Scala analysis: 277_C19
Chromatic tetrachord 28/27 * 99/91 * 13/11
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: 44/39 208.835280 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 13/11 289.2097 tridecimal minor third 1: 28/27 62.9609 Archytas' 1/3-tone 2: 99/91 145.8744 3: 13/11 289.2097 tridecimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 99/91 145.874 cents 1: 1 13/11 289.210 cents tridecimal minor third 2: 1 44/39 208.835 cents 2: 1 364/297 352.171 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 : 63.0 208.8 498.0 63.0 : 145.9 435.1 498.0 208.8: 289.2 352.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 289.2097 cents 351/308, 226.2488 cents 28/27, 62.9609 cents 2: 208.8353 .. 435.0841 cents 351/308, 226.2488 cents 484/507,-80.3744 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 : 13/11, 289.2097 cents Average / Smallest step : 2.636795 Largest / Average step : 1.742070 Largest / Smallest step : 4.593481 Median interval of one step : 99/91, 145.8744 cents, amount: 1 Least squares average step : 141.05475 cents, oct.: 423.16424 cents Scale is not proper Scale has trivalence property Scale is a mode of a 973-tone equal temperament with octave 4/3 degrees: 123 408 973 Least number of segments generator : 487 of 249.278 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 801 of 410.004 cents and inv. generated superset size: 30 = 27 more = 1000.000% 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 : 0.982829 Lumma stability : 0.252832 Lumma impropriety factor : 0.161380 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 : 28/27, 62.9609 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% -- Rational properties -- Prime limit : 13 Odd number limit : 297 (O: 99 U: 297) Highest odd numerator or denominator: 39 Scale harmonicity : 0.016496 Average absolute harmonicity : 0.095267 Specific harmonicity : 0.087977 Fundamental : 1/351, -8.4553 octaves, 0.7454 Hz. Guide tone : 308, 8.2668 octaves, 80580.674 Hz. Exponens Consonantiae : 1.081080E+05, 16.72211 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 72.5, average 24.16667 Mersenne's string divisions : 31955 Sum of van Prooijen's expressibility: 3.49955, average 1.16652 Sum of Tenney's harmonic distance : 7.19222, average 2.39741 Vogel's harmonic complexity : 20.66667 Wille's k value : 58 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 14.91951, average 2.48658 Lattice compactness (without 2's) : 12.19036, average 2.03173 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -3 ..-1 -1.66667 5 1 7: 0 .. 1 0.33333 1 1 11: 0 .. 1 0.33333 1 13: -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 23 27| Scale is weakly epimorphic with val: <6 10 21 23 30| Scale is weakly epimorphic with val: <6 10 21 24 25| Scale is weakly epimorphic with val: <6 10 21 24 28| Scale is weakly epimorphic with val: <6 10 21 25 26| Scale is weakly epimorphic with val: <6 10 21 25 29| Scale is weakly epimorphic with val: <6 10 21 26 27| Scale is weakly epimorphic with val: <6 10 21 26 30| Scale is weakly epimorphic with val: <6 10 21 27 28| Scale is weakly epimorphic with val: <7 10 18 24 25| Scale is weakly epimorphic with val: <7 10 18 25 26| Scale is weakly epimorphic with val: <7 10 18 26 27| Scale is weakly epimorphic with val: <7 10 18 27 28| Scale is weakly epimorphic with val: <7 10 19 23 25| Scale is weakly epimorphic with val: <7 10 19 23 28| Scale is weakly epimorphic with val: <7 10 19 24 26| Scale is weakly epimorphic with val: <7 10 19 24 29| Scale is weakly epimorphic with val: <7 10 19 25 27| Scale is weakly epimorphic with val: <7 10 19 25 30| Scale is weakly epimorphic with val: <7 10 19 26 28| Scale is weakly epimorphic with val: <7 10 19 27 29| Scale is weakly epimorphic with val: <7 10 21 24 25| Scale is weakly epimorphic with val: <7 10 21 25 26| Scale is weakly epimorphic with val: <7 10 21 26 27| Scale is weakly epimorphic with val: <7 10 21 27 28| Scale is weakly epimorphic with val: <7 11 18 23 25| Scale is weakly epimorphic with val: <7 11 18 23 28| Scale is weakly epimorphic with val: <7 11 18 24 26| Scale is weakly epimorphic with val: <7 11 18 24 29| Scale is weakly epimorphic with val: <7 11 18 25 27| Scale is weakly epimorphic with val: <7 11 18 25 30| Scale is weakly epimorphic