Scala analysis: 449_D14
Diatonic tetrachord 135/121 * 121/114 * 152/135
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 135/121 189.542832 2: 45/38 292.710699 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 152/135 205.3343 1: 135/121 189.5428 2: 121/114 103.1679 3: 152/135 205.3343
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 121/114 103.168 cents 1: 1 135/121 189.543 cents 1: 1 152/135 205.334 cents 2: 1 45/38 292.711 cents 2: 1 484/405 308.502 cents 2: 1 152/121 394.877 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 : 189.5 292.7 498.0 189.5: 103.2 308.5 498.0 292.7: 205.3 394.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 103.1679 .. 205.3343 cents 5776/5445, 102.1664 cents 121/114, 103.1679 cents 2: 292.7107 .. 394.8771 cents 5776/5445, 102.1664 cents 6075/5776, 87.3764 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 121/114, 103.1679 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 152/135, 205.3343 cents Average / Smallest step : 1.609174 Largest / Average step : 1.236842 Largest / Smallest step : 1.990293 Median interval of one step : 135/121, 189.5428 cents, amount: 1 Least squares average step : 162.07852 cents, oct.: 486.23555 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1009-tone equal temperament with octave 4/3 degrees: 384 593 1009 Least number of segments generator : 505 of 249.269 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 977 of 482.250 cents and inv. generated superset size: 26 = 23 more = 866.667% 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 87.37640 cents Scale diversity : 1.163270 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.589730 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 : 18392/18225, 15.7915 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 19 Odd number limit : 405 (O: 135 U: 405) Highest odd numerator or denominator: 135 Scale harmonicity : 0.011045 Average absolute harmonicity : 0.085111 Specific harmonicity : 0.056469 Fundamental : 1/13794, -13.7518 octaves, 0.0190 Hz. Guide tone : 540, 9.0768 octaves, 141277.805 Hz. Exponens Consonantiae : 7.448760E+06, 22.82857 octaves Euler's gradus suavitatis : 54 Sum of Mann's harmonic distance : 173.0, average 57.66667 Mersenne's string divisions : 148736 Sum of van Prooijen's expressibility: 4.26067, average 1.42022 Sum of Tenney's harmonic distance : 8.52530, average 2.84177 Vogel's harmonic complexity : 39.00000 Wille's k value : 8167 Wilson's harmonic complexity : 58 Rectangular lattice diameter : 8 Triangular lattice diameter : 5 Lattice compactness : 20.74136, average 3.45689 Lattice compactness (without 2's) : 17.53984, average 2.92331 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -1 .. 3 1.33333 6 1 5: 0 .. 1 0.66667 2 11: -2 .. 0 -0.66667 2 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 3 / 3 = 1.00000 Average absolute exponent except 2's: 11 / 3 = 3.66667 Scale is weakly epimorphic with val: <6 10 17 23 28| Scale is weakly epimorphic with val: <6 10 17 26 28| Scale is weakly epimorphic with val: <6 10 18 25 29| Scale is weakly epimorphic with val: <6 10 19 23 29| Scale is weakly epimorphic with val: <6 10 19 23 32| Scale is weakly epimorphic with val: <6 10 19 24 30| Scale is weakly epimorphic with val: <6 10 19 27 30| Scale is weakly epimorphic with val: <6 11 