Scala analysis: 445_D13
Diatonic tetrachord 39/37 * 37/33 * 44/39
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 39/37 91.138624 2: 13/11 289.209719 tridecimal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 44/39 208.8353 1: 39/37 91.1386 2: 37/33 198.0711 3: 44/39 208.8353
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 39/37 91.139 cents 1: 1 37/33 198.071 cents 1: 1 44/39 208.835 cents 2: 1 13/11 289.210 cents tridecimal minor third 2: 1 44/37 299.974 cents 2: 1 148/117 406.906 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 : 91.1 289.2 498.0 91.1 : 198.1 406.9 498.0 289.2: 208.8 300.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 91.1386 .. 208.8353 cents 1628/1521, 117.6967 cents 39/37, 91.1386 cents 2: 289.2097 .. 406.9064 cents 1628/1521, 117.6967 cents 507/484, 80.3744 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 39/37, 91.1386 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 44/39, 208.8353 cents Average / Smallest step : 1.821566 Largest / Average step : 1.257930 Largest / Smallest step : 2.291403 Median interval of one step : 37/33, 198.0711 cents, amount: 1 Least squares average step : 154.54950 cents, oct.: 463.64851 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 694-tone equal temperament with octave 4/3 degrees: 127 403 694 Least number of segments generator : 349 of 250.458 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 597 of 428.434 cents and inv. generated superset size: 14 = 11 more = 466.667% 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 80.37444 cents Scale diversity : 1.053692 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.527365 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 : 484/481, 10.7642 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 increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 106.9325 cents: 1 -- Rational properties -- Prime limit : 37 Odd number limit : 117 (O: 39 U: 117) Highest odd numerator or denominator: 39 Scale harmonicity : 0.020978 Fundamental : 1/1221, -10.2538 octaves, 0.2143 Hz. Guide tone : 156, 7.2854 octaves, 40813.588 Hz. Exponens Consonantiae : 1.904760E+05, 17.53925 octaves Euler's gradus suavitatis : 65 Sum of Mann's harmonic distance : 53.5, average 17.83333 Mersenne's string divisions : 3192 Sum of van Prooijen's expressibility: 3.18213, average 1.06071 Sum of Tenney's harmonic distance : 6.39378, average 2.13126 Vogel's harmonic complexity : 44.33333 Wille's k value : 721 Wilson's harmonic complexity : 67 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 12.12446, average 2.02074 Lattice compactness (without 2's) : 9.21076, average 1.53513 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -1 .. 1 0.00000 2 1 11: -1 .. 0 -0.33333 1 13: 0 .. 1 0.66667 2 1 37: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 23 26 35| Scale is weakly epimorphic with val: <6 10 23 26 38| Scale is weakly epimorphic with val: <6 10 23 26 41| Scale is weakly epimorphic with val: <6 10 23 30 37| Scale is weakly epimorphic with val: <6 10 24 27 36| Scale is weakly epimorphic with val: <6 10 24 27 39| Scale is weakly epimorphic with val: <6 10 24 28 35| Scale is weakly epimorphic with val: <6 10 25 28 37| Scale is weakly epimorphic with val: <6 10 25 28 40| Scale is weakly epimorphic with val: <6 10 25 29 36| Scale is weakly epimorphic with val: <6 10 26 29 35| Scale is weakly epimorphic with val: <6 10 26 29 38| Scale is weakly epimorphic with val: <6 10 26 29 41| Scale is weakly epimorphic with val: <6 10 26 30 37| Scale is weakly epimorphic with val: <6 10 27 28 35| Scale is weakly epimorphic with val: <6 10 27 30 36| Scale is weakly epimorphic with val: <6 10 27 30 39| Scale is weakly epimorphic with val: <6 11 23 26 35| Scale is weakly epimorphic with val: <6 11 23 26 38| Scale is weakly epimorphic with val: <6 11 23 26 41| Scale is weakly epimorphic with val: <6 11 23 28 36| Scale is weakly epimorphic with val: <6 11 24 27 36| Scale is weakly epimorphic with val: <6 11 24 27 39| Scale is weakly epimorphic with val: <6 