Scala analysis: 398_D6
Diatonic tetrachord 35/34 * 17/15 * 8/7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 35/34 50.184211 septendecimal 1/4-tone 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: 35/34 50.1842 septendecimal 1/4-tone 2: 17/15 216.6867 septendecimal whole tone 3: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 35/34 50.184 cents septendecimal 1/4-tone 1: 1 17/15 216.687 cents septendecimal whole tone 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 20/17 281.358 cents septendecimal augmented second 2: 1 136/105 447.861 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 : 50.2 266.9 498.0 50.2 : 216.7 447.9 498.0 266.9: 231.2 281.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 50.1842 .. 231.1741 cents 272/245, 180.9899 cents 35/34, 50.1842 cents 2: 266.8709 .. 447.8608 cents 272/245, 180.9899 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 35/34, 50.1842 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 3.308112 Largest / Average step : 1.392489 Largest / Smallest step : 4.606510 Median interval of one step : 17/15, 216.6867 cents, amount: 1 Least squares average step : 148.43293 cents, oct.: 445.29879 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1995-tone equal temperament with octave 4/3 degrees: 201 1069 1995 Least number of segments generator : 998 of 249.147 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1868 of 466.340 cents and inv. generated superset size: 57 = 54 more = 1900.000% 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 35.69681 cents Scale diversity : 0.677693 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.273199 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 : 120/119, 14.4874 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 Limited inverse transpositions with margin 166.5025 cents: 1 -- Rational properties -- Prime limit : 17 Odd number limit : 105 (O: 35 U: 105) Highest odd numerator or denominator: 35 Scale harmonicity : 0.019058 Average absolute harmonicity : 0.102292 Specific harmonicity : 0.093369 Fundamental : 1/102, -6.6724 octaves, 2.5650 Hz. Guide tone : 140, 7.1293 octaves, 36627.579 Hz. Exponens Consonantiae : 1.428000E+04, 13.80171 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 44.5, average 14.83333 Mersenne's string divisions : 6279 Sum of van Prooijen's expressibility: 2.86629, average 0.95543 Sum of Tenney's harmonic distance : 5.77798, average 1.92599 Vogel's harmonic complexity : 19.66667 Wille's k value : 59 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 14.46800, average 2.41133 Lattice compactness (without 2's) : 8.87832, average 1.47972 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.00000 4 3: -1 .. 0 -0.66667 2 1 5: 0 .. 1 0.33333 1 7: 0 .. 1 0.66667 2 1 17: -1 .. 0 -0.33333 1 1 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 19 27| Scale is weakly epimorphic with val: <6 10 15 19 30| Scale is weakly epimorphic with val: <6 10 15 19 33| Scale is weakly epimorphic with val: <6 10 16 19 28| Scale is weakly epimorphic with val: <6 10 16 19 31| Scale is weakly epimorphic with val: <6 10 16 20 27| Scale is weakly epimorphic with val: <6 10 17 19 29| Scale is weakly epimorphic with val: <6 10 17 19 32| Scale is weakly epimorphic with val: <6 10 17 20 28| Scale is weakly epimorphic with val: <6 10 18 19 27| Scale is weakly epimorphic with val: <6 10 18 19 30| Scale is weakly epimorphic with val: <6 10 18 19 33| Scale is weakly epimorphic with val: <6 10 18 20 29| Scale is weakly epimorphic with val: <6 10 19 19 28| Scale is weakly epimorphic with val: <6 10 19 19 31| Scale is weakly epimorphic with val: <6 10 19 20 30| Scale is weakly epimorphic with val: <6 11 15 20 27| Scale is weakly epimorphic with val: <6 11 15 20 30| Scale is weakly epimorphic with val: <6 11 15 20 33| Scale is weakly epimorphic with val: <6 11 15 22 28| Scale is weakly epimorphic with val: <6 11 16 20 28| Scale is weakly epimorphic with val: <6 11 16 20 31| Scale is weakly epimorphic with val: <6 11 16 22 29| Scale is weakly epimorphic with val: <6 11 17 19 27| Scale is weakly epimorphic with val: <6 11 17 20 29| Scale is weakly epimorphic with val: <6 11 17 20 32| Scale is weakly epimorphic with val: <6 11 17 22 30| Scale is weakly epimorphic with val: <6 11 18 19 28| Scale is weakly epimorphic with val: <6 11 18 20 27| Scale is weakly epimorphic with val: <6 11 18 20 30| Scale is weakly epimorphic with val: <6 11 18 20 33| Scale is weakly epimorphic with val: <6 11 18 22 31| Scale is weakly epimorphic with val: <6 11 19 19 29| Scale is weakly epimorphic with val: <6 11 19 20 28| Scale is weakly epimorphic with val: <6 11 19 20 31| Scale is weakly epimorphic with val: <6 11 19 22 32| Scale is weakly epimorphic with val: <7 10 15 20 29| Scale is weakly epimorphic with val: <7 10 15 20 32| Scale is weakly epimorphic with val: <7 10 15 22 27| Scale is weakly epimorphic with val: <7 10 16 20 27| Scale is weakly epimorphic with val: <7 10 16 20 30| Scale is weakly epimorphic with val: <7 10 16 20 33| Scale is weakly epimorphic with val: <7 10 16 22 28| Scale is weakly epimorphic with val: <7 10 17 20 28| Scale is weakly epimorphic with val: <7 10 17 20 31| Scale is weakly epimorphic with val: <7 10 17 22 29| Scale is weakly epimorphic with val: <7 10 18 19 27| Scale is weakly epimorphic with val: <7 10 18 20 29| Scale is weakly epimorphic with val: <7 10 18 20 32| Scale is weakly epimorphic with val: <7 10 18 22 30| Scale is weakly epimorphic with val: <7 10 19 19 28| Scale is weakly epimorphic with val: <7 10 19 20 27| Scale is weakly epimorphic with val: <7 10 19 20 30| Scale is weakly epimorphic with val: <7 10 19 20 33| Scale is weakly epimorphic with val: <7 10 19 22 31| Scale is weakly epimorphic with val: <7 11 15 19 28| Scale is weakly epimorphic with val: <7 11 15 19 31| Scale is JI-epimorphic with val: <7 11 15 20 27| Scale is weakly epimorphic with val: <7 11 15 20 30| Scale is weakly epimorphic with val: <7 11 15 20 33| Scale is weakly epimorphic with val: <7 11 15 22 28| Scale is weakly epimorphic with val: <7 11 15 22 31| Scale is weakly epimorphic with val: <7 11 16 19 29| Scale is weakly epimorphic with val: <7 11 16 19 32| Scale is JI-epimorphic with val: <7 11 16 20 28| Scale is weakly epimorphic with val: <7 11 16 20 31| Scale is weakly epimorphic with val: <7 11 16 22 29| Scale is weakly epimorphic with val: <7 11 16 22 32| Scale is weakly epimorphic with val: <7 11 17 19 27| Scale is weakly epimorphic with val: <7 11 17 19 30| Scale is weakly epimorphic with val: <7 11 17 19 33| Scale is JI-epimorphic with val: <7 11 17 20 29| Scale is weakly epimorphic with val: <7 11 17 20 32| Scale is weakly epimorphic with val: <7 11 17 22 27| Scale is weakly epimorphic with val: <7 11 17 22 30| Scale is weakly epimorphic with val: <7 11 17 22 33| Scale is weakly epimorphic with val: <7 11 18 19 28| Scale is weakly epimorphic with val: <7 11 18 19 31| Scale is weakly epimorphic with val: <7 11 18 20 27| Scale is JI-epimorphic with val: <7 11 18 20 30| Scale is weakly epimorphic with val: <7 11 18 20 33| Scale is weakly epimorphic with val: <7 11 18 22 28| Scale is weakly epimorphic with val: <7 11 18 22 31| Scale is weakly epimorphic with val: <7 11 19 19 29| Scale is weakly