Scala analysis: 393_D6
Diatonic tetrachord 28/27 * 8/7 * 9/8, Archytas
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 8/7 231.1741 septimal whole tone 3: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/7 435.084 cents septimal major third, BP 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 : 63.0 294.1 498.0 63.0 : 231.2 435.1 498.0 294.1: 203.9 266.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 231.1741 cents 54/49, 168.2132 cents 28/27, 62.9609 cents 2: 266.8709 .. 435.0841 cents 54/49, 168.2132 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.636795 Largest / Average step : 1.392489 Largest / Smallest step : 3.671709 Median interval of one step : 9/8, 203.9100 cents, amount: 1 Least squares average step : 153.24042 cents, oct.: 459.72126 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1424-tone equal temperament with octave 4/3 degrees: 180 841 1424 Least number of segments generator : 713 of 249.372 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 715 of 250.072 cents and inv. generated superset size: 61 = 58 more = 2033.333% 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 35.69681 cents Scale diversity : 0.839614 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.324506 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 : 64/63, 27.2641 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 1 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 differentially coherent in interval class 1 Limited inverse transpositions with margin 168.2132 cents: 1 -- Rational properties -- Prime limit : 7 Odd number limit : 27 (O: 9 U: 27) Highest odd numerator or denominator: 27 Scale harmonicity : 0.042945 Average absolute harmonicity : 0.113501 Specific harmonicity : 0.212792 Fundamental : 1/27, -4.7549 octaves, 9.6898 Hz. Guide tone : 224, 7.8074 octaves, 58604.127 Hz. Exponens Consonantiae : 6.048000E+03, 12.56224 octaves Euler's gradus suavitatis : 18 Sum of Mann's harmonic distance : 60.5, average 20.16667 Mersenne's string divisions : 22715 Sum of van Prooijen's expressibility: 3.33985, average 1.11328 Sum of Tenney's harmonic distance : 6.89422, average 2.29807 Vogel's harmonic complexity : 7.33333 Wille's k value : 4 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 20.81257, average 3.46876 Lattice compactness (without 2's) : 12.39835, average 2.06639 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 2 .. 5 3.00000 9 3: -3 ..-1 -2.33333 7 2 7: 0 .. 1 0.33333 1 1 Average exponent except 2's :-6 / 3 =-2.00000 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 10 19| Scale is JI-epimorphic with val: <7 11 20| = patent Scale is weakly epimorphic with val: <8 11 20|
FIT/MODE
3: 0 2 1 N G T3 SD: 42.4268 c. M: 62.9609 c. 4: 0 2 2 P M DE S SD: 44.7184 c. M: 62.9609 c. 5: 1 2 2 SP M ME S SD: 21.3315 c. M:-36.6481 c. 6: 1 3 2 P T3 SD: 24.7514 c. M:-37.8950 c. 7: 1 3 3 SP M DE S SD: 7.2576 c. M: 9.5379 c. 15: 2 7 6 SP T3 SD: 3.3607 c. M:-4.6920 c. 17: 2 8 7 SP T3 SD: 2.6100 c. M: 4.3674 c. 24: 3 11 10 SP T3 SD: 2.1229 c. M: 3.6087 c. 32: 4 15 13 SP T3 SD: 0.9986 c. M:-1.5792 c. 39: 5 18 16 SP T3 SD: 0.5678 c. M:-0.8910 c. 56: 7 26 23 SP T3 SD: 0.5515 c. M: 0.7053 c. 71: 9 33 29 SP T3 SD: 0.2960 c. M:-0.4832 c. 110: 14 51 45 SP T3 SD: 0.2640 c. M:-0.4266 c. 127: 16 59 52 SP T3 SD: 0.1244 c. M: 0.2151 c. 166: 21 77 68 SP T3 SD: 0.0677 c. M: 0.1084 c. 237: 30 110 97 SP T3 SD: 0.0621 c. M:-0.0828 c. 293: 37 136 120 SP T3 SD: 0.0552 c. M: 0.0678 c. 364: 46 169 149 SP T3 SD: 0.0261 c. M:-0.0399 c. 530: 67 246 217 SP T3 SD: 0.0038 c. M: 0.0065 c. 1424: 180 661 583 SP T3 SD: 0.0045 c. M: 0.0058 c. 1954: 247 907 800 SP T3 SD: 0.0028 c. M: 0.0043 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: 92.1787 cents 5 x 6:7 S SD: 43.5810 cents 6 x 7:8 S SD: 13.6320 cents 7 x 8:9 S SD: 44.5201 cents 8 x 9:11 SD: 52.3893 cents 9 x 11:12 SD: 26.6365 cents 14:15:17:19 SD: 25.5879 cents 15:16:18:20 S SD: 17.7672 cents 16:17:19:21 SD: 16.7275 cents 17:18:20:23 SD: 15.2664 cents 18:19:21:24 SD: 13.6718 cents 20:21:24:27 S SD: 12.4167 cents 21:22:25:28 SD: 6.3978 cents 27:28:32:36 S SD: 0.0000 cents