Scala analysis: 061_E4
Enharmonic tetrachord 14/11 * 143/140 * 40/39
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/11 417.507964 undecimal diminished fourth or major third 2: 13/10 454.213948 tridecimal semi-diminished fourth 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 40/39 43.8311 tridecimal minor diesis 1: 14/11 417.5080 undecimal diminished fourth or major third 2: 143/140 36.7060 3: 40/39 43.8311 tridecimal minor diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 143/140 36.706 cents 1: 1 40/39 43.831 cents tridecimal minor diesis 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 13/10 454.214 cents tridecimal semi-diminished fourth 2: 1 560/429 461.339 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 : 417.5 454.2 498.0 417.5: 36.7 80.5 498.0 454.2: 43.8 461.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 36.7060 .. 417.5080 cents 1960/1573, 380.8020 cents 143/140, 36.7060 cents 2: 80.5370 .. 461.3390 cents 1960/1573, 380.8020 cents 121/147,-336.9709 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 143/140, 36.7060 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 14/11, 417.5080 cents Average / Smallest step : 4.522832 Largest / Average step : 2.514881 Largest / Smallest step : 11.374384 Median interval of one step : 40/39, 43.8311 cents, amount: 1 Least squares average step : 201.43363 cents, oct.: 604.30090 cents Scale is not proper Scale has trivalence property Scale is a mode of a 909-tone equal temperament with octave 4/3 degrees: 762 829 909 Least number of segments generator : 455 of 249.296 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 655 of 358.877 cents and inv. generated superset size: 15 = 12 more = 500.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LSM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 36.70598 cents Scale diversity : 0.279179 Lumma stability : 0.147400 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 : 5600/5577, 7.1251 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% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Limited inverse transpositions with margin 380.8020 cents: 1 -- Rational properties -- Prime limit : 13 Odd number limit : 429 (O: 143 U: 429) Highest odd numerator or denominator: 13 Scale harmonicity : 0.015952 Average absolute harmonicity : 0.094019 Specific harmonicity : 0.084627 Fundamental : 1/330, -8.3663 octaves, 0.7928 Hz. Guide tone : 364, 8.5078 octaves, 95231.706 Hz. Exponens Consonantiae : 1.201200E+05, 16.87412 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 27.5, average 9.16667 Mersenne's string divisions : 4025 Sum of van Prooijen's expressibility: 2.63246, average 0.87749 Sum of Tenney's harmonic distance : 5.38065, average 1.79355 Vogel's harmonic complexity : 21.00000 Wille's k value : 214 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 13.99270, average 2.33212 Lattice compactness (without 2's) : 9.29253, average 1.54875 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -1 .. 0 -0.33333 1 1 5: -1 .. 0 -0.33333 1 7: 0 .. 1 0.33333 1 11: -1 .. 0 -0.33333 1 1 13: 0 .. 1 0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <7 11 16 19 24 27| Scale is weakly epimorphic with val: <7 11 16 19 25 28| Scale is weakly epimorphic with val: <7 11 16 20 25 27| Scale is weakly epimorphic with val: <7 11 16 20 26 28| Scale is weakly epimorphic with val: <7 11 16 21 24 28| Scale is weakly epimorphic with val: <7 11 16 21 26 27| Scale is weakly epimorphic with val: <7 11 17 19 24 28| Scale is JI-epimorphic with val: <7 11 17 19 25 26| Scale is weakly epimorphic with val: <7 11 17 20 25 28| Scale is JI-epimorphic with val: <7 11 17 20 26 26| Scale is weakly epimorphic