Scala analysis: 316_C24
Chromatic tetrachord 18/17 * 7/6 * 68/63
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: 21/17 365.825498 submajor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 68/63 132.2195 supraminor second 1: 18/17 98.9546 Arabic lute index finger 2: 7/6 266.8709 septimal minor third 3: 68/63 132.2195 supraminor second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 18/17 98.955 cents Arabic lute index finger 1: 1 68/63 132.220 cents supraminor second 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 21/17 365.825 cents submajor third 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 : 99.0 365.8 498.0 99.0 : 266.9 399.1 498.0 365.8: 132.2 231.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 98.9546 .. 266.8709 cents 119/108, 167.9163 cents 18/17, 98.9546 cents 2: 231.1741 .. 399.0904 cents 119/108, 167.9163 cents 48/49,-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 : 7/6, 266.8709 cents Average / Smallest step : 1.677689 Largest / Average step : 1.607511 Largest / Smallest step : 2.696903 Median interval of one step : 68/63, 132.2195 cents, amount: 1 Least squares average step : 166.05290 cents, oct.: 498.15870 cents Scale is not proper Scale has trivalence property Scale is a mode of a 614-tone equal temperament with octave 4/3 degrees: 122 451 614 Least number of segments generator : 309 of 250.645 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 573 of 464.788 cents and inv. generated superset size: 24 = 21 more = 800.000% Number of contiguous 1-step segments: 0 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 35.69681 cents Scale diversity : 1.153203 Lumma stability : 0.397372 Lumma impropriety factor : 0.071674 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 : 578/567, 33.2649 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 : 63 (O: 21 U: 63) Highest odd numerator or denominator: 21 Scale harmonicity : 0.019840 Average absolute harmonicity : 0.088312 Specific harmonicity : 0.086489 Fundamental : 1/51, -5.6724 octaves, 5.1299 Hz. Guide tone : 252, 7.9773 octaves, 65929.642 Hz. Exponens Consonantiae : 1.285200E+04, 13.64971 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 40.0, average 13.33333 Mersenne's string divisions : 1330 Sum of van Prooijen's expressibility: 3.02979, average 1.00993 Sum of Tenney's harmonic distance : 6.11757, average 2.03919 Vogel's harmonic complexity : 14.00000 Wille's k value : 31 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.62856, average 2.43809 Lattice compactness (without 2's) : 11.99410, average 1.99902 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.00000 3 3: -1 .. 2 0.66667 4 1 7: 0 .. 1 0.33333 1 17: -1 .. 0 -0.66667 2 2 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 21 28| Scale is weakly epimorphic with val: <6 11 21 29| Scale is weakly epimorphic with val: <7 10 21 28| Scale is JI-epimorphic with val: <7 11 19 28| Scale is weakly epimorphic with val: <7 11 19 31| Scale is weakly epimorphic with val: <7 11 20 27| Scale is weakly epimorphic with val: <7 11 20 30| = patent Scale is weakly epimorphic with val: <7 11 20 33| Scale is weakly epimorphic with val: <7 11 22 28| Scale is weakly epimorphic with val: <7 11 22 31| Scale is weakly epimorphic with val: <7 12 18 27| Scale is weakly epimorphic with val: <7 12 20 28| Scale is weakly epimorphic with val: <7 12 21 30| Scale is weakly epimorphic with val: <8 11 20 27| Scale is weakly epimorphic with val: <8 11 21 29| Scale is weakly epimorphic with val: <8 12 18 27| Scale is weakly epimorphic with val: <8 12 19 29| Scale is weakly epimorphic with val: <8 12 21 30| Scale is weakly epimorphic with val: <8 12 22 29|
FIT/MODE
3: 0 2 1 N G T3 SD: 60.3715 c. M: 98.9546 c. 4: 1 2 1 P M ME I SD: 15.4117 c. M:-25.5567 c. 9: 2 5 2 N M DE I SD: 14.1598 c. M:-21.5428 c. 10: 2 5 3 P T3 SD: 9.9341 c. M: 17.1940 c. 11: 2 6 3 N T3 SD: 5.2794 c. M: 8.4010 c. 15: 3 8 4 N T3 SD: 0.5097 c. M:-0.6544 c. 101: 20 54 27 N T3 SD: 0.5653 c. M: 0.9212 c. 106: 21 57 28 N T3 SD: 0.4154 c. M:-0.6604 c. 121: 24 65 32 N T3 SD: 0.3075 c. M:-0.5051 c. 136: 27 73 36 N T3 SD: 0.2263 c. M:-0.3841 c. 151: 30 81 40 N T3 SD: 0.1658 c. M:-0.2871 c. 166: 33 89 44 N T3 SD: 0.1239 c. M:-0.2076 c. 181: 36 97 48 N T3 SD: 0.1013 c. M:-0.1413 c. 196: 39 105 52 N T3 SD: 0.0977 c. M:-0.1462 c. 373: 74 200 99 N T3 SD: 0.0865 c. M: 0.1467 c. 377: 75 202 100 N T3 SD: 0.0974 c. M:-0.1260 c. 388: 77 208 103 N T3 SD: 0.0669 c. M: 0.1158 c. 403: 80 216 107 N T3 SD: 0.0511 c. M: 0.0871 c. 418: 83 224 111 N T3 SD: 0.0408 c. M: 0.0605 c. 433: 86 232 115 N T3 SD: 0.0382 c. M: 0.0557 c. 569: 113 305 151 N T3 SD: 0.0389 c. M:-0.0494 c. 584: 116 313 155 N T3 SD: 0.0249 c. M:-0.0329 c. 599: 119 321 159 N T3 SD: 0.0117 c. M:-0.0172 c. 614: 122 329 163 N T3 SD: 0.0034 c. M:-0.0055 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: 20.4882 cents 5 x 6:7 S SD: 49.1253 cents 6 x 7:8 S SD: 49.4773 cents 7:8 x 9 S SD: 73.2224 cents 8:9:10:11 H SD: 39.8238 cents 9:10:11:12 H SD: 28.4858 cents 11:12:14:15 S SD: 27.5999 cents 12:13:15:16 SD: 14.8674 cents 16:17:20:21 SD: 11.5427 cents 17:18:21:23 SD: 8.4246 cents 18:19:22:24 SD: 6.3931 cents 21:22:26:28 SD: 6.2768 cents 30:32:37:40 SD: 4.3564 cents 33:35:41:44 SD: 3.4603 cents 51:54:63:68 SD: 0.0000 cents