Scala analysis: 096_E11
Enharmonic tetrachord 40/39 * 117/113 * 113/90
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: 120/113 104.053960 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 113/90 393.9910 1: 40/39 43.8311 tridecimal minor diesis 2: 117/113 60.2229 3: 113/90 393.9910
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 117/113 60.223 cents 1: 1 113/90 393.991 cents 2: 1 120/113 104.054 cents 2: 1 452/351 437.822 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 : 43.8 104.1 498.0 43.8 : 60.2 454.2 498.0 104.1: 394.0 437.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 393.9910 cents 1469/1200, 350.1600 cents 40/39, 43.8311 cents 2: 104.0540 .. 454.2139 cents 1469/1200, 350.1600 cents 10800/12769,-289.9371 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 : 113/90, 393.9910 cents Average / Smallest step : 3.787612 Largest / Average step : 2.373226 Largest / Smallest step : 8.988857 Median interval of one step : 117/113, 60.2229 cents, amount: 1 Least squares average step : 124.71957 cents, oct.: 374.15871 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2216-tone equal temperament with octave 4/3 degrees: 195 463 2216 Least number of segments generator : 1109 of 249.247 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1315 of 295.546 cents and inv. generated superset size: 30 = 27 more = 1000.000% 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 : 0.448040 Lumma stability : 0.176012 Lumma impropriety factor : 0.582150 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 : 4563/4520, 16.3919 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% Limited inverse transpositions with margin 333.7681 cents: 2 -- Rational properties -- Prime limit : 113 Odd number limit : 351 (O: 117 U: 351) Highest odd numerator or denominator: 113 Scale harmonicity : 0.027110 Fundamental : 1/4407, -12.1056 octaves, 0.0594 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 5.288400E+05, 19.01247 octaves Euler's gradus suavitatis : 136 Sum of Mann's harmonic distance : 159.5, average 53.16667 Mersenne's string divisions : 128849 Sum of van Prooijen's expressibility: 4.12126, average 1.37375 Sum of Tenney's harmonic distance : 8.40457, average 2.80152 Vogel's harmonic complexity : 92.00000 Wille's k value : 734 Wilson's harmonic complexity : 137 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 15.43440, average 2.57240 Lattice compactness (without 2's) : 10.03261, average 1.67210 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -1 .. 1 -0.33333 3 1 5: 0 .. 1 0.66667 2 13: -1 .. 0 -0.33333 1 1 113: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <7 10 17 25 49| Scale is weakly epimorphic with val: <7 10 18 26 50| Scale is weakly epimorphic with val: <7 10 19 27 48| Scale is weakly epimorphic with val: <7 11 15 26 49| Scale is weakly epimorphic with val: <7 11 15 27 48| Scale is weakly epimorphic with val: <7 11 15 29 49| Scale is weakly epimorphic with val: <7 11 15 30 48| Scale is weakly epimorphic with val: <7 11 16 25 49| Scale is weakly epimorphic with val: <7 11 16 27 50| Scale is weakly epimorphic with val: <7 11 16 28 49| Scale is weakly epimorphic with val: <7 11 16 30 50| Scale is weakly epimorphic with val: <7 11 17 25 48| Scale is weakly epimorphic with val: <7 11 17 26 50| Scale is weakly epimorphic with val: <7 11 17 28 48| Scale is weakly epimorphic with val: <7 11 17 29 50| Scale is weakly epimorphic with val: <7 11 18 26 49| Scale is JI-epimorphic with val: <7 11 18 27 48| Scale is weakly epimorphic with val: <7 11 18 29 49| Scale is weakly epimorphic with val: <7 11 18 30 48| Scale is weakly epimorphic with val: <7 11 19 25 49| Scale is weakly epimorphic with val: <7 11 19 27 50| Scale is JI-epimorphic with val: <7 11 19 28 49| Scale is weakly epimorphic with val: <7 11 19 30 50| Scale is weakly epimorphic with val: <7 12 18 26 48| Scale is weakly epimorphic with val: <7 12 18 29 48| Scale is weakly epimorphic with val: <7 12 19 25 48| Scale is weakly epimorphic with val: <7 12 19 27 49| Scale is weakly epimorphic with val: <7 12 19 30 49| Scale is weakly epimorphic with val: <8 11 15 25 49| Scale is weakly epimorphic with val: <8 11 16 25 48| Scale is weakly epimorphic with val: <8 11 16 26 50| Scale is weakly epimorphic with val: <8 11 16 28 48| Scale is weakly epimorphic with val: <8 11 17 26 49| Scale is weakly epimorphic with val: <8 11 17 27 48| Scale is weakly epimorphic with val: <8 11 17 29 49| Scale is weakly epimorphic with val: <8 11 18 27 50| Scale is weakly epimorphic with val: <8 11 18 28 49| Scale is weakly epimorphic with val: <8 11 18 30 50| Scale is weakly epimorphic with val: <8 11 19 29 50| Scale is weakly epimorphic with val: <8 12 15 25 48| Scale is weakly epimorphic with val: <8 12 15 28 48| Scale is weakly epimorphic with val: <8 12 16 25 50| Scale is weakly epimorphic with val: <8 12 16 26 49| Scale is weakly epimorphic with val: <8 12 16 29 49| Scale is weakly epimorphic with val: <8 12 17 26 48| Scale is weakly epimorphic with val: <8 12 17 27 50| Scale is weakly epimorphic with val: <8 12 17 30 50| Scale is weakly epimorphic with val: <8 12 18 27 49| Scale is weakly epimorphic with val: <8 12 19 28 50|
FIT/MODE
3: 0 0 3 N M DE S SD: 65.1879 c. M: 104.0540 c. 4: 0 1 3 N G T3 SD: 27.9265 c. M: 43.8311 c. 5: 0 1 4 N G T3 SD: 25.4357 c. M: 43.8311 c. 6: 0 1 5 N G T3 SD: 28.0720 c. M: 43.8311 c. 8: 1 1 6 N M DE S SD: 15.8951 c. M:-20.4573 c. 9: 1 1 7 N M DE S SD: 7.6655 c. M:-11.5073 c. 10: 1 1 8 N M DE S SD: 4.2988 c. M:-5.9734 c. 19: 2 2 15 N M DE S SD: 4.9835 c. M:-8.5947 c. 23: 2 3 18 N T3 SD: 2.4531 c. M:-4.2167 c. 24: 2 3 19 N T3 SD: 1.3544 c. M: 2.3273 c. 33: 3 4 26 N T3 SD: 1.2416 c. M:-1.5919 c. 34: 3 4 27 N T3 SD: 0.8773 c. M: 1.5153 c. 57: 5 7 45 N T3 SD: 0.4678 c. M:-0.7976 c. 67: 6 8 53 N T3 SD: 0.4446 c. M:-0.7700 c. 91: 8 11 72 N T3 SD: 0.0470 c. M: 0.0665 c. 421: 37 51 333 N T3 SD: 0.0452 c. M: 0.0599 c. 488: 43 59 386 N T3 SD: 0.0408 c. M:-0.0541 c. 512: 45 62 405 N T3 SD: 0.0374 c. M: 0.0576 c. 579: 51 70 458 N T3 SD: 0.0273 c. M:-0.0382 c. 670: 59 81 530 N T3 SD: 0.0177 c. M:-0.0266 c. 761: 67 92 602 N T3 SD: 0.0108 c. M:-0.0179 c. 852: 75 103 674 N T3 SD: 0.0065 c. M:-0.0109 c. 943: 83 114 746 N T3 SD: 0.0058 c. M: 0.0085 c. 1795: 158 217 1420 N T3 SD: 0.0056 c. M:-0.0080 c. 2125: 187 257 1681 N T3 SD: 0.0050 c. M:-0.0081 c. 2216: 195 268 1753 N T3 SD: 0.0041 c. M:-0.0051 c. 2307: 203 279 1825 N T3 SD: 0.0040 c. M: 0.0065 c. 2398: 211 290 1897 N T3 SD: 0.0047 c. M: 0.0081 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: 81.4085 cents 7 x 8:9 S SD: 70.9288 cents 8 x 9:11 SD: 56.5889 cents 9 x 10:12 S SD: 39.1749 cents 10 x 11:13 SD: 37.5370 cents 11 x 12:15 S SD: 30.3465 cents 12 x 13:16 SD: 17.2594 cents 13 x 14:17 SD: 20.7238 cents 14 x 15:19 SD: 17.1446 cents 15 x 16:20 S SD: 3.8387 cents 16 x 17:21 SD: 13.6395 cents 17 x 18:23 SD: 12.8916 cents 18 x 19:24 SD: 5.2255 cents 19 x 20:25 S SD: 13.7702 cents 20 x 21:27 SD: 14.5444 cents 21 x 22:28 SD: 11.7585 cents 22 x 23:29 SD: 16.7761 cents 23:24 x 31 SD: 17.6160 cents 24:25 x 32 SD: 13.4207 cents 26:27:28:35 S SD: 12.1325 cents 27:28:29:36 SD: 9.1433 cents 29:30:31:39 SD: 7.9703 cents 30:31:32:40 S SD: 5.0142 cents 33:34:35:44 SD: 2.7168 cents 75:77:80:100 SD: 2.6233 cents 77:79:82:103 SD: 2.4827 cents 78:80:83:104 SD: 1.1702 cents 81:83:86:108 SD: 0.5476 cents 114:117:121:152 SD: 0.4809 cents 192:197:204:256 SD: 0.3756 cents 195:200:207:260 SD: 0.2220 cents 273:280:290:364 SD: 0.1761 cents 354:363:376:472 SD: 0.1636 cents 387:397:411:516 SD: 0.1179 cents 468:480:497:624 SD: 0.0103 cents