with val: <7 11 17 21 24 26| Scale is weakly epimorphic with val: <7 11 17 21 26 28| Scale is weakly epimorphic with val: <7 11 18 19 24 26| Scale is JI-epimorphic with val: <7 11 18 19 25 27| Scale is weakly epimorphic with val: <7 11 18 20 25 26| Scale is JI-epimorphic with val: <7 11 18 20 26 27| Scale is weakly epimorphic with val: <7 11 18 21 24 27| Scale is weakly epimorphic with val: <7 11 18 21 26 26| Scale is weakly epimorphic with val: <7 12 16 19 25 26| Scale is weakly epimorphic with val: <7 12 16 20 24 27| Scale is weakly epimorphic with val: <7 12 16 20 26 26| Scale is weakly epimorphic with val: <7 12 16 21 24 26| Scale is weakly epimorphic with val: <7 12 16 21 25 27| Scale is weakly epimorphic with val: <7 12 17 19 25 27| Scale is weakly epimorphic with val: <7 12 17 20 24 28| Scale is weakly epimorphic with val: <7 12 17 20 26 27| Scale is weakly epimorphic with val: <7 12 17 21 24 27| Scale is weakly epimorphic with val: <7 12 17 21 25 28| Scale is weakly epimorphic with val: <7 12 18 19 25 28| Scale is weakly epimorphic with val: <7 12 18 20 24 26| Scale is weakly epimorphic with val: <7 12 18 20 26 28| Scale is weakly epimorphic with val: <7 12 18 21 24 28| Scale is weakly epimorphic with val: <7 12 18 21 25 26|
FIT/MODE
3: 2 0 1 N G T3 SD: 86.0918 c. M: 122.1839 c. 4: 3 1 0 N G T3 SD: 35.8464 c. M: 43.9742 c. 5: 4 0 1 N G T3 SD: 34.0339 c. M: 55.7779 c. 6: 5 0 1 N G T3 SD: 22.6635 c. M: 39.1764 c. 7: 6 0 1 N G T3 SD: 16.6775 c. M: 27.3182 c. 8: 7 0 1 N G T3 SD: 14.9853 c. M: 18.4246 c. 10: 8 1 1 N M DE S SD: 11.5387 c. M: 19.0720 c. 11: 9 1 1 N M DE S SD: 5.8430 c. M: 10.0166 c. 12: 10 1 1 N M DE S SD: 1.9596 c. M: 2.4705 c. 37: 31 3 3 N M DE S SD: 1.9956 c. M:-3.4490 c. 43: 36 3 4 N T3 SD: 1.4759 c. M: 2.4987 c. 44: 37 3 4 N T3 SD: 1.1235 c. M: 1.4458 c. 55: 46 4 5 N T3 SD: 1.0024 c. M: 1.4458 c. 56: 47 4 5 N T3 SD: 0.4656 c. M: 0.6373 c. 68: 57 5 6 N T3 SD: 0.0680 c. M: 0.1141 c. 352: 295 26 31 N T3 SD: 0.0672 c. M: 0.1123 c. 420: 352 31 37 N T3 SD: 0.0625 c. M: 0.0988 c. 421: 353 31 37 N T3 SD: 0.0637 c. M:-0.0927 c. 488: 409 36 43 N T3 SD: 0.0602 c. M: 0.0891 c. 489: 410 36 43 N T3 SD: 0.0484 c. M:-0.0758 c. 557: 467 41 49 N T3 SD: 0.0377 c. M:-0.0630 c. 625: 524 46 55 N T3 SD: 0.0306 c. M:-0.0530 c. 637: 534 47 56 N T3 SD: 0.0272 c. M:-0.0469 c. 693: 581 51 61 N T3 SD: 0.0264 c. M:-0.0449 c. 705: 591 52 62 N T3 SD: 0.0181 c. M:-0.0313 c. 773: 648 57 68 N T3 SD: 0.0107 c. M:-0.0186 c. 841: 705 62 74 N T3 SD: 0.0048 c. M:-0.0078 c. 909: 762 67 80 N T3 SD: 0.0029 c. M: 0.0049 c. 1750: 1467 129 154 N T3 SD: 0.0029 c. M: 0.0040 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 4:5 x x S SD: 31.1943 cents 5:6 x 7 S SD: 66.1656 cents 6 x x 8 S SD: 0.0000 cents 7:9 x x SD: 17.5761 cents 8:10 x 11 S SD: 30.8670 cents 9:11 x 12 SD: 35.0500 cents 10 x 13 x SD: 0.0000 cents 11:14 x 15 SD: 19.4529 cents 12:15 x 16 S SD: 15.5971 cents 13 x 17 x SD: 10.2138 cents 14:18 x 19 SD: 17.6625 cents 15:19 x 20 SD: 4.1318 cents 16:20:21 x S SD: 17.6603 cents 17 x 22:23 SD: 13.2327 cents 18:23 x 24 SD: 3.4282 cents 19:24:25 x SD: 12.3243 cents 21:27 x 28 SD: 8.7881 cents 22:28 x 29 SD: 9.8929 cents 23:29:30:31 SD: 8.4742 cents 24 x 31:32 SD: 5.5667 cents 25:32 x 33 SD: 10.0007 cents 26:33:34:35 SD: 6.6789 cents 27:34:35:36 SD: 6.3561 cents 28:36 x 37 SD: 11.7261 cents 29:37:38:39 SD: 6.8901 cents 30:38:39:40 SD: 2.7546 cents 33:42:43:44 SD: 1.3436 cents 84:107:109:112 SD: 1.1661 cents 114:145:148:152 SD: 0.8592 cents 117:149:152:156 SD: 0.5178 cents 147:187:191:196 SD: 0.4122 cents 150:191:195:200 SD: 0.2747 cents 180:229:234:240 SD: 0.2290 cents 297:378:386:396 SD: 0.1495 cents 330:420:429:440 SD: 0.0000 cents