11 24 29 37| Scale is weakly epimorphic with val: <6 11 25 27 35| Scale is weakly epimorphic with val: <6 11 25 28 37| Scale is weakly epimorphic with val: <6 11 25 28 40| Scale is weakly epimorphic with val: <6 11 25 30 38| Scale is weakly epimorphic with val: <6 11 26 28 36| Scale is weakly epimorphic with val: <6 11 26 29 35| Scale is weakly epimorphic with val: <6 11 26 29 38| Scale is weakly epimorphic with val: <6 11 26 29 41| Scale is weakly epimorphic with val: <6 11 27 29 37| Scale is weakly epimorphic with val: <6 11 27 30 36| Scale is weakly epimorphic with val: <6 11 27 30 39| Scale is weakly epimorphic with val: <7 10 23 26 37| Scale is weakly epimorphic with val: <7 10 23 26 40| Scale is weakly epimorphic with val: <7 10 23 28 35| Scale is weakly epimorphic with val: <7 10 24 27 35| Scale is weakly epimorphic with val: <7 10 24 27 38| Scale is weakly epimorphic with val: <7 10 24 27 41| Scale is weakly epimorphic with val: <7 10 24 29 36| Scale is weakly epimorphic with val: <7 10 25 28 36| Scale is weakly epimorphic with val: <7 10 25 28 39| Scale is weakly epimorphic with val: <7 10 25 30 37| Scale is weakly epimorphic with val: <7 10 26 28 35| Scale is weakly epimorphic with val: <7 10 26 29 37| Scale is weakly epimorphic with val: <7 10 26 29 40| Scale is weakly epimorphic with val: <7 10 27 29 36| Scale is weakly epimorphic with val: <7 10 27 30 35| Scale is weakly epimorphic with val: <7 10 27 30 38| Scale is weakly epimorphic with val: <7 10 27 30 41| Scale is JI-epimorphic with val: <7 11 23 25 35| Scale is weakly epimorphic with val: <7 11 23 25 38| Scale is weakly epimorphic with val: <7 11 23 25 41| Scale is weakly epimorphic with val: <7 11 23 27 36| Scale is weakly epimorphic with val: <7 11 23 27 39| Scale is weakly epimorphic with val: <7 11 23 28 35| Scale is weakly epimorphic with val: <7 11 23 28 38| Scale is weakly epimorphic with val: <7 11 23 28 41| Scale is weakly epimorphic with val: <7 11 23 30 36| Scale is weakly epimorphic with val: <7 11 23 30 39| Scale is weakly epimorphic with val: <7 11 24 25 37| Scale is weakly epimorphic with val: <7 11 24 25 40| Scale is JI-epimorphic with val: <7 11 24 26 36| Scale is weakly epimorphic with val: <7 11 24 26 39| Scale is weakly epimorphic with val: <7 11 24 28 37| Scale is weakly epimorphic with val: <7 11 24 28 40| Scale is weakly epimorphic with val: <7 11 24 29 36| Scale is weakly epimorphic with val: <7 11 24 29 39| Scale is weakly epimorphic with val: <7 11 25 26 35| Scale is weakly epimorphic with val: <7 11 25 26 38| Scale is weakly epimorphic with val: <7 11 25 26 41| Scale is JI-epimorphic with val: <7 11 25 27 37| Scale is weakly epimorphic with val: <7 11 25 27 40| Scale is weakly epimorphic with val: <7 11 25 29 35| Scale is weakly epimorphic with val: <7 11 25 29 38| Scale is weakly epimorphic with val: <7 11 25 29 41| Scale is weakly epimorphic with val: <7 11 25 30 37| Scale is weakly epimorphic with val: <7 11 25 30 40| Scale is weakly epimorphic with val: <7 11 26 27 36| Scale is weakly epimorphic with val: <7 11 26 27 39| Scale is weakly epimorphic with val: <7 11 26 28 35| Scale is JI-epimorphic with val: <7 11 26 28 38| Scale is weakly epimorphic with val: <7 11 26 28 41| Scale is weakly epimorphic with val: <7 11 26 30 36| Scale is weakly epimorphic with val: <7 11 26 30 39| Scale is weakly epimorphic with val: <7 11 27 28 37| Scale is weakly epimorphic with val: <7 11 27 28 40| Scale is weakly epimorphic with val: <7 11 27 29 36| Scale is JI-epimorphic with val: <7 11 27 29 39| Scale is weakly epimorphic with val: <7 12 23 26 37| Scale is weakly epimorphic with val: <7 12 23 26 40| Scale is weakly epimorphic with val: <7 12 23 27 36| Scale is weakly epimorphic with val: <7 12 23 30 39| Scale is weakly epimorphic with val: <7 12 24 27 35| Scale is weakly epimorphic with val: <7 12 24 27 38| Scale is weakly epimorphic with val: <7 12 24 27 41| Scale is weakly epimorphic with val: <7 12 24 28 37| Scale is weakly epimorphic with val: <7 12 25 26 35| Scale is weakly