Scala analysis: 435_D11
Diatonic tetrachord 120/113 * 113/102 * 17/15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 120/113 104.053960 2: 20/17 281.358304 septendecimal augmented second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 17/15 216.6867 septendecimal whole tone 1: 120/113 104.0540 2: 113/102 177.3043 3: 17/15 216.6867 septendecimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 120/113 104.054 cents 1: 1 113/102 177.304 cents 1: 1 17/15 216.687 cents septendecimal whole tone 2: 1 20/17 281.358 cents septendecimal augmented second 2: 1 136/113 320.741 cents 2: 1 113/90 393.991 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 : 104.1 281.4 498.0 104.1: 177.3 394.0 498.0 281.4: 216.7 320.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 104.0540 .. 216.6867 cents 1921/1800, 112.6327 cents 120/113, 104.0540 cents 2: 281.3583 .. 393.9910 cents 1921/1800, 112.6327 cents 300/289, 64.6716 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 120/113, 104.0540 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/15, 216.6867 cents Average / Smallest step : 1.595470 Largest / Average step : 1.305224 Largest / Smallest step : 2.082445 Median interval of one step : 113/102, 177.3043 cents, amount: 1 Least squares average step : 154.35040 cents, oct.: 463.05119 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 2149-tone equal temperament with octave 4/3 degrees: 449 1214 2149 Least number of segments generator : 1075 of 249.138 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 2064 of 478.346 cents and inv. generated superset size: 21 = 18 more = 700.000% 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 64.67161 cents Scale diversity : 1.234307 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.547701 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 : 578/565, 39.3824 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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% -- Rational properties -- Prime limit : 113 Odd number limit : 113 (O: 113 U: 113) Highest odd numerator or denominator: 113 Scale harmonicity : 0.022296 Fundamental : 1/5763, -12.4926 octaves, 0.0454 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 6.915600E+05, 19.39949 octaves Euler's gradus suavitatis : 140 Sum of Mann's harmonic distance : 138.5, average 46.16667 Mersenne's string divisions : 60347 Sum of van Prooijen's expressibility: 3.76065, average 1.25355 Sum of Tenney's harmonic distance : 7.74292, average 2.58097 Vogel's harmonic complexity : 95.33333 Wille's k value : 960 Wilson's harmonic complexity : 141 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.91577, average 2.31930 Lattice compactness (without 2's) : 9.21076, average 1.53513 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.66667 2 17: -1 .. 0 -0.33333 1 1 113: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 18 27 48| Scale is weakly epimorphic with val: <6 10 19 28 49| Scale is weakly epimorphic with val: <6 11 18 27 48| Scale is weakly epimorphic with val: <6 11 19 28 49| Scale is weakly epimorphic with val: <7 10 16 27 48| Scale is weakly epimorphic with val: <7 10 17 28 49| Scale is weakly epimorphic with val: <7 10 18 29 50| Scale is weakly epimorphic with val: <7 10 19 30 48| Scale is weakly epimorphic with val: <7 11 15 27 49| Scale is weakly epimorphic with val: <7 11 15 28 48| Scale is weakly epimorphic with val: <7 11 15 30 49| Scale is weakly epimorphic with val: <7 11 15 31 48| Scale is weakly epimorphic with val: <7 11 15 33 49| Scale is weakly epimorphic with val: <7 11 16 28 50| Scale is weakly epimorphic with val: <7 11 16 29 49| Scale is weakly epimorphic with val: <7 11 16 31 50| Scale is weakly epimorphic with val: <7 11 16 32 49| Scale is weakly epimorphic with val: <7 11 17 27 50| Scale is JI-epimorphic with val: <7 11 17 29 48| Scale is weakly epimorphic with val: <7 11 17 30 