Scala analysis: 082_E8
Enharmonic tetrachord 36/35 * 2240/2187 * 81/64
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 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: 36/35 48.7704 septimal diesis, 1/4-tone 2: 2240/2187 41.4546 3: 81/64 407.8200 Pythagorean major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 2240/2187 41.455 cents 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 81/64 407.820 cents Pythagorean major third 2: 1 256/243 90.225 cents limma, Pythagorean minor second 2: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 2: 1 729/560 456.590 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 : 48.8 90.2 498.0 48.8 : 41.5 449.3 498.0 90.2 : 407.8 456.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.4546 .. 407.8200 cents 177147/143360, 366.3654 cents 2240/2187, 41.4546 cents 2: 90.2250 .. 456.5904 cents 177147/143360, 366.3654 cents 16384/19683,-317.5950 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 2240/2187, 41.4546 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 81/64, 407.8200 cents Average / Smallest step : 4.004741 Largest / Average step : 2.456525 Largest / Smallest step : 9.837747 Median interval of one step : 36/35, 48.7704 cents, amount: 1 Least squares average step : 123.09681 cents, oct.: 369.29044 cents Scale is not proper Scale has trivalence property Scale is a mode of a 817-tone equal temperament with octave 4/3 degrees: 80 148 817 Least number of segments generator : 409 of 249.327 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 743 of 452.934 cents and inv. generated superset size: 24 = 21 more = 800.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 41.45461 cents Scale diversity : 0.351599 Lumma stability : 0.166469 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 : 19683/19600, 7.3158 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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% Limited inverse transpositions with margin 366.3654 cents: 2 -- Rational properties -- Prime limit : 7 Odd number limit : 2187 (O: 729 U: 2187) Highest odd numerator or denominator: 243 Scale harmonicity : 0.023067 Average absolute harmonicity : 0.100931 Specific harmonicity : 0.120551 Fundamental : 1/8505, -13.0541 octaves, 0.0308 Hz. Guide tone : 2304, 11.1699 octaves, 602785.302 Hz. Exponens Consonantiae : 1.959552E+07, 24.22402 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 288.5, average 96.16667 Mersenne's string divisions : 248003 Sum of van Prooijen's expressibility: 4.40680, average 1.46893 Sum of Tenney's harmonic distance : 8.97340, average 2.99113 Vogel's harmonic complexity : 23.00000 Wille's k value : 1417 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 9 Triangular lattice diameter : 7 Lattice compactness : 34.68743, average 5.78124 Lattice compactness (without 2's) : 22.90754, average 3.81792 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 8 4.00000 12 3: -5 .. 2 -1.33333 8 2 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-6 / 3 =-2.00000 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <7 11 15 19| Scale is weakly epimorphic with val: <7 11 15 22| Scale is weakly epimorphic with val: <7 11 16 18| Scale is weakly epimorphic with val: <7 11 16 21| Scale is weakly epimorphic with val: <7 11 17 20| = patent Scale is weakly epimorphic with val: <7 11 18 19| Scale is weakly epimorphic with val: <7 11 18 22| Scale is weakly epimorphic with val: <7 11 19 21|
FIT/MODE
3: 0 0 3 N M DE S SD: 59.2146 c. M: 90.2250 c. 4: 0 1 3 N G T3 SD: 34.4195 c. M: 48.7704 c. 5: 0 1 4 N G T3 SD: 28.6741 c. M: 48.7704 c. 6: 1 0 5 N G T3 SD: 20.2013 c. M:-34.2371 c. 7: 1 0 6 N G T3 SD: 16.9774 c. M:-22.3789 c. 9: 1 1 7 N M DE S SD: 12.4017 c. M:-20.4517 c. 10: 1 1 8 N M DE S SD: 5.4507 c. M:-9.3840 c. 11: 1 1 9 N M DE S SD: 2.0259 c. M: 3.4936 c. 32: 3 3 26 N M DE S SD: 2.1830 c. M:-3.1584 c. 38: 4 3 31 N T3 SD: 2.2857 c. M:-3.6554 c. 39: 4 3 32 N T3 SD: 1.4182 c. M:-2.3112 c. 49: 5 4 40 N T3 SD: 1.3873 c. M:-2.0505 c. 50: 5 4 41 N T3 SD: 0.6837 c. M:-1.0341 c. 61: 6 5 50 N T3 SD: 0.2698 c. M: 0.4136 c. 72: 7 6 59 N T3 SD: 0.2659 c. M: 0.3493 c. 132: 13 11 108 N T3 SD: 0.2491 c. M:-0.3286 c. 133: 13 11 109 N T3 SD: 0.2098 c. M: 0.3522 c. 143: 14 12 117 N T3 SD: 0.1898 c. M:-0.3286 c. 193: 19 16 158 N T3 SD: 0.1596 c. M:-0.2600 c. 204: 20 17 167 N T3 SD: 0.0700 c. M:-0.1067 c. 265: 26 22 217 N T3 SD: 0.0550 c. M:-0.0944 c. 276: 27 23 226 N T3 SD: 0.0281 c. M: 0.0486 c. 480: 47 40 393 N T3 SD: 0.0264 c. M:-0.0457 c. 541: 53 45 443 N T3 SD: 0.0129 c. M:-0.0215 c. 817: 80 68 669 N T3 SD: 0.0026 c. M: 0.0039 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 25:26 x 33 SD: 12.9296 cents 26:27 x 35 SD: 11.7146 cents 27:28 x 36 SD: 7.0953 cents 32:33:34:43 SD: 6.8213 cents 33:34:35:44 SD: 4.0001 cents 36:37:38:48 SD: 1.2109 cents 75:77:79:100 SD: 1.0734 cents 111:114:117:148 SD: 0.9191 cents 147:151:155:196 SD: 0.9161 cents 168:173:177:224 SD: 0.6687 cents 171:176:180:228 SD: 0.6049 cents 204:210:215:272 SD: 0.5253 cents 207:213:218:276 SD: 0.3040 cents 243:250:256:324 SD: 0.1319 cents 522:537:550:696 SD: 0.1205 cents 525:540:553:700 SD: 0.0902 cents 561:577:591:748 SD: 0.0310 cents