Scala analysis: 031_H8
Hyperenharmonic tetrachord 40/39 * 91/90 * 9/7
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: 28/27 62.960904 Archytas' 1/3-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 9/7 435.0841 septimal major third, BP third 1: 40/39 43.8311 tridecimal minor diesis 2: 91/90 19.1299 medium tridecimal comma, superleap 3: 9/7 435.0841 septimal major third, BP third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 91/90 19.130 cents medium tridecimal comma, superleap 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 9/7 435.084 cents septimal major third, BP third 2: 1 28/27 62.961 cents Archytas' 1/3-tone 2: 1 13/10 454.214 cents tridecimal semi-diminished fourth 2: 1 120/91 478.915 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 : 43.8 63.0 498.0 43.8 : 19.1 454.2 498.0 63.0 : 435.1 478.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 19.1299 .. 435.0841 cents 810/637, 415.9542 cents 91/90, 19.1299 cents 2: 62.9609 .. 478.9151 cents 810/637, 415.9542 cents 196/243,-372.1232 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 91/90, 19.1299 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/7, 435.0841 cents Average / Smallest step : 8.678321 Largest / Average step : 2.620752 Largest / Smallest step : 22.743724 Median interval of one step : 40/39, 43.8311 cents, amount: 1 Least squares average step : 118.84913 cents, oct.: 356.54740 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1068-tone equal temperament with octave 4/3 degrees: 94 135 1068 Least number of segments generator : 535 of 249.489 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 757 of 353.015 cents and inv. generated superset size: 11 = 8 more = 366.667% 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 19.12985 cents Scale diversity : 0.130615 Lumma stability : 0.076820 Lumma impropriety factor : 0.747168 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 : 91/90, 19.1299 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 415.9542 cents: 2 -- Rational properties -- Prime limit : 13 Odd number limit : 91 (O: 91 U: 91) Highest odd numerator or denominator: 39 Scale harmonicity : 0.020064 Average absolute harmonicity : 0.097601 Specific harmonicity : 0.107010 Fundamental : 1/351, -8.4553 octaves, 0.7454 Hz. Guide tone : 280, 8.1293 octaves, 73255.158 Hz. Exponens Consonantiae : 9.828000E+04, 16.58461 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 70.5, average 23.50000 Mersenne's string divisions : 30415 Sum of van Prooijen's expressibility: 3.49955, average 1.16652 Sum of Tenney's harmonic distance : 7.15083, average 2.38361 Vogel's harmonic complexity : 19.00000 Wille's k value : 58 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 16.23837, average 2.70640 Lattice compactness (without 2's) : 12.19036, average 2.03173 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -3 ..-1 -1.66667 5 1 5: 0 .. 1 0.33333 1 7: 0 .. 