Scala analysis: 430_D11
Diatonic tetrachord 20/19 * 19/17 * 17/15, Ptolemy
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 20/19 88.800698 small undevicesimal semitone 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: 20/19 88.8007 small undevicesimal semitone 2: 19/17 192.5576 quasi-meantone 3: 17/15 216.6867 septendecimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 20/19 88.801 cents small undevicesimal semitone 1: 1 19/17 192.558 cents quasi-meantone 1: 1 17/15 216.687 cents septendecimal whole tone 2: 1 20/17 281.358 cents septendecimal augmented second 2: 1 68/57 305.487 cents 2: 1 19/15 409.244 cents undevicesimal ditone 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 : 88.8 281.4 498.0 88.8 : 192.6 409.2 498.0 281.4: 216.7 305.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.8007 .. 216.6867 cents 323/300, 127.8860 cents 20/19, 88.8007 cents 2: 281.3583 .. 409.2443 cents 323/300, 127.8860 cents 300/289, 64.6716 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 20/19, 88.8007 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/15, 216.6867 cents Average / Smallest step : 1.869524 Largest / Average step : 1.305224 Largest / Smallest step : 2.440146 Median interval of one step : 19/17, 192.5576 cents, amount: 1 Least squares average step : 153.26088 cents, oct.: 459.78264 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1032-tone equal temperament with octave 4/3 degrees: 184 583 1032 Least number of segments generator : 517 of 249.505 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 979 of 472.467 cents and inv. generated superset size: 28 = 25 more = 933.333% 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 : 1.079298 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.486448 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 : 289/285, 24.1291 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 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% Limited inverse transpositions with margin 103.7569 cents: 1 -- Rational properties -- Prime limit : 19 Odd number limit : 57 (O: 19 U: 57) Highest odd numerator or denominator: 19 Scale harmonicity : 0.013282 Average absolute harmonicity : 0.087924 Specific harmonicity : 0.068885 Fundamental : 1/969, -9.9204 octaves, 0.2700 Hz. Guide tone : 20, 4.3219 octaves, 5232.511 Hz. Exponens Consonantiae : 1.938000E+04, 14.24228 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 41.5, average 13.83333 Mersenne's string divisions : 10101 Sum of van Prooijen's expressibility: 2.98632, average 0.99544 Sum of Tenney's harmonic distance : 6.19044, average 2.06348 Vogel's harmonic complexity : 31.33333 Wille's k value : 161 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 12.01336, average 2.00223 Lattice compactness (without 2's) : 8.70674, average 1.45112 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -1 .. 0 -0.33333 1 1 5: 0 .. 1 0.66667 2 17: -1 .. 0 -0.33333 1 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 18 27 29| Scale is weakly epimorphic with val: <6 10 18 27 32| Scale is weakly epimorphic with val: <6 10 19 27 28| Scale is weakly epimorphic with val: <6 10 19 28 30| Scale is weakly epimorphic with val: <6 10 19 28 33| Scale is weakly epimorphic with val: <6 11 18 27 28| Scale is weakly epimorphic with val: <6 11 18 27 31| Scale is weakly epimorphic with val: <6 11 18 27 34| Scale is weakly epimorphic with val: <6 11 19 28 29| Scale is weakly epimorphic with val: <6 11 19 28 32| Scale is weakly epimorphic with val: <7 10 16 27 28| Scale is weakly epimorphic with val: <7 10 16 27 31| Scale is weakly epimorphic with val: <7 10 16 27 34| Scale is weakly epimorphic with val: <7 10 17 28 29| Scale is weakly epimorphic with val: <7 10 17 28 32| Scale is weakly epimorphic with val: <7 10 18 27 29| Scale is weakly epimorphic with val: <7 10 18 29 30| Scale is weakly epimorphic with val: <7 10 18 29 33| Scale is weakly epimorphic with val: <7 10 19 28 30| Scale is weakly epimorphic with val: <7 10 19 30 31| Scale is weakly epimorphic with val: <7 10 19 30 34| Scale is JI-epimorphic with val: <7 11 15 27 28| Scale is weakly epimorphic with val: <7 11 15 27 31| Scale is weakly epimorphic with val: <7 11 15 27 34| Scale is weakly epimorphic with val: <7 11 15 28 30| Scale is weakly epimorphic with val: <7 11 15 28 33| Scale is weakly epimorphic with val: <7 11 15 30 31| Scale is weakly epimorphic with val: <7 11 15 30 34| Scale is weakly epimorphic with val: <7 11 15 31 33| Scale is weakly epimorphic with val: <7 11 15 33 34| Scale is JI-epimorphic with val: <7 11 16 28 29| Scale is weakly epimorphic with val: <7 11 16 28 32| Scale is weakly epimorphic with val: <7 11 16 29 31| Scale is weakly epimorphic