Scala analysis: 444_D13
Diatonic tetrachord 39/35 * 35/33 * 44/39
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 39/35 187.343042 2: 13/11 289.209719 tridecimal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 44/39 208.8353 1: 39/35 187.3430 2: 35/33 101.8667 3: 44/39 208.8353
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 35/33 101.867 cents 1: 1 39/35 187.343 cents 1: 1 44/39 208.835 cents 2: 1 13/11 289.210 cents tridecimal minor third 2: 1 140/117 310.702 cents 2: 1 44/35 396.178 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 : 187.3 289.2 498.0 187.3: 101.9 310.7 498.0 289.2: 208.8 396.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 101.8667 .. 208.8353 cents 484/455, 106.9686 cents 35/33, 101.8667 cents 2: 289.2097 .. 396.1783 cents 484/455, 106.9686 cents 507/484, 80.3744 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 35/33, 101.8667 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 44/39, 208.8353 cents Average / Smallest step : 1.629728 Largest / Average step : 1.257930 Largest / Smallest step : 2.050084 Median interval of one step : 39/35, 187.3430 cents, amount: 1 Least squares average step : 161.42125 cents, oct.: 484.26375 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 973-tone equal temperament with octave 4/3 degrees: 366 565 973 Least number of segments generator : 487 of 249.278 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 837 of 428.431 cents and inv. generated superset size: 21 = 18 more = 700.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 80.37444 cents Scale diversity : 1.174318 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.570446 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 : 1540/1521, 21.4922 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 13 Odd number limit : 117 (O: 39 U: 117) Highest odd numerator or denominator: 39 Scale harmonicity : 0.015539 Average absolute harmonicity : 0.087723 Specific harmonicity : 0.074343 Fundamental : 1/1155, -10.1737 octaves, 0.2265 Hz. Guide tone : 156, 7.2854 octaves, 40813.588 Hz. Exponens Consonantiae : 1.801800E+05, 17.45908 octaves Euler's gradus suavitatis : 39 Sum of Mann's harmonic distance : 52.5, average 17.50000 Mersenne's string divisions : 6216 Sum of van Prooijen's expressibility: 3.18213, average 1.06071 Sum of Tenney's harmonic distance : 6.36965, average 2.12322 Vogel's harmonic complexity : 27.66667 Wille's k value : 682 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 13.61266, average 2.26878 Lattice compactness (without 2's) : 10.79202, average 1.79867 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -1 .. 1 0.00000 2 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.33333 1 13: 0 .. 1 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: <7 11 16 19 25 26| Scale is weakly epimorphic with val: <7 11 16 19 26 28| Scale is JI-epimorphic with val: <7 11 16 20 24 26| Scale is weakly epimorphic with val: <7 11 16 20 26 27| Scale is weakly epimorphic with val: <7 11 16 21 24 28| Scale is JI-epimorphic with val: <7 11 16 21 25 27| Scale is JI-epimorphic with val: <7 11 17 19 24 26| Scale is weakly epimorphic with val: <7 11 17 19 26 27| Scale is weakly epimorphic with val: <7 11 17 20 24 28| Scale is JI-epimorphic with val: <7 11 17 20 25 27| = patent Scale is weakly epimorphic with val: <7 11 17 21 25 26| Scale is JI-epimorphic with val: <7 11 17 21 26 28| Scale is weakly epimorphic with val: <7 11 18 19 24 28| Scale is JI-epimorphic with val: <7 11 18 19 25 27| Scale is weakly epimorphic with val: <7 11 18 20 25 26| Scale is JI-epimorphic with val: <7 11 18 20 26 28| Scale is weakly epimorphic with val: <7 11 18 21 24 26| Scale is weakly epimorphic with val: <7 11 18 21 26 27| Scale is weakly epimorphic with val: <7 12 16 19 24 27| Scale is weakly epimorphic with val: <7 12 16 19 25 26| Scale is weakly epimorphic with val: <7 12 16 20 25 28| Scale is weakly epimorphic with val: <7 12 16 20 26 27| Scale is weakly epimorphic with val: <7 12 16 21 24 28| Scale is weakly epimorphic with val: <7 12 17 19 25 28| Scale is weakly epimorphic with val: <7 12 17 19 26 27| Scale is weakly epimorphic with val: <7 12 17 20 24 28| Scale is weakly epimorphic with val: <7 12 17 21 24 27| Scale is weakly epimorphic with val: <7 12 18 19 24 28| Scale is weakly epimorphic with val: <7 12 18 20 24 27| Scale is weakly epimorphic with val: <7 12 18 21 25 28|
FIT/MODE
3: 1 1 1 SP B ME I SD: 27.6192 c. M:-42.8203 c. 5: 2 1 2 SP M ME I SD: 8.8224 c. M:-11.8750 c. 14: 5 3 6 SP T3 SD: 6.0815 c. M: 9.4698 c. 16: 6 3 7 SP T3 SD: 5.2410 c. M: 9.0594 c. 19: 7 4 8 SP T3 SD: 2.2801 c. M: 3.8528 c. 24: 9 5 10 SP T3 SD: 0.8297 c. M:-1.3165 c. 64: 24 13 27 SP T3 SD: 0.8091 c. M: 1.2775 c. 69: 26 14 29 SP T3 SD: 0.3389 c. M: 0.4880 c. 93: 35 19 39 SP T3 SD: 0.0554 c. M:-0.0932 c. 303: 114 62 127 SP T3 SD: 0.0536 c. M:-0.0837 c. 396: 149 81 166 SP T3 SD: 0.0456 c. M:-0.0588 c. 489: 184 100 205 SP T3 SD: 0.0429 c. M:-0.0604 c. 577: 217 118 242 SP T3 SD: 0.0359 c. M: 0.0501 c. 601: 226 123 252 SP T3 SD: 0.0337 c. M: 0.0582 c. 670: 252 137 281 SP T3 SD: 0.0288 c. M: 0.0463 c. 694: 261 142 291 SP T3 SD: 0.0219 c. M: 0.0379 c. 787: 296 161 330 SP T3 SD: 0.0130 c. M: 0.0224 c. 880: 331 180 369 SP T3 SD: 0.0063 c. M: 0.0102 c. 973: 366 199 408 SP T3 SD: 0.0033 c. M: 0.0058 c. 1853: 697 379 777 SP T3 SD: 0.0041 c. M: 0.0050 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: 97.1040 cents 5 x 6:7 S SD: 44.2531 cents 6 x 7:8 S SD: 11.1694 cents 7:8 x 9 S SD: 38.3576 cents 8:9 x 11 SD: 27.8948 cents 9:10:11:12 H SD: 19.4691 cents 10:11:12:13 H SD: 18.6154 cents 11:12:13:15 SD: 17.8294 cents 15:17:18:20 SD: 13.1643 cents 16:18:19:21 SD: 10.9886 cents 17:19:20:23 SD: 8.9914 cents 18:20:21:24 S SD: 7.6261 cents 26:29:31:35 SD: 7.5381 cents 27:30:32:36 S SD: 2.3251 cents 60:67:71:80 SD: 1.4366 cents 78:87:92:104 SD: 1.2734 cents 87:97:103:116 SD: 1.0748 cents 105:117:124:140 SD: 0.4229 cents 132:147:156:176 SD: 0.3364 cents 192:214:227:256 SD: 0.2778 cents 237:264:280:316 SD: 0.2649 cents 297:331:351:396 SD: 0.0996 cents 429:478:507:572 SD: 0.0345 cents