Scala analysis: 418_D8
Diatonic tetrachord 26/25 * 44/39 * 25/22
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 26/25 67.900234 tridecimal 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: 26/25 67.9002 tridecimal 1/3-tone 2: 44/39 208.8353 3: 25/22 221.3095 undecimal acute whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 26/25 67.900 cents tridecimal 1/3-tone 1: 1 44/39 208.835 cents 1: 1 25/22 221.309 cents undecimal acute whole tone 2: 1 88/75 276.736 cents 2: 1 13/11 289.210 cents tridecimal minor third 2: 1 50/39 430.145 cents 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 : 67.9 276.7 498.0 67.9 : 208.8 430.1 498.0 276.7: 221.3 289.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 67.9002 .. 221.3095 cents 625/572, 153.4093 cents 26/25, 67.9002 cents 2: 276.7355 .. 430.1448 cents 625/572, 153.4093 cents 1936/1875, 55.4260 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 26/25, 67.9002 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 25/22, 221.3095 cents Average / Smallest step : 2.444984 Largest / Average step : 1.333069 Largest / Smallest step : 3.259333 Median interval of one step : 44/39, 208.8353 cents, amount: 1 Least squares average step : 151.10759 cents, oct.: 453.32277 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1159-tone equal temperament with octave 4/3 degrees: 158 644 1159 Least number of segments generator : 580 of 249.237 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 919 of 394.912 cents and inv. generated superset size: 32 = 29 more = 1066.667% 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 55.42603 cents Scale diversity : 0.848620 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.383954 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 : 975/968, 12.4742 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 140.9350 cents: 1 -- Rational properties -- Prime limit : 13 Odd number limit : 75 (O: 25 U: 75) Highest odd numerator or denominator: 75 Scale harmonicity : 0.017006 Average absolute harmonicity : 0.089795 Specific harmonicity : 0.082955 Fundamental : 1/75, -6.2288 octaves, 3.4883 Hz. Guide tone : 1144, 10.1599 octaves, 299299.647 Hz. Exponens Consonantiae : 8.580000E+04, 16.38869 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 110.5, average 36.83333 Mersenne's string divisions : 58191 Sum of van Prooijen's expressibility: 3.75012, average 1.25004 Sum of Tenney's harmonic distance : 7.71164, average 2.57055 Vogel's harmonic complexity : 14.33333 Wille's k value : 19 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 16.29953, average 2.71659 Lattice compactness (without 2's) : 12.10317, average 2.01719 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -1 .. 0 -0.66667 2 1 5: -2 .. 0 -1.33333 4 11: 0 .. 1 0.33333 1 1 13: 0 .. 1 0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 15 23 27| Scale is weakly epimorphic with val: <6 10 15 25 25| Scale is weakly epimorphic with val: <6 10 15 25 28| Scale is weakly epimorphic with val: <6 10 15 26 27| Scale is weakly epimorphic with val: <6 10 16 25 29| Scale is weakly epimorphic with val: <6 10 16 27 27| Scale is weakly epimorphic with val: <6 10 16 27 30| Scale is weakly epimorphic with val: <6 11 15 25 27| Scale is weakly epimorphic with val: <6 11 15 26 26| Scale is weakly epimorphic with val: <6 11 15 26 29| Scale is weakly epimorphic with val: <6 11 16 24 29| Scale is weakly epimorphic with val: <6 11 16 27 29| Scale is weakly epimorphic with val: <7 10 15 24 26| Scale is weakly epimorphic with val: <7 10 16 23 28| Scale is weakly epimorphic with val: <7 10 16 24 27| Scale is weakly epimorphic with val: <7 10 16 24 30| Scale is weakly epimorphic with val: <7 10 16 26 28| Scale is weakly epimorphic with val: <7 10 17 25 30| Scale is weakly epimorphic with val: <7 10 17 26 26| Scale is weakly epimorphic with val: <7 10 17 26 29| Scale is weakly epimorphic with val: <7 11 15 24 25| Scale is weakly epimorphic with val: <7 11 15 24 28| Scale is weakly epimorphic with val: <7 11 15 25 27| Scale is weakly epimorphic with val: <7 11 15 25 30| Scale is weakly epimorphic with val: <7 11 15 27 28| Scale is weakly epimorphic with val: <7 11 16 23 27| Scale