Scala analysis: 071_E7
Enharmonic tetrachord 40/39 * 39/38 * 19/15, Eratosthenes
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40/39 43.831051 tridecimal minor diesis 2: 20/19 88.800698 small undevicesimal semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 19/15 409.2443 undevicesimal ditone 1: 40/39 43.8311 tridecimal minor diesis 2: 39/38 44.9696 3: 19/15 409.2443 undevicesimal ditone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 39/38 44.970 cents 1: 1 19/15 409.244 cents undevicesimal ditone 2: 1 20/19 88.801 cents small undevicesimal semitone 2: 1 152/117 453.075 cents 2: 1 13/10 454.214 cents tridecimal semi-diminished 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 : 43.8 88.8 498.0 43.8 : 45.0 454.2 498.0 88.8 : 409.2 453.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 409.2443 cents 247/200, 365.4133 cents 40/39, 43.8311 cents 2: 88.8007 .. 454.2139 cents 247/200, 365.4133 cents 300/361,-320.4436 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 19/15, 409.2443 cents Average / Smallest step : 3.787612 Largest / Average step : 2.465104 Largest / Smallest step : 9.336858 Median interval of one step : 39/38, 44.9696 cents, amount: 1 Least squares average step : 122.54053 cents, oct.: 367.62160 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1318-tone equal temperament with octave 4/3 degrees: 116 235 1318 Least number of segments generator : 661 of 249.778 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 839 of 317.041 cents and inv. generated superset size: 18 = 15 more = 600.000% 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 43.83105 cents Scale diversity : 0.345469 Lumma stability : 0.176012 Lumma impropriety factor : 0.643403 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 : 1521/1520, 1.1386 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 : 2 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 Limited inverse transpositions with margin 364.2747 cents: 2 -- Rational properties -- Prime limit : 19 Odd number limit : 117 (O: 39 U: 117) Highest odd numerator or denominator: 39 Scale harmonicity : 0.014636 Average absolute harmonicity : 0.089011 Specific harmonicity : 0.074751 Fundamental : 1/741, -9.5333 octaves, 0.3531 Hz. Guide tone : 40, 5.3219 octaves, 10465.023 Hz. Exponens Consonantiae : 2.964000E+04, 14.85526 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 62.5, average 20.83333 Mersenne's string divisions : 21567 Sum of van Prooijen's expressibility: 3.34694, average 1.11565 Sum of Tenney's harmonic distance : 6.85209, average 2.28403 Vogel's harmonic complexity : 28.00000 Wille's k value : 123 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 13.61376, average 2.26896 Lattice compactness (without 2's) : 9.02458, average 1.50410 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 0 -0.66667 2 1 5: 0 .. 1 0.66667 2 13: -1 .. 0 -0.33333 1 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 19 26 28| Scale is weakly epimorphic with val: <6 11 19 27 28| Scale is weakly epimorphic with val: <7 10 17 25 29| Scale is weakly epimorphic with val: <7 10 17 25 32| Scale is weakly epimorphic with val: <7 10 17 26 28| Scale is weakly epimorphic with val: <7 10 18 26 30| Scale is weakly epimorphic with val: <7 10 18 26 33| Scale is weakly epimorphic with val: <7 10 18 27 29| Scale is weakly epimorphic with val: <7 10 19 25 30| Scale is weakly epimorphic with val: <7 10 19 27 28| Scale is weakly epimorphic with val: <7 10 19 27 31| Scale is weakly epimorphic with val: <7 10 19 27 34| Scale is weakly epimorphic with val: <7 10 19 28 30| Scale is weakly epimorphic with val: <7 11 15 26 28| Scale is weakly epimorphic with val: <7 11 15 26 31| Scale is weakly epimorphic with val: <7 11 15 26 34| Scale is weakly epimorphic with val: <7 11 15 27 30| Scale is weakly epimorphic with val: <7 11 15 27 33| Scale is weakly epimorphic with val: <7 11 15 29 