Scala analysis: 368_D1
Diatonic tetrachord 46/45 * 26/23 * 15/13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 46/45 38.050632 23rd-partial chroma 2: 52/45 250.303946 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 15/13 247.7411 tridecimal 5/4-tone 1: 46/45 38.0506 23rd-partial chroma 2: 26/23 212.2533 3: 15/13 247.7411 tridecimal 5/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 46/45 38.051 cents 23rd-partial chroma 1: 1 26/23 212.253 cents 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 1 46/39 285.792 cents 2: 1 30/23 459.994 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 : 38.1 250.3 498.0 38.1 : 212.3 460.0 498.0 250.3: 247.7 285.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.0506 .. 247.7411 cents 675/598, 209.6904 cents 46/45, 38.0506 cents 2: 250.3039 .. 459.9944 cents 675/598, 209.6904 cents 676/675, 2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 46/45, 38.0506 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 15/13, 247.7411 cents Average / Smallest step : 4.363002 Largest / Average step : 1.492281 Largest / Smallest step : 6.510826 Median interval of one step : 26/23, 212.2533 cents, amount: 1 Least squares average step : 145.19954 cents, oct.: 435.59861 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1741-tone equal temperament with octave 4/3 degrees: 133 875 1741 Least number of segments generator : 871 of 249.166 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1414 of 404.501 cents and inv. generated superset size: 44 = 41 more = 1466.667% 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 : 0.596393 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.157946 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 : 23 Odd number limit : 45 (O: 23 U: 45) Highest odd numerator or denominator: 45 Scale harmonicity : 0.012825 Average absolute harmonicity : 0.086797 Specific harmonicity : 0.065576 Fundamental : 1/45, -5.4919 octaves, 5.8139 Hz. Guide tone : 1196, 10.2240 octaves, 312904.176 Hz. Exponens Consonantiae : 5.382000E+04, 15.71585 octaves Euler's gradus suavitatis : 45 Sum of Mann's harmonic distance : 97.5, average 32.50000 Mersenne's string divisions : 8827 Sum of van Prooijen's expressibility: 3.78355, average 1.26118 Sum of Tenney's harmonic distance : 7.76437, average 2.58812 Vogel's harmonic complexity : 16.33333 Wille's k value : 11 Wilson's harmonic complexity : 47 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 13.50820, average 2.25137 Lattice compactness (without 2's) : 10.77729, average 1.79622 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -2 ..-1 -1.66667 5 1 5: -1 .. 0 -0.66667 2 13: 0 .. 1 0.33333 1 1 23: 0 .. 1 0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 15 26 30| Scale is weakly epimorphic with val: <6 10 15 26 33| Scale is weakly epimorphic with val: <6 10 15 26 36| Scale is weakly epimorphic with val: <6 10 15 27 32| Scale is weakly epimorphic with val: <6 10 15 30 32| Scale is weakly epimorphic with val: <6 10 16 25 33| Scale is weakly epimorphic with val: <6 10 16 27 31| Scale is weakly epimorphic with val: <6 10 16 27 34| Scale is weakly epimorphic with val: <6 10 16 28 33| Scale is weakly