Scala analysis: 424_D10
Diatonic tetrachord 67/62 * 62/57 * 76/67
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 67/62 134.271456 2: 67/57 279.839012 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 76/67 218.2060 1: 67/62 134.2715 2: 62/57 145.5676 3: 76/67 218.2060
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 67/62 134.271 cents 1: 1 62/57 145.568 cents 1: 1 76/67 218.206 cents 2: 1 67/57 279.839 cents 2: 1 38/31 352.477 cents 2: 1 248/201 363.774 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 : 134.3 279.8 498.0 134.3: 145.6 363.8 498.0 279.8: 218.2 352.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 134.2715 .. 218.2060 cents 4712/4489, 83.9345 cents 67/62, 134.2715 cents 2: 279.8390 .. 363.7735 cents 4712/4489, 83.9345 cents 4489/4332, 61.6330 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 67/62, 134.2715 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 76/67, 218.2060 cents Average / Smallest step : 1.236413 Largest / Average step : 1.314375 Largest / Smallest step : 1.625111 Median interval of one step : 62/57, 145.5676 cents, amount: 1 Least squares average step : 156.29175 cents, oct.: 468.87524 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 61.63302 cents Scale diversity : 1.333715 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.662944 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 : 3844/3819, 11.2961 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 72.6384 cents: 2 -- Rational properties -- Prime limit : 67 Odd number limit : 201 (O: 67 U: 201) Highest odd numerator or denominator: 67 Scale harmonicity : 0.025143 Fundamental : 1/3534, -11.7871 octaves, 0.0740 Hz. Guide tone : 268, 8.0661 octaves, 70115.652 Hz. Exponens Consonantiae : 9.471120E+05, 19.85318 octaves Euler's gradus suavitatis : 120 Sum of Mann's harmonic distance : 130.0, average 43.33333 Mersenne's string divisions : 111972 Sum of van Prooijen's expressibility: 4.12927, average 1.37642 Sum of Tenney's harmonic distance : 8.27960, average 2.75987 Vogel's harmonic complexity : 80.33333 Wille's k value : 1909 Wilson's harmonic complexity : 120 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 11.78068, average 1.96345 Lattice compactness (without 2's) : 5.82843, average 0.97140 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -1 .. 0 -0.66667 2 1 19: -1 .. 0 -0.33333 1 31: -1 .. 0 -0.33333 1 67: 0 .. 1 0.66667 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 28 36 45| Scale is weakly epimorphic with val: <6 10 29 34 43| Scale is weakly epimorphic with val: <6 10 30 33 43| Scale is weakly epimorphic with val: <6 10 30 35 44| Scale is weakly epimorphic with val: <6 10 30 36 43| Scale is weakly epimorphic with val: <6 10 30 39 43| Scale is weakly epimorphic with val: <6 10 31 34 44| Scale is weakly epimorphic with val: <6 10 31 36 45| Scale is weakly epimorphic with val: <6 10 31 37 44| Scale is weakly epimorphic with val: <6 10 32 34 43| Scale is weakly epimorphic with val: <6 10 32 35 45| Scale is weakly epimorphic with val: <6 10 32 38 45| Scale is weakly epimorphic with val: <6 10 33 35 44| Scale is weakly epimorphic with val: <6 10 34 36 45| Scale is weakly epimorphic with val: <6 11 28 35 44| Scale is weakly epimorphic with val: <6 11 29 35 43| Scale is weakly epimorphic with val: <6 11 29 36 45| Scale is weakly epimorphic with