1 0.33333 1 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 15 21 25| Scale is weakly epimorphic with val: <6 10 15 21 28| Scale is weakly epimorphic with val: <6 10 16 21 26| Scale is weakly epimorphic with val: <6 10 16 21 29| Scale is weakly epimorphic with val: <6 10 17 21 27| Scale is weakly epimorphic with val: <6 10 17 21 30| Scale is weakly epimorphic with val: <6 10 18 21 25| Scale is weakly epimorphic with val: <6 10 18 21 28| Scale is weakly epimorphic with val: <6 10 19 21 26| Scale is weakly epimorphic with val: <6 10 19 21 29| Scale is weakly epimorphic with val: <7 10 15 19 27| Scale is weakly epimorphic with val: <7 10 15 19 30| Scale is weakly epimorphic with val: <7 10 16 19 25| Scale is weakly epimorphic with val: <7 10 16 19 28| Scale is weakly epimorphic with val: <7 10 17 18 25| Scale is weakly epimorphic with val: <7 10 17 19 26| Scale is weakly epimorphic with val: <7 10 17 19 29| Scale is weakly epimorphic with val: <7 10 17 21 25| Scale is weakly epimorphic with val: <7 10 18 18 26| Scale is weakly epimorphic with val: <7 10 18 19 27| Scale is weakly epimorphic with val: <7 10 18 19 30| Scale is weakly epimorphic with val: <7 10 18 21 26| Scale is weakly epimorphic with val: <7 10 19 19 25| Scale is weakly epimorphic with val: <7 10 19 19 28| Scale is weakly epimorphic with val: <7 10 19 21 27| Scale is weakly epimorphic with val: <7 11 15 18 27| Scale is weakly epimorphic with val: <7 11 15 18 30| Scale is weakly epimorphic with val: <7 11 15 20 26| Scale is weakly epimorphic with val: <7 11 15 20 29| Scale is weakly epimorphic with val: <7 11 15 21 27| Scale is weakly epimorphic with val: <7 11 15 21 30| Scale is weakly epimorphic with val: <7 11 16 18 25| Scale is weakly epimorphic with val: <7 11 16 18 28| Scale is weakly epimorphic with val: <7 11 16 20 27| Scale is weakly epimorphic with val: <7 11 16 20 30| Scale is JI-epimorphic with val: <7 11 16 21 25| Scale is weakly epimorphic with val: <7 11 16 21 28| Scale is weakly epimorphic with val: <7 11 17 18 26| Scale is weakly epimorphic with val: <7 11 17 18 29| Scale is weakly epimorphic with val: <7 11 17 20 25| Scale is weakly epimorphic with val: <7 11 17 20 28| Scale is JI-epimorphic with val: <7 11 17 21 26| Scale is weakly epimorphic with val: <7 11 17 21 29| Scale is weakly epimorphic with val: <7 11 18 18 27| Scale is weakly epimorphic with val: <7 11 18 18 30| Scale is weakly epimorphic with val: <7 11 18 20 26| Scale is weakly epimorphic with val: <7 11 18 20 29| Scale is JI-epimorphic with val: <7 11 18 21 27| Scale is weakly epimorphic with val: <7 11 18 21 30| Scale is weakly epimorphic with val: <7 11 19 20 27| Scale is weakly epimorphic with val: <7 11 19 20 30| Scale is weakly epimorphic with val: <7 11 19 21 25| Scale is JI-epimorphic with val: <7 11 19 21 28| Scale is weakly epimorphic with val: <7 12 19 20 25| Scale is weakly epimorphic with val: <8 11 15 18 25| Scale is weakly epimorphic with val: <8 11 15 20 27| Scale is weakly epimorphic with val: <8 11 15 20 30| Scale is weakly epimorphic with val: <8 11 15 21 25| Scale is weakly epimorphic with val: <8 11 16 18 26| Scale is weakly epimorphic with val: <8 11 16 20 25| Scale is weakly epimorphic with val: <8 11 16 20 28| Scale is weakly epimorphic with val: <8 11 16 21 26| Scale is weakly epimorphic with val: <8 11 17 18 27| Scale is weakly epimorphic with val: <8 11 17 20 26| Scale is weakly epimorphic with val: <8 11 17 20 29| Scale is weakly epimorphic with val: <8 11 17 21 27| Scale is weakly epimorphic with val: <8 11 18 18 28| Scale is weakly epimorphic with val: <8 11 18 20 27| Scale is weakly epimorphic with val: <8 11 18 20 30| Scale is weakly epimorphic with val: <8 11 18 21 28| Scale is weakly epimorphic