Scala analysis: 341_C28
Chromatic tetrachord 57/52 * 104/99 * 22/19
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 57/52 158.940355 2: 38/33 244.240073 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 22/19 253.8049 Godzilla third 1: 57/52 158.9404 2: 104/99 85.2997 3: 22/19 253.8049 Godzilla third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 104/99 85.300 cents 1: 1 57/52 158.940 cents 1: 1 22/19 253.805 cents Godzilla third 2: 1 38/33 244.240 cents 2: 1 208/171 339.105 cents 2: 1 33/26 412.745 cents tridecimal 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 : 158.9 244.2 498.0 158.9: 85.3 339.1 498.0 244.2: 253.8 412.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 85.2997 .. 253.8049 cents 1089/988, 168.5052 cents 104/99, 85.2997 cents 2: 244.2401 .. 412.7453 cents 1089/988, 168.5052 cents 361/363,-9.5649 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 104/99, 85.2997 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 22/19, 253.8049 cents Average / Smallest step : 1.946255 Largest / Average step : 1.528807 Largest / Smallest step : 2.975449 Median interval of one step : 57/52, 158.9404 cents, amount: 1 Least squares average step : 152.96825 cents, oct.: 458.90475 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1197-tone equal temperament with octave 4/3 degrees: 382 587 1197 Least number of segments generator : 599 of 249.231 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 857 of 356.579 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 : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 9.56485 cents Scale diversity : 1.086140 Lumma stability : 0.342538 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 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 19 Odd number limit : 171 (O: 57 U: 171) Highest odd numerator or denominator: 57 Scale harmonicity : 0.011937 Average absolute harmonicity : 0.082857 Specific harmonicity : 0.055345 Fundamental : 1/1716, -10.7448 octaves, 0.1525 Hz. Guide tone : 228, 7.8329 octaves, 59650.629 Hz. Exponens Consonantiae : 3.912480E+05, 18.57772 octaves Euler's gradus suavitatis : 49 Sum of Mann's harmonic distance : 93.5, average 31.16667 Mersenne's string divisions : 54173 Sum of van Prooijen's expressibility: 3.75151, average 1.25050 Sum of Tenney's harmonic distance : 7.64936, average 2.54979 Vogel's harmonic complexity : 33.00000 Wille's k value : 940 Wilson's harmonic complexity : 49 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 17.17727, average 2.86288 Lattice compactness (without 2's) : 10.77729, average 1.79622 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.33333 5 3: -1 .. 1 -0.33333 3 1 11: -1 .. 0 -0.33333 1 13: -1 .. 0 -0.33333 1 19: 0 .. 1 0.66667 2 2 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 26 31| Scale is weakly epimorphic with val: <6 10 23 27 30| Scale is weakly epimorphic with val: <6 10 23 29 34| Scale is weakly epimorphic with val: <6 10 23 30 30| Scale is weakly epimorphic with val: <6 10 24 25 31| Scale is weakly epimorphic with val: <6 10 24 27 32| Scale is weakly epimorphic with val: <6 10 24 28 31| Scale is weakly epimorphic with val: <6 10 25 25 30| Scale is weakly epimorphic with val: <6 10 25 26 32| Scale is weakly epimorphic with val: <6 10 25 28 33| Scale is weakly epimorphic with val: <6 10 25 29 32| Scale is weakly epimorphic with val: <6 10 26 26 31| Scale is weakly epimorphic with val: <6 10 26 27 33| Scale is weakly epimorphic with val: <6 10 26 29 34| Scale is weakly epimorphic with val: <6 10 26 30 33| Scale is weakly epimorphic with val: <6 10 27 27 32| Scale is weakly epimorphic with val: <6 10 27 28 34| Scale is weakly