Scala analysis: 060_E4
Enharmonic tetrachord 50/49 * 77/75 * 14/11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 50/49 34.975615 Erlich's decatonic comma, tritonic diesis 2: 22/21 80.537035 undecimal minor semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 14/11 417.5080 undecimal diminished fourth or major third 1: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 2: 77/75 45.5614 3: 14/11 417.5080 undecimal diminished fourth or major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 1 77/75 45.561 cents 1: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 22/21 80.537 cents undecimal minor semitone 2: 1 100/77 452.484 cents 2: 1 98/75 463.069 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 : 35.0 80.5 498.0 35.0 : 45.6 463.1 498.0 80.5 : 417.5 452.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.9756 .. 417.5080 cents 343/275, 382.5323 cents 50/49, 34.9756 cents 2: 80.5370 .. 463.0694 cents 343/275, 382.5323 cents 121/147,-336.9709 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 50/49, 34.9756 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 14/11, 417.5080 cents Average / Smallest step : 4.746593 Largest / Average step : 2.514881 Largest / Smallest step : 11.937116 Median interval of one step : 77/75, 45.5614 cents, amount: 1 Least squares average step : 120.72748 cents, oct.: 362.18243 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1979-tone equal temperament with octave 4/3 degrees: 139 320 1979 Least number of segments generator : 990 of 249.148 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1899 of 477.912 cents and inv. generated superset size: 28 = 25 more = 933.333% 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 34.97561 cents Scale diversity : 0.276020 Lumma stability : 0.140452 Lumma impropriety factor : 0.676587 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 : 3773/3750, 10.5858 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 371.9465 cents: 2 -- Rational properties -- Prime limit : 11 Odd number limit : 77 (O: 77 U: 77) Highest odd numerator or denominator: 49 Scale harmonicity : 0.017787 Average absolute harmonicity : 0.091499 Specific harmonicity : 0.088099 Fundamental : 1/147, -7.1997 octaves, 1.7798 Hz. Guide tone : 1100, 10.1033 octaves, 287788.122 Hz. Exponens Consonantiae : 1.617000E+05, 17.30296 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 74.5, average 24.83333 Mersenne's string divisions : 29799 Sum of van Prooijen's expressibility: 3.48954, average 1.16318 Sum of Tenney's harmonic distance : 7.13299, average 2.37766 Vogel's harmonic complexity : 16.33333 Wille's k value : 38 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 14.77615, average 2.46269 Lattice compactness (without 2's) : 12.62044, average 2.10341 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.33333 4 3: -1 .. 0 -0.66667 2 1 5: 0 .. 2 0.66667 2 7: -2 .. 0 -1.00000 3 1 11: 0 .. 1 0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 15 19 26| Scale is weakly epimorphic with val: <6 10 16 20 27| Scale is weakly epimorphic with val: <6 10 17 18 25| Scale is weakly epimorphic with val: <6 10 18 19 26| Scale is weakly epimorphic with val: <6 10 19 20 27| Scale is weakly epimorphic with val: <6 11 16 18 26| Scale is weakly epimorphic with val: <6 11 17 19 27| Scale is weakly epimorphic with val: <7 10 15 19 25| Scale is weakly epimorphic with val: <7 10 16 18 23| Scale is weakly epimorphic with val: <7 10 16 18 26| Scale is weakly epimorphic with val: <7 10 16 20 26| Scale is weakly epimorphic with val: <7 10 17 18 24| Scale is weakly epimorphic with val: <7 10 17 19 24| Scale is weakly epimorphic with val: <7 10 17 19 27| Scale is weakly epimorphic with val: <7 10 17 21 27| Scale is weakly epimorphic with val: <7 10 18 19 25| Scale is weakly epimorphic with val: <7 10 18 20 25| Scale is weakly epimorphic with val: <7 10 19 20 26| Scale is weakly epimorphic with val: <7 10 19 21 23| Scale is weakly epimorphic with val: <7 10 19 21 26| Scale is JI-epimorphic with val: <7 11 15 18 24| Scale is weakly epimorphic with val: <7 11 15 18 27| Scale is weakly epimorphic with val: <7 11 15 19 24| Scale is weakly epimorphic with val: <7 11 15 19 27| Scale is weakly epimorphic with val: <7 11 15 21 24| Scale is weakly epimorphic with val: <7 11 15 21 27| Scale is weakly epimorphic with val: <7 11 15 22 24| Scale is weakly epimorphic with val: <7 11 15 22 27| Scale is JI-epimorphic with val: <7 11 16 19 