Scala analysis: 287_C21
Chromatic tetrachord 34/33 * 11/10 * 20/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 34/33 51.682466 2: 17/15 216.686695 septendecimal whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 20/17 281.3583 septendecimal augmented second 1: 34/33 51.6825 2: 11/10 165.0042 Ptolemy's second, 4/5-tone 3: 20/17 281.3583 septendecimal augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 34/33 51.682 cents 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 20/17 281.358 cents septendecimal augmented second 2: 1 17/15 216.687 cents septendecimal whole tone 2: 1 40/33 333.041 cents 2: 1 22/17 446.363 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 : 51.7 216.7 498.0 51.7 : 165.0 446.4 498.0 216.7: 281.4 333.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.6825 .. 281.3583 cents 330/289, 229.6758 cents 34/33, 51.6825 cents 2: 216.6867 .. 446.3625 cents 330/289, 229.6758 cents 289/300,-64.6716 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 34/33, 51.6825 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 20/17, 281.3583 cents Average / Smallest step : 3.212211 Largest / Average step : 1.694776 Largest / Smallest step : 5.443980 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 141.37078 cents, oct.: 424.11233 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1648-tone equal temperament with octave 4/3 degrees: 171 717 1648 Least number of segments generator : 825 of 249.325 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1523 of 460.269 cents and inv. generated superset size: 48 = 45 more = 1600.000% 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 51.68247 cents Scale diversity : 0.870598 Lumma stability : 0.207541 Lumma impropriety factor : 0.129851 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 : 34/33, 51.6825 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 : 33 (O: 17 U: 33) Highest odd numerator or denominator: 33 Scale harmonicity : 0.016845 Average absolute harmonicity : 0.086349 Specific harmonicity : 0.076476 Fundamental : 1/165, -7.3663 octaves, 1.5856 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 1.122000E+04, 13.45379 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 53.0, average 17.66667 Mersenne's string divisions : 15008 Sum of van Prooijen's expressibility: 3.22608, average 1.07536 Sum of Tenney's harmonic distance : 6.53571, average 2.17857 Vogel's harmonic complexity : 23.00000 Wille's k value : 93 Wilson's harmonic complexity : 36 Rectangular lattice diameter : 4 Triangular lattice diameter : 1 Lattice compactness : 11.88171, average 1.98029 Lattice compactness (without 2's) : 8.70674, average 1.45112 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.00000 3 3: -1 ..-1 -1.00000 3 1 5: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 2 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 15 23 28| Scale is weakly epimorphic with val: <6 10 15 25 32| Scale is weakly epimorphic with val: <6 10 15 26 28| Scale is weakly epimorphic with val: <6 10 16 23 30| Scale is weakly epimorphic with val: <6 10 16 24 29| Scale is weakly epimorphic with val: <6 10 16 26 33| Scale is weakly epimorphic with val: <6 10 16 27 29| Scale is weakly epimorphic with val: <6 10 17 24 31| Scale is weakly epimorphic with val: <6 10 17 25 30| Scale is weakly epimorphic with val: <6 10 18 23 31| Scale is weakly epimorphic with val: <6 10 18 25 32| Scale is weakly epimorphic with val: <6 10 18 26 31| Scale is weakly epimorphic with val: <6 10 19 23 30| Scale is weakly epimorphic with val: <6 10 19 24 32| Scale is weakly epimorphic with val: <6 10 19 26 33| Scale is weakly epimorphic with val: <6 10 19 27 32| Scale is weakly epimorphic with val: <6 11 15 23 31| Scale is weakly epimorphic with val: <6 11 15 25 29| Scale is weakly epimorphic with val: <6 