epimorphic with val: <6 11 23 25 31| Scale is weakly epimorphic with val: <6 11 23 26 30| Scale is weakly epimorphic with val: <6 11 23 28 31| Scale is weakly epimorphic with val: <6 11 23 29 33| Scale is weakly epimorphic with val: <6 11 24 26 32| Scale is weakly epimorphic with val: <6 11 24 27 31| Scale is weakly epimorphic with val: <6 11 24 29 32| Scale is weakly epimorphic with val: <6 11 24 30 34| Scale is weakly epimorphic with val: <6 11 25 25 29| Scale is weakly epimorphic with val: <6 11 25 27 33| Scale is weakly epimorphic with val: <6 11 25 28 32| Scale is weakly epimorphic with val: <6 11 25 30 33| Scale is weakly epimorphic with val: <6 11 26 26 30| Scale is weakly epimorphic with val: <6 11 26 28 34| Scale is weakly epimorphic with val: <6 11 26 29 33| Scale is weakly epimorphic with val: <6 11 27 27 31| Scale is weakly epimorphic with val: <6 11 27 30 34| Scale is weakly epimorphic with val: <7 10 23 26 29| Scale is weakly epimorphic with val: <7 10 23 27 34| Scale is weakly epimorphic with val: <7 10 23 29 29| Scale is weakly epimorphic with val: <7 10 24 25 32| Scale is weakly epimorphic with val: <7 10 24 27 30| Scale is weakly epimorphic with val: <7 10 24 30 30| Scale is weakly epimorphic with val: <7 10 25 25 31| Scale is weakly epimorphic with val: <7 10 25 26 33| Scale is weakly epimorphic with val: <7 10 25 28 31| Scale is weakly epimorphic with val: <7 10 26 26 32| Scale is weakly epimorphic with val: <7 10 26 27 34| Scale is weakly epimorphic with val: <7 10 26 29 32| Scale is weakly epimorphic with val: <7 10 27 27 33| Scale is weakly epimorphic with val: <7 10 27 30 33| Scale is JI-epimorphic with val: <7 11 23 25 29| Scale is weakly epimorphic with val: <7 11 23 25 32| Scale is weakly epimorphic with val: <7 11 23 26 28| Scale is weakly epimorphic with val: <7 11 23 26 31| Scale is weakly epimorphic with val: <7 11 23 26 34| Scale is weakly epimorphic with val: <7 11 23 28 29| Scale is weakly epimorphic with val: <7 11 23 28 32| Scale is weakly epimorphic with val: <7 11 23 29 31| Scale is weakly epimorphic with val: <7 11 23 29 34| Scale is JI-epimorphic with val: <7 11 24 26 30| Scale is weakly epimorphic with val: <7 11 24 26 33| Scale is weakly epimorphic with val: <7 11 24 27 29| Scale is weakly epimorphic with val: <7 11 24 27 32| Scale is weakly epimorphic with val: <7 11 24 29 30| Scale is weakly epimorphic with val: <7 11 24 29 33| Scale is weakly epimorphic with val: <7 11 24 30 32| Scale is weakly epimorphic with val: <7 11 25 25 30| Scale is weakly epimorphic with val: <7 11 25 25 33| Scale is weakly epimorphic with val: <7 11 25 27 28| Scale is JI-epimorphic with val: <7 11 25 27 31| = patent Scale is weakly epimorphic with val: <7 11 25 27 34| Scale is weakly epimorphic with val: <7 11 25 28 30| Scale is weakly epimorphic with val: <7 11 25 28 33| Scale is weakly epimorphic with val: <7 11 25 30 31| Scale is weakly epimorphic with val: <7 11 25 30 34| Scale is weakly epimorphic with val: <7 11 26 26 28| Scale is weakly epimorphic with val: <7 11 26 26 31| Scale is weakly epimorphic with val: <7 11 26 26 34| Scale is weakly epimorphic with val: <7 11 26 28 29| Scale is JI-epimorphic with val: <7 11 26 28 32| Scale is weakly epimorphic with val: <7 11 26 29 31| Scale is weakly epimorphic with val: <7 11 26 29 34| Scale is weakly epimorphic with val: <7 11 27 27 29| Scale is weakly epimorphic with val: <7 11 27 27 32| Scale is weakly epimorphic with val: <7 11 27 29 30| Scale is JI-epimorphic with val: <7 11 27 29 33| Scale is weakly epimorphic with val: <7 11 27 30 32| Scale is weakly epimorphic with val: <7 12 23 25 31| Scale is weakly