with val: <7 11 16 29 34| Scale is weakly epimorphic with val: <7 11 16 31 32| Scale is weakly epimorphic with val: <7 11 16 32 34| Scale is weakly epimorphic with val: <7 11 17 27 29| Scale is weakly epimorphic with val: <7 11 17 27 32| Scale is JI-epimorphic with val: <7 11 17 29 30| Scale is weakly epimorphic with val: <7 11 17 29 33| Scale is weakly epimorphic with val: <7 11 17 30 32| Scale is weakly epimorphic with val: <7 11 17 32 33| Scale is weakly epimorphic with val: <7 11 18 27 28| Scale is weakly epimorphic with val: <7 11 18 27 31| Scale is weakly epimorphic with val: <7 11 18 27 34| Scale is weakly epimorphic with val: <7 11 18 28 30| Scale is weakly epimorphic with val: <7 11 18 28 33| Scale is JI-epimorphic with val: <7 11 18 30 31| Scale is weakly epimorphic with val: <7 11 18 30 34| Scale is weakly epimorphic with val: <7 11 18 31 33| Scale is weakly epimorphic with val: <7 11 18 33 34| Scale is weakly epimorphic with val: <7 11 19 28 29| Scale is weakly epimorphic with val: <7 11 19 28 32| Scale is weakly epimorphic with val: <7 11 19 29 31| Scale is weakly epimorphic with val: <7 11 19 29 34| Scale is JI-epimorphic with val: <7 11 19 31 32| Scale is weakly epimorphic with val: <7 11 19 32 34| Scale is weakly epimorphic with val: <7 12 16 27 29| Scale is weakly epimorphic with val: <7 12 16 27 32| Scale is weakly epimorphic with val: <7 12 17 27 28| Scale is weakly epimorphic with val: <7 12 17 28 30| Scale is weakly epimorphic with val: <7 12 17 28 33| Scale is weakly epimorphic with val: <7 12 18 28 29| Scale is weakly epimorphic with val: <7 12 18 29 31| Scale is weakly epimorphic with val: <7 12 18 29 34| Scale is weakly epimorphic with val: <7 12 19 29 30| Scale is weakly epimorphic with val: <7 12 19 30 32| Scale is weakly epimorphic with val: <8 11 15 27 28| Scale is weakly epimorphic with val: <8 11 15 28 30| Scale is weakly epimorphic with val: <8 11 15 28 33| Scale is weakly epimorphic with val: <8 11 16 28 29| Scale is weakly epimorphic with val: <8 11 16 29 31| Scale is weakly epimorphic with val: <8 11 16 29 34| Scale is weakly epimorphic with val: <8 11 17 29 30| Scale is weakly epimorphic with val: <8 11 17 30 32| Scale is weakly epimorphic with val: <8 11 18 27 31| Scale is weakly epimorphic with val: <8 11 18 30 31| Scale is weakly epimorphic with val: <8 11 18 31 33| Scale is weakly epimorphic with val: <8 11 19 28 32| Scale is weakly epimorphic with val: <8 11 19 31 32| Scale is weakly epimorphic with val: <8 11 19 32 34| Scale is weakly epimorphic with val: <8 12 15 28 29| Scale is weakly epimorphic with val: <8 12 15 28 32| Scale is weakly epimorphic with val: <8 12 16 27 29| Scale is weakly epimorphic with val: <8 12 16 29 30| Scale is weakly epimorphic with val: <8 12 16 29 33| Scale is weakly epimorphic with val: <8 12 17 28 30| Scale is weakly epimorphic with val: <8 12 17 30 31| Scale is weakly epimorphic with val: <8 12 17 30 34| Scale is weakly epimorphic with val: <8 12 18 29 31| Scale is weakly epimorphic with val: <8 12 18 31 32| Scale is weakly epimorphic with val: <8 12 19 27 32| Scale is weakly epimorphic with val: <8 12 19 30 32| Scale is weakly epimorphic with val: <8 12 19 32 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 84.0429 c. M: 115.3433 c. 4: 1 1 2 P M ME S SD: 27.8140 c. M:-35.7106 c. 5: 1 2 2 SP M ME S SD: 11.8599 c. M:-17.4687 c. 7: 1 3 3 SP M DE S SD: 10.3612 c. M: 17.6514 c. 11: 2 4 5 SP T3 SD: 5.6895 c. M: 9.6974 c. 12: 2 5 5 SP M DE S SD: 6.2613 c. M:-9.1679 c. 16: 3 6 7 SP T3 SD: 2.7362 c. M:-4.5827 c. 23: 4 9 10 SP T3 SD: 1.2638 c. M: 2.1842 c. 39: 7 15 17 SP T3 SD: 0.4157 c. M:-0.5920 c. 62: 11 24 27 SP T3 SD: 0.2789 c. M: 0.4379 c. 101: 18 39 44 SP T3 SD: 0.1653 c. M: 0.2834 c. 163: 29 63 71 SP T3 SD: 0.1833 c. M: 0.2532 c. 168: 30 65 73 SP T3 SD: 0.1767 c. M:-0.2743 c. 191: 34 74 83 SP T3 SD: 0.1708 c. M:-0.2588 c. 207: 37 80 90 SP T3 SD: 0.1531 c. M:-0.2218 c. 230: 41 89 100 SP T3 SD: 0.0846 c. M:-0.1454 c. 269: 48 104 117 SP T3 SD: 0.0550 c. M:-0.0698 c. 331: 59 128 144 SP T3 SD: 0.0169 c. M: 0.0253 c. 701: 125 271 305 SP T3 SD: 0.0074 c. M: 0.0091 c. 1032: 184 399 449 SP T3 SD: 0.0014 c. M: 0.0020 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: 38.1868 cents 10:11:12:13 H SD: 31.4527 cents 11:12:13:15 SD: 24.4927 cents 12:13:14:16 S SD: 17.2792 cents 15:16:18:20 S SD: 13.7483 cents 16:17:19:21 SD: 11.8569 cents 17:18:20:23 SD: 9.0791 cents 18:19:21:24 SD: 5.0875 cents 33:35:39:44 SD: 5.0812 cents 39:41:46:52 SD: 1.6529 cents 57:60:67:76 SD: 0.5064 cents 96:101:113:128 SD: 0.4251 cents 153:161:180:204 SD: 0.1886 cents 363:382:427:484 SD: 0.1778 cents 510:537:600:680 SD: 0.1697 cents 549:578:646:732 SD: 0.1486 cents