11 16 23 30| Scale is weakly epimorphic with val: <6 11 16 24 32| Scale is weakly epimorphic with val: <6 11 16 26 30| Scale is weakly epimorphic with val: <6 11 17 24 31| Scale is weakly epimorphic with val: <6 11 17 25 33| Scale is weakly epimorphic with val: <6 11 17 27 31| Scale is weakly epimorphic with val: <6 11 18 23 31| Scale is weakly epimorphic with val: <6 11 18 25 32| Scale is weakly epimorphic with val: <6 11 19 23 33| Scale is weakly epimorphic with val: <6 11 19 24 32| Scale is weakly epimorphic with val: <6 11 19 26 33| Scale is weakly epimorphic with val: <7 10 15 23 28| Scale is weakly epimorphic with val: <7 10 15 24 30| Scale is weakly epimorphic with val: <7 10 15 26 28| Scale is weakly epimorphic with val: <7 10 15 27 33| Scale is weakly epimorphic with val: <7 10 16 24 29| Scale is weakly epimorphic with val: <7 10 16 25 31| Scale is weakly epimorphic with val: <7 10 16 27 29| Scale is weakly epimorphic with val: <7 10 17 23 29| Scale is weakly epimorphic with val: <7 10 17 25 30| Scale is weakly epimorphic with val: <7 10 17 26 32| Scale is weakly epimorphic with val: <7 10 18 23 31| Scale is weakly epimorphic with val: <7 10 18 24 30| Scale is weakly epimorphic with val: <7 10 18 26 31| Scale is weakly epimorphic with val: <7 10 18 27 33| Scale is weakly epimorphic with val: <7 10 19 24 32| Scale is weakly epimorphic with val: <7 10 19 25 31| Scale is weakly epimorphic with val: <7 10 19 27 32| Scale is JI-epimorphic with val: <7 11 15 23 28| Scale is weakly epimorphic with val: <7 11 15 23 31| Scale is weakly epimorphic with val: <7 11 15 24 27| Scale is weakly epimorphic with val: <7 11 15 24 30| Scale is weakly epimorphic with val: <7 11 15 24 33| Scale is weakly epimorphic with val: <7 11 15 26 28| Scale is weakly epimorphic with val: <7 11 15 26 31| Scale is weakly epimorphic with val: <7 11 15 27 27| Scale is weakly epimorphic with val: <7 11 15 27 30| Scale is weakly epimorphic with val: <7 11 15 27 33| Scale is JI-epimorphic with val: <7 11 16 24 29| Scale is weakly epimorphic with val: <7 11 16 24 32| Scale is weakly epimorphic with val: <7 11 16 25 28| Scale is weakly epimorphic with val: <7 11 16 25 31| Scale is weakly epimorphic with val: <7 11 16 27 29| Scale is weakly epimorphic with val: <7 11 16 27 32| Scale is weakly epimorphic with val: <7 11 17 23 29| Scale is weakly epimorphic with val: <7 11 17 23 32| Scale is weakly epimorphic with val: <7 11 17 25 27| Scale is JI-epimorphic with val: <7 11 17 25 30| = patent Scale is weakly epimorphic with val: <7 11 17 25 33| Scale is weakly epimorphic with val: <7 11 17 26 29| Scale is weakly epimorphic with val: <7 11 17 26 32| Scale is weakly epimorphic with val: <7 11 18 23 28| Scale is weakly epimorphic with val: <7 11 18 23 31| Scale is weakly epimorphic with val: <7 11 18 24 27| Scale is weakly epimorphic with val: <7 11 18 24 30| Scale is weakly epimorphic with val: <7 11 18 24 33| Scale is weakly epimorphic with val: <7 11 18 26 28| Scale is JI-epimorphic with val: <7 11 18 26 31| Scale is weakly epimorphic with val: <7 11 18 27 27| Scale is weakly epimorphic with val: <7 11 18 27 30| Scale is weakly epimorphic with val: <7 11 18 27 33| Scale is weakly epimorphic with val: <7 11 19 24 29| Scale is weakly epimorphic with val: <7 11 19 24 32| Scale is weakly epimorphic with val: <7 11 19 25 28| Scale is weakly epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 27 29| Scale is JI-epimorphic with val: <7 11 19 27 32| Scale is weakly epimorphic with val: <7 12 15 23 31| Scale is weakly epimorphic with val: <7 12 15 24 30| Scale is weakly epimorphic with val: <7 12 15 27 30| Scale is weakly epimorphic with val: <7 12 16 24 32| Scale is weakly epimorphic with val: <7 12 16 25 31| Scale is weakly epimorphic with val: <7 12 17 23 32| Scale is weakly