Scala analysis: 397_D6
Diatonic tetrachord 16/15 * 35/32 * 8/7, Vogel
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: 7/6 266.870906 septimal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 16/15 111.7313 minor diatonic semitone 2: 35/32 155.1396 septimal neutral second 3: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 35/32 155.140 cents septimal neutral second 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 128/105 342.905 cents septimal 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 : 111.7 266.9 498.0 111.7: 155.1 386.3 498.0 266.9: 231.2 342.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 231.1741 cents 15/14, 119.4428 cents 16/15, 111.7313 cents 2: 266.8709 .. 386.3137 cents 15/14, 119.4428 cents 49/48, 35.6968 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 : 8/7, 231.1741 cents Average / Smallest step : 1.485842 Largest / Average step : 1.392489 Largest / Smallest step : 2.069018 Median interval of one step : 35/32, 155.1396 cents, amount: 1 Least squares average step : 152.82915 cents, oct.: 458.48745 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1618-tone equal temperament with octave 4/3 degrees: 363 867 1618 Least number of segments generator : 811 of 249.638 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1245 of 383.230 cents and inv. generated superset size: 28 = 25 more = 933.333% 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 35.69681 cents Scale diversity : 1.271667 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.520353 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 : 49/48, 35.6968 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing 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 Scale is n-1 differentially coherent in interval class 2 -- Rational properties -- Prime limit : 7 Odd number limit : 105 (O: 35 U: 105) Highest odd numerator or denominator: 15 Scale harmonicity : 0.041064 Average absolute harmonicity : 0.120829 Specific harmonicity : 0.213170 Fundamental : 1/30, -4.9069 octaves, 8.7209 Hz. Guide tone : 112, 6.8074 octaves, 29302.063 Hz. Exponens Consonantiae : 3.360000E+03, 11.71425 octaves Euler's gradus suavitatis : 18 Sum of Mann's harmonic distance : 25.5, average 8.50000 Mersenne's string divisions : 2821 Sum of van Prooijen's expressibility: 2.49831, average 0.83277 Sum of Tenney's harmonic distance : 5.08264, average 1.69421 Vogel's harmonic complexity : 8.33333 Wille's k value : 17 Wilson's harmonic complexity : 15 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 18.80526, average 3.13421 Lattice compactness (without 2's) : 7.24264, average 1.20711 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.66667 7 3: -1 ..-1 -1.00000 3 1 5: -1 .. 0 -0.33333 1 1 7: 0 .. 1 0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 16 19| Scale is weakly epimorphic with val: <6 10 19 19| Scale is weakly epimorphic with val: <6 11 17 20| Scale is weakly epimorphic with val: <7 10 15 19| Scale is weakly epimorphic with val: <7 10 15 22| Scale is weakly epimorphic with val: <7 10 16 20| Scale is weakly epimorphic with val: <7 10 19 20| Scale is weakly epimorphic with val: <7 11 15 19| Scale is weakly epimorphic with val: <7 11 15 22| Scale is JI-epimorphic with val: <7 11 16 20| Scale is weakly epimorphic with val: <7 11 18 19| Scale is weakly epimorphic with val: <7 11 18 22| Scale is weakly epimorphic with val: <7 11 19 20| Scale is weakly epimorphic with val: <7 12 15 22| Scale is weakly epimorphic with val: <7 12 18 22| Scale is weakly epimorphic with val: <8 11 17 22| Scale is weakly epimorphic with val: <8 11 18 20| Scale is weakly epimorphic with val: <8 12 17 19| Scale is weakly epimorphic with val: <8 12 17 22|
FIT/MODE
3: 1 1 1 SP B ME I SD: 48.9640 c. M:-65.1591 c. 4: 1 1 2 P M ME S SD: 12.6740 c. M: 17.8484 c. 9: 2 3 4 SP T3 SD: 5.7026 c. M:-9.8208 c. 13: 3 4 6 SP T3 SD: 1.9969 c. M:-3.2022 c. 32: 7 10 15 SP T3 SD: 2.0792 c. M: 2.7839 c. 41: 9 13 19 SP T3 SD: 1.4047 c. M: 2.4043 c. 45: 10 14 21 SP T3 SD: 0.9429 c. M: 1.2469 c. 54: 12 17 25 SP T3 SD: 0.6999 c. M: 1.0546 c. 58: 13 18 27 SP T3 SD: 0.3937 c. M: 0.6744 c. 71: 16 22 33 SP T3 SD: 0.3422 c. M:-0.5042 c. 112: 25 35 52 SP T3 SD: 0.3255 c. M: 0.5605 c. 125: 28 39 58 SP T3 SD: 0.1084 c. M: 0.1692 c. 183: 41 57 85 SP T3 SD: 0.1249 c. M: 0.1583 c. 196: 44 61 91 SP T3 SD: 0.0557 c. M:-0.0747 c. 321: 72 100 149 SP T3 SD: 0.0121 c. M: 0.0203 c. 838: 188 261 389 SP T3 SD: 0.0108 c. M: 0.0186 c. 1159: 260 361 538 SP T3 SD: 0.0090 c. M: 0.0150 c. 1297: 291 404 602 SP T3 SD: 0.0082 c. M:-0.0120 c. 1618: 363 504 751 SP T3 SD: 0.0043 c. M:-0.0056 c. 1939: 435 604 900 SP T3 SD: 0.0020 c. M:-0.0031 c. 2260: 507 704 1049 SP T3 SD: 0.0015 c. M:-0.0019 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 x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 48.7680 cents 6 x 7:8 S SD: 0.0000 cents 7 x 8:9 S SD: 36.1882 cents 8 x 9:11 SD: 41.2374 cents 9:10:11:12 H SD: 35.7162 cents 10:11:12:13 H SD: 28.1617 cents 11:12:13:15 SD: 19.7943 cents 12:13:14:16 S SD: 8.9471 cents 18:19:21:24 SD: 6.0428 cents 29:31:34:39 SD: 5.8414 cents 30:32:35:40 SD: 0.0000 cents