Scala analysis: 214_C14
Chromatic tetrachord 30/29 * 29/27 * 6/5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 30/29 58.691521 2: 10/9 182.403712 minor whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 30/29 58.6915 2: 29/27 123.7122 3: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 30/29 58.692 cents 1: 1 29/27 123.712 cents 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 36/29 374.333 cents 2: 1 58/45 439.353 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 : 58.7 182.4 498.0 58.7 : 123.7 439.4 498.0 182.4: 315.6 374.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.6915 .. 315.6413 cents 29/25, 256.9498 cents 30/29, 58.6915 cents 2: 182.4037 .. 439.3535 cents 29/25, 256.9498 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 30/29, 58.6915 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 2.828603 Largest / Average step : 1.901282 Largest / Smallest step : 5.377971 Median interval of one step : 29/27, 123.7122 cents, amount: 1 Least squares average step : 136.97385 cents, oct.: 410.92156 cents Scale is not proper Scale has trivalence property Scale is a mode of a 314-tone equal temperament with octave 4/3 degrees: 37 115 314 Least number of segments generator : 159 of 252.195 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 275 of 436.186 cents and inv. generated superset size: 12 = 9 more = 400.000% 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 58.69152 cents Scale diversity : 0.916105 Lumma stability : 0.235688 Lumma impropriety factor : 0.267521 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 : 30/29, 58.6915 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 : 29 Odd number limit : 45 (O: 29 U: 45) Highest odd numerator or denominator: 29 Scale harmonicity : 0.014191 Average absolute harmonicity : 0.102803 Specific harmonicity : 0.072571 Fundamental : 1/261, -8.0279 octaves, 1.0024 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 1.566000E+04, 13.93480 octaves Euler's gradus suavitatis : 41 Sum of Mann's harmonic distance : 42.5, average 14.16667 Mersenne's string divisions : 7847 Sum of van Prooijen's expressibility: 2.89376, average 0.96459 Sum of Tenney's harmonic distance : 5.97294, average 1.99098 Vogel's harmonic complexity : 28.00000 Wille's k value : 72 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.22564, average 2.37094 Lattice compactness (without 2's) : 11.99410, average 1.99902 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.33333 4 3: -2 .. 1 -0.66667 4 1 5: 0 .. 1 0.66667 2 1 29: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 17 32| Scale is weakly epimorphic with val: <6 10 17 35| Scale is weakly epimorphic with val: <6 10 17 38| Scale is weakly epimorphic with val: <6 11 18 32| Scale is weakly epimorphic with val: <6 11 19 34| Scale is weakly epimorphic with val: <6 11 19 37| Scale is weakly epimorphic with val: <7 10 16 34| Scale is weakly epimorphic with val: <7 10 16 37| Scale is weakly epimorphic with val: <7 10 18 32| Scale is weakly epimorphic with val: <7 11 16 32| Scale is weakly epimorphic with val: <7 11 16 35| Scale is weakly epimorphic with val: <7 11 16 38| Scale is JI-epimorphic with val: <7 11 17 34| Scale is weakly epimorphic with val: <7 11 17 37| Scale is weakly epimorphic with val: <7 11 19 32| Scale is weakly epimorphic with val: <7 11 19 35| Scale is weakly epimorphic with val: <7 11 19 38| Scale is weakly epimorphic with val: <7 12 18 34| Scale is weakly epimorphic with val: <8 11 17 32| Scale is weakly epimorphic with val: <8 11 17 35| Scale is weakly epimorphic with val: <8 11 17 38| Scale is weakly epimorphic with val: <8 11 18 34| Scale is weakly epimorphic with val: <8 12 15 32| Scale is weakly epimorphic with val: <8 12 18 35| Scale is weakly epimorphic with val: <8 12 19 34| Scale is weakly epimorphic with val: <8 12 19 37|
FIT/MODE
3: 0 1 2 N G T3 SD: 35.1818 c. M: 58.6915 c. 5: 1 1 3 N M DE S SD: 25.5406 c. M:-40.9175 c. 6: 1 1 4 N M DE S SD: 16.9298 c. M:-24.3160 c. 7: 1 2 4 N T3 SD: 19.3126 c. M:-31.0441 c. 8: 1 2 5 N T3 SD: 3.2527 c. M:-4.3632 c. 25: 3 6 16 N T3 SD: 1.8982 c. M: 3.1075 c. 33: 4 8 21 N T3 SD: 1.2241 c. M:-1.6776 c. 41: 5 10 26 N T3 SD: 1.1863 c. M:-2.0457 c. 44: 5 11 28 N T3 SD: 1.4227 c. M: 2.0955 c. 49: 6 12 31 N T3 SD: 1.3620 c. M:-2.2936 c. 52: 6 13 33 N T3 SD: 0.7486 c. M: 1.2248 c. 60: 7 15 38 N T3 SD: 0.3601 c. M: 0.5863 c. 93: 11 23 59 N T3 SD: 0.2245 c. M: 0.3227 c. 153: 18 38 97 N T3 SD: 0.0862 c. M: 0.1127 c. 161: 19 40 102 N T3 SD: 0.0797 c. M:-0.1097 c. 314: 37 78 199 N T3 SD: 0.0028 c. M: 0.0047 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: 78.8780 cents 6 x 7:8 S SD: 42.2336 cents 7 x 8:9 S SD: 39.8203 cents 8 x 9:11 SD: 28.7251 cents 9 x 10:12 S SD: 0.0000 cents 10 x 11:13 SD: 23.5791 cents 11 x 12:15 S SD: 25.1136 cents 12 x 13:16 SD: 21.9155 cents 13 x 14:17 SD: 31.8493 cents 14:15:16:19 SD: 27.9050 cents 15:16:17:20 SD: 21.0516 cents 16:17:18:21 S SD: 19.2821 cents 17:18:19:23 SD: 16.2035 cents 18:19:20:24 S SD: 11.6372 cents 21:22:23:28 SD: 11.0441 cents 24:25:27:32 SD: 8.2061 cents 25:26:28:33 SD: 8.0128 cents 26:27:29:35 SD: 6.3491 cents 27:28:30:36 S SD: 1.4231 cents 90:93:100:120 SD: 0.6416 cents 117:121:130:156 SD: 0.1644 cents 144:149:160:192 SD: 0.1336 cents 261:270:290:348 SD: 0.0000 cents