Scala analysis: 371_D1
Diatonic tetrachord 91/90 * 8/7 * 15/13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 91/90 19.129853 medium tridecimal comma, superleap 2: 52/45 250.303946 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 15/13 247.7411 tridecimal 5/4-tone 1: 91/90 19.1299 medium tridecimal comma, superleap 2: 8/7 231.1741 septimal whole tone 3: 15/13 247.7411 tridecimal 5/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 91/90 19.130 cents medium tridecimal comma, superleap 1: 1 8/7 231.174 cents septimal whole tone 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 1 7/6 266.871 cents septimal minor third 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 : 19.1 250.3 498.0 19.1 : 231.2 478.9 498.0 250.3: 247.7 266.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 19.1299 .. 247.7411 cents 1350/1183, 228.6112 cents 91/90, 19.1299 cents 2: 250.3039 .. 478.9151 cents 1350/1183, 228.6112 cents 676/675, 2.5629 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 : 15/13, 247.7411 cents Average / Smallest step : 8.678321 Largest / Average step : 1.492281 Largest / Smallest step : 12.950495 Median interval of one step : 8/7, 231.1741 cents, amount: 1 Least squares average step : 143.84805 cents, oct.: 431.54416 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 2135-tone equal temperament with octave 4/3 degrees: 82 1073 2135 Least number of segments generator : 1068 of 249.139 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1328 of 309.791 cents and inv. generated superset size: 42 = 39 more = 1400.000% 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 2.56289 cents Scale diversity : 0.371395 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.081966 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 : 676/675, 2.5629 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% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 212.0442 cents: 1 -- Rational properties -- Prime limit : 13 Odd number limit : 91 (O: 91 U: 91) Highest odd numerator or denominator: 91 Scale harmonicity : 0.021199 Average absolute harmonicity : 0.088096 Specific harmonicity : 0.091565 Fundamental : 1/90, -6.4919 octaves, 2.9070 Hz. Guide tone : 364, 8.5078 octaves, 95231.706 Hz. Exponens Consonantiae : 3.276000E+04, 14.99965 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 142.5, average 47.50000 Mersenne's string divisions : 122899 Sum of van Prooijen's expressibility: 4.08938, average 1.36313 Sum of Tenney's harmonic distance : 8.36168, average 2.78723 Vogel's harmonic complexity : 15.66667 Wille's k value : 45 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 16.72665, average 2.78778 Lattice compactness (without 2's) : 10.82729, average 1.80455 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 1.00000 5 3: -2 ..-1 -1.66667 5 1 5: -1 .. 0 -0.66667 2 7: 0 .. 1 0.33333 1 13: 0 .. 1 0.66667 2 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <6 10 15 19 26| Scale is weakly epimorphic with val: <6 10 15 22 26| Scale is weakly epimorphic with val: <6 10 16 19 27| Scale is weakly epimorphic with val: <6 10 16 20 25| Scale is weakly epimorphic with val: <6 10 16 22 27| Scale is weakly epimorphic with val: <6 10 17 19 28| Scale is weakly epimorphic with val: <6 10 17 20 26| Scale is weakly epimorphic with val: <6 10 17 22 28| Scale is weakly epimorphic with val: <6 10 18 19 29| Scale is weakly epimorphic with val: <6 10 18 20 27| Scale is weakly epimorphic with val: <6 10 18 22 29| Scale is