Scala analysis: 417_D8
Diatonic tetrachord 28/27 * 198/175 * 25/22
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: 88/75 276.735514 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 25/22 221.3095 undecimal acute whole tone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 198/175 213.7746 3: 25/22 221.3095 undecimal acute whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 198/175 213.775 cents 1: 1 25/22 221.309 cents undecimal acute whole tone 2: 1 88/75 276.736 cents 2: 1 350/297 284.270 cents 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 : 63.0 276.7 498.0 63.0 : 213.8 435.1 498.0 276.7: 221.3 284.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 221.3095 cents 675/616, 158.3486 cents 28/27, 62.9609 cents 2: 276.7355 .. 435.0841 cents 675/616, 158.3486 cents 1936/1875, 55.4260 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 : 25/22, 221.3095 cents Average / Smallest step : 2.636795 Largest / Average step : 1.333069 Largest / Smallest step : 3.515030 Median interval of one step : 198/175, 213.7746 cents, amount: 1 Least squares average step : 150.75478 cents, oct.: 452.26434 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1321-tone equal temperament with octave 4/3 degrees: 167 734 1321 Least number of segments generator : 661 of 249.211 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1073 of 404.544 cents and inv. generated superset size: 36 = 33 more = 1200.000% 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 55.42603 cents Scale diversity : 0.784279 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.364119 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 : 4375/4356, 7.5349 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major 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% Limited inverse transpositions with margin 150.8137 cents: 1 -- Rational properties -- Prime limit : 11 Odd number limit : 297 (O: 175 U: 297) Highest odd numerator or denominator: 75 Scale harmonicity : 0.019132 Average absolute harmonicity : 0.096955 Specific harmonicity : 0.102039 Fundamental : 1/675, -9.3987 octaves, 0.3876 Hz. Guide tone : 616, 9.2668 octaves, 161161.348 Hz. Exponens Consonantiae : 4.158000E+05, 18.66553 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 112.5, average 37.50000 Mersenne's string divisions : 62755 Sum of van Prooijen's expressibility: 3.78355, average 1.26118 Sum of Tenney's harmonic distance : 7.77725, average 2.59242 Vogel's harmonic complexity : 19.00000 Wille's k value : 112 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 17.85289, average 2.97548 Lattice compactness (without 2's) : 14.24618, average 2.37436 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -3 ..-1 -1.66667 5 1 5: -2 .. 0 -0.66667 2 7: 0 .. 1 0.33333 1 1 11: 0 .. 1 0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 15 19 25| Scale is weakly epimorphic with val: <6 10 15 21 23| Scale is weakly epimorphic with val: <6 10 15 21 26| Scale is weakly epimorphic with val: <6 10 15 22 25| Scale is weakly epimorphic with val: <6 10 16 19 27| Scale is weakly epimorphic with val: <6 10 16 21 25| Scale is weakly epimorphic with val: <6 10 16 22 27| Scale is weakly epimorphic with val: <6 10 17 21 24| Scale is weakly epimorphic with val: <6 10 17 21 27| Scale is weakly epimorphic with val: <6 10 18 21 23| Scale is weakly epimorphic with val: <6 10 18 21 26| Scale is weakly epimorphic with val: <6 10 19 21 25| Scale is weakly epimorphic with val: <6 11 15 20 26| Scale is weakly epimorphic with val: <7 10 15 19 24| Scale is weakly epimorphic with val: <7 10 15 19 27| Scale is weakly epimorphic with val: <7 10 16 18 24| Scale is weakly epimorphic with val: <7 10 16 19 23| Scale is weakly epimorphic with val: <7 10 16 19 26| Scale is weakly epimorphic with val: <7 10 16 21 24| Scale is weakly epimorphic with val: <7 10 17 18 26| Scale is weakly epimorphic with val: <7 10 17 19 25| Scale is weakly epimorphic with val: <7 10 17 21 26| Scale is weakly epimorphic with val: <7 10 18 19 24| Scale is weakly epimorphic with val: <7 10 18 19 27| Scale is weakly epimorphic with val: <7 10 19 19 23| Scale is weakly epimorphic with val: <7 10 19 19 26| Scale is weakly epimorphic with val: <7 11 15 18 24| Scale is weakly epimorphic with val: <7 11 15 18 27| Scale is weakly epimorphic