Scala analysis: 331_C25
Chromatic tetrachord 117/107 * 107/102 * 136/117
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 117/107 154.677280 2: 39/34 237.527253 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 136/117 260.5177 1: 117/107 154.6773 2: 107/102 82.8500 3: 136/117 260.5177
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 107/102 82.850 cents 1: 1 117/107 154.677 cents 1: 1 136/117 260.518 cents 2: 1 39/34 237.527 cents 2: 1 428/351 343.368 cents 2: 1 136/107 415.195 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 : 154.7 237.5 498.0 154.7: 82.8 343.4 498.0 237.5: 260.5 415.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 82.8500 .. 260.5177 cents 4624/4173, 177.6678 cents 107/102, 82.8500 cents 2: 237.5273 .. 415.1950 cents 4624/4173, 177.6678 cents 4563/4624,-22.9905 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 107/102, 82.8500 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 136/117, 260.5177 cents Average / Smallest step : 2.003803 Largest / Average step : 1.569242 Largest / Smallest step : 3.144452 Median interval of one step : 117/107, 154.6773 cents, amount: 1 Least squares average step : 151.70477 cents, oct.: 455.11431 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1040-tone equal temperament with octave 4/3 degrees: 323 496 1040 Least number of segments generator : 521 of 249.501 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 619 of 296.433 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 : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 22.99049 cents Scale diversity : 1.089909 Lumma stability : 0.332701 Lumma impropriety factor : 0.046161 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 : 4624/4563, 22.9905 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 107 Odd number limit : 351 (O: 117 U: 351) Highest odd numerator or denominator: 117 Scale harmonicity : 0.015805 Fundamental : 1/10914, -13.4139 octaves, 0.0240 Hz. Guide tone : 468, 8.8704 octaves, 122440.765 Hz. Exponens Consonantiae : 5.107752E+06, 22.28426 octaves Euler's gradus suavitatis : 144 Sum of Mann's harmonic distance : 152.0, average 50.66667 Mersenne's string divisions : 16352 Sum of van Prooijen's expressibility: 4.13637, average 1.37879 Sum of Tenney's harmonic distance : 8.29929, average 2.76643 Vogel's harmonic complexity : 97.66667 Wille's k value : 6259 Wilson's harmonic complexity : 146 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 15.81883, average 2.63647 Lattice compactness (without 2's) : 11.99410, average 1.99902 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -1 .. 2 0.66667 4 1 13: 0 .. 1 0.66667 2 17: -1 .. 0 -0.33333 1 1 107: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 2 / 3 = 0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 26 27 48| Scale is weakly epimorphic with val: <6 10 27 28 49| Scale is weakly epimorphic with val: <6 10 28 29 50| Scale is weakly epimorphic with val: <6 10 29 30 48| Scale is weakly epimorphic with val: <6 10 30 31 49| Scale is weakly epimorphic with val: <6 11 25 27 48| Scale is weakly epimorphic with val: <6 11 26 28 49| Scale is weakly epimorphic with val: <6 11 27 29 50| Scale is weakly epimorphic with val: <6 11 28 30 48| Scale is weakly epimorphic with val: <6 11 29 29 48| Scale is weakly epimorphic with val: <6 11 29 31 49| Scale is weakly epimorphic with val: <6 11 29 32 48| Scale is weakly epimorphic with val: <6 11 30 30 49| Scale is weakly epimorphic with val: <6 11 30 32 50| Scale is weakly epimorphic with val: <6 11 30 33 49| Scale is weakly epimorphic with val: <7 10 27 27 48| Scale is weakly epimorphic with val: <7 10 28 28 49| Scale is weakly epimorphic with val: <7 10 29 29 50| Scale is weakly epimorphic with val: <7 10 30 30 48| Scale is weakly epimorphic with val: <7 11 25 27 49| Scale is weakly epimorphic with val: <7 11 25 28 48| Scale is weakly epimorphic with val: <7 11 25 30 49| Scale is weakly 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 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 weakly epimorphic with val: <7 11 26 32 49| Scale is weakly epimorphic with val: <7 11 27 27 50| Scale is JI-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 weakly epimorphic with val: <7 11 27 33 50| Scale is weakly epimorphic with val: <7 11 28 28 48| Scale is JI-epimorphic with val: <7 11 28 30 49| Scale is weakly epimorphic with val: <7 11 28 31 48| Scale is weakly epimorphic with val: <7 11 28 33 49| Scale is weakly epimorphic with val: <7 11 29 29 49| Scale is JI-epimorphic with val: <7 11 29 31 50| Scale is weakly epimorphic with val: <7 11 29 32 49| Scale is weakly epimorphic with val: <7 11 30 30 50| Scale is weakly epimorphic with val: <7 11 30 32 48| Scale is weakly epimorphic with val: <7 11 30 33 50| Scale is weakly epimorphic with val: <7 12 25 27 48| Scale is weakly epimorphic with val: <7 12 26 28 49| Scale is weakly epimorphic with val: <7 12 27 28 48| Scale is weakly epimorphic with val: <7 12 27 29 50| Scale is weakly epimorphic with val: <7 12 27 31 48| Scale is weakly epimorphic with val: <7 12 28 29 49| Scale is weakly epimorphic with val: <7 12 28 30 48| Scale is weakly epimorphic with val: <7 12 28 32 49| Scale is weakly epimorphic with val: <7 12 29 30 50| Scale is weakly epimorphic with val: <7 12 29 31 49| Scale is weakly epimorphic with val: <7 12 29 33 50| Scale is weakly epimorphic with val: <7 12 30 32 50| Scale is weakly epimorphic with val: <8 11 27 27 48| Scale is weakly epimorphic with val: <8 11 28 28 49| Scale is weakly epimorphic with val: <8 11 29 29 50| Scale is weakly epimorphic with val: <8 11 29 31 48| Scale is weakly epimorphic with val: <8 11 30 30 48| Scale is weakly epimorphic with val: <8 11 30 32 49| Scale is weakly epimorphic with val: <8 12 26 27 48| Scale is weakly epimorphic with val: <8 12 27 28 49| Scale is weakly epimorphic with val: <8 12 27 29 48| Scale is weakly epimorphic with val: <8 12 27 32 48| Scale is weakly epimorphic with val: <8 12 28 29 50| Scale is weakly epimorphic with val: <8 12 28 30 49| Scale is weakly epimorphic with val: <8 12 28 33 49| Scale is weakly epimorphic with val: <8 12 29 30 48| Scale is weakly epimorphic with val: <8 12 29 31 50| Scale is weakly epimorphic with val: <8 12 30 31 49|
FIT/MODE
3: 1 0 2 N G T3 SD: 41.8033 c. M: 71.5123 c. 4: 1 1 2 P M ME S SD: 18.6380 c. M: 30.1660 c. 6: 2 1 3 P T3 SD: 9.3217 c. M:-11.4952 c. 10: 3 2 5 P T3 SD: 7.2995 c. M:-11.4952 c. 13: 4 2 7 N T3 SD: 4.4994 c. M: 7.6603 c. 19: 6 3 10 N T3 SD: 1.7660 c. M:-2.6001 c. 23: 7 4 12 N T3 SD: 1.8300 c. M: 3.0984 c. 29: 9 5 15 N T3 SD: 1.6803 c. M:-2.9083 c. 36: 11 6 19 N T3 SD: 1.9754 c. M: 2.4969 c. 42: 13 7 22 N T3 SD: 0.3664 c. M: 0.5205 c. 90: 28 15 47 N T3 SD: 0.2920 c. M:-0.4276 c. 132: 41 22 69 N T3 SD: 0.1022 c. M:-0.1760 c. 174: 54 29 91 N T3 SD: 0.0697 c. M: 0.1116 c. 306: 95 51 160 N T3 SD: 0.0671 c. M:-0.1021 c. 325: 101 54 170 N T3 SD: 0.0576 c. M:-0.0998 c. 367: 114 61 192 N T3 SD: 0.0284 c. M: 0.0399 c. 499: 155 83 261 N T3 SD: 0.0181 c. M:-0.0261 c. 541: 168 90 283 N T3 SD: 0.0118 c. M: 0.0164 c. 1040: 323 173 544 N T3 SD: 0.0026 c. M:-0.0040 c. 1581: 491 263 827 N T3 SD: 0.0024 c. M: 0.0030 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: 57.5250 cents 6 x 7:8 S SD: 14.6718 cents 7 x 8:9 S SD: 31.6403 cents 8 x 9:11 SD: 31.4965 cents 9:10 x 12 S SD: 13.8632 cents 10:11 x 13 SD: 22.5156 cents 11:12:13:15 SD: 21.6052 cents 12:13:14:16 S SD: 11.1575 cents 16 x 18:21 S SD: 21.6417 cents 17:19:20:23 SD: 21.0683 cents 18:20:21:24 S SD: 13.4569 cents 19:21:22:25 SD: 11.2368 cents 20:22:23:27 SD: 8.0885 cents 21:23:24:28 SD: 2.3164 cents 54:59:62:72 SD: 0.7133 cents 75:82:86:100 SD: 0.2080 cents 204:223:234:272 SD: 0.1693 cents 279:305:320:372 SD: 0.1511 cents 354:387:406:472 SD: 0.1507 cents