Scala analysis: 443_D13
Diatonic tetrachord 12/11 * 13/12 * 44/39, Young
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 12/11 150.637059 undecimal neutral second, 3/4-tone 2: 13/11 289.209719 tridecimal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 44/39 208.8353 1: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 13/12 138.5727 tridecimal 2/3-tone 3: 44/39 208.8353
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 44/39 208.835 cents 2: 1 13/11 289.210 cents tridecimal minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 16/13 359.472 cents tridecimal neutral 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 : 150.6 289.2 498.0 150.6: 138.6 347.4 498.0 289.2: 208.8 359.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 138.5727 .. 208.8353 cents 176/169, 70.2626 cents 13/12, 138.5727 cents 2: 289.2097 .. 359.4723 cents 176/169, 70.2626 cents 507/484, 80.3744 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 13/12, 138.5727 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 44/39, 208.8353 cents Average / Smallest step : 1.198036 Largest / Average step : 1.257930 Largest / Smallest step : 1.507045 Median interval of one step : 12/11, 150.6371 cents, amount: 1 Least squares average step : 158.79939 cents, oct.: 476.39818 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 2311-tone equal temperament with octave 4/3 degrees: 699 1342 2311 Least number of segments generator : 1156 of 249.130 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1258 of 271.112 cents and inv. generated superset size: 33 = 30 more = 1100.000% 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 : 1.353634 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.717846 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 : 144/143, 12.0644 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 Length of longest harmonic part : 2 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 Limited inverse transpositions with margin 70.2626 cents: 2 -- Rational properties -- Prime limit : 13 Odd number limit : 39 (O: 13 U: 39) Highest odd numerator or denominator: 13 Scale harmonicity : 0.020978 Average absolute harmonicity : 0.094281 Specific harmonicity : 0.098045 Fundamental : 1/33, -5.0444 octaves, 7.9280 Hz. Guide tone : 156, 7.2854 octaves, 40813.588 Hz. Exponens Consonantiae : 5.148000E+03, 12.32980 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 27.0, average 9.00000 Mersenne's string divisions : 3864 Sum of van Prooijen's expressibility: 2.63246, average 0.87749 Sum of Tenney's harmonic distance : 5.35509, average 1.78503 Vogel's harmonic complexity : 12.33333 Wille's k value : 19 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 13.43108, average 2.23851 Lattice compactness (without 2's) : 9.21076, average 1.53513 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.33333 4 3: -1 .. 1 0.00000 2 1 11: -1 .. 0 -0.66667 2 1 13: 0 .. 1 0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 24 27| Scale is weakly epimorphic with val: <6 10 27 30| Scale is weakly epimorphic with val: <6 11 24 27| Scale is weakly epimorphic with val: <6 11 27 30| Scale is weakly epimorphic with val: <7 10 25 28| Scale is weakly epimorphic with val: <7 11 23 27| Scale is weakly epimorphic with val: <7 11 23 30| Scale is JI-epimorphic with val: <7 11 24 26| Scale is weakly epimorphic with val: <7 11 24 29| Scale is weakly epimorphic with val: <7 11 26 27| Scale is weakly epimorphic with val: <7 11 26 30| Scale is weakly epimorphic with val: <7 11 27 29| Scale is weakly epimorphic with val: <7 12 23 27| Scale is weakly epimorphic with val: <7 12 23 30| Scale is weakly epimorphic with val: <7 12 25 28| Scale is weakly epimorphic with val: <8 11 23 26| Scale is weakly epimorphic with val: <8 11 24 25| Scale is weakly epimorphic with val: <8 11 24 28| Scale is weakly epimorphic with val: <8 11 26 29| Scale is weakly epimorphic with val: <8 12 23 26| Scale is weakly epimorphic with val: <8 12 25 27| Scale is weakly epimorphic with val: <8 12 25 30| Scale is weakly epimorphic with val: <8 12 26 29|
FIT/MODE
3: 1 1 1 SP B ME I SD: 26.2682 c. M:-42.8203 c. 4: 1 1 2 P M ME S SD: 27.6741 c. M: 40.1872 c. 6: 2 1 3 P T3 SD: 24.8428 c. M: 40.1872 c. 7: 2 2 3 SP M ME S SD: 5.5017 c. M: 8.3385 c. 17: 5 5 7 SP M DE S SD: 3.2337 c. M: 4.1532 c. 24: 7 7 10 SP M DE S SD: 3.1944 c. M: 5.3739 c. 26: 8 7 11 SP T3 SD: 1.8546 c. M:-2.6076 c. 33: 10 9 14 SP T3 SD: 1.4278 c. M: 2.4565 c. 36: 11 10 15 SP T3 SD: 1.1712 c. M:-1.5434 c. 43: 13 12 18 SP T3 SD: 0.2063 c. M:-0.3513 c. 162: 49 45 68 SP T3 SD: 0.1274 c. M: 0.2206 c. 205: 62 57 86 SP T3 SD: 0.0583 c. M: 0.1007 c. 248: 75 69 104 SP T3 SD: 0.0168 c. M: 0.0223 c. 539: 163 150 226 SP T3 SD: 0.0136 c. M: 0.0223 c. 787: 238 219 330 SP T3 SD: 0.0123 c. M: 0.0212 c. 1035: 313 288 434 SP T3 SD: 0.0125 c. M: 0.0206 c. 1283: 388 357 538 SP T3 SD: 0.0129 c. M: 0.0202 c. 1326: 401 369 556 SP T3 SD: 0.0125 c. M: 0.0216 c. 1481: 448 412 621 SP T3 SD: 0.0120 c. M:-0.0207 c. 1524: 461 424 639 SP T3 SD: 0.0119 c. M:-0.0183 c. 1686: 510 469 707 SP T3 SD: 0.0123 c. M:-0.0171 c. 1729: 523 481 725 SP T3 SD: 0.0090 c. M:-0.0151 c. 1772: 536 493 743 SP T3 SD: 0.0081 c. M:-0.0131 c. 1815: 549 505 761 SP T3 SD: 0.0100 c. M:-0.0131 c. 1977: 598 550 829 SP T3 SD: 0.0072 c. M:-0.0108 c. 2020: 611 562 847 SP T3 SD: 0.0054 c. M:-0.0092 c. 2063: 624 574 865 SP T3 SD: 0.0068 c. M:-0.0089 c. 2225: 673 619 933 SP T3 SD: 0.0063 c. M: 0.0079 c. 2268: 686 631 951 SP T3 SD: 0.0036 c. M:-0.0062 c. 2311: 699 643 969 SP T3 SD: 0.0042 c. M:-0.0055 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 x 8:9 S SD: 42.8142 cents 8:9 x 11 SD: 37.6697 cents 9:10:11:12 H SD: 22.1012 cents 10:11:12:13 H SD: 17.7207 cents 11:12:13:15 SD: 12.9686 cents 12:13:14:16 S SD: 8.4628 cents 21:23:25:28 SD: 4.7923 cents 33:36:39:44 SD: 0.0000 cents