Scala analysis: 416_D8
Diatonic tetrachord 22/21 * 25/22 * 28/25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 22/21 80.537035 undecimal minor semitone 2: 25/21 301.846520 BP second, quasi-equal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 28/25 196.1985 middle second 1: 22/21 80.5370 undecimal minor semitone 2: 25/22 221.3095 undecimal acute whole tone 3: 28/25 196.1985 middle second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 28/25 196.198 cents middle second 1: 1 25/22 221.309 cents undecimal acute whole tone 2: 1 88/75 276.736 cents 2: 1 25/21 301.847 cents BP second, quasi-equal minor third 2: 1 14/11 417.508 cents undecimal diminished fourth or 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 : 80.5 301.8 498.0 80.5 : 221.3 417.5 498.0 301.8: 196.2 276.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 221.3095 cents 525/484, 140.7725 cents 22/21, 80.5370 cents 2: 276.7355 .. 417.5080 cents 525/484, 140.7725 cents 1936/1875, 55.4260 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 25/22, 221.3095 cents Average / Smallest step : 2.061350 Largest / Average step : 1.333069 Largest / Smallest step : 2.747922 Median interval of one step : 28/25, 196.1985 cents, amount: 1 Least squares average step : 155.59751 cents, oct.: 466.79252 cents Scale is strictly proper Scale has trivalence property 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 55.42603 cents Scale diversity : 1.007423 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.434700 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 : 625/616, 25.1110 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle 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 140.7725 cents: 1 -- Rational properties -- Prime limit : 11 Odd number limit : 75 (O: 25 U: 75) Highest odd numerator or denominator: 25 Scale harmonicity : 0.021770 Average absolute harmonicity : 0.094745 Specific harmonicity : 0.107318 Fundamental : 1/21, -4.3923 octaves, 12.4584 Hz. Guide tone : 1100, 10.1033 octaves, 287788.122 Hz. Exponens Consonantiae : 2.310000E+04, 14.49561 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 48.0, average 16.00000 Mersenne's string divisions : 13846 Sum of van Prooijen's expressibility: 3.19728, average 1.06576 Sum of Tenney's harmonic distance : 6.46398, average 2.15466 Vogel's harmonic complexity : 10.33333 Wille's k value : 12 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 13.86710, average 2.31118 Lattice compactness (without 2's) : 11.06789, average 1.84465 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.00000 3 3: -1 ..-1 -1.00000 3 1 5: 0 .. 2 0.66667 2 7: -1 .. 0 -0.66667 2 1 11: 0 .. 1 0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 15 19 26| Scale is weakly epimorphic with val: <6 10 16 18 25| Scale is weakly epimorphic with val: <6 10 16 19 24| Scale is weakly epimorphic with val: <6 10 16 19 27| Scale is weakly epimorphic with val: <6 10 17 20 27| Scale is weakly epimorphic with val: <6 10 17 21 23| Scale is weakly epimorphic with val: <6 10 17 21 26| Scale is weakly epimorphic with val: <6 10 18 19 26| Scale is weakly epimorphic with val: <6 11 16 18 25| Scale is weakly epimorphic with val: <6 11 16 19 27| Scale is weakly epimorphic with val: <6 11 17 18 26| Scale is weakly epimorphic with val: <6 11 17 20 24| Scale is weakly epimorphic with val: <6 11 17 20 27| Scale is weakly epimorphic with val: <6 11 18 22 23| Scale is weakly epimorphic with val: <6 11 18 22 26| Scale is weakly epimorphic with val: <6 11 19 19 27| Scale is weakly epimorphic with val: <7 10 15 18 24| Scale is weakly epimorphic with val: <7 10 15 21 27| Scale is weakly epimorphic with val: <7 10 16 19 24| Scale is weakly epimorphic with val: <7 10 16 19 27| Scale is weakly epimorphic with val: <7 10 16 20 26| Scale is weakly epimorphic with val: <7 10 17 19 25| Scale is weakly epimorphic with val: <7 10 17 21 23| Scale is weakly epimorphic with val: <7 10 17 21 26| Scale is weakly epimorphic with val: <7 10 18 18 24| Scale is weakly epimorphic with val: <7 10 18 21 27| Scale is weakly epimorphic with val: <7 10 19 20 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 JI-epimorphic with val: <7 11 16 19 24| Scale is weakly