25| Scale is weakly epimorphic with val: <7 11 16 20 25| Scale is weakly epimorphic with val: <7 11 16 22 25| Scale is weakly epimorphic with val: <7 11 17 18 23| Scale is weakly epimorphic with val: <7 11 17 18 26| Scale is weakly epimorphic with val: <7 11 17 20 23| Scale is JI-epimorphic with val: <7 11 17 20 26| Scale is weakly epimorphic with val: <7 11 17 21 23| Scale is weakly epimorphic with val: <7 11 17 21 26| Scale is weakly epimorphic with val: <7 11 18 18 24| Scale is weakly epimorphic with val: <7 11 18 18 27| Scale is weakly epimorphic with val: <7 11 18 19 24| Scale is weakly epimorphic with val: <7 11 18 19 27| Scale is weakly epimorphic with val: <7 11 18 21 24| Scale is JI-epimorphic with val: <7 11 18 21 27| Scale is weakly epimorphic with val: <7 11 18 22 24| Scale is weakly epimorphic with val: <7 11 18 22 27| Scale is weakly epimorphic with val: <7 11 19 19 25| Scale is weakly epimorphic with val: <7 11 19 20 25| Scale is weakly epimorphic with val: <7 11 19 22 25| Scale is weakly epimorphic with val: <7 12 15 18 26| Scale is weakly epimorphic with val: <7 12 16 18 24| Scale is weakly epimorphic with val: <7 12 16 18 27| Scale is weakly epimorphic with val: <7 12 16 19 27| Scale is weakly epimorphic with val: <7 12 17 19 25| Scale is weakly epimorphic with val: <7 12 18 18 26| Scale is weakly epimorphic with val: <7 12 18 20 23| Scale is weakly epimorphic with val: <7 12 18 20 26| Scale is weakly epimorphic with val: <7 12 19 19 27| Scale is weakly epimorphic with val: <7 12 19 21 24| Scale is weakly epimorphic with val: <7 12 19 21 27| Scale is weakly epimorphic with val: <8 11 15 20 26| Scale is weakly epimorphic with val: <8 11 16 18 24| Scale is weakly epimorphic with val: <8 11 16 21 27| Scale is weakly epimorphic with val: <8 11 17 19 25| Scale is weakly epimorphic with val: <8 11 18 20 26| Scale is weakly epimorphic with val: <8 11 19 21 27| Scale is weakly epimorphic with val: <8 12 15 18 25| Scale is weakly epimorphic with val: <8 12 16 19 26| Scale is weakly epimorphic with val: <8 12 17 20 27| Scale is weakly epimorphic with val: <8 12 18 18 25| Scale is weakly epimorphic with val: <8 12 19 19 26|
FIT/MODE
3: 0 0 3 N M DE S SD: 50.6935 c. M: 80.5370 c. 4: 0 1 3 N G T3 SD: 32.4398 c. M:-43.9742 c. 5: 0 1 4 N G T3 SD: 23.0002 c. M: 34.9756 c. 6: 0 1 5 N G T3 SD: 20.2435 c. M: 34.9756 c. 7: 0 1 6 N G T3 SD: 20.9079 c. M: 34.9756 c. 8: 0 1 7 N G T3 SD: 22.7853 c. M: 34.9756 c. 10: 1 1 8 N M DE S SD: 13.9479 c. M:-19.0720 c. 11: 1 1 9 N M DE S SD: 8.2955 c. M:-10.3012 c. 12: 1 1 10 N M DE S SD: 4.0299 c. M:-6.5281 c. 13: 1 1 11 N M DE S SD: 2.9693 c. M: 3.9147 c. 25: 2 2 21 N M DE S SD: 2.8530 c. M:-4.8680 c. 30: 2 3 25 N T3 SD: 1.7555 c. M:-2.4705 c. 31: 2 3 26 N T3 SD: 1.6462 c. M: 2.8437 c. 42: 3 4 35 N T3 SD: 1.4677 c. M:-2.4705 c. 43: 3 4 36 N T3 SD: 0.3385 c. M:-0.5401 c. 99: 7 9 83 N T3 SD: 0.1408 c. M:-0.2397 c. 142: 10 13 119 N T3 SD: 0.0950 c. M:-0.1322 c. 285: 20 26 239 N T3 SD: 0.0883 c. M: 0.1508 c. 328: 23 30 275 N T3 SD: 0.0458 c. M: 0.0603 c. 371: 26 34 311 N T3 SD: 0.0420 c. M: 0.0722 c. 427: 30 39 358 N T3 SD: 0.0340 c. M: 0.0567 c. 470: 33 43 394 N T3 SD: 0.0039 c. M: 0.0065 c. 1979: 139 181 1659 N T3 SD: 0.0042 c. M:-0.0058 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: 93.1669 cents 7 x 8:9 S SD: 81.6327 cents 8 x 9:11 SD: 67.1917 cents 9 x 10:12 S SD: 50.9333 cents 10 x 11:13 SD: 47.5812 cents 11 x 12:15 S SD: 40.0864 cents 12 x 13:16 SD: 29.0178 cents 13 x 14:17 SD: 29.2030 cents 14 x 15:19 SD: 24.7619 cents 15 x 16:20 S SD: 15.5971 cents 16 x 17:21 SD: 18.3002 cents 17 x 18:23 SD: 15.6363 cents 18 x 19:24 SD: 6.5330 cents 19 x 20:25 S SD: 12.1871 cents 20 x 21:27 SD: 10.9312 cents 21 x 22:28 SD: 0.0000 cents 22 x 23:29 SD: 10.0536 cents 23 x 24:31 SD: 9.9663 cents 24 x 25:32 SD: 4.9323 cents 25 x 26:33 SD: 10.7521 cents 26 x 27:35 SD: 11.2416 cents 27 x 28:36 SD: 8.7881 cents 28 x 29:37 SD: 12.5754 cents 29 x 30:39 SD: 13.2104 cents 30:31 x 40 SD: 10.8956 cents 31:32 x 41 SD: 12.2072 cents 32:33:34:43 SD: 11.1184 cents 33:34:35:44 SD: 9.0313 cents 34:35:36:45 S SD: 9.0293 cents 35:36:37:47 SD: 8.0801 cents 36:37:38:48 SD: 6.0179 cents 38:39:40:51 SD: 5.7450 cents 39:40:41:52 SD: 3.5736 cents 42:43:44:56 SD: 1.9204 cents 87:89:91:116 SD: 1.7157 cents 99:101:104:132 SD: 1.5918 cents 102:104:107:136 SD: 0.8941 cents 105:107:110:140 SD: 0.7700 cents 144:147:151:192 SD: 0.5968 cents 147:150:154:196 SD: 0.0000 cents