val: <6 11 29 38 43| Scale is weakly epimorphic with val: <6 11 30 33 44| Scale is weakly epimorphic with val: <6 11 30 34 43| Scale is weakly epimorphic with val: <6 11 30 36 44| Scale is weakly epimorphic with val: <6 11 30 39 44| Scale is weakly epimorphic with val: <6 11 31 34 45| Scale is weakly epimorphic with val: <6 11 31 35 44| Scale is weakly epimorphic with val: <6 11 31 37 45| Scale is weakly epimorphic with val: <6 11 32 36 45| Scale is weakly epimorphic with val: <6 11 33 34 43| Scale is weakly epimorphic with val: <6 11 34 35 44| Scale is weakly epimorphic with val: <7 10 28 33 43| Scale is weakly epimorphic with val: <7 10 29 34 44| Scale is weakly epimorphic with val: <7 10 30 34 43| Scale is weakly epimorphic with val: <7 10 30 35 45| Scale is weakly epimorphic with val: <7 10 30 37 43| Scale is weakly epimorphic with val: <7 10 31 33 43| Scale is weakly epimorphic with val: <7 10 31 35 44| Scale is weakly epimorphic with val: <7 10 31 38 44| Scale is weakly epimorphic with val: <7 10 32 33 45| Scale is weakly epimorphic with val: <7 10 32 34 44| Scale is weakly epimorphic with val: <7 10 32 36 45| Scale is weakly epimorphic with val: <7 10 32 39 45| Scale is weakly epimorphic with val: <7 10 33 35 45| Scale is weakly epimorphic with val: <7 11 28 33 44| Scale is weakly epimorphic with val: <7 11 28 34 43| Scale is weakly epimorphic with val: <7 11 28 36 44| Scale is weakly epimorphic with val: <7 11 28 37 43| Scale is weakly epimorphic with val: <7 11 28 39 44| Scale is weakly epimorphic with val: <7 11 29 34 45| Scale is weakly epimorphic with val: <7 11 29 35 44| Scale is weakly epimorphic with val: <7 11 29 37 45| Scale is weakly epimorphic with val: <7 11 29 38 44| Scale is weakly epimorphic with val: <7 11 30 33 45| Scale is JI-epimorphic with val: <7 11 30 35 43| Scale is weakly epimorphic with val: <7 11 30 36 45| Scale is weakly epimorphic with val: <7 11 30 38 43| Scale is weakly epimorphic with val: <7 11 30 39 45| Scale is weakly epimorphic with val: <7 11 31 33 44| Scale is weakly epimorphic with val: <7 11 31 34 43| Scale is JI-epimorphic with val: <7 11 31 36 44| = patent Scale is weakly epimorphic with val: <7 11 31 37 43| Scale is weakly epimorphic with val: <7 11 31 39 44| Scale is weakly epimorphic with val: <7 11 32 34 45| Scale is weakly epimorphic with val: <7 11 32 35 44| Scale is JI-epimorphic with val: <7 11 32 37 45| Scale is weakly epimorphic with val: <7 11 32 38 44| Scale is weakly epimorphic with val: <7 11 33 33 45| Scale is weakly epimorphic with val: <7 11 33 35 43| Scale is weakly epimorphic with val: <7 11 33 36 45| Scale is weakly epimorphic with val: <7 11 33 38 43| Scale is weakly epimorphic with val: <7 11 33 39 45| Scale is weakly epimorphic with val: <7 11 34 34 43| Scale is weakly epimorphic with val: <7 11 34 36 44| Scale is weakly epimorphic with val: <7 11 34 37 43| Scale is weakly epimorphic with val: <7 11 34 39 44| Scale is weakly epimorphic with val: <7 12 28 34 44| Scale is weakly epimorphic with val: <7 12 28 35 43| Scale is weakly epimorphic with val: <7 12 28 38 43| Scale is weakly epimorphic with val: <7 12 29 33 44| Scale is weakly epimorphic with val: <7 12 29 35 45| Scale is weakly epimorphic with val: <7 12 29 36 44| Scale is weakly epimorphic with val: <7 12 29 39 44| Scale is weakly epimorphic with val: <7 12 30 