epimorphic with val: <7 12 25 28 36| Scale is weakly epimorphic with val: <7 12 25 28 39| Scale is weakly epimorphic with val: <7 12 25 29 38| Scale is weakly epimorphic with val: <7 12 26 27 36| Scale is weakly epimorphic with val: <7 12 26 29 37| Scale is weakly epimorphic with val: <7 12 26 29 40| Scale is weakly epimorphic with val: <7 12 26 30 39| Scale is weakly epimorphic with val: <7 12 27 28 37| Scale is weakly epimorphic with val: <7 12 27 30 35| Scale is weakly epimorphic with val: <7 12 27 30 38| Scale is weakly epimorphic with val: <7 12 27 30 41| Scale is weakly epimorphic with val: <8 11 23 26 36| Scale is weakly epimorphic with val: <8 11 23 26 39| Scale is weakly epimorphic with val: <8 11 23 27 35| Scale is weakly epimorphic with val: <8 11 23 30 38| Scale is weakly epimorphic with val: <8 11 24 27 37| Scale is weakly epimorphic with val: <8 11 24 27 40| Scale is weakly epimorphic with val: <8 11 24 28 36| Scale is weakly epimorphic with val: <8 11 25 28 35| Scale is weakly epimorphic with val: <8 11 25 28 38| Scale is weakly epimorphic with val: <8 11 25 28 41| Scale is weakly epimorphic with val: <8 11 25 29 37| Scale is weakly epimorphic with val: <8 11 26 27 35| Scale is weakly epimorphic with val: <8 11 26 29 36| Scale is weakly epimorphic with val: <8 11 26 29 39| Scale is weakly epimorphic with val: <8 11 26 30 38| Scale is weakly epimorphic with val: <8 11 27 28 36| Scale is weakly epimorphic with val: <8 11 27 30 37| Scale is weakly epimorphic with val: <8 11 27 30 40| Scale is weakly epimorphic with val: <8 12 23 26 36| Scale is weakly epimorphic with val: <8 12 23 26 39| Scale is weakly epimorphic with val: <8 12 23 28 37| Scale is weakly epimorphic with val: <8 12 24 26 35| Scale is weakly epimorphic with val: <8 12 24 27 37| Scale is weakly epimorphic with val: <8 12 24 27 40| Scale is weakly epimorphic with val: <8 12 24 29 38| Scale is weakly epimorphic with val: <8 12 25 27 36| Scale is weakly epimorphic with val: <8 12 25 28 35| Scale is weakly epimorphic with val: <8 12 25 28 38| Scale is weakly epimorphic with val: <8 12 25 28 41| Scale is weakly epimorphic with val: <8 12 25 30 39| Scale is weakly epimorphic with val: <8 12 26 28 37| Scale is weakly epimorphic with val: <8 12 26 29 36| Scale is weakly epimorphic with val: <8 12 26 29 39| Scale is weakly epimorphic with val: <8 12 27 29 38| Scale is weakly epimorphic with val: <8 12 27 30 37| Scale is weakly epimorphic with val: <8 12 27 30 40|
FIT/MODE
3: 1 1 1 SP B ME I SD: 49.7998 c. M:-74.8764 c. 4: 1 1 2 P M ME S SD: 30.1593 c. M: 40.1872 c. 5: 1 2 2 SP M ME S SD: 7.3991 c. M:-9.6173 c. 12: 2 5 5 SP M DE S SD: 4.7556 c. M: 8.1311 c. 17: 3 7 7 SP M DE S SD: 2.8678 c. M:-3.7579 c. 22: 4 9 9 SP M DE S SD: 2.9578 c. M:-5.0896 c. 26: 5 10 11 SP T3 SD: 2.8892 c. M:-4.6393 c. 28: 5 11 12 SP T3 SD: 2.9510 c. M: 4.6126 c. 33: 6 13 14 SP T3 SD: 1.4579 c. M: 2.4565 c. 38: 7 15 16 SP T3 SD: 0.6113 c. M: 0.8679 c. 55: 10 22 23 SP T3 SD: 0.4683 c. M: 0.5850 c. 88: 16 35 37 SP T3 SD: 0.4716 c. M: 0.5850 c. 93: 17 37 39 SP T3 SD: 0.0581 c. M: 0.0981 c. 410: 75 163 172 SP T3 SD: 0.0611 c. M: 0.1007 c. 415: 76 165 174 SP T3 SD: 0.0413 c. M:-0.0696 c. 508: 93 202 213 SP T3 SD: 0.0231 c. M:-0.0389 c. 601: 110 239 252 SP T3 SD: 0.0105 c. M:-0.0177 c. 694: 127 276 291 SP T3 SD: 0.0013 c. M:-0.0022 c. 2175: 398 865 912 SP T3 SD: 0.0012 c. M: 0.0021 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 x 9:11 SD: 50.2843 cents 9:10:11:12 H SD: 36.0807 cents 10:11:12:13 H SD: 29.9554 cents 11:12:13:15 SD: 23.6965 cents 12:13:14:16 S SD: 17.4770 cents 15:16:18:20 S SD: 11.1688 cents 16:17:19:21 SD: 10.5577 cents 17:18:20:23 SD: 9.1985 cents 18:19:21:24 SD: 7.4914 cents 21:22:25:28 SD: 5.4983 cents 33:35:39:44 SD: 3.5760 cents 39:41:46:52 SD: 1.8993 cents 54:57:64:72 SD: 1.8358 cents 72:76:85:96 SD: 1.0273 cents 93:98:110:124 SD: 0.5030 cents 165:174:195:220 SD: 0.2690 cents 204:215:241:272 SD: 0.2294 cents 258:272:305:344 SD: 0.2068 cents 297:313:351:396 SD: 0.0997 cents 462:487:546:616 SD: 0.0320 cents