Scala analysis: 412_D8
Diatonic tetrachord 132/119 * 238/225 * 25/22
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 132/119 179.491627 2: 88/75 276.735514 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 25/22 221.3095 undecimal acute whole tone 1: 132/119 179.4916 2: 238/225 97.2439 3: 25/22 221.3095 undecimal acute whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 238/225 97.244 cents 1: 1 132/119 179.492 cents 1: 1 25/22 221.309 cents undecimal acute whole tone 2: 1 88/75 276.736 cents 2: 1 119/99 318.553 cents 2: 1 150/119 400.801 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 : 179.5 276.7 498.0 179.5: 97.2 318.6 498.0 276.7: 221.3 400.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 97.2439 .. 221.3095 cents 5625/5236, 124.0656 cents 238/225, 97.2439 cents 2: 276.7355 .. 400.8011 cents 5625/5236, 124.0656 cents 1936/1875, 55.4260 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 238/225, 97.2439 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 25/22, 221.3095 cents Average / Smallest step : 1.707202 Largest / Average step : 1.333069 Largest / Smallest step : 2.275819 Median interval of one step : 132/119, 179.4916 cents, amount: 1 Least squares average step : 159.07840 cents, oct.: 477.23521 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1429-tone equal temperament with octave 4/3 degrees: 515 794 1429 Least number of segments generator : 715 of 249.197 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 987 of 343.996 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 55.42603 cents Scale diversity : 1.188355 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.501790 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 : 2975/2904, 41.8179 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 : 17 Odd number limit : 225 (O: 119 U: 225) Highest odd numerator or denominator: 119 Scale harmonicity : 0.012544 Average absolute harmonicity : 0.085793 Specific harmonicity : 0.061537 Fundamental : 1/8925, -13.1236 octaves, 0.0293 Hz. Guide tone : 264, 8.0444 octaves, 69069.149 Hz. Exponens Consonantiae : 2.356200E+06, 21.16803 octaves Euler's gradus suavitatis : 48 Sum of Mann's harmonic distance : 210.5, average 70.16667 Mersenne's string divisions : 286391 Sum of van Prooijen's expressibility: 4.42773, average 1.47591 Sum of Tenney's harmonic distance : 9.09485, average 3.03162 Vogel's harmonic complexity : 34.33333 Wille's k value : 1487 Wilson's harmonic complexity : 51 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 17.34934, average 2.89156 Lattice compactness (without 2's) : 13.49359, average 2.24893 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 1 -0.33333 3 1 5: -2 .. 0 -0.66667 2 7: -1 .. 0 -0.33333 1 11: 0 .. 1 0.66667 2 1 17: -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 JI-epimorphic with val: <7 11 16 19 24 29| Scale is weakly epimorphic with val: <7 11 16 19 26 30| Scale is weakly epimorphic with val: <7 11 16 20 24 31| Scale is weakly epimorphic with val: <7 11 16 20 26 29| Scale is weakly epimorphic with val: <7 11 16 21 24 30| Scale is weakly epimorphic with val: <7 11 16 21 26 31| Scale is weakly epimorphic with val: <7 11 17 19 25 29| Scale is JI-epimorphic with val: <7 11 17 19 26 31| Scale is weakly epimorphic with val: <7 11 17 20 25 31| Scale is JI-epimorphic with val: <7 11 17 20 26 30| Scale is weakly epimorphic with val: <7 11 17 21 25 30| Scale is JI-epimorphic with val: <7 11 17 21 26 29| Scale is weakly epimorphic with val: <7 11 18 19 24 31| Scale is weakly epimorphic with val: <7 11 18 19 25 30| Scale is weakly epimorphic with val: <7 11 18 20 24 30| Scale is weakly epimorphic with val: <7 11 18 20 25 29| Scale is weakly epimorphic with val: <7 11 18 21 24 29| Scale is weakly epimorphic with val: <7 11 18 21 25 31| Scale is weakly epimorphic with val: <7 12 16 19 26 29| Scale is weakly epimorphic with val: <7 12 16 20 26 31| Scale is weakly epimorphic with val: <7 12 16 21 26 30| Scale is weakly epimorphic with val: <7 12 17 19 26 30| Scale is weakly epimorphic with val: <7 12 17 20 26 29| Scale is weakly epimorphic with val: <7 12 18 19 25 29|
FIT/MODE
3: 1 1 1 SP B ME I SD: 32.8588 c. M:-55.2945 c. 4: 1 1 2 P M ME S SD: 35.5474 c. M: 54.9804 c. 5: 2 1 2 SP M ME I SD: 17.0994 c. M:-22.0915 c. 8: 3 1 4 P T3 SD: 16.5423 c. M: 27.7130 c. 9: 3 2 4 SP T3 SD: 7.7808 c. M: 13.4766 c. 11: 4 2 5 SP T3 SD: 3.0747 c. M: 5.0746 c. 20: 7 4 9 SP T3 SD: 3.4005 c. M: 5.1759 c. 25: 9 5 11 SP T3 SD: 1.2577 c. M:-2.1697 c. 36: 13 7 16 SP T3 SD: 0.2082 c. M:-0.3580 c. 169: 61 33 75 SP T3 SD: 0.2285 c. M:-0.2836 c. 189: 68 37 84 SP T3 SD: 0.1755 c. M: 0.3008 c. 225: 81 44 100 SP T3 SD: 0.1156 c. M: 0.1954 c. 261: 94 51 116 SP T3 SD: 0.0733 c. M: 0.1191 c. 297: 107 58 132 SP T3 SD: 0.0435 c. M: 0.0613 c. 333: 120 65 148 SP T3 SD: 0.0269 c. M: 0.0438 c. 655: 236 128 291 SP T3 SD: 0.0343 c. M: 0.0434 c. 691: 249 135 307 SP T3 SD: 0.0246 c. M:-0.0362 c. 727: 262 142 323 SP T3 SD: 0.0187 c. M:-0.0323 c. 763: 275 149 339 SP T3 SD: 0.0183 c. M:-0.0287 c. 1024: 369 200 455 SP T3 SD: 0.0131 c. M: 0.0203 c. 1060: 382 207 471 SP T3 SD: 0.0065 c. M:-0.0084 c. 1096: 395 214 487 SP T3 SD: 0.0046 c. M:-0.0066 c. 1429: 515 279 635 SP T3 SD: 0.0030 c. M: 0.0051 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: 109.5782 cents 5 x 6:7 S SD: 46.4983 cents 6 x 7:8 S SD: 4.9323 cents 7 x 8:9 S SD: 38.8585 cents 8:9 x 11 SD: 29.3013 cents 9:10:11:12 H SD: 23.5775 cents 10:11:12:13 H SD: 20.1238 cents 11:12:13:15 SD: 16.6728 cents 12:13:14:16 S SD: 14.0304 cents 14 x 16:19 SD: 27.4535 cents 15:17:18:20 SD: 17.9417 cents 16:18:19:21 SD: 14.0289 cents 17:19:20:23 SD: 9.6082 cents 18:20:21:24 S SD: 3.4285 cents 45:50:53:60 SD: 2.3880 cents 57:63:67:76 SD: 2.3182 cents 63:70:74:84 SD: 1.1541 cents 81:90:95:108 SD: 1.0006 cents 120:133:141:160 SD: 0.9463 cents 138:153:162:184 SD: 0.4032 cents 156:173:183:208 SD: 0.1885 cents 357:396:419:476 SD: 0.1653 cents 375:416:440:500 SD: 0.0466 cents 531:589:623:708 SD: 0.0380 cents