Scala analysis: 342_C28
Chromatic tetrachord 114/109 * 109/99 * 22/19
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 114/109 77.646827 2: 38/33 244.240073 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 22/19 253.8049 Godzilla third 1: 114/109 77.6468 2: 109/99 166.5932 3: 22/19 253.8049 Godzilla third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 114/109 77.647 cents 1: 1 109/99 166.593 cents 1: 1 22/19 253.805 cents Godzilla third 2: 1 38/33 244.240 cents 2: 1 132/109 331.452 cents 2: 1 218/171 420.398 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 : 77.6 244.2 498.0 77.6 : 166.6 420.4 498.0 244.2: 253.8 331.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 77.6468 .. 253.8049 cents 1199/1083, 176.1581 cents 114/109, 77.6468 cents 2: 244.2401 .. 420.3982 cents 1199/1083, 176.1581 cents 361/363,-9.5649 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 114/109, 77.6468 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 22/19, 253.8049 cents Average / Smallest step : 2.138078 Largest / Average step : 1.528807 Largest / Smallest step : 3.268710 Median interval of one step : 109/99, 166.5932 cents, amount: 1 Least squares average step : 147.16157 cents, oct.: 441.48471 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1719-tone equal temperament with octave 4/3 degrees: 268 843 1719 Least number of segments generator : 860 of 249.167 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1433 of 415.182 cents and inv. generated superset size: 38 = 35 more = 1266.667% 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 9.56485 cents Scale diversity : 1.033842 Lumma stability : 0.311806 Lumma impropriety factor : 0.019205 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 : 363/361, 9.5649 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 109 Odd number limit : 171 (O: 109 U: 171) Highest odd numerator or denominator: 109 Scale harmonicity : 0.016773 Fundamental : 1/3597, -11.8126 octaves, 0.0727 Hz. Guide tone : 228, 7.8329 octaves, 59650.629 Hz. Exponens Consonantiae : 8.201160E+05, 19.64547 octaves Euler's gradus suavitatis : 143 Sum of Mann's harmonic distance : 150.5, average 50.16667 Mersenne's string divisions : 110831 Sum of van Prooijen's expressibility: 4.03306, average 1.34435 Sum of Tenney's harmonic distance : 8.27181, average 2.75727 Vogel's harmonic complexity : 96.00000 Wille's k value : 1035 Wilson's harmonic complexity : 145 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 12.38573, average 2.06429 Lattice compactness (without 2's) : 10.03261, average 1.67210 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.33333 4 3: -1 .. 1 -0.33333 3 1 11: -1 .. 0 -0.33333 1 19: 0 .. 1 0.66667 2 1 109: -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 23 30 48| Scale is weakly epimorphic with val: <6 10 24 31 49| Scale is weakly epimorphic with val: <6 10 25 32 50| Scale is weakly epimorphic with val: <6 10 26 33 48| Scale is weakly epimorphic with val: <6 10 27 34 49| Scale is weakly epimorphic with val: <6 11 23 31 49| Scale is weakly epimorphic with val: <6 11 24 32 50| Scale is weakly epimorphic with val: <6 11 24 34 48| Scale is weakly epimorphic with val: <6 11 25 33 48| Scale is weakly epimorphic with val: <6 11 26 34 49| Scale is weakly epimorphic with val: <6 11 27 34 48| Scale is weakly epimorphic with val: <7 10 23 29 50| Scale is weakly epimorphic with val: <7 10 23 34 48| Scale is weakly epimorphic with val: <7 10 24 30 48| Scale is weakly epimorphic with val: <7 10 25 31 49| Scale is weakly epimorphic with val: <7 10 26 32 50| Scale is weakly epimorphic with val: <7 10 26 34 48| Scale is weakly epimorphic with val: <7 10 27 33 48| Scale is weakly epimorphic with val: <7 11 23 28 50| Scale is weakly epimorphic with val: <7 11 23 29 49| Scale is weakly epimorphic with val: <7 11 23 31 50| Scale is weakly epimorphic with val: <7 11 23 32 49| Scale is weakly epimorphic with val: <7 11 23 34 50| Scale is weakly epimorphic with val: <7 11 24 29 48| Scale is weakly epimorphic with val: <7 11 24 30 50| Scale is weakly epimorphic with val: <7 11 24 32 48| Scale is weakly epimorphic with val: <7 11 24 33 50| Scale is weakly epimorphic with