weakly epimorphic with val: <6 10 19 19 30| Scale is weakly epimorphic with val: <6 10 19 20 28| Scale is weakly epimorphic with val: <6 10 19 22 30| Scale is weakly epimorphic with val: <6 11 15 19 27| Scale is weakly epimorphic with val: <6 11 15 20 28| Scale is weakly epimorphic with val: <6 11 16 19 28| Scale is weakly epimorphic with val: <6 11 16 20 29| Scale is weakly epimorphic with val: <6 11 16 22 25| Scale is weakly epimorphic with val: <6 11 17 19 29| Scale is weakly epimorphic with val: <6 11 17 20 30| Scale is weakly epimorphic with val: <6 11 17 22 26| Scale is weakly epimorphic with val: <6 11 18 19 30| Scale is weakly epimorphic with val: <6 11 18 22 27| Scale is weakly epimorphic with val: <6 11 19 22 28| Scale is weakly epimorphic with val: <7 10 15 19 26| Scale is weakly epimorphic with val: <7 10 16 19 27| Scale is weakly epimorphic with val: <7 10 16 20 25| Scale is weakly epimorphic with val: <7 10 17 19 28| Scale is weakly epimorphic with val: <7 10 17 20 26| Scale is weakly epimorphic with val: <7 10 17 22 25| Scale is weakly epimorphic with val: <7 10 18 19 29| Scale is weakly epimorphic with val: <7 10 18 20 27| Scale is weakly epimorphic with val: <7 10 18 22 26| Scale is weakly epimorphic with val: <7 10 19 19 30| Scale is weakly epimorphic with val: <7 10 19 20 28| Scale is weakly epimorphic with val: <7 10 19 22 27| Scale is weakly epimorphic with val: <7 11 15 19 27| Scale is weakly epimorphic with val: <7 11 15 19 30| Scale is JI-epimorphic with val: <7 11 15 20 25| Scale is weakly epimorphic with val: <7 11 15 20 28| Scale is weakly epimorphic with val: <7 11 15 22 27| Scale is weakly epimorphic with val: <7 11 15 22 30| Scale is weakly epimorphic with val: <7 11 16 19 25| Scale is weakly epimorphic with val: <7 11 16 19 28| Scale is JI-epimorphic with val: <7 11 16 20 26| Scale is weakly epimorphic with val: <7 11 16 20 29| Scale is weakly epimorphic with val: <7 11 16 22 25| Scale is weakly epimorphic with val: <7 11 16 22 28| Scale is weakly epimorphic with val: <7 11 17 19 26| Scale is weakly epimorphic with val: <7 11 17 19 29| Scale is JI-epimorphic with val: <7 11 17 20 27| = patent Scale is weakly epimorphic with val: <7 11 17 20 30| Scale is weakly epimorphic with val: <7 11 17 22 26| Scale is weakly epimorphic with val: <7 11 17 22 29| Scale is weakly epimorphic with val: <7 11 18 19 27| Scale is weakly epimorphic with val: <7 11 18 19 30| Scale is weakly epimorphic with val: <7 11 18 20 25| Scale is JI-epimorphic with val: <7 11 18 20 28| Scale is weakly epimorphic with val: <7 11 18 22 27| Scale is weakly epimorphic with val: <7 11 18 22 30| Scale is weakly epimorphic with val: <7 11 19 19 25| Scale is weakly epimorphic with val: <7 11 19 19 28| Scale is weakly epimorphic with val: <7 11 19 20 26| Scale is JI-epimorphic with val: <7 11 19 20 29| Scale is weakly epimorphic with val: <7 11 19 22 25| Scale is weakly epimorphic with val: <7 11 19 22 28| Scale is weakly epimorphic with val: <7 12 15 19 28| Scale is weakly epimorphic with val: <7 12 15 20 29| Scale is weakly epimorphic with val: <7 12 15 22 28| Scale is weakly epimorphic with val: <7 12 16 19 29| Scale is weakly epimorphic with val: <7 12 16 20 30| Scale is weakly epimorphic with val: <7 12 16 22 29| Scale is weakly epimorphic with val: <7 12 17 19 30| Scale is weakly epimorphic with val: <7 12 17 22 30| Scale is weakly epimorphic with val: <8 11 15 20 28| Scale is weakly epimorphic with val: <8 11 16 19 25| Scale