31| Scale is weakly epimorphic with val: <7 11 15 29 34| Scale is weakly epimorphic with val: <7 11 15 30 30| Scale is weakly epimorphic with val: <7 11 15 30 33| Scale is JI-epimorphic with val: <7 11 16 25 28| Scale is weakly epimorphic with val: <7 11 16 25 31| Scale is weakly epimorphic with val: <7 11 16 25 34| Scale is weakly epimorphic with val: <7 11 16 27 29| Scale is weakly epimorphic with val: <7 11 16 27 32| Scale is weakly epimorphic with val: <7 11 16 28 28| Scale is weakly epimorphic with val: <7 11 16 28 31| Scale is weakly epimorphic with val: <7 11 16 28 34| Scale is weakly epimorphic with val: <7 11 16 30 32| Scale is weakly epimorphic with val: <7 11 17 25 30| Scale is weakly epimorphic with val: <7 11 17 25 33| Scale is JI-epimorphic with val: <7 11 17 26 29| Scale is weakly epimorphic with val: <7 11 17 26 32| Scale is weakly epimorphic with val: <7 11 17 28 30| Scale is weakly epimorphic with val: <7 11 17 28 33| Scale is weakly epimorphic with val: <7 11 17 29 29| Scale is weakly epimorphic with val: <7 11 17 29 32| Scale is weakly epimorphic with val: <7 11 18 26 28| Scale is weakly epimorphic with val: <7 11 18 26 31| Scale is weakly epimorphic with val: <7 11 18 26 34| Scale is JI-epimorphic with val: <7 11 18 27 30| Scale is weakly epimorphic with val: <7 11 18 27 33| Scale is weakly epimorphic with val: <7 11 18 29 31| Scale is weakly epimorphic with val: <7 11 18 29 34| Scale is weakly epimorphic with val: <7 11 18 30 30| Scale is weakly epimorphic with val: <7 11 18 30 33| Scale is weakly epimorphic with val: <7 11 19 25 28| Scale is weakly epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 25 34| Scale is weakly epimorphic with val: <7 11 19 27 29| Scale is weakly epimorphic with val: <7 11 19 27 32| Scale is weakly epimorphic with val: <7 11 19 28 28| Scale is JI-epimorphic with val: <7 11 19 28 31| Scale is weakly epimorphic with val: <7 11 19 28 34| Scale is weakly epimorphic with val: <7 11 19 30 32| Scale is weakly epimorphic with val: <7 12 17 25 28| Scale is weakly epimorphic with val: <7 12 17 28 28| Scale is weakly epimorphic with val: <7 12 18 26 29| Scale is weakly epimorphic with val: <7 12 18 29 29| Scale is weakly epimorphic with val: <7 12 19 25 29| Scale is weakly epimorphic with val: <7 12 19 25 32| Scale is weakly epimorphic with val: <7 12 19 27 30| Scale is weakly epimorphic with val: <7 12 19 30 30| Scale is weakly epimorphic with val: <8 11 15 25 30| Scale is weakly epimorphic with val: <8 11 15 25 33| Scale is weakly epimorphic with val: <8 11 15 27 28| Scale is weakly epimorphic with val: <8 11 16 25 29| Scale is weakly epimorphic with val: <8 11 16 26 28| Scale is weakly epimorphic with val: <8 11 16 26 31| Scale is weakly epimorphic with val: <8 11 16 26 34| Scale is weakly epimorphic with val: <8 11 16 28 29| Scale is weakly epimorphic with val: <8 11 17 26 30| Scale is weakly epimorphic with val: <8 11 17 27 29| Scale is weakly epimorphic with val: <8 11 17 27 32| Scale is weakly epimorphic with val: <8 11 17 29 30| Scale is weakly epimorphic with val: <8 11 18 27 31| Scale is weakly epimorphic with val: <8 11 18 28 30| Scale is weakly epimorphic with val: <8 11 18 28 33| Scale is weakly epimorphic with val: <8 11 18 30 31| Scale is weakly epimorphic with val: <8 11 19 25 32| Scale is weakly epimorphic with val: <8 11 19 28 32| Scale is weakly epimorphic with val: <8 11 19 29 31| Scale is weakly epimorphic with val: <8 11 19 29 34| Scale is weakly epimorphic with val: <8 12 15 25 28| Scale is weakly epimorphic with val: <8 12 15 28 28| Scale is weakly epimorphic with val: <8 12 16 25 30| Scale is weakly epimorphic with val: <8 12 16 25 33| Scale is weakly epimorphic with val: <8 12 16 26 29| Scale is weakly epimorphic with val: <8 12 16 29 29| Scale is weakly epimorphic with val: <8 12 17 26 28| Scale is weakly epimorphic with val: <8 12 17 26 31| Scale is weakly epimorphic with val: <8 12 17 26 34| Scale is weakly epimorphic with val: <8 12 17 27 30| Scale is weakly epimorphic with val: <8 12 17 30 30| Scale is weakly epimorphic with val: <8 12 18 25 31| Scale is weakly epimorphic with val: <8 12 18 27 29| Scale is weakly epimorphic with val: <8 12 18 27 32| Scale is weakly epimorphic with val: <8 12 18 28 31| Scale is weakly epimorphic with val: <8 12 19 26 32| Scale is weakly epimorphic with val: <8 12 19 28 30| Scale is weakly epimorphic with val: <8 12 19 28 33| Scale is weakly epimorphic with val: <8 12 19 29 32|
