Scala analysis: 265_C18
Chromatic tetrachord 456/439 * 439/405 * 45/38
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 456/439 65.775462 2: 152/135 205.334300 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 45/38 292.7107 1: 456/439 65.7755 2: 439/405 139.5588 3: 45/38 292.7107
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 456/439 65.775 cents 1: 1 439/405 139.559 cents 1: 1 45/38 292.711 cents 2: 1 152/135 205.334 cents 2: 1 540/439 358.486 cents 2: 1 439/342 432.270 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 : 65.8 205.3 498.0 65.8 : 139.6 432.3 498.0 205.3: 292.7 358.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 65.7755 .. 292.7107 cents 6585/5776, 226.9352 cents 456/439, 65.7755 cents 2: 205.3343 .. 432.2695 cents 6585/5776, 226.9352 cents 5776/6075,-87.3764 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 456/439, 65.7755 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 45/38, 292.7107 cents Average / Smallest step : 2.523966 Largest / Average step : 1.763158 Largest / Smallest step : 4.450150 Median interval of one step : 439/405, 139.5588 cents, amount: 1 Least squares average step : 140.75565 cents, oct.: 422.26694 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2052-tone equal temperament with octave 4/3 degrees: 271 846 2052 Least number of segments generator : 1027 of 249.265 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1435 of 348.292 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 : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 65.77546 cents Scale diversity : 1.003340 Lumma stability : 0.264135 Lumma impropriety factor : 0.175439 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 : 456/439, 65.7755 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 439 Odd number limit : 439 (O: 439 U: 439) Highest odd numerator or denominator: 439 Scale harmonicity : 0.018460 Fundamental : 1/59265, -15.8549 octaves, 0.0044 Hz. Guide tone : 456, 8.8329 octaves, 119301.258 Hz. Exponens Consonantiae : 2.702484E+07, 24.68778 octaves Euler's gradus suavitatis : 472 Sum of Mann's harmonic distance : 594.5, average 198.16667 Mersenne's string divisions : 256865 Sum of van Prooijen's expressibility: 5.24992, average 1.74997 Sum of Tenney's harmonic distance : 10.69279, average 3.56426 Vogel's harmonic complexity : 317.33333 Wille's k value : 9877 Wilson's harmonic complexity : 475 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 19.24318, average 3.20720 Lattice compactness (without 2's) : 14.53950, average 2.42325 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -3 .. 1 -1.00000 5 1 5: -1 .. 0 -0.33333 1 19: 0 .. 1 0.66667 2 1 439: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 15 30 63| Scale is weakly epimorphic with val: <6 10 16 31 64| Scale is weakly epimorphic with val: <6 10 17 32 62| Scale is weakly epimorphic with val: <6 10 18 33 63| Scale is weakly epimorphic with val: <6 10 19 34 64| Scale is weakly epimorphic with val: <6 11 15 33 63| Scale is weakly epimorphic with val: <6 11 16 34 64| Scale is weakly epimorphic with val: <7 10 16 28 63| Scale is weakly epimorphic with val: <7 10 17 29 64| Scale is weakly epimorphic with val: <7 10 17 34 62| Scale is weakly epimorphic with val: <7 10 18 30 62| Scale is weakly epimorphic with val: <7 10 19 31 63| Scale is weakly epimorphic with val: <7 11 15 28 64| Scale is weakly epimorphic with val: <7 11 15 29 63| Scale is weakly epimorphic with val: <7 11 15 31 64| Scale is weakly epimorphic with val: <7 11 15 32 63| Scale is weakly epimorphic with val: <7 11 15 34 64| Scale is weakly epimorphic with val: <7 11 16 29 62| Scale is weakly epimorphic with val: <7 11 16 30 64| Scale is weakly epimorphic with val: <7 11 16 32 62| Scale is weakly epimorphic with val: <7 11 16 33 64| Scale is weakly epimorphic with val: <7 11 17 28 62| Scale is weakly