Scala analysis: 308_C24
Chromatic tetrachord 22/21 * 12/11 * 7/6, Ptolemy
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 22/21 80.537035 undecimal minor semitone 2: 8/7 231.174094 septimal whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 22/21 80.5370 undecimal minor semitone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 14/11 417.508 cents undecimal diminished fourth or major 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 : 80.5 231.2 498.0 80.5 : 150.6 417.5 498.0 231.2: 266.9 347.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 266.8709 cents 49/44, 186.3339 cents 22/21, 80.5370 cents 2: 231.1741 .. 417.5080 cents 49/44, 186.3339 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 2.061350 Largest / Average step : 1.607511 Largest / Smallest step : 3.313642 Median interval of one step : 12/11, 150.6371 cents, amount: 1 Least squares average step : 145.50144 cents, oct.: 436.50433 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1144-tone equal temperament with octave 4/3 degrees: 185 531 1144 Least number of segments generator : 573 of 249.458 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 679 of 295.605 cents and inv. generated superset size: 47 = 44 more = 1566.667% 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 35.69681 cents Scale diversity : 1.088798 Lumma stability : 0.323413 Lumma impropriety factor : 0.071674 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 : 49/48, 35.6968 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle All steps are superparticular (epimoric) 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 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 21 (O: 11 U: 21) Highest odd numerator or denominator: 21 Scale harmonicity : 0.029296 Average absolute harmonicity : 0.106891 Specific harmonicity : 0.137510 Fundamental : 1/21, -4.3923 octaves, 12.4584 Hz. Guide tone : 88, 6.4594 octaves, 23023.050 Hz. Exponens Consonantiae : 1.848000E+03, 10.85175 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 32.5, average 10.83333 Mersenne's string divisions : 4515 Sum of van Prooijen's expressibility: 2.64444, average 0.88148 Sum of Tenney's harmonic distance : 5.49201, average 1.83067 Vogel's harmonic complexity : 9.00000 Wille's k value : 5 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 3 Triangular lattice diameter : 1 Lattice compactness : 13.31194, average 2.21866 Lattice compactness (without 2's) : 7.97469, average 1.32912 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -1 .. 0 -0.66667 2 1 7: -1 .. 0 -0.66667 2 1 11: 0 .. 1 0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 20 27| Scale is weakly epimorphic with val: <6 11 19 27| Scale is weakly epimorphic with val: <7 10 18 23| Scale is weakly epimorphic with val: <7 10 18 26| Scale is weakly epimorphic with val: <7 10 19 25| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 19 27| Scale is weakly 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 22 24| Scale is weakly epimorphic with val: <7 11 22 27| Scale is weakly epimorphic with val: <7 12 18 24| Scale is weakly epimorphic with val: <7 12 18 27| Scale is weakly epimorphic with val: <8 11 20 26| Scale is weakly epimorphic with val: <8 11 21 25| Scale is weakly epimorphic with val: <8 12 19 26| Scale is weakly epimorphic with val: <8 12 21 24| Scale is weakly epimorphic with val: <8 12 21 27|
FIT/MODE
3: 0 1 2 N G T3 SD: 59.8106 c. M: 80.5370 c. 4: 1 1 2 P M ME S SD: 27.4001 c. M:-43.9742 c. 5: 1 1 3 N M DE S SD: 21.4859 c. M: 31.9561 c. 6: 1 2 3 P T3 SD: 10.4030 c. M:-17.8484 c. 7: 1 2 4 N T3 SD: 11.5809 c. M: 17.7262 c. 11: 2 3 6 N T3 SD: 6.4103 c. M:-10.0166 c. 13: 2 4 7 N T3 SD: 2.3828 c. M: 3.9147 c. 24: 4 7 13 N T3 SD: 2.2010 c. M: 2.9035 c. 30: 5 9 16 N T3 SD: 1.5977 c. M:-2.4705 c. 37: 6 11 20 N T3 SD: 1.3588 c. M: 2.3426 c. 43: 7 13 23 N T3 SD: 0.4151 c. M:-0.5401 c. 56: 9 17 30 N T3 SD: 0.2874 c. M: 0.4941 c. 99: 16 30 53 N T3 SD: 0.1414 c. M:-0.2408 c. 155: 25 47 83 N T3 SD: 0.1569 c. M: 0.2072 c. 222: 36 67 119 N T3 SD: 0.1430 c. M:-0.2270 c. 235: 38 71 126 N T3 SD: 0.0958 c. M: 0.1660 c. 278: 45 84 149 N T3 SD: 0.0610 c. M:-0.0818 c. 334: 54 101 179 N T3 SD: 0.0276 c. M: 0.0454 c. 433: 70 131 232 N T3 SD: 0.0170 c. M: 0.0217 c. 711: 115 215 381 N T3 SD: 0.0135 c. M:-0.0188 c. 767: 124 232 411 N T3 SD: 0.0118 c. M: 0.0187 c. 810: 131 245 434 N T3 SD: 0.0118 c. M:-0.0172 c. 1144: 185 346 613 N T3 SD: 0.0021 c. M:-0.0035 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: 59.7273 cents 6 x 7:8 S SD: 17.8484 cents 7 x 8:9 S SD: 31.4805 cents 8 x 9:11 SD: 29.9221 cents 9 x 10:12 S SD: 24.3852 cents 10 x 11:13 SD: 39.6850 cents 11:12:13:15 SD: 32.9913 cents 12:13:14:16 S SD: 22.7117 cents 13:14:15:17 SD: 20.2367 cents 14:15:16:19 SD: 16.5079 cents 15:16:17:20 SD: 11.4648 cents 19:20:22:25 SD: 11.0868 cents 20:21:23:27 SD: 8.1262 cents 21:22:24:28 S SD: 0.0000 cents