epimorphic with val: <6 10 17 26 34| Scale is weakly epimorphic with val: <6 10 17 28 32| Scale is weakly epimorphic with val: <6 10 17 28 35| Scale is weakly epimorphic with val: <6 10 17 29 34| Scale is weakly epimorphic with val: <6 10 18 27 35| Scale is weakly epimorphic with val: <6 10 18 29 30| Scale is weakly epimorphic with val: <6 10 18 29 33| Scale is weakly epimorphic with val: <6 10 18 29 36| Scale is weakly epimorphic with val: <6 10 18 30 35| Scale is weakly epimorphic with val: <6 10 19 25 36| Scale is weakly epimorphic with val: <6 10 19 28 36| Scale is weakly epimorphic with val: <6 10 19 30 31| Scale is weakly epimorphic with val: <6 10 19 30 34| Scale is weakly epimorphic with val: <6 11 15 27 34| Scale is weakly epimorphic with val: <6 11 15 28 30| Scale is weakly epimorphic with val: <6 11 15 28 33| Scale is weakly epimorphic with val: <6 11 15 28 36| Scale is weakly epimorphic with val: <6 11 15 30 34| Scale is weakly epimorphic with val: <6 11 16 25 35| Scale is weakly epimorphic with val: <6 11 16 28 35| Scale is weakly epimorphic with val: <6 11 16 29 31| Scale is weakly epimorphic with val: <6 11 16 29 34| Scale is weakly epimorphic with val: <6 11 17 26 36| Scale is weakly epimorphic with val: <6 11 17 29 36| Scale is weakly epimorphic with val: <6 11 17 30 32| Scale is weakly epimorphic with val: <6 11 17 30 35| Scale is weakly epimorphic with val: <7 10 15 26 31| Scale is weakly epimorphic with val: <7 10 15 29 31| Scale is weakly epimorphic with val: <7 10 16 25 31| Scale is weakly epimorphic with val: <7 10 16 25 34| Scale is weakly epimorphic with val: <7 10 16 27 32| Scale is weakly epimorphic with val: <7 10 16 30 32| Scale is weakly epimorphic with val: <7 10 17 25 33| Scale is weakly epimorphic with val: <7 10 17 26 32| Scale is weakly epimorphic with val: <7 10 17 26 35| Scale is weakly epimorphic with val: <7 10 17 28 33| Scale is weakly epimorphic with val: <7 10 18 26 34| Scale is weakly epimorphic with val: <7 10 18 27 30| Scale is weakly epimorphic with val: <7 10 18 27 33| Scale is weakly epimorphic with val: <7 10 18 27 36| Scale is weakly epimorphic with val: <7 10 18 29 34| Scale is weakly epimorphic with val: <7 10 19 27 35| Scale is weakly epimorphic with val: <7 10 19 28 31| Scale is weakly epimorphic with val: <7 10 19 28 34| Scale is weakly epimorphic with val: <7 10 19 30 35| Scale is JI-epimorphic with val: <7 11 15 25 31| Scale is weakly epimorphic with val: <7 11 15 25 34| Scale is weakly epimorphic with val: <7 11 15 27 32| Scale is weakly epimorphic with val: <7 11 15 27 35| Scale is weakly epimorphic with val: <7 11 15 28 31| Scale is weakly epimorphic with val: <7 11 15 28 34| Scale is weakly epimorphic with val: <7 11 15 30 32| Scale is weakly epimorphic with val: <7 11 15 30 35| Scale is weakly epimorphic with val: <7 11 16 25 30| Scale is weakly epimorphic with val: <7 11 16 25 33| Scale is weakly epimorphic with val: <7 11 16 25 36| Scale is JI-epimorphic with val: <7 11 16 26 32| Scale is weakly epimorphic with val: <7 11 16 26 35| Scale is weakly epimorphic with val: <7 11 16 28 30| Scale is weakly epimorphic with val: <7 11 16 28 33| Scale is weakly