Scala analysis: 271_C19
Chromatic tetrachord 66/61 * 122/117 * 13/11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 66/61 136.388138 2: 44/39 208.835280 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 13/11 289.2097 tridecimal minor third 1: 66/61 136.3881 2: 122/117 72.4471 3: 13/11 289.2097 tridecimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 122/117 72.447 cents 1: 1 66/61 136.388 cents 1: 1 13/11 289.210 cents tridecimal minor third 2: 1 44/39 208.835 cents 2: 1 122/99 361.657 cents 2: 1 78/61 425.598 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 : 136.4 208.8 498.0 136.4: 72.4 361.7 498.0 208.8: 289.2 425.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 72.4471 .. 289.2097 cents 1521/1342, 216.7626 cents 122/117, 72.4471 cents 2: 208.8353 .. 425.5979 cents 1521/1342, 216.7626 cents 484/507,-80.3744 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 122/117, 72.4471 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 13/11, 289.2097 cents Average / Smallest step : 2.291533 Largest / Average step : 1.742070 Largest / Smallest step : 3.992010 Median interval of one step : 66/61, 136.3881 cents, amount: 1 Least squares average step : 146.29955 cents, oct.: 438.89865 cents Scale is not proper Scale has trivalence property Scale is a mode of a 818-tone equal temperament with octave 4/3 degrees: 224 343 818 Least number of segments generator : 411 of 250.240 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 425 of 258.764 cents and inv. generated superset size: 48 = 45 more = 1600.000% 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 72.44714 cents Scale diversity : 1.049626 Lumma stability : 0.290926 Lumma impropriety factor : 0.161380 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 : 3861/3721, 63.9410 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 : 61 Odd number limit : 117 (O: 61 U: 117) Highest odd numerator or denominator: 61 Scale harmonicity : 0.020978 Fundamental : 1/2379, -11.2161 octaves, 0.1100 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 3.140280E+05, 18.26053 octaves Euler's gradus suavitatis : 89 Sum of Mann's harmonic distance : 108.5, average 36.16667 Mersenne's string divisions : 73787 Sum of van Prooijen's expressibility: 3.85352, average 1.28451 Sum of Tenney's harmonic distance : 7.91857, average 2.63952 Vogel's harmonic complexity : 60.33333 Wille's k value : 643 Wilson's harmonic complexity : 91 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 12.92706, average 2.15451 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 1.66667 5 3: -1 .. 1 -0.33333 3 1 11: 0 .. 1 0.66667 2 13: -1 .. 0 -0.33333 1 1 61: -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: <7 10 24 25 42| Scale is weakly epimorphic with val: <7 10 25 26 43| Scale is weakly epimorphic with val: <7 10 26 27 44| Scale is weakly epimorphic with val: <7 10 27 28 42| Scale is weakly epimorphic with val: <7 11 23 25 42| Scale is weakly epimorphic with val: <7 11 23 27 43| Scale is weakly epimorphic with val: <7 11 23 28 42| Scale is weakly epimorphic with val: <7 11 23 30 43| Scale is weakly epimorphic with val: <7 11 24 25 44| Scale is weakly epimorphic with val: <7 11 24 26 43| Scale is weakly epimorphic with val: <7 11 24 28 44| Scale is weakly epimorphic with val: <7 11 24 29 43| Scale is JI-epimorphic with val: <7 11 25 26 42| Scale is weakly epimorphic with val: <7 11 25 27 44| Scale is weakly epimorphic with val: <7 11 25 29 42| Scale is weakly epimorphic with val: <7 11 25 30 44| Scale is JI-epimorphic with val: <7 11 26 27 43| Scale is weakly epimorphic with val: <7 11 26 28 42| Scale is weakly epimorphic with val: <7 11 26 30 43| Scale is JI-epimorphic with val: <7 11 27 28 44| Scale is weakly epimorphic with val: <7 11 27 29 43| Scale is weakly epimorphic with val: <7 12 26 27 42| Scale is weakly epimorphic with val: <7 12 26 30 42| Scale is weakly epimorphic with val: <7 12 27 28 43| Scale is weakly epimorphic with val: <8 11 23 25 44| Scale is weakly epimorphic with val: <8 11 24 26 42| Scale is weakly epimorphic with val: <8 11 25 27 43| Scale is weakly epimorphic with val: <8 11 26 27 42| Scale is weakly epimorphic with val: <8 11 26 28 44| Scale is weakly epimorphic with val: <8 11 26 30 42| Scale is weakly epimorphic with val: <8 11 27 28 43| Scale is weakly epimorphic with val: <8 11 27 29 42| Scale is weakly epimorphic with val: <8 12 24 25 42| Scale is weakly epimorphic with val: <8 12 25 26 43| Scale is weakly epimorphic with val: <8 12 25 27 42| Scale is weakly epimorphic with val: <8 12 25 30 42| Scale is weakly epimorphic with val: <8 12 26 27 44| Scale is weakly epimorphic with val: <8 12 26 28 43| Scale is weakly epimorphic with val: <8 12 27 28 42| Scale is weakly epimorphic with val: <8 12 27 29 44|
FIT/MODE
3: 1 0 2 N G T3 SD: 30.0629 c. M: 42.8203 c. 4: 1 1 2 P M ME S SD: 24.1942 c. M:-40.1872 c. 5: 1 1 3 N M DE S SD: 21.9484 c. M: 36.7791 c. 7: 2 1 4 N T3 SD: 4.3286 c. M:-5.9104 c. 19: 5 3 11 N T3 SD: 3.1142 c. M: 5.3237 c. 22: 6 3 13 N T3 SD: 2.9561 c. M: 5.0896 c. 26: 7 4 15 N T3 SD: 1.7132 c. M: 2.2991 c. 29: 8 4 17 N T3 SD: 1.6889 c. M: 2.7477 c. 33: 9 5 19 N T3 SD: 1.4544 c. M:-2.4565 c. 36: 10 5 21 N T3 SD: 1.3621 c. M:-1.9577 c. 48: 13 7 28 N T3 SD: 1.1527 c. M: 1.5010 c. 55: 15 8 32 N T3 SD: 0.4571 c. M: 0.5619 c. 62: 17 9 36 N T3 SD: 0.1005 c. M:-0.1726 c. 179: 49 26 104 N T3 SD: 0.0956 c. M: 0.1572 c. 241: 66 35 140 N T3 SD: 0.0642 c. M: 0.1110 c. 303: 83 44 176 N T3 SD: 0.0536 c. M: 0.0837 c. 365: 100 53 212 N T3 SD: 0.0524 c. M: 0.0657 c. 453: 124 66 263 N T3 SD: 0.0472 c. M: 0.0579 c. 515: 141 75 299 N T3 SD: 0.0355 c. M:-0.0535 c. 577: 158 84 335 N T3 SD: 0.0294 c. M:-0.0501 c. 632: 173 92 367 N T3 SD: 0.0325 c. M: 0.0562 c. 639: 175 93 371 N T3 SD: 0.0279 c. M:-0.0474 c. 694: 190 101 403 N T3 SD: 0.0207 c. M: 0.0358 c. 756: 207 110 439 N T3 SD: 0.0108 c. M: 0.0187 c. 818: 224 119 475 N T3 SD: 0.0029 c. M: 0.0042 c. 1698: 465 247 986 N T3 SD: 0.0024 c. M:-0.0034 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: 68.0849 cents 6 x 7:8 S SD: 29.0178 cents 7 x 8:9 S SD: 33.4032 cents 8 x 9:11 SD: 26.7501 cents 9 x 10:12 S SD: 13.2158 cents 10:11 x 13 SD: 26.1727 cents 11:12 x 15 S SD: 20.7165 cents 12:13:14:16 S SD: 19.3589 cents 13:14:15:17 SD: 17.3501 cents 14:15:16:19 SD: 13.8448 cents 15:16:17:20 SD: 8.6256 cents 19 x 21:25 SD: 21.1592 cents 20:22:23:27 SD: 16.2573 cents 21:23:24:28 SD: 10.2440 cents 22:24:25:29 SD: 9.1294 cents 23:25:26:31 SD: 6.8752 cents 24:26:27:32 SD: 1.7960 cents 63:68:71:84 SD: 1.5236 cents 87:94:98:116 SD: 1.2111 cents 108:117:122:144 SD: 1.0298 cents 123:133:139:164 SD: 1.0227 cents 132:143:149:176 SD: 0.7868 cents 147:159:166:196 SD: 0.5641 cents 171:185:193:228 SD: 0.2357 cents 195:211:220:260 SD: 0.0448 cents