Scala analysis: 369_D1
Diatonic tetrachord 40/39 * 169/150 * 15/13
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: 52/45 250.303946 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 15/13 247.7411 tridecimal 5/4-tone 1: 40/39 43.8311 tridecimal minor diesis 2: 169/150 206.4729 3: 15/13 247.7411 tridecimal 5/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 169/150 206.473 cents 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 1 200/169 291.572 cents 2: 1 13/10 454.214 cents tridecimal 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 : 43.8 250.3 498.0 43.8 : 206.5 454.2 498.0 250.3: 247.7 291.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 247.7411 cents 9/8, 203.9100 cents 40/39, 43.8311 cents 2: 250.3039 .. 454.2139 cents 9/8, 203.9100 cents 676/675, 2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 15/13, 247.7411 cents Average / Smallest step : 3.787612 Largest / Average step : 1.492281 Largest / Smallest step : 5.652181 Median interval of one step : 169/150, 206.4729 cents, amount: 1 Least squares average step : 145.61242 cents, oct.: 436.83727 cents Scale is strictly proper Scale has trivalence property 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 : 0.664771 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.181158 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% -- Rational properties -- Prime limit : 13 Odd number limit : 169 (O: 169 U: 169) Highest odd numerator or denominator: 45 Scale harmonicity : 0.015281 Average absolute harmonicity : 0.090457 Specific harmonicity : 0.081498 Fundamental : 1/585, -9.1923 octaves, 0.4472 Hz. Guide tone : 520, 9.0224 octaves, 136045.294 Hz. Exponens Consonantiae : 3.042000E+05, 18.21466 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 91.5, average 30.50000 Mersenne's string divisions : 53641 Sum of van Prooijen's expressibility: 3.72140, average 1.24047 Sum of Tenney's harmonic distance : 7.64152, average 2.54717 Vogel's harmonic complexity : 22.33333 Wille's k value : 97 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 15.48883, average 2.58147 Lattice compactness (without 2's) : 11.32780, average 1.88797 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -2 ..-1 -1.33333 4 1 5: -1 .. 1 0.00000 2 13: -1 .. 1 0.00000 2 2 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: <7 10 16 25| Scale is weakly epimorphic with val: <7 10 17 25| Scale is weakly epimorphic with val: <7 10 17 26| Scale is weakly epimorphic with val: <7 10 18 26| Scale is weakly epimorphic with val: <7 10 18 27| Scale is weakly epimorphic with val: <7 10 19 27| Scale is weakly epimorphic with val: <7 10 19 28| Scale is weakly epimorphic with val: <8 11 15 25| Scale is weakly epimorphic with val: <8 11 16 25| Scale is weakly epimorphic with val: <8 11 16 26| Scale is weakly epimorphic with val: <8 11 17 26| Scale is weakly epimorphic with val: <8 11 17 27| Scale is weakly epimorphic with val: <8 11 18 27| Scale is weakly epimorphic with val: <8 11 18 28| Scale is weakly epimorphic with val: <8 11 19 28| Scale is weakly epimorphic with val: <8 11 19 29|
FIT/MODE
3: 0 1 2 N G T3 SD: 54.8507 c. M: 84.2889 c. 4: 0 2 2 P M DE S SD: 25.3167 c. M: 43.8311 c. 8: 1 3 4 P T3 SD: 10.6631 c. M:-18.4246 c. 10: 1 4 5 P T3 SD: 3.5272 c. M:-5.9734 c. 12: 1 5 6 P T3 SD: 1.5339 c. M: 2.3273 c. 22: 2 9 11 P T3 SD: 1.1154 c. M:-1.4458 c. 34: 3 14 17 P T3 SD: 0.7428 c. M: 1.2814 c. 46: 4 19 23 P T3 SD: 0.7990 c. M: 1.2814 c. 78: 7 32 39 P T3 SD: 0.8927 c. M: 1.2814 c. 80: 7 33 40 P T3 SD: 0.7540 c. M: 1.2814 c. 101: 9 42 50 SP T3 SD: 0.7536 c. M:-1.1841 c. 103: 9 43 51 SP T3 SD: 0.6804 c. M:-1.1362 c. 111: 10 46 55 SP T3 SD: 0.8170 c. M:-1.0379 c. 113: 10 47 56 SP T3 SD: 0.5508 c. M:-0.9223 c. 115: 10 48 57 SP T3 SD: 0.5929 c. M:-0.8840 c. 123: 11 51 61 SP T3 SD: 0.5932 c. M:-0.7431 c. 125: 11 52 62 SP T3 SD: 0.4103 c. M:-0.7107 c. 127: 11 53 63 SP T3 SD: 0.5604 c. M: 0.6933 c. 135: 12 56 67 SP T3 SD: 0.4125 c. M:-0.5632 c. 137: 12 57 68 SP T3 SD: 0.3318 c. M:-0.5362 c. 147: 13 61 73 SP T3 SD: 0.2683 c. M:-0.4126 c. 149: 13 62 74 SP T3 SD: 0.3133 c. M:-0.3898 c. 159: 14 66 79 SP T3 SD: 0.1649 c. M:-0.2847 c. 171: 15 71 85 SP T3 SD: 0.1304 c. M:-0.1748 c. 181: 16 75 90 SP T3 SD: 0.1251 c. M:-0.1950 c. 193: 17 80 96 SP T3 SD: 0.0226 c. M:-0.0382 c. 398: 35 165 198 SP T3 SD: 0.0258 c. M: 0.0331 c. 591: 52 245 294 SP T3 SD: 0.0115 c. M: 0.0174 c. 784: 69 325 390 SP T3 SD: 0.0064 c. M: 0.0109 c. 977: 86 405 486 SP T3 SD: 0.0067 c. M:-0.0091 c. 1761: 155 730 876 SP T3 SD: 0.0061 c. M: 0.0088 c. 1932: 170 801 961 SP T3 SD: 0.0060 c. M:-0.0075 c. 2125: 187 881 1057 SP T3 SD: 0.0047 c. M:-0.0076 c. 2318: 204 961 1153 SP T3 SD: 0.0045 c. M:-0.0077 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 15:16:17:20 SD: 25.2555 cents 17:18:20:23 SD: 22.7101 cents 18:19:21:24 SD: 17.4856 cents 19:20:22:25 SD: 16.8666 cents 20:21:23:27 SD: 15.5757 cents 21:22:24:28 S SD: 13.7973 cents 24:25:28:32 SD: 10.5141 cents 25:26:29:33 SD: 10.1447 cents 26:27:30:35 S SD: 9.0894 cents 27:28:31:36 SD: 7.3779 cents 30:31:35:40 SD: 7.0063 cents 31:32:36:41 SD: 6.6158 cents 32:33:37:43 SD: 5.4949 cents 33:34:38:44 SD: 3.3068 cents 39:40:45:52 SD: 0.8543 cents 153:157:177:204 SD: 0.7111 cents 192:197:222:256 SD: 0.4135 cents 231:237:267:308 SD: 0.2363 cents 270:277:312:360 SD: 0.1603 cents 315:323:364:420 SD: 0.1374 cents 507:520:586:676 SD: 0.1313 cents 546:560:631:728 SD: 0.0610 cents 585:600:676:780 SD: 0.0000 cents