Scala analysis: 431_D11
Diatonic tetrachord 15/14 * 56/51 * 17/15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic 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: 15/14 119.4428 major diatonic semitone 2: 56/51 161.9155 3: 17/15 216.6867 septendecimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 56/51 161.915 cents 1: 1 17/15 216.687 cents septendecimal whole tone 2: 1 20/17 281.358 cents septendecimal augmented second 2: 1 17/14 336.130 cents supraminor third 2: 1 56/45 378.602 cents septimal narrow 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 : 119.4 281.4 498.0 119.4: 161.9 378.6 498.0 281.4: 216.7 336.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 119.4428 .. 216.6867 cents 238/225, 97.2439 cents 15/14, 119.4428 cents 2: 281.3583 .. 378.6022 cents 238/225, 97.2439 cents 300/289, 64.6716 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 15/14, 119.4428 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/15, 216.6867 cents Average / Smallest step : 1.389912 Largest / Average step : 1.305224 Largest / Smallest step : 1.814146 Median interval of one step : 56/51, 161.9155 cents, amount: 1 Least squares average step : 155.44960 cents, oct.: 466.34880 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 2064-tone equal temperament with octave 4/3 degrees: 495 1166 2064 Least number of segments generator : 1033 of 249.264 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1865 of 450.026 cents and inv. generated superset size: 47 = 44 more = 1566.667% 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 : 1.328972 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.609498 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 : 784/765, 42.4727 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% -- Rational properties -- Prime limit : 17 Odd number limit : 51 (O: 17 U: 51) Highest odd numerator or denominator: 17 Scale harmonicity : 0.018137 Average absolute harmonicity : 0.096460 Specific harmonicity : 0.092054 Fundamental : 1/714, -9.4798 octaves, 0.3664 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 4.284000E+04, 15.38667 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 36.5, average 12.16667 Mersenne's string divisions : 7511 Sum of van Prooijen's expressibility: 2.88366, average 0.96122 Sum of Tenney's harmonic distance : 5.93288, average 1.97763 Vogel's harmonic complexity : 24.33333 Wille's k value : 382 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 15.75469, average 2.62578 Lattice compactness (without 2's) : 10.05986, average 1.67664 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 1.00000 5 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.66667 2 7: -1 .. 0 -0.33333 1 1 17: -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 17 18 28| Scale is weakly epimorphic with val: <6 10 17 18 31| Scale is weakly epimorphic with val: <6 10 18 18 27| Scale is weakly epimorphic with val: <6 10 18 19 29| Scale is weakly epimorphic with val: <6 10 18 19 32| Scale is weakly epimorphic with val: <6 10 18 21 27| Scale is weakly epimorphic with val: <6 10 19 19 28| Scale is weakly epimorphic with val: <6 10 19 20 27| Scale is weakly epimorphic with val: <6 10 19 20 30| Scale is weakly epimorphic with val: <6 10 19 20 33| Scale is weakly epimorphic with val: <6 10 19 22 28| Scale is weakly epimorphic with val: <6 11 16 18 29| Scale is weakly epimorphic with val: <6 11 16 18 32| Scale is weakly