Scala analysis: 184_C8
Chromatic tetrachord 28/27 * 81/77 * 11/9
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: 12/11 150.637059 undecimal neutral second, 3/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 11/9 347.4079 undecimal neutral third 1: 28/27 62.9609 Archytas' 1/3-tone 2: 81/77 87.6762 3: 11/9 347.4079 undecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 81/77 87.676 cents 1: 1 11/9 347.408 cents undecimal neutral third 2: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 1 308/243 410.369 cents 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 : 63.0 150.6 498.0 63.0 : 87.7 435.1 498.0 150.6: 347.4 410.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 347.4079 cents 33/28, 284.4470 cents 28/27, 62.9609 cents 2: 150.6371 .. 435.0841 cents 33/28, 284.4470 cents 108/121,-196.7709 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 : 11/9, 347.4079 cents Average / Smallest step : 2.636795 Largest / Average step : 2.092630 Largest / Smallest step : 5.517836 Median interval of one step : 81/77, 87.6762 cents, amount: 1 Least squares average step : 132.74072 cents, oct.: 398.22215 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1511-tone equal temperament with octave 4/3 degrees: 191 457 1511 Least number of segments generator : 756 of 249.187 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1071 of 353.015 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 : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 62.96090 cents Scale diversity : 0.791311 Lumma stability : 0.252832 Lumma impropriety factor : 0.395087 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 : 2187/2156, 24.7153 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 259.7318 cents: 2 -- Rational properties -- Prime limit : 11 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.024311 Average absolute harmonicity : 0.102449 Specific harmonicity : 0.126914 Fundamental : 1/297, -8.2143 octaves, 0.8809 Hz. Guide tone : 84, 6.3923 octaves, 21976.547 Hz. Exponens Consonantiae : 2.494800E+04, 14.60664 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 42.5, average 14.16667 Mersenne's string divisions : 8855 Sum of van Prooijen's expressibility: 2.94988, average 0.98329 Sum of Tenney's harmonic distance : 6.07828, average 2.02609 Vogel's harmonic complexity : 17.66667 Wille's k value : 49 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 17.14199, average 2.85700 Lattice compactness (without 2's) : 14.29127, average 2.38188 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -3 .. 1 -1.00000 5 1 7: 0 .. 1 0.33333 1 1 11: -1 .. 0 -0.33333 1 1 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 21 24| Scale is weakly epimorphic with val: <6 10 21 27| Scale is weakly epimorphic with val: <7 10 19 25| Scale is weakly epimorphic with val: <7 11 18 24| Scale is weakly epimorphic with val: <7 11 18 27| Scale is JI-epimorphic with val: <7 11 20 23| Scale is weakly epimorphic with val: <7 11 20 26| Scale is weakly epimorphic with val: <7 11 21 24| Scale is weakly epimorphic with val: <7 11 21 27| Scale is weakly epimorphic with val: <7 12 20 23| Scale is weakly epimorphic with val: <8 11 18 24| Scale is weakly epimorphic with val: <8 11 20 23| Scale is weakly epimorphic with val: <8 11 20 26| Scale is weakly epimorphic with val: <8 11 21 24| Scale is weakly epimorphic with val: <8 12 19 25| Scale is weakly epimorphic with val: <8 12 22 25|
FIT/MODE
3: 0 1 2 N G T3 SD: 37.4191 c. M: 62.9609 c. 4: 0 1 3 N G T3 SD: 39.3558 c. M: 62.9609 c. 6: 1 1 4 N M DE S SD: 14.5871 c. M:-20.0466 c. 7: 1 1 5 N M DE S SD: 6.7473 c. M: 8.3385 c. 10: 1 2 7 N T3 SD: 7.6286 c. M: 13.1564 c. 13: 2 2 9 N M DE S SD: 8.0298 c. M:-13.6614 c. 16: 2 3 11 N T3 SD: 2.9165 c. M:-5.0020 c. 17: 2 3 12 N T3 SD: 3.4796 c. M: 4.3674 c. 23: 3 4 16 N T3 SD: 1.2771 c. M:-2.0015 c. 40: 5 7 28 N T3 SD: 0.8154 c. M: 1.2236 c. 56: 7 10 39 N T3 SD: 0.5182 c. M: 0.7053 c. 63: 8 11 44 N T3 SD: 0.2986 c. M: 0.4330 c. 119: 15 21 83 N T3 SD: 0.1068 c. M: 0.1821 c. 142: 18 25 99 N T3 SD: 0.1433 c. M:-0.1794 c. 182: 23 32 127 N T3 SD: 0.0754 c. M: 0.1290 c. 261: 33 46 182 N T3 SD: 0.0650 c. M:-0.1122 c. 301: 38 53 210 N T3 SD: 0.0618 c. M: 0.0848 c. 324: 41 57 226 N T3 SD: 0.0367 c. M:-0.0633 c. 443: 56 78 309 N T3 SD: 0.0077 c. M:-0.0131 c. 1068: 135 188 745 N T3 SD: 0.0072 c. M: 0.0111 c. 1392: 176 245 971 N T3 SD: 0.0072 c. M:-0.0103 c. 1511: 191 266 1054 N T3 SD: 0.0036 c. M: 0.0049 c. 1954: 247 344 1363 N T3 SD: 0.0025 c. M: 0.0043 c. 2397: 303 422 1672 N T3 SD: 0.0027 c. M: 0.0040 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: 92.6837 cents 6 x 7:8 S SD: 58.1169 cents 7 x 8:9 S SD: 51.1133 cents 8 x 9:11 SD: 37.6697 cents 9 x 10:12 S SD: 15.8833 cents 10 x 11:13 SD: 23.0628 cents 11 x 12:15 S SD: 19.4529 cents 12 x 13:16 SD: 6.0322 cents 13 x 14:17 SD: 20.1813 cents 14 x 15:19 SD: 21.8633 cents 15 x 16:20 S SD: 19.4529 cents 16:17 x 21 SD: 25.0343 cents 17:18:19:23 SD: 20.2530 cents 18:19:20:24 S SD: 14.7123 cents 19:20:21:25 SD: 13.7666 cents 20:21:22:27 SD: 11.2124 cents 21:22:23:28 SD: 6.2887 cents 24:25:26:32 SD: 4.7728 cents 33:34:36:44 SD: 3.7595 cents 53:55:58:71 SD: 3.2877 cents 54:56:59:72 SD: 0.8899 cents 111:115:121:148 SD: 0.7060 cents 132:137:144:176 SD: 0.4682 cents 165:171:180:220 SD: 0.3748 cents 219:227:239:292 SD: 0.3577 cents 243:252:265:324 SD: 0.1979 cents 297:308:324:396 SD: 0.0000 cents