epimorphic with val: <7 11 16 19 27| Scale is weakly epimorphic with val: <7 11 16 20 23| Scale is weakly epimorphic with val: <7 11 16 20 26| Scale is weakly epimorphic with val: <7 11 16 22 24| Scale is weakly epimorphic with val: <7 11 16 22 27| Scale is weakly epimorphic with val: <7 11 17 18 23| Scale is weakly epimorphic with val: <7 11 17 18 26| Scale is weakly epimorphic with val: <7 11 17 19 25| Scale is weakly epimorphic with val: <7 11 17 21 23| Scale is JI-epimorphic with val: <7 11 17 21 26| Scale is weakly epimorphic with val: <7 11 17 22 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 19 24| Scale is weakly epimorphic with val: <7 11 19 19 27| Scale is weakly epimorphic with val: <7 11 19 20 23| Scale is weakly epimorphic with val: <7 11 19 20 26| Scale is weakly epimorphic with val: <7 11 19 22 24| Scale is weakly epimorphic with val: <7 11 19 22 27| Scale is weakly epimorphic with val: <7 12 16 19 27| Scale is weakly epimorphic with val: <7 12 17 18 26| Scale is weakly epimorphic with val: <7 12 17 19 25| Scale is weakly epimorphic with val: <7 12 18 21 24| Scale is weakly epimorphic with val: <7 12 18 21 27| Scale is weakly epimorphic with val: <7 12 19 19 27| Scale is weakly epimorphic with val: <8 11 15 18 24| Scale is weakly epimorphic with val: <8 11 15 21 27| Scale is weakly epimorphic with val: <8 11 16 18 25| Scale is weakly epimorphic with val: <8 11 16 20 26| Scale is weakly epimorphic with val: <8 11 17 19 25| Scale is weakly epimorphic with val: <8 11 17 20 24| Scale is weakly epimorphic with val: <8 11 17 20 27| Scale is weakly epimorphic with val: <8 11 18 18 24| Scale is weakly epimorphic with val: <8 11 18 21 27| Scale is weakly epimorphic with val: <8 11 18 22 23| Scale is weakly epimorphic with val: <8 11 18 22 26| Scale is weakly epimorphic with val: <8 11 19 20 26| Scale is weakly epimorphic with val: <8 12 15 19 26| Scale is weakly epimorphic with val: <8 12 16 18 25| Scale is weakly epimorphic with val: <8 12 17 19 25| Scale is weakly epimorphic with val: <8 12 17 20 27| Scale is weakly epimorphic with val: <8 12 18 19 26| Scale is weakly epimorphic with val: <8 12 18 21 24| Scale is weakly epimorphic with val: <8 12 18 21 27|
FIT/MODE
3: 0 2 1 N G T3 SD: 49.6563 c. M: 80.5370 c. 4: 1 1 2 P M ME S SD: 39.6825 c. M: 52.8240 c. 5: 1 2 2 SP M ME S SD: 11.1484 c. M:-19.0720 c. 7: 1 3 3 SP M DE S SD: 11.3383 c. M: 17.2494 c. 11: 2 5 4 SP T3 SD: 10.4575 c. M:-15.0912 c. 12: 2 5 5 SP M DE S SD: 6.6896 c. M: 11.3203 c. 13: 2 6 5 SP T3 SD: 3.5062 c. M:-4.6427 c. 18: 3 8 7 SP T3 SD: 2.0351 c. M:-2.5143 c. 25: 4 11 10 SP T3 SD: 1.8111 c. M: 3.0195 c. 38: 6 17 15 SP T3 SD: 1.1199 c. M: 1.8984 c. 43: 7 19 17 SP T3 SD: 0.5118 c. M: 0.7030 c. 56: 9 25 22 SP T3 SD: 0.4217 c. M:-0.5379 c. 81: 13 36 32 SP T3 SD: 0.4755 c. M: 0.6039 c. 99: 16 44 39 SP T3 SD: 0.0259 c. M: 0.0449 c. 736: 119 327 290 SP T3 SD: 0.0251 c. M: 0.0421 c. 835: 135 371 329 SP T3 SD: 0.0231 c. M: 0.0372 c. 934: 151 415 368 SP T3 SD: 0.0219 c. M: 0.0334 c. 952: 154 423 375 SP T3 SD: 0.0188 c. M:-0.0291 c. 1051: 170 467 414 SP T3 SD: 0.0149 c. M:-0.0221 c. 1150: 186 511 453 SP T3 SD: 0.0117 c. M:-0.0163 c. 1249: 202 555 492 SP T3 SD: 0.0092 c. M:-0.0115 c. 1348: 218 599 531 SP T3 SD: 0.0072 c. M:-0.0101 c. 1447: 234 643 570 SP T3 SD: 0.0058 c. M:-0.0094 c. 1546: 250 687 609 SP T3 SD: 0.0050 c. M:-0.0087 c. 1645: 266 731 648 SP T3 SD: 0.0048 c. M:-0.0081 c. 1744: 282 775 687 SP T3 SD: 0.0051 c. M:-0.0076 c. 1843: 298 819 726 SP T3 SD: 0.0056 c. M:-0.0071 c. 1985: 321 882 782 SP T3 SD: 0.0053 c. M: 0.0087 c. 2084: 337 926 821 SP T3 SD: 0.0048 c. M: 0.0083 c. 2183: 353 970 860 SP T3 SD: 0.0047 c. M: 0.0080 c. 2282: 369 1014 899 SP T3 SD: 0.0048 c. M: 0.0077 c. 2381: 385 1058 938 SP T3 SD: 0.0051 c. M: 0.0074 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: 84.4672 cents 5 x 6:7 S SD: 42.7931 cents 6 x 7:8 S SD: 17.4878 cents 7 x 8:9 S SD: 47.3251 cents 8 x 10:11 S SD: 49.9317 cents 9:10:11:12 H SD: 37.1972 cents 10:11:12:13 H SD: 32.0523 cents 11:12:13:15 SD: 27.0542 cents 12:13:14:16 S SD: 22.5867 cents 14:15:17:19 SD: 20.0774 cents 15:16:18:20 S SD: 11.3694 cents 20:21:24:27 S SD: 8.6169 cents 21:22:25:28 SD: 0.0000 cents