epimorphic with val: <6 11 17 19 27| Scale is weakly epimorphic with val: <6 11 17 19 30| Scale is weakly epimorphic with val: <6 11 17 19 33| Scale is weakly epimorphic with val: <6 11 18 18 27| Scale is weakly epimorphic with val: <6 11 18 20 28| Scale is weakly epimorphic with val: <6 11 18 20 31| Scale is weakly epimorphic with val: <6 11 18 21 27| Scale is weakly epimorphic with val: <6 11 19 19 28| Scale is weakly epimorphic with val: <6 11 19 21 29| Scale is weakly epimorphic with val: <6 11 19 21 32| Scale is weakly epimorphic with val: <6 11 19 22 28| Scale is weakly epimorphic with val: <7 10 16 20 27| Scale is weakly epimorphic with val: <7 10 17 18 28| Scale is weakly epimorphic with val: <7 10 17 21 28| Scale is weakly epimorphic with val: <7 10 18 18 27| Scale is weakly epimorphic with val: <7 10 18 18 30| Scale is weakly epimorphic with val: <7 10 18 18 33| Scale is weakly epimorphic with val: <7 10 18 19 29| Scale is weakly epimorphic with val: <7 10 18 22 29| Scale is weakly epimorphic with val: <7 10 19 19 28| Scale is weakly epimorphic with val: <7 10 19 19 31| Scale is weakly epimorphic with val: <7 10 19 20 30| Scale is JI-epimorphic with val: <7 11 15 18 27| Scale is weakly epimorphic with val: <7 11 15 18 30| Scale is weakly epimorphic with val: <7 11 15 18 33| Scale is weakly epimorphic with val: <7 11 15 20 28| Scale is weakly epimorphic with val: <7 11 15 20 31| Scale is weakly epimorphic with val: <7 11 15 21 27| Scale is weakly epimorphic with val: <7 11 15 21 30| Scale is weakly epimorphic with val: <7 11 15 21 33| Scale is weakly epimorphic with val: <7 11 16 18 29| Scale is weakly epimorphic with val: <7 11 16 18 32| Scale is JI-epimorphic with val: <7 11 16 19 28| Scale is weakly epimorphic with val: <7 11 16 19 31| Scale is weakly epimorphic with val: <7 11 16 21 29| Scale is weakly epimorphic with val: <7 11 16 21 32| Scale is weakly epimorphic with val: <7 11 16 22 28| Scale is weakly epimorphic with val: <7 11 16 22 31| Scale is weakly epimorphic with val: <7 11 17 19 27| Scale is weakly epimorphic with val: <7 11 17 19 30| Scale is weakly epimorphic with val: <7 11 17 19 33| Scale is JI-epimorphic with val: <7 11 17 20 29| Scale is weakly epimorphic with val: <7 11 17 20 32| Scale is weakly epimorphic with val: <7 11 17 22 27| Scale is weakly epimorphic with val: <7 11 17 22 30| Scale is weakly epimorphic with val: <7 11 17 22 33| Scale is weakly epimorphic with val: <7 11 18 18 27| Scale is weakly epimorphic with val: <7 11 18 18 30| Scale is weakly epimorphic with val: <7 11 18 18 33| Scale is weakly epimorphic with val: <7 11 18 20 28| Scale is weakly epimorphic with val: <7 11 18 20 31| Scale is weakly epimorphic with val: <7 11 18 21 27| Scale is JI-epimorphic with val: <7 11 18 21 30| Scale is weakly epimorphic with val: <7 11 18 21 33| Scale is weakly epimorphic with val: <7 11 19 19 28| Scale is weakly epimorphic with val: <7 11 19 19 31| Scale is weakly epimorphic with val: <7 11 19 21 29| Scale is weakly epimorphic with val: <7 11 19 21 32| Scale is weakly epimorphic with val: <7 11 19 22 28| Scale is JI-epimorphic with val: <7 11 19 22 31| Scale is weakly epimorphic with val: <7 12 16 18 29| Scale is weakly epimorphic with val: <7 12 16 18 32| Scale is weakly epimorphic with val: <7 12 16 20 27| Scale is weakly epimorphic with val: <7 12 17 18 28| Scale is weakly epimorphic with val: <7 12 17 19 27| Scale is weakly