epimorphic with val: <7 11 16 28 36| Scale is weakly epimorphic with val: <7 11 16 29 32| Scale is weakly epimorphic with val: <7 11 16 29 35| Scale is weakly epimorphic with val: <7 11 17 26 31| Scale is weakly epimorphic with val: <7 11 17 26 34| Scale is weakly epimorphic with val: <7 11 17 27 30| Scale is JI-epimorphic with val: <7 11 17 27 33| = patent Scale is weakly epimorphic with val: <7 11 17 27 36| Scale is weakly epimorphic with val: <7 11 17 29 31| Scale is weakly epimorphic with val: <7 11 17 29 34| Scale is weakly epimorphic with val: <7 11 17 30 30| Scale is weakly epimorphic with val: <7 11 17 30 33| Scale is weakly epimorphic with val: <7 11 17 30 36| Scale is weakly epimorphic with val: <7 11 18 25 31| Scale is weakly epimorphic with val: <7 11 18 25 34| Scale is weakly epimorphic with val: <7 11 18 27 32| Scale is weakly epimorphic with val: <7 11 18 27 35| Scale is weakly epimorphic with val: <7 11 18 28 31| Scale is JI-epimorphic with val: <7 11 18 28 34| Scale is weakly epimorphic with val: <7 11 18 30 32| Scale is weakly epimorphic with val: <7 11 18 30 35| Scale is weakly epimorphic with val: <7 11 19 25 30| Scale is weakly epimorphic with val: <7 11 19 25 33| Scale is weakly epimorphic with val: <7 11 19 25 36| Scale is weakly epimorphic with val: <7 11 19 26 32| Scale is weakly epimorphic with val: <7 11 19 26 35| Scale is weakly epimorphic with val: <7 11 19 28 30| Scale is weakly epimorphic with val: <7 11 19 28 33| Scale is weakly epimorphic with val: <7 11 19 28 36| Scale is weakly epimorphic with val: <7 11 19 29 32| Scale is JI-epimorphic with val: <7 11 19 29 35| Scale is weakly epimorphic with val: <7 12 15 26 35| Scale is weakly epimorphic with val: <7 12 15 28 30| Scale is weakly epimorphic with val: <7 12 15 28 33| Scale is weakly epimorphic with val: <7 12 15 28 36| Scale is weakly epimorphic with val: <7 12 15 29 35| Scale is weakly epimorphic with val: <7 12 16 27 36| Scale is weakly epimorphic with val: <7 12 16 29 31| Scale is weakly epimorphic with val: <7 12 16 29 34| Scale is weakly epimorphic with val: <7 12 16 30 36| Scale is weakly epimorphic with val: <7 12 17 30 32| Scale is weakly epimorphic with val: <7 12 17 30 35| Scale is weakly epimorphic with val: <8 11 15 25 32| Scale is weakly epimorphic with val: <8 11 15 28 32| Scale is weakly epimorphic with val: <8 11 16 25 31| Scale is weakly epimorphic with val: <8 11 16 25 34| Scale is weakly epimorphic with val: <8 11 16 26 33| Scale is weakly epimorphic with val: <8 11 16 29 33| Scale is weakly epimorphic with val: <8 11 17 26 32| Scale is weakly epimorphic with val: <8 11 17 26 35| Scale is weakly epimorphic with val: <8 11 17 27 34| Scale is weakly epimorphic with val: <8 11 17 30 34| Scale is weakly epimorphic with val: <8 11 18 25 35| Scale is weakly epimorphic with val: <8 11 18 27 30| Scale is weakly epimorphic with val: <8 11 18 27 33| Scale is weakly epimorphic with val: <8 11 18 27 36| Scale is weakly epimorphic with val: <8 11 18 28 35| Scale is weakly epimorphic with val: <8 11 19 26 36| Scale is weakly epimorphic with val: <8 11 19 28 31| Scale is weakly epimorphic with val: <8 11 19 28 34| Scale is weakly