Scala analysis: 471_D15
Diatonic tetrachord 9/8 * 7168/6561 * 243/224
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 896/729 357.095901 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 243/224 140.9491 Archytas' 2/3-tone 1: 9/8 203.9100 major whole tone 2: 7168/6561 153.1859 3: 243/224 140.9491 Archytas' 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 243/224 140.949 cents Archytas' 2/3-tone 1: 1 7168/6561 153.186 cents 1: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 2187/1792 344.859 cents 2: 1 896/729 357.096 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 : 203.9 357.1 498.0 203.9: 153.2 294.1 498.0 357.1: 140.9 344.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 140.9491 .. 203.9100 cents 28/27, 62.9609 cents 243/224, 140.9491 cents 2: 294.1350 .. 357.0959 cents 28/27, 62.9609 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 243/224, 140.9491 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.177837 Largest / Average step : 1.228263 Largest / Smallest step : 1.446692 Median interval of one step : 7168/6561, 153.1859 cents, amount: 1 Least squares average step : 172.30263 cents, oct.: 516.90789 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1424-tone equal temperament with octave 4/3 degrees: 583 1021 1424 Least number of segments generator : 713 of 249.372 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1351 of 472.513 cents and inv. generated superset size: 54 = 51 more = 1800.000% 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 90.22500 cents Scale diversity : 1.353560 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.747168 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 : 1605632/1594323, 12.2368 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 Steps are strictly decreasing 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% Limited inverse transpositions with margin 50.7241 cents: 1 -- Rational properties -- Prime limit : 7 Odd number limit : 6561 (O: 2187 U: 6561) Highest odd numerator or denominator: 729 Scale harmonicity : 0.024027 Average absolute harmonicity : 0.121442 Specific harmonicity : 0.123529 Fundamental : 1/5832, -12.5098 octaves, 0.0449 Hz. Guide tone : 8064, 12.9773 octaves, 2109748.559 Hz. Exponens Consonantiae : 4.702925E+07, 25.48705 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 824.5, average 274.83333 Mersenne's string divisions : 193375 Sum of van Prooijen's expressibility: 4.29409, average 1.43136 Sum of Tenney's harmonic distance : 8.75155, average 2.91718 Vogel's harmonic complexity : 20.33333 Wille's k value : 3280 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 9 Triangular lattice diameter : 8 Lattice compactness : 40.93285, average 6.82214 Lattice compactness (without 2's) : 25.24404, average 4.20734 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 7 2.00000 12 3: -6 .. 2 -1.66667 9 2 7: 0 .. 1 0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is JI-epimorphic with val: <7 11 19| Scale is weakly epimorphic with val: <7 11 22| Scale is weakly epimorphic with val: <7 12 18| Scale is weakly epimorphic with val: <7 12 21|
FIT/MODE
3: 1 1 1 SP B ME I SD: 26.2319 c. M: 37.8950 c. 5: 2 2 1 SP M ME S SD: 24.0210 c. M:-41.3401 c. 7: 3 2 2 SP M ME S SD: 5.5615 c. M:-9.5379 c. 10: 4 3 3 SP M ME S SD: 5.5875 c. M: 8.4644 c. 15: 6 5 4 SP T3 SD: 5.4230 c. M:-8.1371 c. 17: 7 5 5 SP M DE S SD: 3.2658 c. M: 5.5347 c. 22: 9 7 6 SP T3 SD: 2.9568 c. M:-5.1186 c. 24: 10 7 7 SP M DE S SD: 3.2472 c. M: 4.3140 c. 25: 10 8 7 SP T3 SD: 2.8434 c. M: 4.6920 c. 29: 12 9 8 SP T3 SD: 2.4081 c. M:-3.5574 c. 32: 13 10 9 SP T3 SD: 1.0421 c. M: 1.5792 c. 39: 16 12 11 SP T3 SD: 0.3645 c. M:-0.4749 c. 88: 36 27 25 SP T3 SD: 0.3264 c. M: 0.5410 c. 127: 52 39 36 SP T3 SD: 0.1325 c. M: 0.2290 c. 166: 68 51 47 SP T3 SD: 0.0726 c. M:-0.1084 c. 325: 133 100 92 SP T3 SD: 0.0585 c. M: 0.0947 c. 364: 149 112 103 SP T3 SD: 0.0255 c. M: 0.0399 c. 491: 201 151 139 SP T3 SD: 0.0302 c. M: 0.0453 c. 530: 217 163 150 SP T3 SD: 0.0055 c. M: 0.0070 c. 1424: 583 438 403 SP T3 SD: 0.0031 c. M: 0.0053 c. 1954: 800 601 553 SP T3 SD: 0.0018 c. M: 0.0022 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: 29.2178 cents 5 x 6:7 S SD: 47.0457 cents 6:7 x 8 S SD: 31.4805 cents 7:8 x 9 S SD: 34.3053 cents 8:9:10:11 H SD: 20.2531 cents 9:10:11:12 H SD: 7.8625 cents 26:29:32:35 SD: 7.4606 cents 30:34:37:40 SD: 4.7022 cents 39:44:48:52 SD: 1.8229 cents 48:54:59:64 SD: 0.0403 cents