epimorphic with val: <7 12 17 19 30| Scale is weakly epimorphic with val: <7 12 17 19 33| Scale is weakly epimorphic with val: <7 12 17 21 28| Scale is weakly epimorphic with val: <7 12 18 19 29| Scale is weakly epimorphic with val: <7 12 18 20 28| Scale is weakly epimorphic with val: <7 12 18 20 31| Scale is weakly epimorphic with val: <7 12 18 22 29| Scale is weakly epimorphic with val: <7 12 19 20 30| Scale is weakly epimorphic with val: <7 12 19 21 29| Scale is weakly epimorphic with val: <7 12 19 21 32| Scale is weakly epimorphic with val: <8 11 15 20 28| Scale is weakly epimorphic with val: <8 11 16 18 29| Scale is weakly epimorphic with val: <8 11 16 21 29| Scale is weakly epimorphic with val: <8 11 17 19 30| Scale is weakly epimorphic with val: <8 11 17 22 30| Scale is weakly epimorphic with val: <8 11 18 18 27| Scale is weakly epimorphic with val: <8 11 18 18 30| Scale is weakly epimorphic with val: <8 11 18 18 33| Scale is weakly epimorphic with val: <8 11 18 20 31| Scale is weakly epimorphic with val: <8 11 19 19 28| Scale is weakly epimorphic with val: <8 11 19 19 31| Scale is weakly epimorphic with val: <8 11 19 21 32| Scale is weakly epimorphic with val: <8 12 15 20 28| Scale is weakly epimorphic with val: <8 12 16 18 29| Scale is weakly epimorphic with val: <8 12 16 21 29| Scale is weakly epimorphic with val: <8 12 17 18 28| Scale is weakly epimorphic with val: <8 12 17 18 31| Scale is weakly epimorphic with val: <8 12 17 19 30| Scale is weakly epimorphic with val: <8 12 17 22 30| Scale is weakly epimorphic with val: <8 12 18 19 29| Scale is weakly epimorphic with val: <8 12 18 19 32| Scale is weakly epimorphic with val: <8 12 18 20 31| Scale is weakly epimorphic with val: <8 12 19 20 27| Scale is weakly epimorphic with val: <8 12 19 20 30| Scale is weakly epimorphic with val: <8 12 19 20 33| Scale is weakly epimorphic with val: <8 12 19 21 32|
FIT/MODE
3: 1 1 1 SP B ME I SD: 39.7349 c. M:-50.6717 c. 4: 1 1 2 P M ME S SD: 18.8970 c. M: 32.3358 c. 5: 1 2 2 SP M ME S SD: 15.2593 c. M: 19.8338 c. 7: 2 2 3 SP M ME S SD: 13.3276 c. M:-22.8558 c. 9: 2 3 4 SP T3 SD: 5.7336 c. M: 8.7661 c. 16: 4 5 7 SP T3 SD: 3.0082 c. M:-5.0684 c. 21: 5 7 9 SP T3 SD: 1.9348 c. M:-3.2388 c. 25: 6 8 11 SP T3 SD: 1.4172 c. M: 2.4531 c. 37: 9 12 16 SP T3 SD: 1.2427 c. M:-1.7033 c. 46: 11 15 20 SP T3 SD: 0.2162 c. M: 0.3451 c. 154: 37 50 67 SP T3 SD: 0.1255 c. M:-0.2174 c. 200: 48 65 87 SP T3 SD: 0.0551 c. M:-0.0880 c. 246: 59 80 107 SP T3 SD: 0.0334 c. M:-0.0574 c. 446: 107 145 194 SP T3 SD: 0.0375 c. M:-0.0483 c. 563: 135 183 245 SP T3 SD: 0.0290 c. M: 0.0469 c. 609: 146 198 265 SP T3 SD: 0.0310 c. M: 0.0429 c. 717: 172 233 312 SP T3 SD: 0.0279 c. M: 0.0358 c. 763: 183 248 332 SP T3 SD: 0.0154 c. M: 0.0249 c. 809: 194 263 352 SP T3 SD: 0.0107 c. M: 0.0152 c. 1009: 242 328 439 SP T3 SD: 0.0059 c. M:-0.0090 c. 1055: 253 343 459 SP T3 SD: 0.0038 c. M: 0.0064 c. 2064: 495 671 898 SP T3 SD: 0.0011 c. M: 0.0015 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: 30.4168 cents 10:11:12:13 H SD: 23.9730 cents 11:12:13:15 SD: 16.8272 cents 12:13:14:16 S SD: 7.9989 cents 27:29:32:36 SD: 4.4904 cents 39:42:46:52 SD: 3.3011 cents 45:48:53:60 SD: 2.6492 cents 57:61:67:76 SD: 0.8441 cents 141:151:166:188 SD: 0.4918 cents 153:164:180:204 SD: 0.2514 cents 210:225:247:280 SD: 0.1374 cents 351:376:413:468 SD: 0.1370 cents 363:389:427:484 SD: 0.1325 cents 504:540:593:672 SD: 0.0572 cents