50| Scale is weakly epimorphic with val: <7 11 17 32 48| Scale is weakly epimorphic with val: <7 11 17 33 50| Scale is weakly epimorphic with val: <7 11 18 27 49| Scale is weakly epimorphic with val: <7 11 18 28 48| Scale is JI-epimorphic with val: <7 11 18 30 49| Scale is weakly epimorphic with val: <7 11 18 31 48| Scale is weakly epimorphic with val: <7 11 18 33 49| Scale is weakly epimorphic with val: <7 11 19 28 50| Scale is weakly epimorphic with val: <7 11 19 29 49| Scale is JI-epimorphic with val: <7 11 19 31 50| Scale is weakly epimorphic with val: <7 11 19 32 49| Scale is weakly epimorphic with val: <7 12 16 27 48| Scale is weakly epimorphic with val: <7 12 17 28 49| Scale is weakly epimorphic with val: <7 12 18 28 48| Scale is weakly epimorphic with val: <7 12 18 29 50| Scale is weakly epimorphic with val: <7 12 18 31 48| Scale is weakly epimorphic with val: <7 12 19 29 49| Scale is weakly epimorphic with val: <7 12 19 30 48| Scale is weakly epimorphic with val: <7 12 19 32 49| Scale is weakly epimorphic with val: <8 11 15 28 49| Scale is weakly epimorphic with val: <8 11 16 28 48| Scale is weakly epimorphic with val: <8 11 16 29 50| Scale is weakly epimorphic with val: <8 11 16 31 48| Scale is weakly epimorphic with val: <8 11 17 29 49| Scale is weakly epimorphic with val: <8 11 17 30 48| Scale is weakly epimorphic with val: <8 11 17 32 49| Scale is weakly epimorphic with val: <8 11 18 27 50| Scale is weakly epimorphic with val: <8 11 18 30 50| Scale is weakly epimorphic with val: <8 11 18 31 49| Scale is weakly epimorphic with val: <8 11 18 33 50| Scale is weakly epimorphic with val: <8 11 19 32 50| Scale is weakly epimorphic with val: <8 12 15 28 49| Scale is weakly epimorphic with val: <8 12 15 29 48| Scale is weakly epimorphic with val: <8 12 15 32 48| Scale is weakly epimorphic with val: <8 12 16 27 49| Scale is weakly epimorphic with val: <8 12 16 29 50| Scale is weakly epimorphic with val: <8 12 16 30 49| Scale is weakly epimorphic with val: <8 12 16 33 49| Scale is weakly epimorphic with val: <8 12 17 28 50| Scale is weakly epimorphic with val: <8 12 17 30 48| Scale is weakly epimorphic with val: <8 12 17 31 50| Scale is weakly epimorphic with val: <8 12 18 31 49| Scale is weakly epimorphic with val: <8 12 19 32 50|
FIT/MODE
3: 1 1 1 SP B ME I SD: 46.2125 c. M:-61.9610 c. 4: 1 1 2 P M ME S SD: 22.0915 c. M: 32.3358 c. 5: 1 2 2 SP M ME S SD: 10.4069 c. M:-17.4687 c. 9: 2 3 4 SP T3 SD: 4.6775 c. M:-6.6227 c. 14: 3 5 6 SP T3 SD: 2.4234 c. M:-3.2388 c. 34: 7 12 15 SP T3 SD: 1.9606 c. M: 3.0390 c. 39: 8 14 17 SP T3 SD: 1.1171 c. M: 1.8909 c. 48: 10 17 21 SP T3 SD: 0.7179 c. M: 1.2080 c. 53: 11 19 23 SP T3 SD: 0.5091 c. M: 0.6861 c. 62: 13 22 27 SP T3 SD: 0.2463 c. M:-0.3748 c. 115: 24 41 50 SP T3 SD: 0.1067 c. M:-0.1454 c. 177: 37 63 77 SP T3 SD: 0.0356 c. M:-0.0571 c. 469: 98 167 204 SP T3 SD: 0.0319 c. M:-0.0530 c. 632: 132 225 275 SP T3 SD: 0.0237 c. M: 0.0319 c. 809: 169 288 352 SP T3 SD: 0.0113 c. M: 0.0152 c. 986: 206 351 429 SP T3 SD: 0.0048 c. M: 0.0083 c. 2087: 436 743 908 SP T3 SD: 0.0036 c. M: 0.0062 c. 2149: 449 765 935 SP T3 SD: 0.0043 c. M: 0.0058 c. 2264: 473 806 985 SP T3 SD: 0.0013 c. M:-0.0019 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: 104.9554 cents 5 x 6:7 S SD: 45.5797 cents 6 x 7:8 S SD: 7.2437 cents 7 x 8:9 S SD: 40.2571 cents 8 x 9:11 SD: 47.0007 cents 9:10:11:12 H SD: 34.1585 cents 10:11:12:13 H SD: 27.5104 cents 11:12:13:15 SD: 20.3996 cents 12:13:14:16 S SD: 12.4785 cents 15:16:18:20 S SD: 11.7107 cents 16:17:19:21 SD: 10.5679 cents 17:18:20:23 SD: 8.5944 cents 18:19:21:24 SD: 5.9545 cents 30:32:35:40 SD: 5.4653 cents 33:35:39:44 SD: 2.7168 cents 45:48:53:60 SD: 2.6381 cents 51:54:60:68 SD: 1.6998 cents 63:67:74:84 SD: 1.2427 cents 96:102:113:128 SD: 0.4249 cents 210:223:247:280 SD: 0.1393 cents 306:325:360:408 SD: 0.0786 cents 516:548:607:688 SD: 0.0672 cents