epimorphic with val: <8 11 19 29 36| Scale is weakly epimorphic with val: <8 12 15 25 34| Scale is weakly epimorphic with val: <8 12 15 26 30| Scale is weakly epimorphic with val: <8 12 15 26 33| Scale is weakly epimorphic with val: <8 12 15 26 36| Scale is weakly epimorphic with val: <8 12 15 28 34| Scale is weakly epimorphic with val: <8 12 16 26 35| Scale is weakly epimorphic with val: <8 12 16 27 31| Scale is weakly epimorphic with val: <8 12 16 27 34| Scale is weakly epimorphic with val: <8 12 16 29 35| Scale is weakly epimorphic with val: <8 12 17 27 36| Scale is weakly epimorphic with val: <8 12 17 28 32| Scale is weakly epimorphic with val: <8 12 17 28 35| Scale is weakly epimorphic with val: <8 12 17 30 36| Scale is weakly epimorphic with val: <8 12 18 29 30| Scale is weakly epimorphic with val: <8 12 18 29 33| Scale is weakly epimorphic with val: <8 12 18 29 36| Scale is weakly epimorphic with val: <8 12 19 30 31| Scale is weakly epimorphic with val: <8 12 19 30 34|
FIT/MODE
3: 0 1 2 N G T3 SD: 53.3931 c. M: 84.2889 c. 4: 0 2 2 P M DE S SD: 21.9810 c. M: 38.0506 c. 8: 1 3 4 P T3 SD: 13.9943 c. M:-24.2050 c. 10: 1 4 5 P T3 SD: 6.8263 c. M:-11.7539 c. 12: 1 5 6 P T3 SD: 2.1265 c. M:-3.4531 c. 14: 1 6 7 P T3 SD: 1.6096 c. M: 2.4760 c. 26: 2 11 13 P T3 SD: 0.7550 c. M: 1.2814 c. 38: 3 16 19 P T3 SD: 1.0411 c. M: 1.2814 c. 40: 3 17 20 P T3 SD: 0.8423 c. M: 1.2814 c. 66: 5 28 33 P T3 SD: 0.7626 c. M: 1.2814 c. 92: 7 39 46 P T3 SD: 0.7453 c. M: 1.2814 c. 103: 8 44 51 SP T3 SD: 0.7508 c. M:-1.1362 c. 105: 8 45 52 SP T3 SD: 0.6323 c. M:-1.0902 c. 107: 8 46 53 SP T3 SD: 0.7650 c. M:-1.0459 c. 115: 9 49 57 SP T3 SD: 0.7395 c. M:-0.9268 c. 117: 9 50 58 SP T3 SD: 0.5116 c. M:-0.8470 c. 119: 9 51 59 SP T3 SD: 0.5180 c. M:-0.8112 c. 129: 10 55 64 SP T3 SD: 0.4940 c. M:-0.6490 c. 131: 10 56 65 SP T3 SD: 0.3581 c. M:-0.6195 c. 133: 10 57 66 SP T3 SD: 0.4877 c. M: 0.6036 c. 143: 11 61 71 SP T3 SD: 0.3052 c. M:-0.4600 c. 145: 11 62 72 SP T3 SD: 0.2954 c. M:-0.4359 c. 157: 12 67 78 SP T3 SD: 0.1762 c. M:-0.3047 c. 169: 13 72 84 SP T3 SD: 0.1869 c. M:-0.2605 c. 171: 13 73 85 SP T3 SD: 0.1480 c. M: 0.1876 c. 183: 14 78 91 SP T3 SD: 0.0545 c. M:-0.0793 c. 380: 29 162 189 SP T3 SD: 0.0295 c. M: 0.0419 c. 406: 31 173 202 SP T3 SD: 0.0342 c. M: 0.0547 c. 563: 43 240 280 SP T3 SD: 0.0271 c. M:-0.0455 c. 589: 45 251 293 SP T3 SD: 0.0076 c. M: 0.0131 c. 772: 59 329 384 SP T3 SD: 0.0088 c. M:-0.0124 c. 1361: 104 580 677 SP T3 SD: 0.0042 c. M:-0.0072 c. 1741: 133 742 866 SP T3 SD: 0.0040 c. M:-0.0059 c. 1950: 149 831 970 SP T3 SD: 0.0039 c. M:-0.0051 c. 2330: 178 993 1159 SP T3 SD: 0.0016 c. M: 0.0026 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: 26.9958 cents 17:18:20:23 SD: 24.2955 cents 18:19:21:24 SD: 19.3234 cents 19:20:22:25 SD: 18.6000 cents 20:21:23:27 SD: 17.2776 cents 21:22:24:28 S SD: 15.5315 cents 24:25:28:32 SD: 12.1958 cents 25:26:29:33 SD: 11.7280 cents 26:27:30:35 S SD: 10.6750 cents 27:28:31:36 SD: 9.0950 cents 30:31:35:40 SD: 8.3317 cents 31:32:36:41 SD: 7.8602 cents 32:33:37:43 SD: 6.7849 cents 33:34:38:44 SD: 4.9732 cents 38:39:44:51 SD: 4.5827 cents 39:40:45:52 SD: 2.1077 cents 45:46:52:60 SD: 0.0000 cents