epimorphic with val: <7 12 23 27 32| Scale is weakly epimorphic with val: <7 12 23 28 31| Scale is weakly epimorphic with val: <7 12 24 25 30| Scale is weakly epimorphic with val: <7 12 24 26 32| Scale is weakly epimorphic with val: <7 12 24 28 33| Scale is weakly epimorphic with val: <7 12 24 29 32| Scale is weakly epimorphic with val: <7 12 25 26 31| Scale is weakly epimorphic with val: <7 12 25 27 33| Scale is weakly epimorphic with val: <7 12 25 29 34| Scale is weakly epimorphic with val: <7 12 25 30 33| Scale is weakly epimorphic with val: <7 12 26 27 32| Scale is weakly epimorphic with val: <7 12 26 28 34| Scale is weakly epimorphic with val: <7 12 27 28 33| Scale is weakly epimorphic with val: <8 11 23 25 33| Scale is weakly epimorphic with val: <8 11 23 26 29| Scale is weakly epimorphic with val: <8 11 23 29 29| Scale is weakly epimorphic with val: <8 11 24 26 34| Scale is weakly epimorphic with val: <8 11 24 27 30| Scale is weakly epimorphic with val: <8 11 24 30 30| Scale is weakly epimorphic with val: <8 11 25 25 31| Scale is weakly epimorphic with val: <8 11 25 28 31| Scale is weakly epimorphic with val: <8 11 26 26 32| Scale is weakly epimorphic with val: <8 11 26 29 32| Scale is weakly epimorphic with val: <8 11 27 27 33| Scale is weakly epimorphic with val: <8 11 27 30 33| Scale is weakly epimorphic with val: <8 12 23 25 32| Scale is weakly epimorphic with val: <8 12 23 27 30| Scale is weakly epimorphic with val: <8 12 23 30 30| Scale is weakly epimorphic with val: <8 12 24 25 31| Scale is weakly epimorphic with val: <8 12 24 26 33| Scale is weakly epimorphic with val: <8 12 24 28 31| Scale is weakly epimorphic with val: <8 12 25 26 32| Scale is weakly epimorphic with val: <8 12 25 27 34| Scale is weakly epimorphic with val: <8 12 25 29 32| Scale is weakly epimorphic with val: <8 12 26 27 33| Scale is weakly epimorphic with val: <8 12 26 30 33| Scale is weakly epimorphic with val: <8 12 27 28 34|
FIT/MODE
3: 1 0 2 N G T3 SD: 45.3476 c. M: 78.2251 c. 4: 1 1 2 P M ME S SD: 20.0685 c. M: 34.4291 c. 6: 2 1 3 P T3 SD: 4.9303 c. M:-7.0746 c. 16: 5 3 8 P T3 SD: 3.3551 c. M:-4.7824 c. 22: 7 4 11 P T3 SD: 2.7745 c. M:-4.7824 c. 28: 9 5 14 P T3 SD: 2.8392 c. M:-4.7824 c. 29: 9 5 15 N T3 SD: 3.3473 c. M: 4.3747 c. 31: 10 5 16 N T3 SD: 2.1231 c. M: 3.2506 c. 35: 11 6 18 N T3 SD: 1.9372 c. M: 2.4119 c. 37: 12 6 19 N T3 SD: 1.8700 c. M:-2.5878 c. 41: 13 7 21 N T3 SD: 0.9514 c. M: 1.2913 c. 47: 15 8 24 N T3 SD: 0.2979 c. M: 0.5159 c. 100: 32 17 51 N T3 SD: 0.2754 c. M:-0.4340 c. 147: 47 25 75 N T3 SD: 0.2442 c. M: 0.2997 c. 157: 50 27 80 N T3 SD: 0.1895 c. M: 0.3273 c. 163: 52 28 83 N T3 SD: 0.1193 c. M:-0.1992 c. 210: 67 36 107 N T3 SD: 0.0324 c. M: 0.0403 c. 467: 149 80 238 N T3 SD: 0.0225 c. M: 0.0352 c. 677: 216 116 345 N T3 SD: 0.0212 c. M: 0.0368 c. 724: 231 124 369 N T3 SD: 0.0272 c. M: 0.0337 c. 730: 233 125 372 N T3 SD: 0.0148 c. M:-0.0247 c. 940: 300 161 479 N T3 SD: 0.0100 c. M:-0.0139 c. 987: 315 169 503 N T3 SD: 0.0088 c. M: 0.0113 c. 1197: 382 205 610 N T3 SD: 0.0016 c. M: 0.0025 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 9:10 x 12 S SD: 11.7317 cents 12:13:14:16 S SD: 10.1489 cents 16 x 18:21 S SD: 24.3405 cents 17:19:20:23 SD: 18.6984 cents 18:20:21:24 S SD: 10.8663 cents 19:21:22:25 SD: 9.5602 cents 20:22:23:27 SD: 7.4869 cents 21:23:24:28 SD: 4.3820 cents 33:36:38:44 SD: 2.7678 cents 54:59:62:72 SD: 2.5263 cents 60:66:69:80 SD: 2.1594 cents 72:79:83:96 SD: 0.8462 cents 93:102:107:124 SD: 0.5889 cents 165:181:190:220 SD: 0.4294 cents 198:217:228:264 SD: 0.1023 cents 468:513:539:624 SD: 0.0973 cents 489:536:563:652 SD: 0.0954 cents 561:615:646:748 SD: 0.0541 cents