Scala analysis: 411_D8
Diatonic tetrachord 176/163 * 163/150 * 25/22
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 176/163 132.844157 2: 88/75 276.735514 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 25/22 221.3095 undecimal acute whole tone 1: 176/163 132.8442 2: 163/150 143.8914 3: 25/22 221.3095 undecimal acute whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 176/163 132.844 cents 1: 1 163/150 143.891 cents 1: 1 25/22 221.309 cents undecimal acute whole tone 2: 1 88/75 276.736 cents 2: 1 200/163 354.154 cents 2: 1 163/132 365.201 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 : 132.8 276.7 498.0 132.8: 143.9 365.2 498.0 276.7: 221.3 354.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 132.8442 .. 221.3095 cents 4075/3872, 88.4653 cents 176/163, 132.8442 cents 2: 276.7355 .. 365.2008 cents 4075/3872, 88.4653 cents 1936/1875, 55.4260 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 176/163, 132.8442 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 25/22, 221.3095 cents Average / Smallest step : 1.249697 Largest / Average step : 1.333069 Largest / Smallest step : 1.665933 Median interval of one step : 163/150, 143.8914 cents, amount: 1 Least squares average step : 155.74644 cents, oct.: 467.23932 cents Scale is strictly proper Scale has trivalence property 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 55.42603 cents Scale diversity : 1.321630 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.644750 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 : 26569/26400, 11.0472 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 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 77.4181 cents: 2 -- Rational properties -- Prime limit : 163 Odd number limit : 163 (O: 163 U: 163) Highest odd numerator or denominator: 163 Scale harmonicity : 0.026561 Fundamental : 1/12225, -13.5775 octaves, 0.0214 Hz. Guide tone : 176, 7.4594 octaves, 46046.099 Hz. Exponens Consonantiae : 2.151600E+06, 21.03698 octaves Euler's gradus suavitatis : 187 Sum of Mann's harmonic distance : 254.5, average 84.83333 Mersenne's string divisions : 386799 Sum of van Prooijen's expressibility: 4.56437, average 1.52146 Sum of Tenney's harmonic distance : 9.35643, average 3.11881 Vogel's harmonic complexity : 126.66667 Wille's k value : 2037 Wilson's harmonic complexity : 187 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 17.58063, average 2.93010 Lattice compactness (without 2's) : 10.33584, average 1.72264 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -1 .. 0 -0.66667 2 1 5: -2 .. 0 -0.66667 2 11: 0 .. 1 0.66667 2 1 163: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 15 25 54| Scale is weakly epimorphic with val: <6 10 16 27 53| Scale is weakly epimorphic with val: <6 11 15 26 54| Scale is weakly epimorphic with val: <7 10 15 27 52| Scale is weakly epimorphic with val: <7 10 16 24 53| Scale is weakly epimorphic with val: <7 10 17 26 52| Scale is weakly epimorphic with val: <7 10 18 27 52| Scale is weakly epimorphic with val: <7 11 15 24 53| Scale is weakly epimorphic with val: <7 11 15 25 52| Scale is weakly epimorphic with val: <7 11 15 27 53| Scale is weakly epimorphic with val: <7 11 16 23 52| Scale is weakly epimorphic with val: <7 11 16 24 54| Scale is weakly epimorphic with val: <7 11 16 26 52| Scale is weakly epimorphic with val: <7 11 16 27 54| Scale is weakly epimorphic