epimorphic with val: <7 11 17 30 63| Scale is JI-epimorphic with val: <7 11 17 31 62| Scale is weakly epimorphic with val: <7 11 17 33 63| Scale is weakly epimorphic with val: <7 11 17 34 62| Scale is weakly epimorphic with val: <7 11 18 28 64| Scale is weakly epimorphic with val: <7 11 18 29 63| Scale is weakly epimorphic with val: <7 11 18 31 64| Scale is JI-epimorphic with val: <7 11 18 32 63| Scale is weakly epimorphic with val: <7 11 18 34 64| Scale is weakly epimorphic with val: <7 11 19 29 62| Scale is weakly epimorphic with val: <7 11 19 30 64| Scale is weakly epimorphic with val: <7 11 19 32 62| Scale is JI-epimorphic with val: <7 11 19 33 64| Scale is weakly epimorphic with val: <7 12 15 33 62| Scale is weakly epimorphic with val: <7 12 15 34 64| Scale is weakly epimorphic with val: <7 12 16 32 62| Scale is weakly epimorphic with val: <7 12 16 34 63| Scale is weakly epimorphic with val: <7 12 17 33 63| Scale is weakly epimorphic with val: <7 12 18 34 64| Scale is weakly epimorphic with val: <7 12 19 32 62| Scale is weakly epimorphic with val: <8 11 15 31 63| Scale is weakly epimorphic with val: <8 11 16 28 62| Scale is weakly epimorphic with val: <8 11 16 32 64| Scale is weakly epimorphic with val: <8 11 17 29 63| Scale is weakly epimorphic with val: <8 11 17 30 62| Scale is weakly epimorphic with val: <8 11 18 30 64| Scale is weakly epimorphic with val: <8 11 18 31 63| Scale is weakly epimorphic with val: <8 11 19 31 62| Scale is weakly epimorphic with val: <8 11 19 32 64| Scale is weakly epimorphic with val: <8 12 15 29 62| Scale is weakly epimorphic with val: <8 12 15 30 64| Scale is weakly epimorphic with val: <8 12 16 30 63| Scale is weakly epimorphic with val: <8 12 16 31 62| Scale is weakly epimorphic with val: <8 12 17 31 64| Scale is weakly epimorphic with val: <8 12 17 32 63| Scale is weakly epimorphic with val: <8 12 18 29 62| Scale is weakly epimorphic with val: <8 12 18 33 64| Scale is weakly epimorphic with val: <8 12 19 30 63| Scale is weakly epimorphic with val: <8 12 19 34 62|
FIT/MODE
3: 0 1 2 N G T3 SD: 44.2433 c. M: 65.7755 c. 5: 1 1 3 N M DE S SD: 19.8504 c. M:-33.8335 c. 7: 1 2 4 N T3 SD: 5.6187 c. M:-8.1136 c. 15: 2 4 9 N T3 SD: 3.5500 c. M: 6.1163 c. 22: 3 6 13 N T3 SD: 1.5386 c. M:-2.1398 c. 29: 4 8 17 N T3 SD: 1.7413 c. M:-2.9204 c. 39: 5 11 23 N T3 SD: 1.2538 c. M: 1.9235 c. 46: 6 13 27 N T3 SD: 0.5181 c. M: 0.8131 c. 68: 9 19 40 N T3 SD: 0.1696 c. M: 0.2569 c. 114: 15 32 67 N T3 SD: 0.1404 c. M: 0.2432 c. 182: 24 51 107 N T3 SD: 0.0797 c. M: 0.0992 c. 303: 40 85 178 N T3 SD: 0.0765 c. M:-0.1298 c. 325: 43 91 191 N T3 SD: 0.0696 c. M:-0.1197 c. 371: 49 104 218 N T3 SD: 0.0341 c. M:-0.0589 c. 439: 58 123 258 N T3 SD: 0.0158 c. M:-0.0255 c. 621: 82 174 365 N T3 SD: 0.0137 c. M: 0.0211 c. 992: 131 278 583 N T3 SD: 0.0060 c. M:-0.0089 c. 1060: 140 297 623 N T3 SD: 0.0053 c. M: 0.0082 c. 1431: 189 401 841 N T3 SD: 0.0058 c. M:-0.0092 c. 1613: 213 452 948 N T3 SD: 0.0046 c. M: 0.0076 c. 2052: 271 575 1206 N T3 SD: 0.0003 c. M: 0.0005 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: 69.4664 cents 6 x 7:8 S SD: 30.7683 cents 7 x 8:9 S SD: 34.0286 cents 8 x 9:11 SD: 26.6460 cents 9 x 10:12 S SD: 11.4653 cents 10 x 11:13 SD: 29.7812 cents 11 x 12:15 S SD: 33.5613 cents 12 x 14:16 S SD: 30.7683 cents 13:14:15:17 SD: 27.5632 cents 14:15:16:19 SD: 22.3279 cents 15:16:17:20 SD: 15.7791 cents 17:18:19:23 SD: 14.5406 cents 18:19:20:24 S SD: 12.0194 cents 21:22:24:28 S SD: 9.9197 cents 22:23:25:29 SD: 9.2598 cents 23:24:26:31 SD: 7.1543 cents 24:25:27:32 SD: 1.7000 cents 78:81:88:104 SD: 1.1761 cents 102:106:115:136 SD: 0.8274 cents 126:131:142:168 SD: 0.7596 cents 159:165:179:212 SD: 0.5541 cents 183:190:206:244 SD: 0.2908 cents 207:215:233:276 SD: 0.1705 cents 309:321:348:412 SD: 0.1597 cents 492:511:554:656 SD: 0.0751 cents 516:536:581:688 SD: 0.0295 cents