Scala analysis: 363_D1
Diatonic tetrachord 26/25 * 10/9 * 15/13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 26/25 67.900234 tridecimal 1/3-tone 2: 52/45 250.303946 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 15/13 247.7411 tridecimal 5/4-tone 1: 26/25 67.9002 tridecimal 1/3-tone 2: 10/9 182.4037 minor whole tone 3: 15/13 247.7411 tridecimal 5/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 26/25 67.900 cents tridecimal 1/3-tone 1: 1 10/9 182.404 cents minor whole tone 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 1 6/5 315.641 cents minor third 2: 1 50/39 430.145 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 : 67.9 250.3 498.0 67.9 : 182.4 430.1 498.0 250.3: 247.7 315.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 67.9002 .. 247.7411 cents 375/338, 179.8408 cents 26/25, 67.9002 cents 2: 250.3039 .. 430.1448 cents 375/338, 179.8408 cents 676/675, 2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 26/25, 67.9002 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 15/13, 247.7411 cents Average / Smallest step : 2.444984 Largest / Average step : 1.492281 Largest / Smallest step : 3.648604 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 147.33165 cents, oct.: 441.99496 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1357-tone equal temperament with octave 4/3 degrees: 185 682 1357 Least number of segments generator : 679 of 249.206 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 964 of 353.806 cents and inv. generated superset size: 36 = 33 more = 1200.000% 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 : 0.929909 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.277813 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 Best minor thirds form a closed circle 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 -- Rational properties -- Prime limit : 13 Odd number limit : 45 (O: 25 U: 45) Highest odd numerator or denominator: 45 Scale harmonicity : 0.023648 Average absolute harmonicity : 0.089988 Specific harmonicity : 0.100577 Fundamental : 1/225, -7.8138 octaves, 1.1628 Hz. Guide tone : 52, 5.7004 octaves, 13604.529 Hz. Exponens Consonantiae : 1.170000E+04, 13.51422 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 77.5, average 25.83333 Mersenne's string divisions : 34629 Sum of van Prooijen's expressibility: 3.52827, average 1.17609 Sum of Tenney's harmonic distance : 7.26131, average 2.42044 Vogel's harmonic complexity : 18.33333 Wille's k value : 58 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 14.67513, average 2.44585 Lattice compactness (without 2's) : 12.10317, average 2.01719 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -2 .. 0 -1.00000 3 1 5: -2 .. 0 -1.00000 3 13: 0 .. 1 0.66667 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: <6 10 15 27| Scale is weakly epimorphic with val: <6 10 16 27| Scale is weakly epimorphic with val: <6 10 19 30| Scale is weakly epimorphic with val: <6 11 15 27| Scale is weakly epimorphic with val: <6 11 17 30| Scale is weakly epimorphic with val: <7 10 15 26| Scale is weakly epimorphic with val: <7 10 17 26| Scale is JI-epimorphic with val: <7 11 16 26| Scale is weakly epimorphic with val: <7 11 16 29| Scale is weakly epimorphic with val: <7 11 17 26| Scale is weakly epimorphic with val: <7 11 17 29| Scale is weakly epimorphic with val: <7 11 19 26| Scale is weakly epimorphic with val: <7 11 19 29| Scale is weakly epimorphic with val: <7 12 15 26| Scale is weakly epimorphic with val: <7 12 16 29| 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 19 28| Scale is weakly epimorphic with val: <8 12 15 25| Scale is weakly epimorphic with val: <8 12 17 28|
FIT/MODE
3: 0 1 2 N G T3 SD: 62.4902 c. M: 84.2889 c. 4: 1 1 2 P M ME S SD: 32.6928 c. M:-56.6110 c. 6: 1 2 3 P T3 SD: 8.7535 c. M:-15.1073 c. 8: 1 3 4 P T3 SD: 3.3418 c. M: 5.6446 c. 14: 2 5 7 P T3 SD: 2.0165 c. M:-3.2491 c. 22: 3 8 11 P T3 SD: 0.7399 c. M: 1.2814 c. 36: 5 13 18 P T3 SD: 1.0427 c. M: 1.2814 c. 52: 7 19 26 P T3 SD: 0.8896 c. M: 1.2814 c. 58: 8 21 29 P T3 SD: 0.8708 c. M: 1.2814 c. 74: 10 27 37 P T3 SD: 0.8162 c. M: 1.2814 c. 80: 11 29 40 P T3 SD: 0.8123 c. M: 1.2814 c. 95: 13 35 47 SP T3 SD: 0.7873 c. M:-1.3398 c. 96: 13 35 48 P T3 SD: 0.7854 c. M: 1.2814 c. 101: 14 37 50 SP T3 SD: 0.9473 c. M:-1.1841 c. 102: 14 37 51 P T3 SD: 0.7858 c. M: 1.2814 c. 103: 14 38 51 SP T3 SD: 0.6666 c. M:-1.1362 c. 109: 15 40 54 SP T3 SD: 0.6864 c. M:-1.0032 c. 111: 15 41 55 SP T3 SD: 0.6536 c. M:-0.9620 c. 117: 16 43 58 SP T3 SD: 0.5036 c. M:-0.8470 c. 125: 17 46 62 SP T3 SD: 0.4214 c. M:-0.7107 c. 131: 18 48 65 SP T3 SD: 0.4720 c. M:-0.6195 c. 133: 18 49 66 SP T3 SD: 0.4453 c. M:-0.5909 c. 139: 19 51 69 SP T3 SD: 0.3119 c. M:-0.5101 c. 147: 20 54 73 SP T3 SD: 0.2514 c. M:-0.4126 c. 161: 22 59 80 SP T3 SD: 0.1776 c. M:-0.2653 c. 169: 23 62 84 SP T3 SD: 0.1304 c. M:-0.1921 c. 183: 25 67 91 SP T3 SD: 0.0923 c. M:-0.1387 c. 191: 26 70 95 SP T3 SD: 0.0611 c. M: 0.1035 c. 374: 51 137 186 SP T3 SD: 0.0303 c. M:-0.0502 c. 396: 54 145 197 SP T3 SD: 0.0162 c. M: 0.0238 c. 587: 80 215 292 SP T3 SD: 0.0145 c. M: 0.0236 c. 770: 105 282 383 SP T3 SD: 0.0112 c. M:-0.0150 c. 961: 131 352 478 SP T3 SD: 0.0096 c. M:-0.0142 c. 983: 134 360 489 SP T3 SD: 0.0097 c. M: 0.0148 c. 1166: 159 427 580 SP T3 SD: 0.0087 c. M:-0.0150 c. 1357: 185 497 675 SP T3 SD: 0.0020 c. M:-0.0031 c. 1753: 239 642 872 SP T3 SD: 0.0021 c. M: 0.0030 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 11:12:13:15 SD: 33.1205 cents 12:13:14:16 S SD: 24.1961 cents 13:14:15:17 SD: 23.0570 cents 14:15:16:19 SD: 20.9802 cents 15:16:17:20 SD: 18.4128 cents 17:18:20:23 SD: 16.8902 cents 18:19:21:24 SD: 10.1931 cents 20:21:23:27 SD: 9.4669 cents 21:22:24:28 S SD: 7.6423 cents 24:25:28:32 SD: 5.5991 cents 27:28:31:36 SD: 4.0600 cents 45:47:52:60 SD: 2.4609 cents 51:53:59:68 SD: 0.7844 cents 123:128:142:164 SD: 0.6508 cents 147:153:170:196 SD: 0.6403 cents 174:181:201:232 SD: 0.2300 cents 225:234:260:300 SD: 0.0000 cents