Scala analysis: 446_D13
Diatonic tetrachord 44/39 * 9/8 * 104/99
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 44/39 208.835280 2: 33/26 412.745281 tridecimal major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 104/99 85.2997 1: 44/39 208.8353 2: 9/8 203.9100 major whole tone 3: 104/99 85.2997
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 104/99 85.300 cents 1: 1 9/8 203.910 cents major whole tone 1: 1 44/39 208.835 cents 2: 1 13/11 289.210 cents tridecimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 33/26 412.745 cents tridecimal major third 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 : 208.8 412.7 498.0 208.8: 203.9 289.2 498.0 412.7: 85.3 294.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 85.2997 .. 208.8353 cents 363/338, 123.5356 cents 104/99, 85.2997 cents 2: 289.2097 .. 412.7453 cents 363/338, 123.5356 cents 507/484, 80.3744 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 104/99, 85.2997 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 44/39, 208.8353 cents Average / Smallest step : 1.946255 Largest / Average step : 1.257930 Largest / Smallest step : 2.448253 Median interval of one step : 9/8, 203.9100 cents, amount: 1 Least squares average step : 180.60435 cents, oct.: 541.81304 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1915-tone equal temperament with octave 4/3 degrees: 803 1587 1915 Least number of segments generator : 958 of 249.153 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1293 of 336.278 cents and inv. generated superset size: 49 = 46 more = 1633.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LMS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 80.37444 cents Scale diversity : 0.981582 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.503918 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 : 352/351, 4.9253 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle Best minor thirds form a closed circle Steps are strictly decreasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 118.6103 cents: 2 -- Rational properties -- Prime limit : 13 Odd number limit : 99 (O: 33 U: 99) Highest odd numerator or denominator: 39 Scale harmonicity : 0.020547 Average absolute harmonicity : 0.086411 Specific harmonicity : 0.083765 Fundamental : 1/78, -6.2854 octaves, 3.3542 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 1.029600E+04, 13.32980 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 74.5, average 24.83333 Mersenne's string divisions : 34279 Sum of van Prooijen's expressibility: 3.58670, average 1.19557 Sum of Tenney's harmonic distance : 7.24719, average 2.41573 Vogel's harmonic complexity : 15.66667 Wille's k value : 49 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 15.77457, average 2.62909 Lattice compactness (without 2's) : 10.32780, average 1.72130 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 1.00000 5 3: -1 .. 1 -0.33333 3 1 11: 0 .. 1 0.66667 2 13: -1 .. 0 -0.66667 2 2 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 24 25| Scale is weakly epimorphic with val: <6 10 25 26| Scale is weakly epimorphic with val: <6 10 26 27| Scale is weakly epimorphic with val: <6 10 27 28| Scale is weakly epimorphic with val: <6 11 23 25| Scale is weakly epimorphic with val: <6 11 24 26| Scale is weakly epimorphic with val: <6 11 25 27| Scale is weakly epimorphic with val: <6 11 26 28| Scale is weakly epimorphic with val: <6 11 27 29| Scale is weakly epimorphic with val: <7 10 24 25| Scale is weakly epimorphic with val: <7 10 25 26| Scale is weakly epimorphic with val: <7 10 26 27| Scale is weakly epimorphic with val: <7 10 27 28| Scale is JI-epimorphic with val: <7 11 23 25| Scale is weakly epimorphic with val: <7 11 23 28| Scale is JI-epimorphic with val: <7 11 24 26| Scale is weakly epimorphic with val: <7 11 24 29| Scale is JI-epimorphic with val: <7 11 25 27| = patent Scale is weakly epimorphic with val: <7 11 25 30| Scale is JI-epimorphic with val: <7 11 26 28| Scale is JI-epimorphic with val: <7 11 27 29| Scale is weakly epimorphic with val: <8 11 23 25| Scale is weakly epimorphic with val: <8 11 24 26| Scale is weakly epimorphic with val: <8 11 25 27| Scale is weakly epimorphic with val: <8 11 26 28| Scale is weakly epimorphic with val: <8 11 27 29|
FIT/MODE
3: 1 1 1 SP B ME I SD: 52.7527 c. M: 80.7153 c. 4: 2 1 1 P M ME S SD: 32.4169 c. M:-40.1872 c. 5: 2 2 1 SP M ME S SD: 9.9540 c. M: 14.3093 c. 7: 3 3 1 SP M DE S SD: 8.5928 c. M:-14.1504 c. 12: 5 5 2 SP M DE S SD: 1.5262 c. M:-2.2922 c. Sansagari: Japan 29: 12 12 5 SP M DE S SD: 1.6202 c. M: 2.7477 c. 41: 17 17 7 SP M DE S SD: 1.3534 c. M: 2.3288 c. 52: 22 21 9 SP T3 SD: 1.2014 c. M:-1.8761 c. 59: 25 24 10 SP T3 SD: 1.3696 c. M:-2.2007 c. 64: 27 26 11 SP T3 SD: 0.7578 c. M:-1.2775 c. 76: 32 31 13 SP T3 SD: 0.5049 c. M:-0.8679 c. 81: 34 33 14 SP T3 SD: 0.4692 c. M: 0.7821 c. 88: 37 36 15 SP T3 SD: 0.4039 c. M:-0.5700 c. 93: 39 38 16 SP T3 SD: 0.2229 c. M: 0.3854 c. 105: 44 43 18 SP T3 SD: 0.0883 c. M: 0.1307 c. 286: 120 117 49 SP T3 SD: 0.0796 c. M:-0.1346 c. 298: 125 122 51 SP T3 SD: 0.0574 c. M:-0.0762 c. 391: 164 160 67 SP T3 SD: 0.0442 c. M:-0.0634 c. 403: 169 165 69 SP T3 SD: 0.0200 c. M:-0.0265 c. 508: 213 208 87 SP T3 SD: 0.0060 c. M: 0.0093 c. 1419: 595 581 243 SP T3 SD: 0.0063 c. M:-0.0108 c. 1915: 803 784 328 SP T3 SD: 0.0043 c. M:-0.0055 c. 2318: 972 949 397 SP T3 SD: 0.0049 c. M:-0.0084 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 5 x S SD: 26.4316 cents 5 x 6:7 S SD: 64.3504 cents 6:7 x 8 S SD: 29.0178 cents 7:8:9 x S SD: 15.7959 cents 10:11:13 x SD: 30.1696 cents 11:12:14:15 S SD: 23.3889 cents 12:14:15:16 S SD: 21.2571 cents 13:15 x 17 SD: 25.7088 cents 14:16:18:19 S SD: 14.6704 cents 15:17:19:20 SD: 2.8655 cents 48:54:61:64 SD: 1.7960 cents 63:71:80:84 SD: 0.6837 cents 78:88:99:104 SD: 0.0000 cents