with val: <7 11 17 23 53| Scale is weakly epimorphic with val: <7 11 17 25 54| Scale is JI-epimorphic with val: <7 11 17 26 53| Scale is weakly epimorphic with val: <7 11 18 24 53| Scale is weakly epimorphic with val: <7 11 18 25 52| Scale is weakly epimorphic with val: <7 11 18 27 53| Scale is weakly epimorphic with val: <7 11 19 23 52| Scale is weakly epimorphic with val: <7 11 19 24 54| Scale is weakly epimorphic with val: <7 11 19 26 52| Scale is weakly epimorphic with val: <7 11 19 27 54| Scale is weakly epimorphic with val: <7 12 15 24 54| Scale is weakly epimorphic with val: <7 12 16 26 53| Scale is weakly epimorphic with val: <7 12 16 27 52| Scale is weakly epimorphic with val: <7 12 19 27 52| Scale is weakly epimorphic with val: <8 11 15 24 53| Scale is weakly epimorphic with val: <8 11 16 23 52| Scale is weakly epimorphic with val: <8 11 17 24 52| Scale is weakly epimorphic with val: <8 11 17 25 54| Scale is weakly epimorphic with val: <8 11 18 24 53| Scale is weakly epimorphic with val: <8 11 18 26 54| Scale is weakly epimorphic with val: <8 11 19 23 52| Scale is weakly epimorphic with val: <8 12 15 23 52| Scale is weakly epimorphic with val: <8 12 16 23 53| Scale is weakly epimorphic with val: <8 12 16 25 54| Scale is weakly epimorphic with val: <8 12 17 24 53| Scale is weakly epimorphic with val: <8 12 17 25 52| Scale is weakly epimorphic with val: <8 12 18 23 52| Scale is weakly epimorphic with val: <8 12 18 27 54| Scale is weakly epimorphic with val: <8 12 19 25 54|
FIT/MODE
3: 1 1 1 SP B ME I SD: 37.2281 c. M:-55.2945 c. 4: 1 1 2 P M ME S SD: 16.7078 c. M: 27.7130 c. 7: 2 2 3 SP M ME S SD: 7.0991 c. M:-9.4544 c. 11: 3 3 5 SP M DE S SD: 3.3995 c. M: 5.0746 c. 18: 5 5 8 SP M DE S SD: 3.1765 c. M:-5.5017 c. 23: 6 7 10 SP T3 SD: 3.2279 c. M:-4.7682 c. 27: 7 8 12 SP T3 SD: 2.1487 c. M: 3.7214 c. 34: 9 10 15 SP T3 SD: 1.0841 c. M:-1.5838 c. 45: 12 13 20 SP T3 SD: 0.0314 c. M: 0.0438 c. 862: 230 249 383 SP T3 SD: 0.0285 c. M:-0.0449 c. 907: 242 262 403 SP T3 SD: 0.0257 c. M:-0.0411 c. 952: 254 275 423 SP T3 SD: 0.0232 c. M:-0.0376 c. 997: 266 288 443 SP T3 SD: 0.0210 c. M:-0.0344 c. 1042: 278 301 463 SP T3 SD: 0.0190 c. M:-0.0316 c. 1087: 290 314 483 SP T3 SD: 0.0172 c. M:-0.0289 c. 1132: 302 327 503 SP T3 SD: 0.0156 c. M:-0.0265 c. 1177: 314 340 523 SP T3 SD: 0.0141 c. M:-0.0243 c. 1222: 326 353 543 SP T3 SD: 0.0128 c. M:-0.0222 c. 1267: 338 366 563 SP T3 SD: 0.0117 c. M:-0.0203 c. 1312: 350 379 583 SP T3 SD: 0.0107 c. M:-0.0185 c. 1357: 362 392 603 SP T3 SD: 0.0098 c. M:-0.0168 c. 1402: 374 405 623 SP T3 SD: 0.0091 c. M:-0.0152 c. 1447: 386 418 643 SP T3 SD: 0.0086 c. M:-0.0137 c. 1492: 398 431 663 SP T3 SD: 0.0081 c. M:-0.0124 c. 1537: 410 444 683 SP T3 SD: 0.0078 c. M:-0.0110 c. 1582: 422 457 703 SP T3 SD: 0.0076 c. M:-0.0098 c. 1627: 434 470 723 SP T3 SD: 0.0076 c. M: 0.0098 c. 1672: 446 483 743 SP T3 SD: 0.0076 c. M: 0.0108 c. 1717: 458 496 763 SP T3 SD: 0.0077 c. M: 0.0116 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: 44.4082 cents 9:10:11:12 H SD: 28.7726 cents 10:11:12:13 H SD: 22.2838 cents 11:12:13:15 SD: 14.8543 cents 12:13:14:16 S SD: 3.8024 cents 39:42:46:52 SD: 3.3777 cents 51:55:60:68 SD: 1.6956 cents 63:68:74:84 SD: 0.6580 cents 75:81:88:100 SD: 0.1311 cents 363:392:426:484 SD: 0.1303 cents 438:473:514:584 SD: 0.1219 cents 513:554:602:684 SD: 0.1178 cents 588:635:690:784 SD: 0.1160 cents