Scala analysis: 076_E8
Enharmonic tetrachord 384/371 * 742/729 * 81/64
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 384/371 59.624549 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: 384/371 59.6245 2: 742/729 30.6004 3: 81/64 407.8200 Pythagorean major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 742/729 30.600 cents 1: 1 384/371 59.625 cents 1: 1 81/64 407.820 cents Pythagorean major third 2: 1 256/243 90.225 cents limma, Pythagorean minor second 2: 1 371/288 438.420 cents 2: 1 486/371 467.445 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 : 59.6 90.2 498.0 59.6 : 30.6 438.4 498.0 90.2 : 407.8 467.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 30.6004 .. 407.8200 cents 59049/47488, 377.2196 cents 742/729, 30.6004 cents 2: 90.2250 .. 467.4446 cents 59049/47488, 377.2196 cents 16384/19683,-317.5950 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 742/729, 30.6004 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 81/64, 407.8200 cents Average / Smallest step : 5.425248 Largest / Average step : 2.456525 Largest / Smallest step : 13.327257 Median interval of one step : 384/371, 59.6245 cents, amount: 1 Least squares average step : 123.87211 cents, oct.: 371.61633 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1253-tone equal temperament with octave 4/3 degrees: 150 227 1253 Least number of segments generator : 627 of 249.221 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 811 of 322.358 cents and inv. generated superset size: 26 = 23 more = 866.667% 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 30.60045 cents Scale diversity : 0.326180 Lumma stability : 0.122882 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 : 139968/137641, 29.0241 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 53 Odd number limit : 729 (O: 371 U: 729) Highest odd numerator or denominator: 371 Scale harmonicity : 0.029167 Fundamental : 1/90153, -16.4601 octaves, 0.0029 Hz. Guide tone : 768, 9.5850 octaves, 200928.434 Hz. Exponens Consonantiae : 6.923750E+07, 26.04505 octaves Euler's gradus suavitatis : 79 Sum of Mann's harmonic distance : 630.5, average 210.16667 Mersenne's string divisions : 2637215 Sum of van Prooijen's expressibility: 5.43210, average 1.81070 Sum of Tenney's harmonic distance : 11.02673, average 3.67558 Vogel's harmonic complexity : 55.66667 Wille's k value : 15025 Wilson's harmonic complexity : 78 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 37.66422, average 6.27737 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 5.66667 17 3: -5 .. 1 -1.66667 7 2 7: -1 .. 0 -0.33333 1 53: -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 18 40| Scale is weakly epimorphic with val: <7 11 19 42| Scale is weakly epimorphic with val: <7 11 20 41| = patent Scale is weakly epimorphic with val: <7 11 21 40| Scale is weakly epimorphic with val: <7 11 22 42|
FIT/MODE
3: 0 0 3 N M DE S SD: 62.4383 c. M: 90.2250 c. 4: 1 0 3 N G T3 SD: 42.3707 c. M:-64.8867 c. 5: 1 0 4 N G T3 SD: 23.7123 c. M:-39.9845 c. 6: 1 0 5 N G T3 SD: 14.1286 c. M:-23.3830 c. 7: 1 0 6 N G T3 SD: 12.8673 c. M: 19.0757 c. 9: 1 1 7 N M DE S SD: 12.0643 c. M:-20.4517 c. 10: 1 1 8 N M DE S SD: 7.8420 c. M: 9.8200 c. 11: 1 1 9 N M DE S SD: 8.2858 c. M: 14.3477 c. 15: 2 1 12 N T3 SD: 6.6845 c. M:-9.3840 c. 16: 2 1 13 N T3 SD: 2.3733 c. M:-3.1584 c. 17: 2 1 14 N T3 SD: 1.4735 c. M: 2.3347 c. 33: 4 2 27 N T3 SD: 0.4699 c. M:-0.7445 c. 50: 6 3 41 N T3 SD: 0.3429 c. M: 0.5769 c. 83: 10 5 68 N T3 SD: 0.2530 c. M:-0.3809 c. 116: 14 7 95 N T3 SD: 0.2819 c. M:-0.4843 c. 133: 16 8 109 N T3 SD: 0.2636 c. M: 0.3522 c. 160: 19 10 131 N T3 SD: 0.2794 c. M: 0.4817 c. 176: 21 11 144 N T3 SD: 0.2217 c. M:-0.3286 c. 193: 23 12 158 N T3 SD: 0.1662 c. M: 0.2720 c. 226: 27 14 185 N T3 SD: 0.1029 c. M:-0.1283 c. 243: 29 15 199 N T3 SD: 0.1110 c. M: 0.1871 c. 259: 31 16 212 N T3 SD: 0.0891 c. M:-0.1538 c. 276: 33 17 226 N T3 SD: 0.0437 c. M: 0.0757 c. 309: 37 19 253 N T3 SD: 0.0217 c. M:-0.0356 c. 585: 70 36 479 N T3 SD: 0.0202 c. M: 0.0294 c. 635: 76 39 520 N T3 SD: 0.0186 c. M: 0.0279 c. 668: 80 41 547 N T3 SD: 0.0138 c. M:-0.0216 c. 944: 113 58 773 N T3 SD: 0.0057 c. M: 0.0071 c. 1253: 150 77 1026 N T3 SD: 0.0024 c. M:-0.0034 c. 2197: 263 135 1799 N T3 SD: 0.0025 c. M: 0.0042 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 23:24 x 31 SD: 11.7033 cents 24:25 x 32 SD: 5.5239 cents 25:26 x 33 SD: 9.6337 cents 26:27 x 35 SD: 8.7621 cents 27:28 x 36 SD: 1.6682 cents 43 x 45:57 SD: 7.6582 cents 44 x 46:59 SD: 8.2502 cents 45 x 47:60 SD: 7.4710 cents 46:48 x 61 SD: 8.4644 cents 47:49:50:63 SD: 7.6492 cents 48:50:51:64 SD: 6.1377 cents 49:51:52:65 SD: 6.0670 cents 50:52:53:67 SD: 5.3387 cents 51:53:54:68 SD: 3.7235 cents 53:55:56:71 SD: 3.5374 cents 54:56:57:72 SD: 1.5826 cents 57:59:60:76 SD: 0.4755 cents 168:174:177:224 SD: 0.3777 cents 225:233:237:300 SD: 0.3010 cents 282:292:297:376 SD: 0.2884 cents 315:326:332:420 SD: 0.2661 cents 318:329:335:424 SD: 0.2514 cents 372:385:392:496 SD: 0.1546 cents 429:444:452:572 SD: 0.0758 cents 486:503:512:648 SD: 0.0340 cents