epimorphic with val: <7 11 19 19 32| Scale is weakly epimorphic with val: <7 11 19 20 28| Scale is JI-epimorphic with val: <7 11 19 20 31| Scale is weakly epimorphic with val: <7 11 19 22 29| Scale is weakly epimorphic with val: <7 11 19 22 32| Scale is weakly epimorphic with val: <7 12 15 22 29| Scale is weakly epimorphic with val: <7 12 15 22 32| Scale is weakly epimorphic with val: <7 12 16 22 27| Scale is weakly epimorphic with val: <7 12 16 22 30| Scale is weakly epimorphic with val: <7 12 16 22 33| Scale is weakly epimorphic with val: <7 12 17 20 27| Scale is weakly epimorphic with val: <7 12 17 22 28| Scale is weakly epimorphic with val: <7 12 17 22 31| Scale is weakly epimorphic with val: <7 12 18 20 28| Scale is weakly epimorphic with val: <7 12 18 22 29| Scale is weakly epimorphic with val: <7 12 18 22 32| Scale is weakly epimorphic with val: <7 12 19 20 29| Scale is weakly epimorphic with val: <7 12 19 22 27| Scale is weakly epimorphic with val: <7 12 19 22 30| Scale is weakly epimorphic with val: <7 12 19 22 33| Scale is weakly epimorphic with val: <8 11 15 22 28| Scale is weakly epimorphic with val: <8 11 15 22 31| Scale is weakly epimorphic with val: <8 11 16 22 29| Scale is weakly epimorphic with val: <8 11 16 22 32| Scale is weakly epimorphic with val: <8 11 17 22 27| Scale is weakly epimorphic with val: <8 11 17 22 30| Scale is weakly epimorphic with val: <8 11 17 22 33| Scale is weakly epimorphic with val: <8 11 18 20 27| Scale is weakly epimorphic with val: <8 11 18 22 28| Scale is weakly epimorphic with val: <8 11 18 22 31| Scale is weakly epimorphic with val: <8 11 19 20 28| Scale is weakly epimorphic with val: <8 11 19 22 29| Scale is weakly epimorphic with val: <8 11 19 22 32| Scale is weakly epimorphic with val: <8 12 16 22 27| Scale is weakly epimorphic with val: <8 12 17 22 28| Scale is weakly epimorphic with val: <8 12 18 22 29| Scale is weakly epimorphic with val: <8 12 19 19 27| Scale is weakly epimorphic with val: <8 12 19 22 30|
FIT/MODE
3: 0 1 2 N G T3 SD: 65.0394 c. M: 100.8559 c. 4: 0 2 2 P M DE S SD: 30.7518 c. M: 50.1842 c. 6: 0 3 3 P M DE S SD: 30.7518 c. M: 50.1842 c. 7: 1 3 3 SP M DE S SD: 15.8509 c. M:-20.9651 c. 8: 1 3 4 P T3 SD: 12.4403 c. M: 17.8484 c. 9: 1 4 4 SP M DE S SD: 6.4034 c. M:-9.8208 c. 11: 1 5 5 SP M DE S SD: 3.9592 c. M: 4.9074 c. 19: 2 8 9 SP T3 SD: 3.0282 c. M: 4.7420 c. 28: 3 12 13 SP T3 SD: 1.8350 c. M:-3.1778 c. 30: 3 13 14 SP T3 SD: 0.7525 c. M: 1.2469 c. 69: 7 30 32 SP T3 SD: 0.2278 c. M:-0.3421 c. 99: 10 43 46 SP T3 SD: 0.1562 c. M: 0.2408 c. 168: 17 73 78 SP T3 SD: 0.1280 c. M:-0.2132 c. 209: 21 91 97 SP T3 SD: 0.0828 c. M: 0.1414 c. 278: 28 121 129 SP T3 SD: 0.0405 c. M:-0.0669 c. 308: 31 134 143 SP T3 SD: 0.0480 c. M: 0.0611 c. 377: 38 164 175 SP T3 SD: 0.0125 c. M:-0.0166 c. 655: 66 285 304 SP T3 SD: 0.0118 c. M:-0.0204 c. 963: 97 419 447 SP T3 SD: 0.0107 c. M: 0.0177 c. 1032: 104 449 479 SP T3 SD: 0.0058 c. M:-0.0079 c. 1409: 142 613 654 SP T3 SD: 0.0054 c. M:-0.0091 c. 1995: 201 868 926 SP T3 SD: 0.0031 c. M: 0.0052 c. 2372: 239 1032 1101 SP T3 SD: 0.0012 c. M: 0.0018 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 x 12:13 S SD: 32.7861 cents 12:13:14:16 S SD: 29.4628 cents 13:14:15:17 SD: 29.0553 cents 14:15:16:19 SD: 27.9085 cents 15:16:18:20 S SD: 26.1759 cents 16:17:19:21 SD: 22.8088 cents 17:18:20:23 SD: 18.9362 cents 18:19:21:24 SD: 14.4729 cents 22:23:26:29 SD: 13.3635 cents 23:24:27:31 SD: 10.6317 cents 24:25:28:32 SD: 6.8294 cents 29:30:34:39 SD: 6.3734 cents 30:31:35:40 SD: 2.1942 cents 36:37:42:48 SD: 0.9167 cents 66:68:77:88 SD: 0.4994 cents 102:105:119:136 SD: 0.0000 cents