407.8200 cents 20385/16384, 378.2644 cents 768/755, 29.5556 cents 2: 90.2250 .. 468.4894 cents 20385/16384, 378.2644 cents 16384/19683,-317.5950 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 768/755, 29.5556 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 81/64, 407.8200 cents Average / Smallest step : 5.617040 Largest / Average step : 2.456525 Largest / Smallest step : 13.798401 Median interval of one step : 755/729, 60.6694 cents, amount: 1 Least squares average step : 121.72433 cents, oct.: 365.17298 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1921-tone equal temperament with octave 4/3 degrees: 114 348 1921 Least number of segments generator : 961 of 249.152 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1630 of 422.599 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 29.55560 cents Scale diversity : 0.322989 Lumma stability : 0.118686 Lumma impropriety factor : 0.637683 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 : 768/755, 29.5556 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 151 Odd number limit : 755 (O: 755 U: 755) Highest odd numerator or denominator: 755 Scale harmonicity : 0.032895 Fundamental : 1/183465, -17.4851 octaves, 0.0014 Hz. Guide tone : 768, 9.5850 octaves, 200928.434 Hz. Exponens Consonantiae : 1.409011E+08, 27.07011 octaves Euler's gradus suavitatis : 175 Sum of Mann's harmonic distance : 1014.5, average 338.16667 Mersenne's string divisions : 5319839 Sum of van Prooijen's expressibility: 5.74067, average 1.91356 Sum of Tenney's harmonic distance : 11.63634, average 3.87878 Vogel's harmonic complexity : 120.00000 Wille's k value : 30577 Wilson's harmonic complexity : 174 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 39.49108, average 6.58185 Lattice compactness (without 2's) : 19.73304, average 3.28884 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 8 6.00000 18 3: -5 .. 1 -1.66667 7 2 5: -1 .. 0 -0.33333 1 151: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-7 / 3 =-2.33333 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <7 11 15 53| Scale is weakly epimorphic with val: <7 11 16 52| Scale is weakly epimorphic with val: <7 11 17 51| Scale is weakly epimorphic with val: <7 11 18 53| Scale is weakly epimorphic with val: <7 11 19 52|
FIT/MODE
3: 0 0 3 N M DE S SD: 54.8151 c. M: 90.2250 c. 4: 0 1 3 N G T3 SD: 26.1348 c. M:-34.2863 c. 5: 0 1 4 N G T3 SD: 17.9034 c. M: 29.5556 c. 6: 0 1 5 N G T3 SD: 17.5654 c. M: 29.5556 c. 7: 0 1 6 N G T3 SD: 20.3094 c. M: 29.5556 c. 10: 1 1 8 N M DE S SD: 12.8851 c. M:-20.2489 c. 11: 1 1 9 N M DE S SD: 9.0786 c. M:-15.7212 c. 12: 1 1 10 N M DE S SD: 8.0592 c. M:-11.9482 c. 15: 1 2 12 N T3 SD: 5.8127 c. M:-9.3840 c. 16: 1 2 13 N T3 SD: 2.0370 c. M:-3.1584 c. 17: 1 2 14 N T3 SD: 1.3562 c. M: 2.3347 c. 33: 2 4 27 N T3 SD: 0.4097 c. M:-0.6289 c. 50: 3 6 41 N T3 SD: 0.3829 c. M: 0.5769 c. 83: 5 10 68 N T3 SD: 0.2869 c. M:-0.4471 c. 116: 7 14 95 N T3 SD: 0.2902 c. M:-0.4988 c. 133: 8 16 109 N T3 SD: 0.3086 c. M:-0.4020 c. 149: 9 18 122 N T3 SD: 0.3050 c. M:-0.5277 c. 171: 10 21 140 N T3 SD: 0.2511 c. M: 0.4302 c. 187: 11 23 153 N T3 SD: 0.2415 c. M:-0.3286 c. 188: 11 23 154 N T3 SD: 0.2552 c. M: 0.4147 c. 204: 12 25 167 N T3 SD: 0.1616 c. M: 0.2588 c. 221: 13 27 181 N T3 SD: 0.1566 c. M: 0.2588 c. 237: 14 29 194 N T3 SD: 0.1114 c. M:-0.1376 c. 254: 15 31 208 N T3 SD: 0.0844 c. M: 0.1435 c. 287: 17 35 235 N T3 SD: 0.0325 c. M: 0.0547 c. 320: 19 39 262 N T3 SD: 0.0279 c. M:-0.0457 c. 607: 36 74 497 N T3 SD: 0.0202 c. M:-0.0303 c. 624: 37 76 511 N T3 SD: 0.0241 c. M: 0.0342 c. 657: 39 80 538 N T3 SD: 0.0105 c. M: 0.0159 c. 944: 56 115 773 N T3 SD: 0.0073 c. M: 0.0106 c. 977: 58 119 800 N T3 SD: 0.0068 c. M:-0.0110 c. 1264: 75 154 1035 N T3 SD: 0.0043 c. M:-0.0063 c. 1921: 114 234 1573 N T3 SD: 0.0008 c. M: 0.0013 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: 88.3230 cents 7 x 8:9 S SD: 77.1860 cents 8 x 9:11 SD: 62.7740 cents 9 x 10:12 S SD: 46.0894 cents 10 x 11:13 SD: 43.3391 cents 11 x 12:15 S SD: 35.9280 cents 12 x 13:16 SD: 24.1738 cents 13 x 14:17 SD: 25.3953 cents 14 x 15:19 SD: 21.1697 cents 15 x 16:20 S SD: 10.7531 cents 16 x 17:21 SD: 15.4945 cents 17 x 18:23 SD: 13.3695 cents 18 x 19:24 SD: 1.6890 cents 19 x 20:25 S SD: 11.4874 cents 20 x 21:27 SD: 11.1319 cents 21 x 22:28 SD: 4.8440 cents 22 x 23:29 SD: 11.9115 cents 23 x 24:31 SD: 12.4901 cents 24 x 25:32 SD: 9.7763 cents 25 x 26:33 SD: 14.1522 cents 26 x 27:35 SD: 14.9487 cents 27 x 28:36 SD: 13.6320 cents 28 x 30:37 SD: 16.5436 cents 29:30:31:39 SD: 13.7698 cents 30:31:32:40 S SD: 11.5613 cents 31:32:33:41 SD: 11.3850 cents 32:33:34:43 SD: 10.3334 cents 33:34:35:44 SD: 8.3342 cents 35:36:37:47 SD: 7.8655 cents 36:37:38:48 SD: 6.0649 cents 39:40:41:52 SD: 4.9112 cents 50:51:53:67 SD: 4.8347 cents 51:52:54:68 SD: 3.2094 cents 54:55:57:72 SD: 1.3458 cents 57:58:60:76 SD: 0.5094 cents 168:171:177:224 SD: 0.3644 cents 225:229:237:300 SD: 0.3297 cents 297:302:313:396 SD: 0.2989 cents 354:360:373:472 SD: 0.1802 cents 411:418:433:548 SD: 0.1073 cents 468:476:493:624 SD: 0.0829 cents 522:531:550:696 SD: 0.0788 cents 579:589:610:772 SD: 0.0379 cents