15 23 28| Scale is weakly epimorphic with val: <6 11 15 26 28| Scale is weakly epimorphic with val: <6 11 16 23 30| Scale is weakly epimorphic with val: <6 11 16 23 33| Scale is weakly epimorphic with val: <6 11 16 25 29| Scale is weakly epimorphic with val: <6 11 17 24 30| Scale is weakly epimorphic with val: <6 11 17 27 30| Scale is weakly epimorphic with val: <6 11 18 23 31| Scale is weakly epimorphic with val: <6 11 18 24 29| Scale is weakly epimorphic with val: <6 11 18 24 32| Scale is weakly epimorphic with val: <6 11 18 26 31| Scale is weakly epimorphic with val: <6 11 19 25 32| Scale is weakly epimorphic with val: <7 10 18 23 28| Scale is weakly epimorphic with val: <7 10 18 26 28| Scale is weakly epimorphic with val: <7 10 19 23 30| Scale is weakly epimorphic with val: <7 10 19 23 33| Scale is weakly epimorphic with val: <7 10 19 25 29| Scale is weakly epimorphic with val: <7 11 15 23 29| Scale is weakly epimorphic with val: <7 11 15 23 32| Scale is weakly epimorphic with val: <7 11 15 25 28| Scale is weakly epimorphic with val: <7 11 15 25 31| Scale is weakly epimorphic with val: <7 11 15 25 34| Scale is weakly epimorphic with val: <7 11 15 26 29| Scale is weakly epimorphic with val: <7 11 15 26 32| Scale is JI-epimorphic with val: <7 11 16 24 29| Scale is weakly epimorphic with val: <7 11 16 24 32| Scale is weakly epimorphic with val: <7 11 16 25 30| Scale is weakly epimorphic with val: <7 11 16 25 33| Scale is weakly epimorphic with val: <7 11 16 27 29| Scale is weakly epimorphic with val: <7 11 16 27 32| Scale is weakly epimorphic with val: <7 11 17 23 30| Scale is weakly epimorphic with val: <7 11 17 23 33| Scale is weakly epimorphic with val: <7 11 17 24 28| Scale is weakly epimorphic with val: <7 11 17 24 31| Scale is weakly epimorphic with val: <7 11 17 24 34| Scale is weakly epimorphic with val: <7 11 17 26 30| Scale is weakly epimorphic with val: <7 11 17 26 33| Scale is weakly epimorphic with val: <7 11 17 27 28| Scale is weakly epimorphic with val: <7 11 17 27 31| Scale is weakly epimorphic with val: <7 11 17 27 34| Scale is weakly epimorphic with val: <7 11 18 23 29| Scale is weakly epimorphic with val: <7 11 18 23 32| Scale is weakly epimorphic with val: <7 11 18 25 28| Scale is JI-epimorphic with val: <7 11 18 25 31| Scale is weakly epimorphic with val: <7 11 18 25 34| Scale is weakly epimorphic with val: <7 11 18 26 29| Scale is weakly epimorphic with val: <7 11 18 26 32| Scale is weakly epimorphic with val: <7 11 19 24 29| Scale is weakly epimorphic with val: <7 11 19 24 32| Scale is weakly epimorphic with val: <7 11 19 25 30| Scale is weakly epimorphic with val: <7 11 19 25 33| Scale is weakly epimorphic with val: <7 11 19 27 29| Scale is weakly epimorphic with val: <7 11 19 27 32| Scale is weakly epimorphic with val: <7 12 15 24 28| Scale is weakly epimorphic with val: <7 12 15 24 31| Scale is weakly epimorphic with val: <7 12 15 24 34| Scale is weakly epimorphic with val: <7 12 15 25 29| Scale is weakly epimorphic with val: <7 12 16 24 30| Scale is weakly epimorphic with val: <7 12 16 27 30| Scale is weakly epimorphic with val: <7 12 17 23 31| Scale is weakly epimorphic with val: <7 12 17 25 30| Scale is weakly epimorphic with val: <7 12 17 25 33| Scale is weakly epimorphic with val: <7 12 17 26 31| Scale is weakly