Scala analysis: 403_D6
Diatonic tetrachord 18/17 * 119/108 * 8/7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 18/17 98.954592 Arabic lute index finger 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: 18/17 98.9546 Arabic lute index finger 2: 119/108 167.9163 3: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 18/17 98.955 cents Arabic lute index finger 1: 1 119/108 167.916 cents 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 144/119 330.129 cents 2: 1 34/27 399.090 cents septendecimal 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 : 99.0 266.9 498.0 99.0 : 167.9 399.1 498.0 266.9: 231.2 330.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 98.9546 .. 231.1741 cents 68/63, 132.2195 cents 18/17, 98.9546 cents 2: 266.8709 .. 399.0904 cents 68/63, 132.2195 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 18/17, 98.9546 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 1.677689 Largest / Average step : 1.392489 Largest / Smallest step : 2.336163 Median interval of one step : 119/108, 167.9163 cents, amount: 1 Least squares average step : 151.91653 cents, oct.: 455.74959 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 614-tone equal temperament with octave 4/3 degrees: 122 329 614 Least number of segments generator : 309 of 250.645 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 441 of 357.716 cents and inv. generated superset size: 23 = 20 more = 766.667% 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 : 1.210774 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.469046 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 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 -- Rational properties -- Prime limit : 17 Odd number limit : 119 (O: 119 U: 119) Highest odd numerator or denominator: 17 Scale harmonicity : 0.019454 Average absolute harmonicity : 0.104464 Specific harmonicity : 0.101344 Fundamental : 1/102, -6.6724 octaves, 2.5650 Hz. Guide tone : 252, 7.9773 octaves, 65929.642 Hz. Exponens Consonantiae : 2.570400E+04, 14.64971 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 27.5, average 9.16667 Mersenne's string divisions : 455 Sum of van Prooijen's expressibility: 2.55267, average 0.85089 Sum of Tenney's harmonic distance : 5.18815, average 1.72938 Vogel's harmonic complexity : 18.33333 Wille's k value : 59 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 16.76949, average 2.79492 Lattice compactness (without 2's) : 12.12918, average 2.02153 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -1 .. 2 0.00000 4 1 7: 0 .. 1 0.33333 1 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 19 28| Scale is weakly epimorphic with val: <6 10 19 31| Scale is weakly epimorphic with val: <6 11 20 29| Scale is weakly epimorphic with val: <6 11 20 32| Scale is weakly epimorphic with val: <7 10 20 28| Scale is weakly epimorphic with val: <7 10 20 31| Scale is weakly epimorphic with val: <7 11 19 27| Scale is weakly epimorphic with val: <7 11 19 30| Scale is weakly epimorphic with val: <7 11 19 33| Scale is JI-epimorphic with val: <7 11 20 28| Scale is weakly epimorphic with val: <7 11 20 31| Scale is weakly epimorphic with val: <7 11 22 27| Scale is weakly epimorphic with val: <7 11 22 30| Scale is weakly epimorphic with val: <7 11 22 33| Scale is weakly epimorphic with val: <7 12 20 28| Scale is weakly epimorphic with val: <7 12 22 27| Scale is weakly epimorphic with val: <7 12 22 30| Scale is weakly epimorphic with val: <7 12 22 33| Scale is weakly epimorphic with val: <8 11 20 27| Scale is weakly epimorphic with val: <8 11 22 29| Scale is weakly epimorphic with val: <8 11 22 32| Scale is weakly epimorphic with val: <8 12 19 29| Scale is weakly epimorphic with val: <8 12 22 29|
FIT/MODE
3: 0 1 2 N G T3 SD: 81.5760 c. M: 100.8559 c. 4: 1 1 2 P M ME S SD: 17.9973 c. M:-25.5567 c. 5: 1 2 2 SP M ME S SD: 18.4537 c. M:-31.9561 c. 6: 1 2 3 P T3 SD: 13.8188 c. M: 17.8484 c. 9: 2 3 4 SP T3 SD: 8.8290 c. M:-11.7221 c. 11: 2 4 5 SP T3 SD: 5.5833 c. M: 8.4010 c. 15: 3 5 7 SP T3 SD: 0.8130 c. M: 1.2469 c. 56: 11 19 26 SP T3 SD: 0.6501 c. M: 1.1243 c. 71: 14 24 33 SP T3 SD: 0.4681 c. M: 0.7485 c. 86: 17 29 40 SP T3 SD: 0.3997 c. M: 0.5038 c. 101: 20 34 47 SP T3 SD: 0.3905 c. M: 0.5894 c. 125: 25 42 58 SP T3 SD: 0.3807 c. M:-0.6544 c. 136: 27 46 63 SP T3 SD: 0.2706 c. M:-0.4621 c. 151: 30 51 70 SP T3 SD: 0.1688 c. M:-0.2923 c. 166: 33 56 77 SP T3 SD: 0.0939 c. M:-0.1532 c. 181: 36 61 84 SP T3 SD: 0.0638 c. M:-0.1041 c. 347: 69 117 161 SP T3 SD: 0.0708 c. M:-0.0927 c. 403: 80 136 187 SP T3 SD: 0.0650 c. M: 0.0871 c. 418: 83 141 194 SP T3 SD: 0.0376 c. M: 0.0605 c. 433: 86 146 201 SP T3 SD: 0.0236 c. M: 0.0357 c. 599: 119 202 278 SP T3 SD: 0.0173 c. M:-0.0280 c. 614: 122 207 285 SP T3 SD: 0.0037 c. M:-0.0055 c. 2275: 452 767 1056 SP T3 SD: 0.0039 c. M: 0.0064 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 9:10:11:12 H SD: 38.6580 cents 10:11:12:13 H SD: 31.0238 cents 11:12:13:15 SD: 22.8127 cents 12:13:14:16 S SD: 13.2060 cents 17:18:20:23 SD: 9.7106 cents 18:19:21:24 SD: 1.7839 cents 66:70:77:88 SD: 0.9707 cents 84:89:98:112 SD: 0.3815 cents 102:108:119:136 SD: 0.0000 cents