Scala analysis: 080_E8
Enharmonic tetrachord 64/63 * 28/27 * 81/64, Wilson
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 64/63 27.264092 septimal comma, Archytas' comma 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: 64/63 27.2641 septimal comma, Archytas' comma 2: 28/27 62.9609 Archytas' 1/3-tone 3: 81/64 407.8200 Pythagorean major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 81/64 407.820 cents Pythagorean major third 2: 1 256/243 90.225 cents limma, Pythagorean minor second 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 21/16 470.781 cents narrow fourth 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 : 27.3 90.2 498.0 27.3 : 63.0 470.8 498.0 90.2 : 407.8 435.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 407.8200 cents 5103/4096, 380.5559 cents 64/63, 27.2641 cents 2: 90.2250 .. 470.7809 cents 5103/4096, 380.5559 cents 16384/19683,-317.5950 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 64/63, 27.2641 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 81/64, 407.8200 cents Average / Smallest step : 6.089145 Largest / Average step : 2.456525 Largest / Smallest step : 14.958136 Median interval of one step : 28/27, 62.9609 cents, amount: 1 Least squares average step : 121.56065 cents, oct.: 364.68195 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1242-tone equal temperament with octave 4/3 degrees: 68 225 1242 Least number of segments generator : 623 of 249.825 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 971 of 389.373 cents and inv. generated superset size: 60 = 57 more = 2000.000% 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 27.26409 cents Scale diversity : 0.315553 Lumma stability : 0.109484 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 : 64/63, 27.2641 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 7 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 243 Scale harmonicity : 0.031627 Average absolute harmonicity : 0.102472 Specific harmonicity : 0.157598 Fundamental : 1/1701, -10.7322 octaves, 0.1538 Hz. Guide tone : 256, 8.0000 octaves, 66976.145 Hz. Exponens Consonantiae : 4.354560E+05, 18.73217 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 316.5, average 105.50000 Mersenne's string divisions : 443611 Sum of van Prooijen's expressibility: 4.66207, average 1.55402 Sum of Tenney's harmonic distance : 9.47855, average 3.15952 Vogel's harmonic complexity : 17.00000 Wille's k value : 283 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 33.26857, average 5.54476 Lattice compactness (without 2's) : 16.81256, average 2.80209 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 2 .. 8 5.33333 16 3: -5 ..-1 -2.66667 8 2 7: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-9 / 3 =-3.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <7 11 18| Scale is weakly epimorphic with val: <7 11 21|
FIT/MODE
3: 0 0 3 N M DE S SD: 54.4178 c. M: 90.2250 c. 4: 0 1 3 N G T3 SD: 25.2908 c. M:-34.2863 c. 5: 0 1 4 N G T3 SD: 16.6472 c. M: 27.2641 c. 6: 0 1 5 N G T3 SD: 16.2832 c. M: 27.2641 c. 7: 0 1 6 N G T3 SD: 19.2112 c. M: 27.2641 c. 10: 1 1 8 N M DE S SD: 14.0964 c. M:-22.5404 c. 11: 1 1 9 N M DE S SD: 10.4014 c. M:-18.0127 c. 12: 1 1 10 N M DE S SD: 9.2170 c. M:-14.2397 c. 13: 1 1 11 N M DE S SD: 10.1172 c. M: 13.6027 c. 14: 1 2 11 N T3 SD: 10.6658 c. M:-16.4989 c. 15: 1 2 12 N T3 SD: 6.4117 c. M:-9.3840 c. 16: 1 2 13 N T3 SD: 2.8812 c. M:-3.8637 c. 17: 1 2 14 N T3 SD: 1.7872 c. M: 2.3347 c. 33: 2 4 27 N T3 SD: 1.6968 c. M:-2.9205 c. 38: 2 5 31 N T3 SD: 1.0671 c. M:-1.5201 c. 39: 2 5 32 N T3 SD: 1.1049 c. M: 1.7233 c. 55: 3 7 45 N T3 SD: 0.1980 c. M:-0.3286 c. 127: 7 16 104 N T3 SD: 0.1093 c. M:-0.1872 c. 182: 10 23 149 N T3 SD: 0.0743 c. M:-0.1010 c. 348: 19 44 285 N T3 SD: 0.0547 c. M: 0.0720 c. 403: 22 51 330 N T3 SD: 0.0439 c. M: 0.0755 c. 475: 26 60 389 N T3 SD: 0.0304 c. M: 0.0526 c. 530: 29 67 434 N T3 SD: 0.0105 c. M: 0.0131 c. 1115: 61 141 913 N T3 SD: 0.0099 c. M: 0.0168 c. 1187: 65 150 972 N T3 SD: 0.0099 c. M: 0.0147 c. 1242: 68 157 1017 N T3 SD: 0.0024 c. M:-0.0041 c. 1772: 97 224 1451 N T3 SD: 0.0021 c. M: 0.0035 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: 14.3188 cents 30:31:32:40 S SD: 12.1698 cents 31:32:33:41 SD: 11.9641 cents 32:33:34:43 SD: 10.9289 cents 33:34:35:44 SD: 9.0172 cents 35:36:37:47 SD: 8.4991 cents 36:37:38:48 SD: 6.8170 cents 39:40:41:52 SD: 5.6544 cents 42:43:44:56 SD: 5.5314 cents 50:51:53:67 SD: 5.1347 cents 51:52:54:68 SD: 3.5989 cents 54:55:57:72 SD: 1.8763 cents 57:58:60:76 SD: 1.0606 cents 129:131:136:172 SD: 0.4688 cents 186:189:196:248 SD: 0.2056 cents 318:323:335:424 SD: 0.0877 cents 504:512:531:672 SD: 0.0403 cents