Scala analysis: 198_C11
Chromatic tetrachord 28/27 * 18/17 * 17/14
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 56/51 161.915496 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 17/14 336.1295 supraminor third 1: 28/27 62.9609 Archytas' 1/3-tone 2: 18/17 98.9546 Arabic lute index finger 3: 17/14 336.1295 supraminor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 18/17 98.955 cents Arabic lute index finger 1: 1 17/14 336.130 cents supraminor third 2: 1 56/51 161.915 cents 2: 1 34/27 399.090 cents septendecimal major third 2: 1 9/7 435.084 cents septimal major third, BP 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 : 63.0 161.9 498.0 63.0 : 99.0 435.1 498.0 161.9: 336.1 399.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 336.1295 cents 459/392, 273.1686 cents 28/27, 62.9609 cents 2: 161.9155 .. 435.0841 cents 459/392, 273.1686 cents 784/867,-174.2140 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/14, 336.1295 cents Average / Smallest step : 2.636795 Largest / Average step : 2.024694 Largest / Smallest step : 5.338702 Median interval of one step : 18/17, 98.9546 cents, amount: 1 Least squares average step : 134.35192 cents, oct.: 403.05576 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1052-tone equal temperament with octave 4/3 degrees: 133 342 1052 Least number of segments generator : 527 of 249.496 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1033 of 489.050 cents and inv. generated superset size: 19 = 16 more = 633.333% 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 62.96090 cents Scale diversity : 0.854733 Lumma stability : 0.252832 Lumma impropriety factor : 0.349796 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 : 243/238, 35.9937 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 -- Rational properties -- Prime limit : 17 Odd number limit : 51 (O: 17 U: 51) Highest odd numerator or denominator: 51 Scale harmonicity : 0.019454 Average absolute harmonicity : 0.095095 Specific harmonicity : 0.097266 Fundamental : 1/459, -8.8424 octaves, 0.5700 Hz. Guide tone : 56, 5.8074 octaves, 14651.032 Hz. Exponens Consonantiae : 2.570400E+04, 14.64971 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 84.5, average 28.16667 Mersenne's string divisions : 41195 Sum of van Prooijen's expressibility: 3.61606, average 1.20535 Sum of Tenney's harmonic distance : 7.41346, average 2.47115 Vogel's harmonic complexity : 22.33333 Wille's k value : 76 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 15.85944, average 2.64324 Lattice compactness (without 2's) : 11.78068, average 1.96345 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -3 ..-1 -1.66667 5 1 7: 0 .. 1 0.66667 2 1 17: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 21 28| Scale is weakly epimorphic with val: <6 10 21 31| Scale is weakly epimorphic with val: <6 10 22 27| Scale is weakly epimorphic with val: <7 10 19 28| Scale is weakly epimorphic with val: <7 10 19 31| Scale is weakly epimorphic with val: <7 10 21 29| Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 11 18 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 21 27| Scale is weakly epimorphic with val: <7 11 21 30| Scale is weakly epimorphic with val: <7 11 21 33| Scale is weakly epimorphic with val: <8 11 18 28| Scale is weakly epimorphic with val: <8 11 20 29| Scale is weakly epimorphic with val: <8 11 20 32| Scale is weakly epimorphic with val: <8 11 21 31| Scale is weakly epimorphic with val: <8 12 19 28| Scale is weakly epimorphic with val: <8 12 22 31|
FIT/MODE
3: 0 1 2 N G T3 SD: 36.4275 c. M: 62.9609 c. 4: 0 1 3 N G T3 SD: 42.2814 c. M: 62.9609 c. 6: 1 1 4 N M DE S SD: 11.8134 c. M:-20.0466 c. 7: 1 1 5 N M DE S SD: 12.2729 c. M: 19.6169 c. 9: 1 2 6 N T3 SD: 4.9970 c. M: 7.6226 c. 15: 2 3 10 N T3 SD: 3.0916 c. M:-4.0995 c. 24: 3 5 16 N T3 SD: 2.4016 c. M:-4.0995 c. 25: 3 5 17 N T3 SD: 2.3571 c. M: 3.1955 c. 31: 4 6 21 N T3 SD: 1.0448 c. M:-1.3030 c. 40: 5 8 27 N T3 SD: 0.4083 c. M: 0.7053 c. 71: 9 14 48 N T3 SD: 0.3475 c. M: 0.5770 c. 95: 12 19 64 N T3 SD: 0.3502 c. M:-0.6045 c. 111: 14 22 75 N T3 SD: 0.2387 c. M: 0.3874 c. 126: 16 25 85 N T3 SD: 0.1840 c. M:-0.2829 c. 166: 21 33 112 N T3 SD: 0.0628 c. M:-0.0991 c. 277: 35 55 187 N T3 SD: 0.0582 c. M: 0.0958 c. 372: 47 74 251 N T3 SD: 0.0522 c. M:-0.0830 c. 403: 51 80 272 N T3 SD: 0.0404 c. M:-0.0671 c. 443: 56 88 299 N T3 SD: 0.0132 c. M: 0.0228 c. 609: 77 121 411 N T3 SD: 0.0085 c. M:-0.0105 c. 1052: 133 209 710 N T3 SD: 0.0035 c. M:-0.0049 c. 1661: 210 330 1121 N T3 SD: 0.0041 c. M:-0.0069 c. 2310: 292 459 1559 N T3 SD: 0.0032 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: 87.7017 cents 6 x 7:8 S SD: 52.4777 cents 7 x 8:9 S SD: 46.7996 cents 8 x 9:11 SD: 33.9173 cents 9 x 10:12 S SD: 10.2441 cents 10 x 11:13 SD: 21.9699 cents 11 x 12:15 S SD: 20.2538 cents 12 x 13:16 SD: 11.6714 cents 13 x 14:17 SD: 23.7710 cents 14 x 15:19 SD: 26.1862 cents 15:16 x 20 S SD: 24.3852 cents 16:17:18:21 S SD: 21.7828 cents 17:18:19:23 SD: 17.8676 cents 18:19:20:24 S SD: 12.2869 cents 19:20:21:25 SD: 12.1215 cents 20:21:22:27 SD: 10.1903 cents 21:22:23:28 SD: 6.0413 cents 29:30:32:39 SD: 5.8825 cents 30:31:33:40 SD: 2.3072 cents 51:53:56:68 SD: 1.2111 cents 81:84:89:108 SD: 0.3815 cents 246:255:270:328 SD: 0.3555 cents 297:308:326:396 SD: 0.2082 cents 378:392:415:504 SD: 0.0818 cents 459:476:504:612 SD: 0.0000 cents