epimorphic with val: <7 12 18 25 32| Scale is weakly epimorphic with val: <7 12 19 24 33| Scale is weakly epimorphic with val: <7 12 19 26 29| Scale is weakly epimorphic with val: <7 12 19 26 32| Scale is weakly epimorphic with val: <7 12 19 27 33| Scale is weakly epimorphic with val: <8 11 16 23 29| Scale is weakly epimorphic with val: <8 11 16 23 32| Scale is weakly epimorphic with val: <8 11 17 23 28| Scale is weakly epimorphic with val: <8 11 17 26 28| Scale is weakly epimorphic with val: <8 11 18 24 28| Scale is weakly epimorphic with val: <8 11 18 24 31| Scale is weakly epimorphic with val: <8 11 18 24 34| Scale is weakly epimorphic with val: <8 11 18 25 29| Scale is weakly epimorphic with val: <8 11 19 24 30| Scale is weakly epimorphic with val: <8 11 19 27 30| Scale is weakly epimorphic with val: <8 12 15 23 28| Scale is weakly epimorphic with val: <8 12 15 24 29| Scale is weakly epimorphic with val: <8 12 15 24 32| Scale is weakly epimorphic with val: <8 12 15 26 28| Scale is weakly epimorphic with val: <8 12 16 25 29| Scale is weakly epimorphic with val: <8 12 17 24 30| Scale is weakly epimorphic with val: <8 12 17 25 28| Scale is weakly epimorphic with val: <8 12 17 25 31| Scale is weakly epimorphic with val: <8 12 17 25 34| Scale is weakly epimorphic with val: <8 12 17 27 30| Scale is weakly epimorphic with val: <8 12 18 23 31| Scale is weakly epimorphic with val: <8 12 18 26 31| Scale is weakly epimorphic with val: <8 12 19 25 32| Scale is weakly epimorphic with val: <8 12 19 26 30| Scale is weakly epimorphic with val: <8 12 19 26 33|
FIT/MODE
3: 1 1 1 SP B ME I SD: 26.4548 c. M:-39.3193 c. 5: 2 1 2 SP M ME I SD: 6.6085 c. M:-9.6752 c. 19: 7 4 8 SP T3 SD: 4.3097 c. M: 6.0526 c. 24: 9 5 10 SP T3 SD: 2.0394 c. M: 2.7760 c. 29: 11 6 12 SP T3 SD: 0.5667 c. M: 0.7533 c. 34: 13 7 14 SP T3 SD: 0.5327 c. M:-0.8861 c. 63: 24 13 26 SP T3 SD: 0.1621 c. M: 0.2081 c. 155: 59 32 64 SP T3 SD: 0.1802 c. M: 0.3101 c. 218: 83 45 90 SP T3 SD: 0.1684 c. M: 0.2806 c. 255: 97 53 105 SP T3 SD: 0.1573 c. M:-0.2569 c. 284: 108 59 117 SP T3 SD: 0.1222 c. M:-0.1538 c. 313: 119 65 129 SP T3 SD: 0.1170 c. M: 0.1903 c. 318: 121 66 131 SP T3 SD: 0.0973 c. M:-0.1648 c. 347: 132 72 143 SP T3 SD: 0.0706 c. M:-0.0881 c. 376: 143 78 155 SP T3 SD: 0.0744 c. M: 0.1268 c. 381: 145 79 157 SP T3 SD: 0.0596 c. M:-0.1032 c. 410: 156 85 169 SP T3 SD: 0.0348 c. M: 0.0428 c. 444: 169 92 183 SP T3 SD: 0.0378 c. M:-0.0590 c. 473: 180 98 195 SP T3 SD: 0.0087 c. M: 0.0120 c. 1009: 384 209 416 SP T3 SD: 0.0025 c. M: 0.0044 c. 1482: 564 307 611 SP T3 SD: 0.0020 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 5 x S SD: 93.6030 cents 5 x 6:7 S SD: 43.7622 cents 6 x 7:8 S SD: 12.9199 cents 7:8 x 9 S SD: 37.7400 cents 8:9 x 11 SD: 27.5881 cents 9:10:11:12 H SD: 18.3871 cents 11:12:13:15 SD: 18.3774 cents 13 x 15:17 SD: 28.0731 cents 14:16:17:19 SD: 22.5026 cents 15:17:18:20 SD: 11.8444 cents 16:18:19:21 SD: 10.3966 cents 17:19:20:23 SD: 9.2900 cents 18:20:21:24 S SD: 8.9360 cents 26:29:31:35 SD: 6.7814 cents 27:30:32:36 S SD: 2.4266 cents 60:67:71:80 SD: 0.6568 cents 87:97:103:116 SD: 0.4199 cents 147:164:174:196 SD: 0.2634 cents 336:375:398:448 SD: 0.2443 cents 363:405:430:484 SD: 0.1766 cents 423:472:501:564 SD: 0.1152 cents 510:569:604:680 SD: 0.0510 cents 570:636:675:760 SD: 0.0450 cents