with val: <7 11 18 26 28| Scale is weakly epimorphic with val: <7 11 18 27 29| Scale is weakly epimorphic with val: <7 11 20 23 27| Scale is weakly epimorphic with val: <7 11 20 23 30| Scale is JI-epimorphic with val: <7 11 20 24 25| Scale is weakly epimorphic with val: <7 11 20 24 28| Scale is JI-epimorphic with val: <7 11 20 25 26| Scale is weakly epimorphic with val: <7 11 20 25 29| Scale is JI-epimorphic with val: <7 11 20 26 27| Scale is weakly epimorphic with val: <7 11 20 26 30| Scale is JI-epimorphic with val: <7 11 20 27 28| Scale is weakly epimorphic with val: <7 11 21 23 25| Scale is weakly epimorphic with val: <7 11 21 23 28| Scale is weakly epimorphic with val: <7 11 21 24 26| Scale is weakly epimorphic with val: <7 11 21 24 29| Scale is weakly epimorphic with val: <7 11 21 25 27| Scale is weakly epimorphic with val: <7 11 21 25 30| Scale is weakly epimorphic with val: <7 11 21 26 28| Scale is weakly epimorphic with val: <7 11 21 27 29| Scale is weakly epimorphic with val: <8 11 18 23 25| Scale is weakly epimorphic with val: <8 11 18 24 26| Scale is weakly epimorphic with val: <8 11 18 25 27| Scale is weakly epimorphic with val: <8 11 18 26 28| Scale is weakly epimorphic with val: <8 11 18 27 29| Scale is weakly epimorphic with val: <8 11 20 23 27| Scale is weakly epimorphic with val: <8 11 20 23 30| Scale is weakly epimorphic with val: <8 11 20 24 25| Scale is weakly epimorphic with val: <8 11 20 24 28| Scale is weakly epimorphic with val: <8 11 20 25 26| Scale is weakly epimorphic with val: <8 11 20 25 29| Scale is weakly epimorphic with val: <8 11 20 26 27| Scale is weakly epimorphic with val: <8 11 20 26 30| Scale is weakly epimorphic with val: <8 11 20 27 28| Scale is weakly epimorphic with val: <8 11 21 23 25| Scale is weakly epimorphic with val: <8 11 21 24 26| Scale is weakly epimorphic with val: <8 11 21 25 27| Scale is weakly epimorphic with val: <8 11 21 26 28| Scale is weakly epimorphic with val: <8 11 21 27 29| Scale is weakly epimorphic with val: <8 12 19 24 25| Scale is weakly epimorphic with val: <8 12 19 25 26| Scale is weakly epimorphic with val: <8 12 19 26 27| Scale is weakly epimorphic with val: <8 12 19 27 28| Scale is weakly epimorphic with val: <8 12 22 24 25| Scale is weakly epimorphic with val: <8 12 22 25 26| Scale is weakly epimorphic with val: <8 12 22 26 27| Scale is weakly epimorphic with val: <8 12 22 27 28|
FIT/MODE
3: 0 1 2 N G T3 SD: 43.9608 c. M: 62.9609 c. 5: 1 1 3 N M DE S SD: 21.8752 c. M:-36.6481 c. 6: 1 2 3 P T3 SD: 25.9286 c. M:-40.1872 c. 7: 1 2 4 N T3 SD: 5.4260 c. M:-8.1884 c. 16: 2 5 9 N T3 SD: 5.2463 c. M:-9.0594 c. 17: 2 5 10 N T3 SD: 3.3265 c. M: 4.3674 c. 24: 3 7 14 N T3 SD: 0.8623 c. M: 1.3165 c. 31: 4 9 18 N T3 SD: 0.7524 c. M:-1.3030 c. 55: 7 16 32 N T3 SD: 0.4073 c. M: 0.5619 c. 79: 10 23 46 N T3 SD: 0.4593 c. M: 0.7912 c. 112: 14 33 65 N T3 SD: 0.4183 c. M: 0.7053 c. 119: 15 35 69 N T3 SD: 0.2682 c. M:-0.4273 c. 143: 18 42 83 N T3 SD: 0.1742 c. M: 0.2699 c. 174: 22 51 101 N T3 SD: 0.0665 c. M:-0.1146 c. 198: 25 58 115 N T3 SD: 0.0557 c. M: 0.0764 c. 372: 47 109 216 N T3 SD: 0.0244 c. M: 0.0359 c. 570: 72 167 331 N T3 SD: 0.0290 c. M: 0.0500 c. 601: 76 176 349 N T3 SD: 0.0117 c. M:-0.0198 c. 799: 101 234 464 N T3 SD: 0.0106 c. M: 0.0179 c. 973: 123 285 565 N T3 SD: 0.0034 c. M:-0.0058 c. 1574: 199 461 914 N T3 SD: 0.0040 c. M:-0.0067 c. 1772: 224 519 1029 N T3 SD: 0.0032 c. M: 0.0049 c. 2373: 300 695 1378 N T3 SD: 0.0033 c. M: 0.0048 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: 68.0849 cents 6 x 7:8 S SD: 29.0178 cents 7 x 8:9 S SD: 33.4032 cents 8 x 9:11 SD: 26.7501 cents 9 x 10:12 S SD: 13.2158 cents 10 x 11:13 SD: 30.9932 cents 11 x 12:15 S SD: 35.0025 cents 12 x 14:16 S SD: 29.0178 cents 13:14:15:17 SD: 27.7143 cents 14:15:16:19 SD: 22.6769 cents 15:16:17:20 SD: 16.4661 cents 17:18:19:23 SD: 15.6322 cents 18:19:20:24 S SD: 13.4890 cents 21:22:24:28 S SD: 9.4748 cents 22:23:25:29 SD: 9.0857 cents 23:24:26:31 SD: 7.2793 cents 24:25:27:32 SD: 3.0501 cents 54:56:61:72 SD: 0.7282 cents 132:137:149:176 SD: 0.5550 cents 186:193:210:248 SD: 0.5379 cents 219:227:247:292 SD: 0.3347 cents 243:252:274:324 SD: 0.3239 cents 273:283:308:364 SD: 0.2265 cents 297:308:335:396 SD: 0.1325 cents 351:364:396:468 SD: 0.0000 cents