Scala analysis: 059_E4
Enharmonic tetrachord 36/35 * 55/54 * 14/11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 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: 36/35 48.7704 septimal diesis, 1/4-tone 2: 55/54 31.7667 telepathma 3: 14/11 417.5080 undecimal diminished fourth or major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 55/54 31.767 cents telepathma 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 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 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 2: 1 72/55 466.278 cents undecimal 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 : 48.8 80.5 498.0 48.8 : 31.8 449.3 498.0 80.5 : 417.5 466.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.7667 .. 417.5080 cents 756/605, 385.7413 cents 55/54, 31.7667 cents 2: 80.5370 .. 466.2783 cents 756/605, 385.7413 cents 121/147,-336.9709 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 55/54, 31.7667 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 14/11, 417.5080 cents Average / Smallest step : 5.226078 Largest / Average step : 2.514881 Largest / Smallest step : 13.142963 Median interval of one step : 36/35, 48.7704 cents, amount: 1 Least squares average step : 121.71282 cents, oct.: 365.13845 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1583-tone equal temperament with octave 4/3 degrees: 155 256 1583 Least number of segments generator : 792 of 249.180 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 970 of 305.182 cents and inv. generated superset size: 9 = 6 more = 300.000% 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 31.76665 cents Scale diversity : 0.269251 Lumma stability : 0.127565 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 : 1944/1925, 17.0037 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 385.7413 cents: 2 -- Rational properties -- Prime limit : 11 Odd number limit : 55 (O: 55 U: 55) Highest odd numerator or denominator: 35 Scale harmonicity : 0.022288 Average absolute harmonicity : 0.095679 Specific harmonicity : 0.107704 Fundamental : 1/105, -6.7142 octaves, 2.4917 Hz. Guide tone : 396, 8.6294 octaves, 103603.724 Hz. Exponens Consonantiae : 4.158000E+04, 15.34360 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 60.5, average 20.16667 Mersenne's string divisions : 21371 Sum of van Prooijen's expressibility: 3.34341, average 1.11447 Sum of Tenney's harmonic distance : 6.84419, average 2.28140 Vogel's harmonic complexity : 14.00000 Wille's k value : 27 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 15.91112, average 2.65185 Lattice compactness (without 2's) : 13.22900, average 2.20483 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 2 0.00000 4 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.66667 2 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 18 25| Scale is weakly epimorphic with val: <6 10 17 20 27| Scale is weakly epimorphic with val: <6 10 18 19 26| Scale is weakly epimorphic with val: <6 11 16 19 27| Scale is weakly epimorphic with val: <6 11 17 18 26| Scale is weakly epimorphic with val: <6 11 19 19 27| Scale is weakly epimorphic with val: <7 10 15 20 26| Scale is weakly epimorphic with val: <7 10 16 19 25| Scale is weakly epimorphic with val: <7 10 17 18 24| Scale is weakly epimorphic with val: <7 10 17 21 27| Scale is weakly epimorphic with val: <7 10 18 20 26| Scale is weakly epimorphic with val: <7 10 19 19 25| 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 20 23| Scale is JI-epimorphic with val: <7 11 15 20 26| Scale is weakly epimorphic with val: <7 11 15 22 24| Scale is weakly epimorphic with val: <7 11 15 22 27| Scale is weakly epimorphic with val: <7 11 16 18 23| Scale is weakly epimorphic with val: <7 11 16 18 26| Scale is JI-epimorphic with val: <7 11 16 19 25| Scale is weakly epimorphic with val: <7 11 16 21 23| Scale