FIT/MODE
3: 0 0 3 N M DE S SD: 57.1744 c. M: 88.8007 c. 4: 0 1 3 N G T3 SD: 32.6415 c. M: 43.8311 c. 5: 0 1 4 N G T3 SD: 26.0639 c. M: 43.8311 c. 6: 0 1 5 N G T3 SD: 25.5259 c. M: 43.8311 c. 7: 0 1 6 N G T3 SD: 27.2808 c. M: 43.8311 c. 8: 1 0 7 N G T3 SD: 18.6557 c. M: 26.5451 c. 9: 1 1 7 N M DE S SD: 14.2709 c. M:-21.8760 c. 10: 1 1 8 N M DE S SD: 7.1298 c. M:-10.8083 c. 11: 1 1 9 N M DE S SD: 1.3119 c. M:-1.7529 c. 23: 2 2 19 N M DE S SD: 1.2967 c. M: 2.1842 c. 34: 3 3 28 N M DE S SD: 0.5297 c. M: 0.9104 c. 45: 4 4 37 N M DE S SD: 0.2947 c. M:-0.4396 c. 101: 9 9 83 N M DE S SD: 0.3179 c. M:-0.5492 c. 124: 11 11 102 N M DE S SD: 0.3238 c. M: 0.4379 c. 146: 13 13 120 N M DE S SD: 0.3040 c. M:-0.5154 c. 157: 14 14 129 N M DE S SD: 0.3355 c. M:-0.5806 c. 169: 15 15 139 N M DE S SD: 0.3122 c. M: 0.3903 c. 191: 17 17 157 N M DE S SD: 0.2990 c. M:-0.4976 c. 214: 19 19 176 N M DE S SD: 0.3066 c. M:-0.3879 c. 218: 19 20 179 N T3 SD: 0.2993 c. M: 0.4235 c. 229: 20 21 188 N T3 SD: 0.2872 c. M:-0.3689 c. 230: 20 21 189 N T3 SD: 0.3020 c. M: 0.5228 c. 236: 21 21 194 N M DE S SD: 0.2967 c. M:-0.4865 c. 240: 21 22 197 N T3 SD: 0.2890 c. M:-0.4324 c. 241: 21 22 198 N T3 SD: 0.2525 c. M: 0.4329 c. 252: 22 23 207 N T3 SD: 0.2173 c. M: 0.3509 c. 263: 23 24 216 N T3 SD: 0.1979 c. M: 0.2758 c. 274: 24 25 225 N T3 SD: 0.1944 c. M:-0.2657 c. 275: 24 25 226 N T3 SD: 0.2136 c. M: 0.3653 c. 285: 25 26 234 N T3 SD: 0.2040 c. M:-0.3231 c. 286: 25 26 235 N T3 SD: 0.1708 c. M: 0.2956 c. 297: 26 27 244 N T3 SD: 0.1405 c. M: 0.2312 c. 308: 27 28 253 N T3 SD: 0.1262 c. M: 0.1713 c. 331: 29 30 272 N T3 SD: 0.1139 c. M: 0.1957 c. 342: 30 31 281 N T3 SD: 0.0845 c. M: 0.1429 c. 353: 31 32 290 N T3 SD: 0.0731 c. M: 0.0934 c. 376: 33 34 309 N T3 SD: 0.0756 c. M: 0.1197 c. 387: 34 35 318 N T3 SD: 0.0434 c. M: 0.0752 c. 398: 35 36 327 N T3 SD: 0.0330 c. M:-0.0465 c. 432: 38 39 355 N T3 SD: 0.0208 c. M: 0.0288 c. 443: 39 40 364 N T3 SD: 0.0124 c. M:-0.0155 c. 875: 77 79 719 N T3 SD: 0.0041 c. M: 0.0064 c. 1318: 116 119 1083 N T3 SD: 0.0018 c. M:-0.0030 c. 2193: 193 198 1802 N T3 SD: 0.0012 c. M: 0.0020 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: 89.0351 cents 7 x 8:9 S SD: 77.8368 cents 8 x 9:11 SD: 63.4196 cents 9 x 10:12 S SD: 46.8015 cents 10 x 11:13 SD: 43.9549 cents 11 x 12:15 S SD: 36.5287 cents 12 x 13:16 SD: 24.8860 cents 13 x 14:17 SD: 25.9335 cents 14 x 15:19 SD: 21.6672 cents 15 x 16:20 S SD: 11.4653 cents 16 x 17:21 SD: 15.8454 cents 17 x 18:23 SD: 13.6187 cents 18 x 19:24 SD: 2.4012 cents 19 x 20:25 S SD: 11.4653 cents 20 x 21:27 SD: 10.9693 cents 21 x 22:28 SD: 4.1318 cents 22 x 23:29 SD: 11.5300 cents 23 x 24:31 SD: 12.0303 cents 24 x 25:32 SD: 9.0641 cents 25 x 26:33 SD: 13.5975 cents 26:27 x 35 SD: 13.5737 cents 27:28 x 36 SD: 9.5649 cents 28:29 x 37 SD: 11.4824 cents 29:30:31:39 SD: 11.3152 cents 30:31:32:40 S SD: 8.7759 cents 32:33:34:43 SD: 7.6858 cents 33:34:35:44 SD: 5.0812 cents 35:36:37:47 SD: 5.0667 cents 36:37:38:48 SD: 2.0012 cents 39:40:41:52 SD: 0.7403 cents 75:77:79:100 SD: 0.6933 cents 114:117:120:152 SD: 0.3795 cents 153:157:161:204 SD: 0.3399 cents 396:406:417:528 SD: 0.3091 cents 435:446:458:580 SD: 0.2392 cents 474:486:499:632 SD: 0.1925 cents 510:523:537:680 SD: 0.1897 cents 513:526:540:684 SD: 0.1688 cents 549:563:578:732 SD: 0.1314 cents 588:603:619:784 SD: 0.0885 cents