val: <7 11 25 28 48| Scale is weakly epimorphic with val: <7 11 25 30 49| Scale is JI-epimorphic with val: <7 11 25 31 48| Scale is weakly epimorphic with val: <7 11 25 33 49| Scale is weakly epimorphic with val: <7 11 25 34 48| Scale is weakly epimorphic with val: <7 11 26 28 50| Scale is weakly epimorphic with val: <7 11 26 29 49| Scale is weakly epimorphic with val: <7 11 26 31 50| Scale is JI-epimorphic with val: <7 11 26 32 49| Scale is weakly epimorphic with val: <7 11 26 34 50| Scale is weakly epimorphic with val: <7 11 27 29 48| Scale is weakly epimorphic with val: <7 11 27 30 50| Scale is weakly epimorphic with val: <7 11 27 32 48| Scale is JI-epimorphic with val: <7 11 27 33 50| Scale is weakly epimorphic with val: <7 12 23 31 49| Scale is weakly epimorphic with val: <7 12 23 32 48| Scale is weakly epimorphic with val: <7 12 24 32 50| Scale is weakly epimorphic with val: <7 12 24 33 49| Scale is weakly epimorphic with val: <7 12 25 33 48| Scale is weakly epimorphic with val: <7 12 25 34 50| Scale is weakly epimorphic with val: <7 12 26 32 48| Scale is weakly epimorphic with val: <7 12 26 34 49| Scale is weakly epimorphic with val: <7 12 27 33 49| Scale is weakly epimorphic with val: <8 11 23 29 50| Scale is weakly epimorphic with val: <8 11 23 33 49| Scale is weakly epimorphic with val: <8 11 24 30 48| Scale is weakly epimorphic with val: <8 11 24 34 50| Scale is weakly epimorphic with val: <8 11 25 31 49| Scale is weakly epimorphic with val: <8 11 25 32 48| Scale is weakly epimorphic with val: <8 11 26 32 50| Scale is weakly epimorphic with val: <8 11 26 33 49| Scale is weakly epimorphic with val: <8 11 27 33 48| Scale is weakly epimorphic with val: <8 11 27 34 50| Scale is weakly epimorphic with val: <8 12 23 30 48| Scale is weakly epimorphic with val: <8 12 23 32 49| Scale is weakly epimorphic with val: <8 12 24 31 49| Scale is weakly epimorphic with val: <8 12 24 33 50| Scale is weakly epimorphic with val: <8 12 25 31 48| Scale is weakly epimorphic with val: <8 12 25 32 50| Scale is weakly epimorphic with val: <8 12 26 32 49| Scale is weakly epimorphic with val: <8 12 26 33 48| Scale is weakly epimorphic with val: <8 12 27 33 50| Scale is weakly epimorphic with val: <8 12 27 34 49|
FIT/MODE
3: 0 1 2 N G T3 SD: 63.6349 c. M: 78.2251 c. 4: 1 1 2 P M ME S SD: 27.1977 c. M:-46.8644 c. 5: 1 1 3 N M DE S SD: 28.9213 c. M: 45.0221 c. 6: 1 2 3 P T3 SD: 4.1476 c. M:-5.3607 c. 20: 3 7 10 P T3 SD: 3.2412 c. M:-4.7824 c. 25: 4 8 13 N T3 SD: 3.2135 c. M: 5.1785 c. 26: 4 9 13 P T3 SD: 2.8238 c. M:-4.7824 c. 27: 4 9 14 N T3 SD: 3.3979 c. M: 4.4406 c. 31: 5 10 16 N T3 SD: 2.4334 c. M: 3.2506 c. 33: 5 11 17 N T3 SD: 2.0342 c. M: 2.7637 c. 39: 6 13 20 N T3 SD: 1.0983 c. M: 1.6028 c. 45: 7 15 23 N T3 SD: 0.4452 c. M: 0.7514 c. 51: 8 17 26 N T3 SD: 0.2819 c. M:-0.4779 c. 96: 15 32 49 N T3 SD: 0.2545 c. M: 0.4055 c. 147: 23 49 75 N T3 SD: 0.2362 c. M: 0.2997 c. 161: 25 54 82 N T3 SD: 0.1973 c. M: 0.3106 c. 167: 26 56 85 N T3 SD: 0.1888 c. M:-0.3090 c. 206: 32 69 105 N T3 SD: 0.1649 c. M: 0.2806 c. 212: 33 71 108 N T3 SD: 0.0850 c. M: 0.1210 c. 257: 40 86 131 N T3 SD: 0.0833 c. M: 0.1301 c. 263: 41 88 134 N T3 SD: 0.0279 c. M:-0.0482 c. 571: 89 191 291 N T3 SD: 0.0135 c. M: 0.0181 c. 834: 130 279 425 N T3 SD: 0.0085 c. M: 0.0139 c. 885: 138 296 451 N T3 SD: 0.0084 c. M:-0.0144 c. 1148: 179 384 585 N T3 SD: 0.0083 c. M:-0.0102 c. 1456: 227 487 742 N T3 SD: 0.0039 c. M: 0.0065 c. 1719: 268 575 876 N T3 SD: 0.0012 c. M:-0.0019 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: 55.3011 cents 6 x 7:8 S SD: 11.3154 cents 7 x 8:9 S SD: 32.1512 cents 8 x 9:11 SD: 33.4085 cents 9 x 10:12 S SD: 30.9182 cents 10 x 12:13 S SD: 41.8906 cents 11:12:13:15 SD: 31.3821 cents 12:13:14:16 S SD: 21.6644 cents 13:14:15:17 SD: 20.2976 cents 14:15:16:19 SD: 17.8156 cents 15:16:17:20 SD: 14.6095 cents 18:19:21:24 SD: 9.2301 cents 19:20:22:25 SD: 9.0781 cents 20:21:23:27 SD: 7.5589 cents 21:22:24:28 S SD: 4.4606 cents 39:41:45:52 SD: 3.1982 cents 45:47:52:60 SD: 2.1695 cents 66:69:76:88 SD: 0.2301 cents 369:386:425:492 SD: 0.1652 cents 435:455:501:580 SD: 0.1198 cents 501:524:577:668 SD: 0.0931 cents 567:593:653:756 SD: 0.0808 cents