Scala analysis: 362_D1
Diatonic tetrachord 16/15 * 15/13 * 13/12, Schlesinger
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 16/13 359.472338 tridecimal neutral third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 13/12 138.5727 tridecimal 2/3-tone 1: 16/15 111.7313 minor diatonic semitone 2: 15/13 247.7411 tridecimal 5/4-tone 3: 13/12 138.5727 tridecimal 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/45 250.304 cents 2: 1 16/13 359.472 cents tridecimal neutral third 2: 1 5/4 386.314 cents 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 : 111.7 359.5 498.0 111.7: 247.7 386.3 498.0 359.5: 138.6 250.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 247.7411 cents 225/208, 136.0098 cents 16/15, 111.7313 cents 2: 250.3039 .. 386.3137 cents 225/208, 136.0098 cents 676/675, 2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 15/13, 247.7411 cents Average / Smallest step : 1.485842 Largest / Average step : 1.492281 Largest / Smallest step : 2.217294 Median interval of one step : 13/12, 138.5727 cents, amount: 1 Least squares average step : 166.05793 cents, oct.: 498.17378 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1948-tone equal temperament with octave 4/3 degrees: 437 1406 1948 Least number of segments generator : 975 of 249.278 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1057 of 270.243 cents and inv. generated superset size: 48 = 45 more = 1600.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.151242 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.453825 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 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 13 Odd number limit : 45 (O: 15 U: 45) Highest odd numerator or denominator: 15 Scale harmonicity : 0.028393 Average absolute harmonicity : 0.109683 Specific harmonicity : 0.145021 Fundamental : 1/195, -7.6073 octaves, 1.3417 Hz. Guide tone : 16, 4.0000 octaves, 4186.009 Hz. Exponens Consonantiae : 3.120000E+03, 11.60733 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 33.5, average 11.16667 Mersenne's string divisions : 6293 Sum of van Prooijen's expressibility: 2.76716, average 0.92239 Sum of Tenney's harmonic distance : 5.77746, average 1.92582 Vogel's harmonic complexity : 16.33333 Wille's k value : 32 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 17.01942, average 2.83657 Lattice compactness (without 2's) : 7.56048, average 1.26008 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.33333 10 3: -1 .. 0 -0.66667 2 1 5: -1 .. 0 -0.33333 1 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is weakly epimorphic with val: <7 10 15 26| Scale is weakly epimorphic with val: <7 10 15 29| Scale is weakly epimorphic with val: <7 10 16 25| Scale is weakly epimorphic with val: <7 10 19 25| Scale is weakly epimorphic with val: <7 11 15 27| Scale is weakly epimorphic with val: <7 11 15 30| Scale is JI-epimorphic with val: <7 11 16 26| Scale is weakly epimorphic with val: <7 11 16 29| Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 11 19 26| Scale is weakly epimorphic with val: <7 11 19 29| Scale is weakly epimorphic with val: <7 12 15 25| Scale is weakly epimorphic with val: <7 12 18 25| Scale is weakly epimorphic with val: <8 11 17 29| Scale is weakly epimorphic with val: <8 11 18 25| Scale is weakly epimorphic with val: <8 11 18 28| Scale is weakly epimorphic with val: <8 12 15 29| Scale is weakly epimorphic with val: <8 12 17 27| Scale is weakly epimorphic with val: <8 12 17 30| Scale is weakly epimorphic with val: <8 12 18 29|
FIT/MODE
3: 1 1 1 SP B ME I SD: 35.1179 c. M:-54.2837 c. 4: 1 2 1 P M ME I SD: 10.9704 c. M:-14.0614 c. 10: 2 5 3 P T3 SD: 9.3892 c. M: 12.1223 c. 13: 3 6 4 SP T3 SD: 8.6703 c. M: 14.6720 c. 14: 3 7 4 P T3 SD: 3.6035 c. M: 5.0074 c. 18: 4 9 5 P T3 SD: 0.6228 c. M: 1.0546 c. 76: 17 38 21 P T3 SD: 0.5827 c. M:-0.9550 c. 93: 21 46 26 SP T3 SD: 0.5706 c. M:-0.7305 c. 94: 21 47 26 P T3 SD: 0.5423 c. M:-0.8155 c. 107: 24 53 30 SP T3 SD: 0.6156 c. M: 1.0661 c. 111: 25 55 31 SP T3 SD: 0.3941 c. M: 0.5210 c. 129: 29 64 36 SP T3 SD: 0.2754 c. M: 0.4166 c. 147: 33 73 41 SP T3 SD: 0.1998 c. M: 0.3378 c. 165: 37 82 46 SP T3 SD: 0.1619 c. M: 0.2762 c. 169: 38 84 47 SP T3 SD: 0.1518 c. M:-0.2552 c. 183: 41 91 51 SP T3 SD: 0.1562 c. M: 0.2268 c. 187: 42 93 52 SP T3 SD: 0.0873 c. M:-0.1291 c. 205: 46 102 57 SP T3 SD: 0.0550 c. M:-0.0919 c. 352: 79 175 98 SP T3 SD: 0.0571 c. M: 0.0876 c. 370: 83 184 103 SP T3 SD: 0.0420 c. M: 0.0723 c. 388: 87 193 108 SP T3 SD: 0.0468 c. M: 0.0584 c. 539: 121 268 150 SP T3 SD: 0.0465 c. M:-0.0747 c. 557: 125 277 155 SP T3 SD: 0.0253 c. M:-0.0382 c. 575: 129 286 160 SP T3 SD: 0.0083 c. M: 0.0138 c. 780: 175 388 217 SP T3 SD: 0.0098 c. M:-0.0140 c. 1168: 262 581 325 SP T3 SD: 0.0092 c. M: 0.0123 c. 1355: 304 674 377 SP T3 SD: 0.0044 c. M:-0.0072 c. 1373: 308 683 382 SP T3 SD: 0.0049 c. M: 0.0067 c. 1930: 433 960 537 SP T3 SD: 0.0039 c. M:-0.0063 c. 1948: 437 969 542 SP T3 SD: 0.0021 c. M: 0.0035 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: 26.8414 cents 5 x 6:7 S SD: 47.5812 cents 6 x 7:8 S SD: 46.3007 cents 7:8 x 9 S SD: 67.5105 cents 8:9:10:11 H SD: 36.5990 cents 9:10:11:12 H SD: 23.8983 cents 12:13:15:16 SD: 12.6531 cents 13:14:16:17 S SD: 12.4926 cents 17:18:21:23 SD: 9.6746 cents 18:19:22:24 SD: 7.2586 cents 27:29:33:36 SD: 5.6676 cents 30:32:37:40 SD: 1.2010 cents 105:112:129:140 SD: 1.0314 cents 117:125:144:156 SD: 0.9241 cents 135:144:166:180 SD: 0.5346 cents 165:176:203:220 SD: 0.2186 cents 195:208:240:260 SD: 0.0000 cents