Scala analysis: 079_E8
Enharmonic tetrachord 128/125 * 250/243 * 81/64, Euler
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 128/125 41.058858 minor diesis, diesis 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: 128/125 41.0589 minor diesis, diesis 2: 250/243 49.1661 maximal diesis, Porcupine comma 3: 81/64 407.8200 Pythagorean major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 128/125 41.059 cents minor diesis, diesis 1: 1 250/243 49.166 cents maximal diesis, Porcupine comma 1: 1 81/64 407.820 cents Pythagorean major third 2: 1 256/243 90.225 cents limma, Pythagorean minor second 2: 1 162/125 448.879 cents 2: 1 125/96 456.986 cents classic augmented third 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 : 41.1 90.2 498.0 41.1 : 49.2 457.0 498.0 90.2 : 407.8 448.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.0589 .. 407.8200 cents 10125/8192, 366.7611 cents 128/125, 41.0589 cents 2: 90.2250 .. 456.9861 cents 10125/8192, 366.7611 cents 16384/19683,-317.5950 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 128/125, 41.0589 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 81/64, 407.8200 cents Average / Smallest step : 4.043342 Largest / Average step : 2.456525 Largest / Smallest step : 9.932570 Median interval of one step : 250/243, 49.1661 cents, amount: 1 Least squares average step : 122.54599 cents, oct.: 367.63797 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1783-tone equal temperament with octave 4/3 degrees: 147 323 1783 Least number of segments generator : 892 of 249.162 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1074 of 300.000 cents and inv. generated superset size: 44 = 41 more = 1466.667% 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 41.05886 cents Scale diversity : 0.350927 Lumma stability : 0.164880 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 : 15625/15552, 8.1073 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% Limited inverse transpositions with margin 358.6539 cents: 2 -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 125 U: 243) Highest odd numerator or denominator: 243 Scale harmonicity : 0.024671 Average absolute harmonicity : 0.099776 Specific harmonicity : 0.123775 Fundamental : 1/30375, -14.8906 octaves, 0.0086 Hz. Guide tone : 256, 8.0000 octaves, 66976.145 Hz. Exponens Consonantiae : 7.776000E+06, 22.89060 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 379.5, average 126.50000 Mersenne's string divisions : 883729 Sum of van Prooijen's expressibility: 4.95964, average 1.65321 Sum of Tenney's harmonic distance : 10.07715, average 3.35905 Vogel's harmonic complexity : 24.66667 Wille's k value : 5062 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 8 Triangular lattice diameter : 5 Lattice compactness : 38.32908, average 6.38818 Lattice compactness (without 2's) : 21.99323, average 3.66554 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 2 .. 8 5.66667 17 3: -5 .. 0 -2.00000 6 2 5: -3 .. 0 -1.00000 3 1 Average exponent except 2's :-9 / 3 =-3.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000
FIT/MODE
3: 0 0 3 N M DE S SD: 57.2316 c. M: 90.2250 c. 4: 0 1 3 N G T3 SD: 30.8835 c. M: 41.0589 c. 5: 0 1 4 N G T3 SD: 24.3166 c. M: 41.0589 c. 6: 0 1 5 N G T3 SD: 24.0688 c. M: 41.0589 c. 7: 0 1 6 N G T3 SD: 26.1388 c. M: 41.0589 c. 8: 1 0 7 N G T3 SD: 20.2615 c. M: 27.9694 c. 9: 1 1 7 N M DE S SD: 14.4011 c. M:-20.4517 c. 10: 1 1 8 N M DE S SD: 7.4060 c. M:-9.3840 c. 11: 1 1 9 N M DE S SD: 2.4426 c. M:-4.2180 c. 23: 2 2 19 N M DE S SD: 2.4550 c. M: 3.6085 c. 34: 3 3 28 N M DE S SD: 2.1433 c. M:-2.8863 c. 38: 3 4 31 N T3 SD: 1.3338 c. M: 1.7395 c. 49: 4 5 40 N T3 SD: 0.7596 c. M:-1.2527 c. 50: 4 5 41 N T3 SD: 0.7767 c. M: 1.2153 c. 60: 5 6 49 N T3 SD: 0.6761 c. M:-1.0833 c. 61: 5 6 50 N T3 SD: 0.2748 c. M: 0.4136 c. 110: 9 11 90 N T3 SD: 0.2607 c. M:-0.3286 c. 121: 10 12 99 N T3 SD: 0.1986 c. M:-0.3286 c. 171: 14 17 140 N T3 SD: 0.1676 c. M: 0.2832 c. 182: 15 18 149 N T3 SD: 0.0466 c. M:-0.0799 c. 243: 20 24 199 N T3 SD: 0.0465 c. M: 0.0675 c. 425: 35 42 348 N T3 SD: 0.0256 c. M: 0.0434 c. 497: 41 49 407 N T3 SD: 0.0260 c. M: 0.0358 c. 607: 50 60 497 N T3 SD: 0.0262 c. M: 0.0337 c. 679: 56 67 556 N T3 SD: 0.0102 c. M:-0.0170 c. 861: 71 85 705 N T3 SD: 0.0099 c. M:-0.0131 c. 922: 76 91 755 N T3 SD: 0.0092 c. M: 0.0151 c. 1104: 91 109 904 N T3 SD: 0.0036 c. M: 0.0062 c. 1783: 147 176 1460 N T3 SD: 0.0017 c. M:-0.0026 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 26:27 x 35 SD: 14.6962 cents 27:28 x 36 SD: 10.9510 cents 30:31:32:40 S SD: 8.8773 cents 32:33:34:43 SD: 7.8009 cents 33:34:35:44 SD: 5.2535 cents 35:36:37:47 SD: 5.2393 cents 36:37:38:48 SD: 2.4049 cents 39:40:41:52 SD: 1.5265 cents 75:77:79:100 SD: 1.5036 cents 93:95:98:124 SD: 1.4151 cents 114:117:120:152 SD: 1.3874 cents 126:129:133:168 SD: 1.1311 cents 129:132:136:172 SD: 0.5931 cents 165:169:174:220 SD: 0.5896 cents 168:172:177:224 SD: 0.1147 cents 375:384:395:500 SD: 0.0902 cents 543:556:572:724 SD: 0.0599 cents