is weakly epimorphic with val: <7 11 16 21 26| Scale is weakly epimorphic with val: <7 11 16 22 25| Scale is JI-epimorphic with val: <7 11 17 18 24| Scale is weakly epimorphic with val: <7 11 17 18 27| Scale is weakly epimorphic with val: <7 11 17 20 25| = patent Scale is weakly epimorphic with val: <7 11 17 21 24| Scale is weakly epimorphic with val: <7 11 17 21 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 20 23| Scale is weakly epimorphic with val: <7 11 18 20 26| 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 21 23| Scale is weakly epimorphic with val: <7 11 19 21 26| Scale is weakly epimorphic with val: <7 11 19 22 25| Scale is weakly epimorphic with val: <7 12 15 19 27| Scale is weakly epimorphic with val: <7 12 15 20 23| Scale is weakly epimorphic with val: <7 12 15 20 26| Scale is weakly epimorphic with val: <7 12 16 18 26| Scale is weakly epimorphic with val: <7 12 16 19 25| Scale is weakly epimorphic with val: <7 12 17 18 24| Scale is weakly epimorphic with val: <7 12 17 18 27| Scale is weakly epimorphic with val: <7 12 18 19 27| Scale is weakly epimorphic with val: <8 11 15 19 25| Scale is weakly epimorphic with val: <8 11 15 20 24| Scale is weakly epimorphic with val: <8 11 15 20 27| Scale is weakly epimorphic with val: <8 11 16 18 24| Scale is weakly epimorphic with val: <8 11 16 19 23| Scale is weakly epimorphic with val: <8 11 16 19 26| Scale is weakly epimorphic with val: <8 11 16 21 27| Scale is weakly epimorphic with val: <8 11 17 18 25| Scale is weakly epimorphic with val: <8 11 17 20 26| Scale is weakly epimorphic with val: <8 11 18 19 25| Scale is weakly epimorphic with val: <8 11 19 21 27| Scale is weakly epimorphic with val: <8 12 15 20 27| Scale is weakly epimorphic with val: <8 12 15 22 25| Scale is weakly epimorphic with val: <8 12 16 19 26| Scale is weakly epimorphic with val: <8 12 16 21 24| Scale is weakly epimorphic with val: <8 12 16 21 27| Scale is weakly epimorphic with val: <8 12 17 18 25| Scale is weakly epimorphic with val: <8 12 17 20 23| Scale is weakly epimorphic with val: <8 12 17 20 26| Scale is weakly epimorphic with val: <8 12 18 19 25| Scale is weakly epimorphic with val: <8 12 18 20 27| Scale is weakly epimorphic with val: <8 12 19 19 26|
FIT/MODE
3: 0 0 3 N M DE S SD: 54.3592 c. M: 80.5370 c. 4: 0 1 3 N G T3 SD: 37.9134 c. M: 48.7704 c. 5: 1 0 4 N G T3 SD: 31.3491 c. M:-50.8386 c. 6: 1 0 5 N G T3 SD: 19.8182 c. M:-34.2371 c. 7: 1 0 6 N G T3 SD: 14.0112 c. M:-22.3789 c. 8: 1 0 7 N G T3 SD: 13.1157 c. M: 18.2814 c. 10: 1 1 8 N M DE S SD: 11.0274 c. M:-19.0720 c. 11: 1 1 9 N M DE S SD: 6.1247 c. M:-10.0166 c. 12: 1 1 10 N M DE S SD: 4.4312 c. M: 7.2666 c. 18: 2 1 15 N T3 SD: 4.0514 c. M:-6.5680 c. 19: 2 1 16 N T3 SD: 2.3781 c. M:-3.6554 c. 30: 3 2 25 N T3 SD: 1.5462 c. M:-2.4705 c. 31: 3 2 26 N T3 SD: 0.3515 c. M: 0.5725 c. 112: 11 7 94 N T3 SD: 0.2973 c. M: 0.4941 c. 123: 12 8 103 N T3 SD: 0.2778 c. M:-0.4459 c. 142: 14 9 119 N T3 SD: 0.2067 c. M:-0.3326 c. 154: 15 10 129 N T3 SD: 0.2354 c. M:-0.3144 c. 173: 17 11 145 N T3 SD: 0.1067 c. M:-0.1705 c. 204: 20 13 171 N T3 SD: 0.0372 c. M:-0.0576 c. 235: 23 15 197 N T3 SD: 0.0148 c. M: 0.0256 c. 439: 43 28 368 N T3 SD: 0.0104 c. M:-0.0131 c. 674: 66 43 565 N T3 SD: 0.0042 c. M:-0.0073 c. 909: 89 58 762 N T3 SD: 0.0049 c. M: 0.0069 c. 1583: 155 101 1327 N T3 SD: 0.0042 c. M:-0.0059 c. 2257: 221 144 1892 N T3 SD: 0.0041 c. M:-0.0064 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 27:28 x 36 SD: 7.0953 cents 28:29 x 37 SD: 9.8059 cents 29:30 x 39 SD: 8.9340 cents 30:31 x 40 SD: 3.9982 cents 31:32 x 41 SD: 7.6628 cents 33:34:35:44 SD: 7.1758 cents 35:36:37:47 SD: 6.6441 cents 36:37:38:48 SD: 4.3780 cents 39:40:41:52 SD: 2.6015 cents 63:65:66:84 SD: 1.7784 cents 66:68:69:88 SD: 1.5384 cents 102:105:107:136 SD: 0.9036 cents 105:108:110:140 SD: 0.0000 cents