Scala analysis: 392_D6
Diatonic tetrachord 21/20 * 10/9 * 8/7, Ptolemy
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor 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: 21/20 84.4672 minor semitone 2: 10/9 182.4037 minor whole tone 3: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 21/20 84.467 cents minor semitone 1: 1 10/9 182.404 cents minor whole tone 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 6/5 315.641 cents minor third 2: 1 80/63 413.578 cents wide 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 : 84.5 266.9 498.0 84.5 : 182.4 413.6 498.0 266.9: 231.2 315.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 231.1741 cents 160/147, 146.7069 cents 21/20, 84.4672 cents 2: 266.8709 .. 413.5778 cents 160/147, 146.7069 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 21/20, 84.4672 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 1.965438 Largest / Average step : 1.392489 Largest / Smallest step : 2.736851 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 150.88171 cents, oct.: 452.64514 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1256-tone equal temperament with octave 4/3 degrees: 213 673 1256 Least number of segments generator : 629 of 249.419 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 743 of 294.624 cents and inv. generated superset size: 56 = 53 more = 1866.667% 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 35.69681 cents Scale diversity : 1.087018 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.410869 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 All steps are superparticular (epimoric) 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 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 -- Rational properties -- Prime limit : 7 Odd number limit : 63 (O: 21 U: 63) Highest odd numerator or denominator: 21 Scale harmonicity : 0.038433 Average absolute harmonicity : 0.110930 Specific harmonicity : 0.173895 Fundamental : 1/60, -5.9069 octaves, 4.3604 Hz. Guide tone : 84, 6.3923 octaves, 21976.547 Hz. Exponens Consonantiae : 5.040000E+03, 12.29921 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 30.5, average 10.16667 Mersenne's string divisions : 3731 Sum of van Prooijen's expressibility: 2.64444, average 0.88148 Sum of Tenney's harmonic distance : 5.32568, average 1.77523 Vogel's harmonic complexity : 11.66667 Wille's k value : 31 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 16.91605, average 2.81934 Lattice compactness (without 2's) : 9.83182, average 1.63864 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.33333 5 3: -1 .. 1 -0.33333 3 1 5: -1 .. 0 -0.33333 1 7: 0 .. 1 0.66667 2 2 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 15 20| 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 15 19| Scale is weakly epimorphic with val: <6 11 17 20| Scale is weakly epimorphic with val: <6 11 18 22| Scale is weakly epimorphic with val: <7 10 15 22| Scale is weakly epimorphic with val: <7 10 17 20| Scale is JI-epimorphic with val: <7 11 16 20| Scale is weakly epimorphic with val: <7 11 17 19| Scale is weakly epimorphic with val: <7 11 17 22| Scale is weakly epimorphic with val: <7 11 19 20| Scale is weakly epimorphic with val: <7 12 15 20| Scale is weakly epimorphic with val: <7 12 16 22| Scale is weakly epimorphic with val: <7 12 19 22| Scale is weakly epimorphic with val: <8 11 16 22| Scale is weakly epimorphic with val: <8 11 19 22| Scale is weakly epimorphic with val: <8 12 15 22|
FIT/MODE
3: 0 1 2 N G T3 SD: 75.9531 c. M: 100.8559 c. 4: 1 1 2 P M ME S SD: 25.3120 c. M:-40.0441 c. 5: 1 2 2 SP M ME S SD: 20.4162 c. M:-31.9561 c. 6: 1 2 3 P T3 SD: 10.3392 c. M: 17.8484 c. 7: 1 3 3 SP M DE S SD: 12.8009 c. M:-17.7262 c. 11: 2 4 5 SP T3 SD: 4.4717 c. M:-6.0864 c. 17: 3 6 8 SP T3 SD: 2.7054 c. M:-3.4231 c. 24: 4 9 11 SP T3 SD: 1.8762 c. M:-2.9035 c. 30: 5 11 14 SP T3 SD: 1.1084 c. M: 1.4597 c. 41: 7 15 19 SP T3 SD: 0.3907 c. M:-0.5649 c. 71: 12 26 33 SP T3 SD: 0.2460 c. M: 0.3116 c. 112: 19 41 52 SP T3 SD: 0.0376 c. M: 0.0611 c. 584: 99 214 271 SP T3 SD: 0.0415 c. M:-0.0607 c. 601: 102 220 279 SP T3 SD: 0.0389 c. M:-0.0596 c. 696: 118 255 323 SP T3 SD: 0.0289 c. M:-0.0411 c. 737: 125 270 342 SP T3 SD: 0.0345 c. M:-0.0596 c. 767: 130 281 356 SP T3 SD: 0.0309 c. M: 0.0528 c. 808: 137 296 375 SP T3 SD: 0.0199 c. M:-0.0270 c. 920: 156 337 427 SP T3 SD: 0.0132 c. M:-0.0163 c. 1032: 175 378 479 SP T3 SD: 0.0082 c. M: 0.0119 c. 1144: 194 419 531 SP T3 SD: 0.0050 c. M: 0.0085 c. 1256: 213 460 583 SP T3 SD: 0.0042 c. M: 0.0057 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 x 11:12 SD: 40.2685 cents 10:11:12:13 H SD: 34.6184 cents 11:12:13:15 SD: 26.6482 cents 12:13:14:16 S SD: 18.0352 cents 16:17:19:21 SD: 15.2827 cents 17:18:20:23 SD: 10.8451 cents 18:19:21:24 SD: 3.0453 cents 42:44:49:56 SD: 1.3101 cents 60:63:70:80 S SD: 0.0000 cents