Scala analysis: 429_D11
Diatonic tetrachord 10/9 * 18/17 * 17/15, Kornerup
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 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: 10/9 182.4037 minor whole tone 2: 18/17 98.9546 Arabic lute index finger 3: 17/15 216.6867 septendecimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 18/17 98.955 cents Arabic lute index finger 1: 1 10/9 182.404 cents minor whole tone 1: 1 17/15 216.687 cents septendecimal whole tone 2: 1 20/17 281.358 cents septendecimal augmented second 2: 1 6/5 315.641 cents minor third 2: 1 34/27 399.090 cents septendecimal major third 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 : 182.4 281.4 498.0 182.4: 99.0 315.6 498.0 281.4: 216.7 399.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 98.9546 .. 216.6867 cents 289/270, 117.7321 cents 18/17, 98.9546 cents 2: 281.3583 .. 399.0904 cents 289/270, 117.7321 cents 300/289, 64.6716 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 18/17, 98.9546 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/15, 216.6867 cents Average / Smallest step : 1.677689 Largest / Average step : 1.305224 Largest / Smallest step : 2.189759 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 159.94681 cents, oct.: 479.84043 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 770-tone equal temperament with octave 4/3 degrees: 282 435 770 Least number of segments generator : 387 of 250.316 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 529 of 342.163 cents and inv. generated superset size: 24 = 21 more = 800.000% 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 64.67161 cents Scale diversity : 1.187865 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.527223 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 : 51/50, 34.2830 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 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 17 Odd number limit : 27 (O: 17 U: 27) Highest odd numerator or denominator: 17 Scale harmonicity : 0.022805 Average absolute harmonicity : 0.106260 Specific harmonicity : 0.112978 Fundamental : 1/153, -7.2574 octaves, 1.7100 Hz. Guide tone : 20, 4.3219 octaves, 5232.511 Hz. Exponens Consonantiae : 3.060000E+03, 11.57932 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 31.5, average 10.50000 Mersenne's string divisions : 4921 Sum of van Prooijen's expressibility: 2.66181, average 0.88727 Sum of Tenney's harmonic distance : 5.56490, average 1.85497 Vogel's harmonic complexity : 19.33333 Wille's k value : 42 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 13.04864, average 2.17477 Lattice compactness (without 2's) : 10.03261, average 1.67210 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -2 .. 0 -1.00000 3 1 5: 0 .. 1 0.66667 2 1 17: -1 .. 0 -0.33333 1 1 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 17 28| Scale is weakly epimorphic with val: <6 10 17 31| Scale is weakly epimorphic with val: <6 10 18 27| Scale is weakly epimorphic with val: <6 11 18 27| Scale is weakly epimorphic with val: <6 11 19 29| Scale is weakly epimorphic with val: <6 11 19 32| Scale is weakly epimorphic with val: <7 10 16 28| Scale is weakly epimorphic with val: <7 10 16 31| Scale is weakly epimorphic with val: <7 10 18 29| Scale is JI-epimorphic with val: <7 11 16 28| Scale is weakly epimorphic with val: <7 11 16 31| Scale is weakly epimorphic with val: <7 11 17 27| Scale is weakly epimorphic with val: <7 11 17 30| = patent Scale is weakly epimorphic with val: <7 11 17 33| Scale is weakly epimorphic with val: <7 11 19 28| Scale is weakly epimorphic with val: <7 11 19 31| Scale is weakly epimorphic with val: <7 12 18 29| Scale is weakly epimorphic with val: <8 11 15 28| Scale is weakly epimorphic with val: <8 11 17 29| Scale is weakly epimorphic with val: <8 11 17 32| Scale is weakly epimorphic with val: <8 11 18 31| Scale is weakly epimorphic with val: <8 12 15 28| Scale is weakly epimorphic with val: <8 12 18 31| Scale is weakly epimorphic with val: <8 12 19 27| Scale is weakly epimorphic with val: <8 12 19 30| Scale is weakly epimorphic with val: <8 12 19 33|
FIT/MODE
3: 1 1 1 SP B ME I SD: 30.7474 c. M:-50.6717 c. 5: 2 1 2 SP M ME I SD: 13.9985 c. M:-17.4687 c. 9: 3 2 4 SP T3 SD: 9.8381 c. M: 16.3887 c. 11: 4 2 5 SP T3 SD: 5.6486 c. M: 9.6974 c. 14: 5 3 6 SP T3 SD: 3.2154 c. M: 4.5305 c. 16: 6 3 7 SP T3 SD: 2.6138 c. M:-4.3632 c. 25: 9 5 11 SP T3 SD: 2.2858 c. M: 3.1075 c. 30: 11 6 13 SP T3 SD: 0.5155 c. M:-0.8672 c. 71: 26 14 31 SP T3 SD: 0.4445 c. M: 0.7696 c. 85: 31 17 37 SP T3 SD: 0.4455 c. M: 0.7638 c. 101: 37 20 44 SP T3 SD: 0.1660 c. M: 0.2834 c. 131: 48 26 57 SP T3 SD: 0.0510 c. M:-0.0861 c. 423: 155 84 184 SP T3 SD: 0.0602 c. M:-0.0950 c. 478: 175 95 208 SP T3 SD: 0.0429 c. M: 0.0651 c. 508: 186 101 221 SP T3 SD: 0.0299 c. M: 0.0487 c. 609: 223 121 265 SP T3 SD: 0.0265 c. M: 0.0326 c. 639: 234 127 278 SP T3 SD: 0.0134 c. M: 0.0210 c. 770: 282 153 335 SP T3 SD: 0.0032 c. M:-0.0048 c. 1671: 612 332 727 SP T3 SD: 0.0029 c. M:-0.0042 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 7:8 x 9 S SD: 39.8203 cents 8:9 x 11 SD: 28.7251 cents 9:10:11:12 H SD: 22.0165 cents 10:11:12:13 H SD: 19.4343 cents 11:12:13:15 SD: 16.9457 cents 12:13:14:16 S SD: 15.3878 cents 14:16 x 19 SD: 28.7988 cents 15:17:18:20 SD: 16.1612 cents 16:18:19:21 SD: 12.7664 cents 17:19:20:23 SD: 9.0791 cents 18:20:21:24 S SD: 4.8291 cents 27:30:32:36 S SD: 4.2589 cents 45:50:53:60 SD: 0.6408 cents 108:120:127:144 SD: 0.2672 cents 153:170:180:204 SD: 0.0000 cents