Scala analysis: 259_C17
Chromatic tetrachord 20/19 * 171/160 * 32/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 20/19 88.800698 small undevicesimal semitone 2: 9/8 203.910002 major whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 32/27 294.1350 Pythagorean minor third 1: 20/19 88.8007 small undevicesimal semitone 2: 171/160 115.1093 3: 32/27 294.1350 Pythagorean minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 20/19 88.801 cents small undevicesimal semitone 1: 1 171/160 115.109 cents 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 640/513 382.936 cents 2: 1 19/15 409.244 cents undevicesimal ditone 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 : 88.8 203.9 498.0 88.8 : 115.1 409.2 498.0 203.9: 294.1 382.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.8007 .. 294.1350 cents 152/135, 205.3343 cents 20/19, 88.8007 cents 2: 203.9100 .. 409.2443 cents 152/135, 205.3343 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 20/19, 88.8007 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 1.869524 Largest / Average step : 1.771737 Largest / Smallest step : 3.312305 Median interval of one step : 171/160, 115.1093 cents, amount: 1 Least squares average step : 142.19684 cents, oct.: 426.59051 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1761-tone equal temperament with octave 4/3 degrees: 314 721 1761 Least number of segments generator : 881 of 249.164 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 932 of 263.588 cents and inv. generated superset size: 26 = 23 more = 866.667% 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 88.80070 cents Scale diversity : 1.098499 Lumma stability : 0.356597 Lumma impropriety factor : 0.181158 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 : 3249/3200, 26.3086 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% Limited inverse transpositions with margin 179.0257 cents: 2 -- Rational properties -- Prime limit : 19 Odd number limit : 513 (O: 171 U: 513) Highest odd numerator or denominator: 19 Scale harmonicity : 0.018690 Average absolute harmonicity : 0.119270 Specific harmonicity : 0.098452 Fundamental : 1/456, -8.8329 octaves, 0.5737 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 8.208000E+04, 16.32474 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 31.5, average 10.50000 Mersenne's string divisions : 4641 Sum of van Prooijen's expressibility: 2.71012, average 0.90337 Sum of Tenney's harmonic distance : 5.51630, average 1.83877 Vogel's harmonic complexity : 21.66667 Wille's k value : 256 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 21.42188, average 3.57031 Lattice compactness (without 2's) : 11.59575, average 1.93263 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 0.33333 7 3: -1 .. 2 0.33333 3 2 5: 0 .. 1 0.33333 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <7 10 17 28| Scale is weakly epimorphic with val: <7 10 18 29| Scale is weakly epimorphic with val: <7 10 19 30| Scale is weakly epimorphic with val: <7 11 15 30| Scale is weakly epimorphic with val: <7 11 15 33| Scale is weakly epimorphic with val: <7 11 16 28| Scale is weakly epimorphic with val: <7 11 16 31| Scale is weakly epimorphic with val: <7 11 16 34| Scale is weakly epimorphic with val: <7 11 17 29| Scale is weakly epimorphic with val: <7 11 17 32| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 11 18 33| Scale is weakly 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 19 34| Scale is weakly epimorphic with val: <7 12 15 28| Scale is weakly epimorphic with val: <7 12 15 31| Scale is weakly epimorphic with val: <7 12 15 34| Scale is weakly epimorphic with val: <7 12 16 29| Scale is weakly epimorphic with val: <7 12 16 32| Scale is weakly epimorphic with val: <7 12 17 30| Scale is weakly epimorphic with val: <7 12 17 33| Scale is weakly epimorphic with val: <7 12 18 28| Scale is weakly epimorphic with val: <7 12 18 31| Scale is weakly epimorphic with val: <7 12 18 34| Scale is weakly epimorphic with val: <7 12 19 29| Scale is weakly epimorphic with val: <7 12 19 32| Scale is weakly epimorphic with val: <8 11 15 28| Scale is weakly epimorphic with val: <8 11 16 29| Scale is weakly epimorphic with val: <8 11 17 30| Scale is weakly epimorphic with val: <8 11 18 31| Scale is weakly epimorphic with val: <8 11 19 32|
FIT/MODE
3: 0 1 2 N G T3 SD: 55.7422 c. M: 88.8007 c. 4: 1 1 2 P M ME S SD: 33.2184 c. M:-45.1125 c. 5: 1 1 3 N M DE S SD: 6.8028 c. M:-10.8083 c. 12: 2 3 7 N T3 SD: 3.9406 c. M: 5.7932 c. 17: 3 4 10 N T3 SD: 0.8547 c. M:-1.1674 c. 39: 7 9 23 N T3 SD: 0.4178 c. M:-0.5920 c. 56: 10 13 33 N T3 SD: 0.3801 c. M:-0.6442 c. 95: 17 22 56 N T3 SD: 0.3686 c. M:-0.5506 c. 134: 24 31 79 N T3 SD: 0.3754 c. M:-0.5115 c. 151: 27 35 89 N T3 SD: 0.3683 c. M:-0.5853 c. 173: 31 40 102 N T3 SD: 0.3819 c. M:-0.4900 c. 186: 33 43 110 N T3 SD: 0.3454 c. M: 0.4379 c. 191: 34 44 113 N T3 SD: 0.3114 c. M: 0.5199 c. 203: 36 47 120 N T3 SD: 0.3184 c. M: 0.4774 c. 208: 37 48 123 N T3 SD: 0.2506 c. M: 0.3820 c. 225: 40 52 133 N T3 SD: 0.2141 c. M: 0.2649 c. 230: 41 53 136 N T3 SD: 0.2088 c. M: 0.3612 c. 242: 43 56 143 N T3 SD: 0.2001 c. M: 0.3051 c. 247: 44 57 146 N T3 SD: 0.1549 c. M: 0.2560 c. 264: 47 61 156 N T3 SD: 0.1223 c. M: 0.1643 c. 281: 50 65 166 N T3 SD: 0.1149 c. M: 0.1806 c. 286: 51 66 169 N T3 SD: 0.0951 c. M: 0.1643 c. 303: 54 70 179 N T3 SD: 0.0567 c. M: 0.0896 c. 320: 57 74 189 N T3 SD: 0.0516 c. M: 0.0864 c. 342: 61 79 202 N T3 SD: 0.0261 c. M: 0.0319 c. 359: 64 83 212 N T3 SD: 0.0161 c. M:-0.0249 c. 701: 125 162 414 N T3 SD: 0.0055 c. M:-0.0090 c. 1060: 189 245 626 N T3 SD: 0.0039 c. M:-0.0065 c. 1761: 314 407 1040 N T3 SD: 0.0031 c. M:-0.0046 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: 70.0332 cents 6 x 7:8 S SD: 31.4805 cents 7 x 8:9 S SD: 34.3053 cents 8 x 9:11 SD: 26.6365 cents 9 x 10:12 S SD: 10.7531 cents 10 x 11:13 SD: 29.3037 cents 11 x 12:15 S SD: 32.9836 cents 12:13:14:16 S SD: 26.7526 cents 13:14:15:17 SD: 22.6356 cents 14:15:16:19 SD: 17.0659 cents 15:16:17:20 SD: 8.7500 cents 18:19:20:24 S SD: 7.3453 cents 24:25:27:32 SD: 6.0428 cents 33:35:37:44 SD: 4.7704 cents 39:41:44:52 SD: 1.8010 cents 57:60:64:76 SD: 1.1260 cents 96:101:108:128 SD: 0.3006 cents 264:278:297:352 SD: 0.2185 cents 360:379:405:480 SD: 0.0801 cents 456:480:513:608 SD: 0.0000 cents