33 43| Scale is weakly epimorphic with val: <7 12 30 34 45| Scale is weakly epimorphic with val: <7 12 30 37 45| Scale is weakly epimorphic with val: <7 12 31 34 44| Scale is weakly epimorphic with val: <7 12 32 35 45| Scale is weakly epimorphic with val: <7 12 33 33 43| Scale is weakly epimorphic with val: <7 12 34 34 44| Scale is weakly epimorphic with val: <8 11 29 33 44| Scale is weakly epimorphic with val: <8 11 29 34 43| Scale is weakly epimorphic with val: <8 11 29 37 43| Scale is weakly epimorphic with val: <8 11 30 34 45| Scale is weakly epimorphic with val: <8 11 30 35 44| Scale is weakly epimorphic with val: <8 11 30 38 44| Scale is weakly epimorphic with val: <8 11 31 33 45| Scale is weakly epimorphic with val: <8 11 31 36 45| Scale is weakly epimorphic with val: <8 11 31 39 45| Scale is weakly epimorphic with val: <8 11 32 33 44| Scale is weakly epimorphic with val: <8 11 33 34 45| Scale is weakly epimorphic with val: <8 12 28 33 43| Scale is weakly epimorphic with val: <8 12 28 34 45| Scale is weakly epimorphic with val: <8 12 28 36 43| Scale is weakly epimorphic with val: <8 12 28 39 43| Scale is weakly epimorphic with val: <8 12 29 34 44| Scale is weakly epimorphic with val: <8 12 29 37 44| Scale is weakly epimorphic with val: <8 12 30 33 44| Scale is weakly epimorphic with val: <8 12 30 35 45| Scale is weakly epimorphic with val: <8 12 30 38 45| Scale is weakly epimorphic with val: <8 12 31 34 45| Scale is weakly epimorphic with val: <8 12 33 33 44| Scale is weakly epimorphic with val: <8 12 34 34 45|
FIT/MODE
3: 1 1 1 SP B ME I SD: 35.2683 c. M:-52.1910 c. 4: 1 1 2 P M ME S SD: 18.6630 c. M: 30.8165 c. 7: 2 2 3 SP M ME S SD: 5.3875 c. M:-8.0271 c. 11: 3 3 5 SP M DE S SD: 4.8067 c. M: 8.1781 c. 18: 5 5 8 SP M DE S SD: 2.9724 c. M:-4.0744 c. 23: 6 7 10 SP T3 SD: 2.6873 c. M: 4.3467 c. 30: 8 9 13 SP T3 SD: 1.6151 c. M:-2.3865 c. 34: 9 10 15 SP T3 SD: 1.6577 c. M: 2.4360 c. 37: 10 11 16 SP T3 SD: 1.6483 c. M:-2.8352 c. 41: 11 12 18 SP T3 SD: 0.4556 c. M: 0.6496 c. 48: 13 14 21 SP T3 SD: 0.3983 c. M:-0.6157 c. 89: 24 26 39 SP T3 SD: 0.0292 c. M: 0.0385 c. 842: 227 246 369 SP T3 SD: 0.0337 c. M: 0.0584 c. 872: 235 255 382 SP T3 SD: 0.0328 c. M: 0.0506 c. 879: 237 257 385 SP T3 SD: 0.0375 c. M:-0.0634 c. 920: 248 269 403 SP T3 SD: 0.0252 c. M:-0.0406 c. 1009: 272 295 442 SP T3 SD: 0.0205 c. M:-0.0336 c. 1098: 296 321 481 SP T3 SD: 0.0167 c. M:-0.0278 c. 1187: 320 347 520 SP T3 SD: 0.0135 c. M:-0.0228 c. 1276: 344 373 559 SP T3 SD: 0.0108 c. M:-0.0186 c. 1365: 368 399 598 SP T3 SD: 0.0086 c. M:-0.0148 c. 1454: 392 425 637 SP T3 SD: 0.0068 c. M:-0.0116 c. 1543: 416 451 676 SP T3 SD: 0.0055 c. M:-0.0087 c. 1632: 440 477 715 SP T3 SD: 0.0047 c. M:-0.0061 c. 1721: 464 503 754 SP T3 SD: 0.0045 c. M:-0.0068 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: 106.4747 cents 5 x 6:7 S SD: 45.8708 cents 6 x 7:8 S SD: 6.4841 cents 7 x 8:9 S SD: 39.7880 cents 8:9 x 11 SD: 43.8393 cents 9:10:11:12 H SD: 27.6532 cents 10:11:12:13 H SD: 21.4669 cents 11:12:13:15 SD: 14.4118 cents 12:13:14:16 S SD: 4.5543 cents 39:42:46:52 SD: 2.8110 cents 51:55:60:68 SD: 1.2872 cents 63:68:74:84 SD: 0.7976 cents 159:172:187:212 SD: 0.6784 cents 171:185:201:228 SD: 0.6544 cents 210:227:247:280 SD: 0.4038 cents 222:240:261:296 SD: 0.2602 cents 273:295:321:364 SD: 0.1919 cents 285:308:335:380 SD: 0.0302 cents