with val: <7 11 15 20 25| Scale is weakly epimorphic with val: <7 11 15 21 24| Scale is weakly epimorphic with val: <7 11 15 21 27| Scale is weakly epimorphic with val: <7 11 16 18 23| Scale is weakly epimorphic with val: <7 11 16 18 26| Scale is JI-epimorphic with val: <7 11 16 20 24| Scale is weakly epimorphic with val: <7 11 16 20 27| Scale is weakly epimorphic with val: <7 11 16 21 23| Scale is weakly epimorphic with val: <7 11 16 21 26| Scale is weakly epimorphic with val: <7 11 17 18 25| Scale is weakly epimorphic with val: <7 11 17 20 23| Scale is JI-epimorphic with val: <7 11 17 20 26| Scale is weakly epimorphic with val: <7 11 17 21 25| Scale is weakly epimorphic with val: <7 11 18 18 24| Scale is weakly epimorphic with val: <7 11 18 18 27| Scale is weakly epimorphic with val: <7 11 18 20 25| Scale is weakly epimorphic with val: <7 11 18 21 24| Scale is weakly epimorphic with val: <7 11 18 21 27| Scale is weakly epimorphic with val: <7 11 19 20 24| Scale is weakly epimorphic with val: <7 11 19 20 27| Scale is weakly epimorphic with val: <7 11 19 21 23| Scale is weakly epimorphic with val: <7 11 19 21 26| Scale is weakly epimorphic with val: <7 12 15 20 24| Scale is weakly epimorphic with val: <7 12 16 20 26| Scale is weakly epimorphic with val: <8 11 15 20 24| Scale is weakly epimorphic with val: <8 11 15 20 27| Scale is weakly epimorphic with val: <8 11 16 20 23| Scale is weakly epimorphic with val: <8 11 16 20 26| Scale is weakly epimorphic with val: <8 11 17 18 24| Scale is weakly epimorphic with val: <8 11 17 20 25| Scale is weakly epimorphic with val: <8 11 17 21 24| Scale is weakly epimorphic with val: <8 11 18 18 26| Scale is weakly epimorphic with val: <8 11 18 20 24| Scale is weakly epimorphic with val: <8 11 18 20 27| Scale is weakly epimorphic with val: <8 11 18 21 26| Scale is weakly epimorphic with val: <8 11 19 20 23| Scale is weakly epimorphic with val: <8 11 19 20 26| Scale is weakly epimorphic with val: <8 12 16 19 23| Scale is weakly epimorphic with val: <8 12 16 22 23| Scale is weakly epimorphic with val: <8 12 17 19 25| Scale is weakly epimorphic with val: <8 12 17 22 25| Scale is weakly epimorphic with val: <8 12 18 19 27| Scale is weakly epimorphic with val: <8 12 18 22 27|
FIT/MODE
3: 0 1 2 N G T3 SD: 73.5371 c. M: 110.7205 c. 4: 0 2 2 P M DE S SD: 39.7160 c. M: 62.9609 c. 5: 1 2 2 SP M ME S SD: 24.7057 c. M:-36.6481 c. 6: 1 2 3 P T3 SD: 19.7474 c. M: 27.7130 c. 7: 1 3 3 SP M DE S SD: 6.5537 c. M:-8.1884 c. 9: 1 4 4 SP M DE S SD: 4.4010 c. M: 7.6226 c. 16: 2 7 7 SP M DE S SD: 2.0131 c. M:-3.4148 c. 25: 3 11 11 SP M DE S SD: 2.2300 c. M: 3.1955 c. 31: 4 13 14 SP T3 SD: 2.2180 c. M: 3.6141 c. 38: 5 16 17 SP T3 SD: 1.7187 c. M:-2.5713 c. 40: 5 17 18 SP T3 SD: 1.6731 c. M: 2.8108 c. 47: 6 20 21 SP T3 SD: 0.7906 c. M: 1.2213 c. 56: 7 24 25 SP T3 SD: 0.7217 c. M: 1.0320 c. 63: 8 27 28 SP T3 SD: 0.1653 c. M:-0.2829 c. 135: 17 58 60 SP T3 SD: 0.1432 c. M: 0.2441 c. 198: 25 85 88 SP T3 SD: 0.0509 c. M: 0.0764 c. 261: 33 112 116 SP T3 SD: 0.0260 c. M: 0.0438 c. 459: 58 197 204 SP T3 SD: 0.0298 c. M: 0.0438 c. 720: 91 309 320 SP T3 SD: 0.0265 c. M: 0.0438 c. 736: 93 316 327 SP T3 SD: 0.0245 c. M:-0.0313 c. 799: 101 343 355 SP T3 SD: 0.0149 c. M:-0.0254 c. 862: 109 370 383 SP T3 SD: 0.0153 c. M:-0.0204 c. 997: 126 428 443 SP T3 SD: 0.0126 c. M: 0.0184 c. 1060: 134 455 471 SP T3 SD: 0.0048 c. M:-0.0084 c. 1321: 167 567 587 SP T3 SD: 0.0015 c. M: 0.0020 c. 2381: 301 1022 1058 SP T3 SD: 0.0016 c. M:-0.0026 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: 109.5782 cents 5 x 6:7 S SD: 46.4983 cents 6 x 7:8 S SD: 4.9323 cents 7 x 8:9 S SD: 38.8585 cents 8 x 9:11 SD: 45.1153 cents 9 x 11:12 SD: 35.3362 cents 11:12:13:15 SD: 32.2428 cents 12:13:14:16 S SD: 25.4175 cents 15:16:18:20 S SD: 20.7959 cents 16:17:19:21 SD: 18.0695 cents 17:18:20:23 SD: 14.7411 cents 18:19:21:24 SD: 10.7303 cents 21:22:25:28 SD: 10.2170 cents 22:23:26:29 SD: 9.0857 cents 23:24:27:31 SD: 7.1952 cents 24:25:28:32 SD: 4.1737 cents 30:31:35:40 SD: 3.8827 cents 51:53:60:68 SD: 1.9599 cents 57:59:67:76 SD: 1.4997 cents 81:84:95:108 SD: 0.2429 cents 294:305:345:392 SD: 0.2207 cents 300:311:352:400 SD: 0.2061 cents 375:389:440:500 SD: 0.1649 cents 432:448:507:576 SD: 0.1366 cents 513:532:602:684 SD: 0.0767 cents 594:616:697:792 SD: 0.0331 cents