epimorphic with val: <7 12 17 25 33| Scale is weakly epimorphic with val: <7 12 17 26 32| Scale is weakly epimorphic with val: <7 12 18 23 31| Scale is weakly epimorphic with val: <7 12 18 24 33| Scale is weakly epimorphic with val: <7 12 18 27 33| Scale is weakly epimorphic with val: <7 12 19 24 32| Scale is weakly epimorphic with val: <8 11 15 24 30| Scale is weakly epimorphic with val: <8 11 15 25 29| Scale is weakly epimorphic with val: <8 11 15 27 33| Scale is weakly epimorphic with val: <8 11 16 23 30| Scale is weakly epimorphic with val: <8 11 16 25 31| Scale is weakly epimorphic with val: <8 11 16 26 30| Scale is weakly epimorphic with val: <8 11 17 23 29| Scale is weakly epimorphic with val: <8 11 17 24 31| Scale is weakly epimorphic with val: <8 11 17 26 32| Scale is weakly epimorphic with val: <8 11 17 27 31| Scale is weakly epimorphic with val: <8 11 18 24 30| Scale is weakly epimorphic with val: <8 11 18 25 32| Scale is weakly epimorphic with val: <8 11 18 27 33| Scale is weakly epimorphic with val: <8 11 19 23 33| Scale is weakly epimorphic with val: <8 11 19 25 31| Scale is weakly epimorphic with val: <8 11 19 26 33| Scale is weakly epimorphic with val: <8 12 15 24 30| Scale is weakly epimorphic with val: <8 12 15 25 32| Scale is weakly epimorphic with val: <8 12 15 27 30| Scale is weakly epimorphic with val: <8 12 16 23 30| Scale is weakly epimorphic with val: <8 12 16 25 31| Scale is weakly epimorphic with val: <8 12 16 26 33| Scale is weakly epimorphic with val: <8 12 17 23 32| Scale is weakly epimorphic with val: <8 12 17 24 31| Scale is weakly epimorphic with val: <8 12 17 26 32| Scale is weakly epimorphic with val: <8 12 18 24 33| Scale is weakly epimorphic with val: <8 12 18 25 32| Scale is weakly epimorphic with val: <8 12 18 27 33| Scale is weakly epimorphic with val: <8 12 19 23 30| Scale is weakly epimorphic with val: <8 12 19 26 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 41.7879 c. M: 51.6825 c. 4: 0 2 2 P M DE S SD: 35.1979 c. M: 51.6825 c. 5: 0 2 3 N G T3 SD: 31.4973 c. M: 51.6825 c. 7: 1 2 4 N T3 SD: 11.3937 c. M:-19.4668 c. 9: 1 3 5 N T3 SD: 3.4226 c. M:-4.6666 c. 21: 2 7 12 N T3 SD: 3.0849 c. M: 4.2496 c. 28: 3 9 16 N T3 SD: 2.1064 c. M: 3.2388 c. 30: 3 10 17 N T3 SD: 1.1943 c. M: 1.8780 c. 39: 4 13 22 N T3 SD: 0.4200 c. M: 0.6009 c. 106: 11 35 60 N T3 SD: 0.3198 c. M: 0.5540 c. 115: 12 38 65 N T3 SD: 0.1860 c. M:-0.2874 c. 145: 15 48 82 N T3 SD: 0.1938 c. M: 0.2947 c. 154: 16 51 87 N T3 SD: 0.0362 c. M:-0.0625 c. 347: 36 115 196 N T3 SD: 0.0251 c. M:-0.0418 c. 501: 52 166 283 N T3 SD: 0.0171 c. M:-0.0275 c. 655: 68 217 370 N T3 SD: 0.0175 c. M:-0.0230 c. 993: 103 329 561 N T3 SD: 0.0153 c. M: 0.0222 c. 1147: 119 380 648 N T3 SD: 0.0099 c. M: 0.0132 c. 1301: 135 431 735 N T3 SD: 0.0072 c. M: 0.0122 c. 1455: 151 482 822 N T3 SD: 0.0071 c. M: 0.0114 c. 1494: 155 495 844 N T3 SD: 0.0064 c. M: 0.0111 c. 1609: 167 533 909 N T3 SD: 0.0086 c. M: 0.0108 c. 1648: 171 546 931 N T3 SD: 0.0025 c. M: 0.0043 c. 1802: 187 597 1018 N T3 SD: 0.0011 c. M:-0.0014 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: 65.0514 cents 6 x 7:8 S SD: 25.0921 cents 7 x 8:9 S SD: 32.3031 cents 8 x 9:11 SD: 27.3918 cents 9 x 10:12 S SD: 17.1415 cents 10 x 11:13 SD: 33.8830 cents 11 x 12:15 S SD: 38.3282 cents 12 x 14:16 S SD: 25.0921 cents 15:16:17:20 SD: 20.0163 cents 17:18:19:23 SD: 19.5949 cents 18:19:20:24 S SD: 18.0513 cents 20:21:23:27 SD: 15.5497 cents 21:22:24:28 S SD: 10.7624 cents 23:24:26:31 SD: 9.7404 cents 24:25:27:32 SD: 7.6293 cents 29:30:33:39 SD: 5.9543 cents 30:31:34:40 SD: 1.6948 cents 66:68:75:88 SD: 1.5409 cents 96:99:109:128 SD: 1.1850 cents 99:102:112:132 SD: 1.0296 cents 105:108:119:140 SD: 0.9707 cents 129:133:146:172 SD: 0.8830 cents 135:139:153:180 SD: 0.3773 cents 165:170:187:220 SD: 0.0000 cents