is weakly epimorphic with val: <8 11 16 20 29| Scale is weakly epimorphic with val: <8 11 16 22 25| Scale is weakly epimorphic with val: <8 11 17 19 26| Scale is weakly epimorphic with val: <8 11 17 20 30| Scale is weakly epimorphic with val: <8 11 17 22 26| Scale is weakly epimorphic with val: <8 11 18 19 27| Scale is weakly epimorphic with val: <8 11 18 22 27| Scale is weakly epimorphic with val: <8 11 19 19 28| Scale is weakly epimorphic with val: <8 11 19 22 28| Scale is weakly epimorphic with val: <8 12 15 20 26| Scale is weakly epimorphic with val: <8 12 15 22 28| Scale is weakly epimorphic with val: <8 12 16 20 27| Scale is weakly epimorphic with val: <8 12 16 22 29| Scale is weakly epimorphic with val: <8 12 17 20 28| Scale is weakly epimorphic with val: <8 12 17 22 30| Scale is weakly epimorphic with val: <8 12 18 20 29| Scale is weakly epimorphic with val: <8 12 19 20 30|
FIT/MODE
3: 0 1 2 N G T3 SD: 49.9018 c. M: 84.2889 c. 4: 0 2 2 P M DE S SD: 11.0694 c. M: 19.1299 c. 10: 0 5 5 P M DE S SD: 11.0694 c. M: 19.1299 c. 12: 0 6 6 P M DE S SD: 11.0694 c. M: 19.1299 c. 16: 1 7 8 P T3 SD: 6.9664 c. M:-11.9980 c. 18: 1 8 9 P T3 SD: 4.9854 c. M:-8.5393 c. 20: 1 9 10 P T3 SD: 3.4138 c. M:-5.7724 c. 22: 1 10 11 P T3 SD: 2.1565 c. M:-3.5086 c. 24: 1 11 12 P T3 SD: 1.1935 c. M:-1.6220 c. 26: 1 12 13 P T3 SD: 0.7400 c. M: 1.2814 c. 50: 2 23 25 P T3 SD: 0.8697 c. M: 1.2814 c. 54: 2 25 27 P T3 SD: 0.8386 c. M: 1.2814 c. 76: 3 35 38 P T3 SD: 0.8006 c. M: 1.2814 c. 80: 3 37 40 P T3 SD: 0.7847 c. M: 1.2814 c. 99: 4 46 49 SP T3 SD: 0.9145 c. M:-1.2339 c. 101: 4 47 50 SP T3 SD: 0.7650 c. M:-1.1841 c. 103: 4 48 51 SP T3 SD: 0.6673 c. M:-1.1362 c. 105: 4 49 52 SP T3 SD: 0.6359 c. M:-1.0902 c. 107: 4 50 53 SP T3 SD: 0.6721 c. M:-1.0459 c. 109: 4 51 54 SP T3 SD: 0.7602 c. M:-1.0032 c. 123: 5 57 61 SP T3 SD: 0.7740 c. M:-1.1159 c. 125: 5 58 62 SP T3 SD: 0.6144 c. M:-0.7919 c. 127: 5 59 63 SP T3 SD: 0.4797 c. M:-0.6794 c. 129: 5 60 64 SP T3 SD: 0.3879 c. M:-0.6490 c. 131: 5 61 65 SP T3 SD: 0.3644 c. M:-0.6195 c. 133: 5 62 66 SP T3 SD: 0.4140 c. M:-0.5909 c. 151: 6 70 75 SP T3 SD: 0.4362 c. M:-0.6600 c. 153: 6 71 76 SP T3 SD: 0.3060 c. M:-0.4013 c. 155: 6 72 77 SP T3 SD: 0.2066 c. M:-0.3252 c. 157: 6 73 78 SP T3 SD: 0.1845 c. M:-0.3047 c. 181: 7 84 90 SP T3 SD: 0.0935 c. M:-0.1316 c. 183: 7 85 91 SP T3 SD: 0.0646 c. M:-0.0793 c. 209: 8 97 104 SP T3 SD: 0.0644 c. M: 0.0900 c. 364: 14 169 181 SP T3 SD: 0.0523 c. M:-0.0868 c. 390: 15 181 194 SP T3 SD: 0.0151 c. M:-0.0257 c. 573: 22 266 285 SP T3 SD: 0.0136 c. M:-0.0223 c. 782: 30 363 389 SP T3 SD: 0.0141 c. M: 0.0233 c. 963: 37 447 479 SP T3 SD: 0.0074 c. M:-0.0115 c. 1172: 45 544 583 SP T3 SD: 0.0055 c. M: 0.0070 c. 1562: 60 725 777 SP T3 SD: 0.0036 c. M: 0.0060 c. 2135: 82 991 1062 SP T3 SD: 0.0011 c. M:-0.0016 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 6:7 S SD: 53.3940 cents 6 x 7:8 S SD: 8.2835 cents 7 x 8:9 S SD: 32.9015 cents 8 x 9:11 SD: 35.3214 cents 9 x 10:12 S SD: 33.9501 cents 10 x 12:13 S SD: 39.3387 cents 11 x 13:15 SD: 27.5105 cents 12 x 14:16 S SD: 8.2835 cents 39:40:45:52 SD: 8.2779 cents 44:45:51:59 SD: 7.5665 cents 45:46:52:60 SD: 6.3069 cents 50:51:58:67 SD: 6.2213 cents 51:52:59:68 SD: 4.8730 cents 57:58:66:76 SD: 3.8413 cents 63:64:73:84 SD: 3.1398 cents 66:67:76:88 SD: 3.0630 cents 69:70:80:92 SD: 2.7249 cents 71:72:82:95 SD: 2.6615 cents 72:73:83:96 SD: 2.1061 cents 78:79:90:104 SD: 1.2962 cents 84:85:97:112 SD: 0.6018 cents 90:91:104:120 SD: 0.0000 cents