with val: <8 11 19 20 25| Scale is weakly epimorphic with val: <8 11 19 20 28| Scale is weakly epimorphic with val: <8 11 19 21 29| Scale is weakly epimorphic with val: <8 12 16 19 25| Scale is weakly epimorphic with val: <8 12 16 22 25| Scale is weakly epimorphic with val: <8 12 17 19 26| Scale is weakly epimorphic with val: <8 12 17 22 26| Scale is weakly epimorphic with val: <8 12 18 19 27| Scale is weakly epimorphic with val: <8 12 18 22 27| Scale is weakly epimorphic with val: <8 12 19 19 28| Scale is weakly epimorphic with val: <8 12 19 22 28|
FIT/MODE
3: 0 0 3 N M DE S SD: 44.2916 c. M: 62.9609 c. 5: 0 1 4 N G T3 SD: 32.9861 c. M: 43.8311 c. 6: 1 0 5 N G T3 SD: 25.4077 c. M:-39.1764 c. 7: 1 0 6 N G T3 SD: 16.4655 c. M:-27.3182 c. 8: 1 0 7 N G T3 SD: 10.6452 c. M:-18.4246 c. 9: 1 0 8 N G T3 SD: 7.9691 c. M:-11.5073 c. 14: 1 1 12 N M DE S SD: 6.7136 c. M: 8.2564 c. 15: 1 1 13 N M DE S SD: 6.4504 c. M: 10.6281 c. 16: 1 1 14 N M DE S SD: 7.3455 c. M: 12.7032 c. 20: 2 1 17 N T3 SD: 7.6080 c. M:-11.7458 c. 21: 2 1 18 N T3 SD: 5.1647 c. M:-8.1884 c. 22: 2 1 19 N T3 SD: 2.9797 c. M:-4.9543 c. 23: 2 1 20 N T3 SD: 1.1943 c. M:-2.0015 c. 24: 2 1 21 N T3 SD: 1.4040 c. M: 2.3273 c. 47: 4 2 41 N T3 SD: 0.9073 c. M: 1.4442 c. 55: 5 2 48 N T3 SD: 0.8703 c. M:-1.4458 c. 56: 5 2 49 N T3 SD: 0.5488 c. M: 0.7053 c. 79: 7 3 69 N T3 SD: 0.1794 c. M:-0.2995 c. 182: 16 7 159 N T3 SD: 0.0297 c. M: 0.0469 c. 443: 39 17 387 N T3 SD: 0.0087 c. M:-0.0149 c. 625: 55 24 546 N T3 SD: 0.0050 c. M: 0.0080 c. 1068: 94 41 933 N T3 SD: 0.0042 c. M: 0.0058 c. 1693: 149 65 1479 N T3 SD: 0.0039 c. M: 0.0066 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: 101.9550 cents 7 x 8:9 S SD: 89.8050 cents 8 x 9:11 SD: 75.3403 cents 9 x 10:12 S SD: 59.7214 cents 10 x 11:13 SD: 55.5293 cents 11 x 12:15 S SD: 47.9603 cents 12 x 13:16 SD: 37.8059 cents 13 x 14:17 SD: 36.7392 cents 14 x 15:19 SD: 32.1292 cents 15 x 16:20 S SD: 24.3852 cents 16 x 17:21 SD: 25.0343 cents 17 x 18:23 SD: 21.9904 cents 18 x 19:24 SD: 15.3211 cents 19 x 20:25 S SD: 17.2736 cents 20 x 21:27 SD: 15.2072 cents 21 x 22:28 SD: 8.7881 cents 22 x 23:29 SD: 12.1177 cents 23 x 24:31 SD: 10.7844 cents 24 x 25:32 SD: 3.8558 cents 25 x 26:33 SD: 9.0435 cents 26 x 27:35 SD: 8.3683 cents 27 x 28:36 SD: 0.0000 cents 28 x 29:37 SD: 7.8417 cents 29 x 30:39 SD: 7.7308 cents 30 x 31:40 SD: 3.0970 cents 31 x 32:41 SD: 8.0693 cents 32:33 x 43 SD: 8.2259 cents 33:34 x 44 SD: 3.9257 cents 34:35 x 45 SD: 7.1345 cents 35:36 x 47 SD: 6.6376 cents 36:37 x 48 SD: 1.8015 cents 37:38 x 49 SD: 5.9839 cents 38:39 x 51 SD: 5.7047 cents 39:40 x 52 SD: 0.0000 cents 40:41 x 53 SD: 5.4540 cents 45:46:47:60 SD: 4.5368 cents 48:49:50:64 SD: 3.7362 cents 51:52:53:68 SD: 3.6136 cents 59 x 61:79 SD: 4.5035 cents 60 x 62:80 SD: 3.0970 cents 61 x 63:81 SD: 5.0274 cents 62 x 64:83 SD: 5.3028 cents 63 x 65:84 SD: 4.4277 cents 64:66 x 85 SD: 5.8108 cents 65:67 x 87 SD: 5.4480 cents 66:68 x 88 SD: 3.9257 cents 67:69 x 89 SD: 4.8003 cents 69:71:72:92 SD: 4.0370 cents 71:73:74:95 SD: 3.8101 cents 72:74:75:96 SD: 2.8372 cents 75:77:78:100 SD: 1.7446 cents 78:80:81:104 SD: 0.7921 cents 81:83:84:108 SD: 0.5346 cents 159:163:165:212 SD: 0.4746 cents 189:194:196:252 SD: 0.4578 cents 192:197:199:256 SD: 0.3931 cents 270:277:280:360 SD: 0.1603 cents 351:360:364:468 SD: 0.0000 cents