is weakly epimorphic with val: <7 11 16 23 30| Scale is JI-epimorphic with val: <7 11 16 24 26| Scale is weakly epimorphic with val: <7 11 16 24 29| Scale is weakly epimorphic with val: <7 11 16 26 27| Scale is weakly epimorphic with val: <7 11 16 26 30| Scale is weakly epimorphic with val: <7 11 16 27 29| Scale is weakly epimorphic with val: <7 11 17 23 25| Scale is weakly epimorphic with val: <7 11 17 23 28| Scale is weakly epimorphic with val: <7 11 17 25 26| Scale is weakly epimorphic with val: <7 11 17 25 29| Scale is JI-epimorphic with val: <7 11 17 26 28| Scale is weakly epimorphic with val: <7 11 18 24 25| Scale is weakly epimorphic with val: <7 11 18 24 28| Scale is weakly epimorphic with val: <7 11 18 25 27| Scale is weakly epimorphic with val: <7 11 18 25 30| Scale is weakly epimorphic with val: <7 11 18 27 28| Scale is weakly epimorphic with val: <7 11 19 23 27| Scale is weakly epimorphic with val: <7 11 19 23 30| Scale is weakly epimorphic with val: <7 11 19 24 26| Scale is weakly epimorphic with val: <7 11 19 24 29| Scale is weakly epimorphic with val: <7 11 19 26 27| Scale is weakly epimorphic with val: <7 11 19 26 30| Scale is weakly epimorphic with val: <7 11 19 27 29| Scale is weakly epimorphic with val: <7 12 15 24 27| Scale is weakly epimorphic with val: <7 12 15 24 30| Scale is weakly epimorphic with val: <7 12 15 25 26| Scale is weakly epimorphic with val: <7 12 16 24 28| Scale is weakly epimorphic with val: <7 12 16 26 26| Scale is weakly epimorphic with val: <7 12 16 26 29| Scale is weakly epimorphic with val: <7 12 16 27 28| Scale is weakly epimorphic with val: <7 12 17 23 30| Scale is weakly epimorphic with val: <7 12 17 26 30| Scale is weakly epimorphic with val: <8 11 15 24 25| Scale is weakly epimorphic with val: <8 11 16 23 27| Scale is weakly epimorphic with val: <8 11 16 26 27| Scale is weakly epimorphic with val: <8 11 17 24 27| Scale is weakly epimorphic with val: <8 11 17 24 30| Scale is weakly epimorphic with val: <8 11 17 25 29| Scale is weakly epimorphic with val: <8 11 18 26 26| Scale is weakly epimorphic with val: <8 11 18 26 29| Scale is weakly epimorphic with val: <8 12 15 23 25| Scale is weakly epimorphic with val: <8 12 16 23 26| Scale is weakly epimorphic with val: <8 12 16 23 29| Scale is weakly epimorphic with val: <8 12 16 25 27| Scale is weakly epimorphic with val: <8 12 17 24 29| Scale is weakly epimorphic with val: <8 12 17 25 25| Scale is weakly epimorphic with val: <8 12 17 25 28| Scale is weakly epimorphic with val: <8 12 17 27 29| Scale is weakly epimorphic with val: <8 12 18 27 27| Scale is weakly epimorphic with val: <8 12 18 27 30|
FIT/MODE
3: 0 2 1 N G T3 SD: 50.5566 c. M: 67.9002 c. 4: 0 2 2 P M DE S SD: 42.3417 c. M: 67.9002 c. 5: 1 2 2 SP M ME S SD: 22.3120 c. M:-31.7088 c. 6: 1 2 3 P T3 SD: 18.2231 c. M: 27.7130 c. 7: 1 3 3 SP M DE S SD: 4.9113 c. M:-7.8616 c. 16: 2 7 7 SP M DE S SD: 3.8089 c. M: 5.6446 c. 22: 3 9 10 SP T3 SD: 2.9298 c. M: 5.0746 c. 23: 3 10 10 SP M DE S SD: 3.2335 c. M:-4.7682 c. 29: 4 12 13 SP T3 SD: 1.2170 c. M: 1.9521 c. 36: 5 15 16 SP T3 SD: 0.7352 c. M:-1.2727 c. 52: 7 22 23 SP T3 SD: 0.7688 c. M:-1.0204 c. 74: 10 31 33 SP T3 SD: 0.5724 c. M: 0.7917 c. 81: 11 34 36 SP T3 SD: 0.1548 c. M: 0.2645 c. 117: 16 49 52 SP T3 SD: 0.1230 c. M:-0.2085 c. 198: 27 83 88 SP T3 SD: 0.0268 c. M: 0.0438 c. 477: 65 200 212 SP T3 SD: 0.0315 c. M: 0.0438 c. 675: 92 283 300 SP T3 SD: 0.0275 c. M: 0.0438 c. 682: 93 286 303 SP T3 SD: 0.0232 c. M:-0.0373 c. 763: 104 320 339 SP T3 SD: 0.0186 c. M:-0.0287 c. 880: 120 369 391 SP T3 SD: 0.0140 c. M:-0.0190 c. 961: 131 403 427 SP T3 SD: 0.0093 c. M:-0.0137 c. 1078: 147 452 479 SP T3 SD: 0.0097 c. M:-0.0150 c. 1159: 158 486 515 SP T3 SD: 0.0035 c. M: 0.0045 c. 1357: 185 569 603 SP T3 SD: 0.0020 c. M: 0.0031 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: 30.7583 cents 12:13:14:16 S SD: 23.7859 cents 15:16:18:20 S SD: 19.5358 cents 16:17:19:21 SD: 16.8263 cents 17:18:20:23 SD: 13.4351 cents 18:19:21:24 SD: 9.1769 cents 22:23:26:29 SD: 8.3606 cents 23:24:27:31 SD: 6.5357 cents 24:25:28:32 SD: 3.4156 cents 45:47:53:60 SD: 3.2888 cents 51:53:60:68 SD: 1.6013 cents 75:78:88:100 SD: 0.0000 cents