Scala analysis: 291_C21
Chromatic tetrachord 21/20 * 20/17 * 68/63
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 21/17 365.825498 submajor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 68/63 132.2195 supraminor second 1: 21/20 84.4672 minor semitone 2: 20/17 281.3583 septendecimal augmented second 3: 68/63 132.2195 supraminor second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 21/20 84.467 cents minor semitone 1: 1 68/63 132.220 cents supraminor second 1: 1 20/17 281.358 cents septendecimal augmented second 2: 1 17/15 216.687 cents septendecimal whole tone 2: 1 21/17 365.825 cents submajor third 2: 1 80/63 413.578 cents wide 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 : 84.5 365.8 498.0 84.5 : 281.4 413.6 498.0 365.8: 132.2 216.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 281.3583 cents 400/357, 196.8911 cents 21/20, 84.4672 cents 2: 216.6867 .. 413.5778 cents 400/357, 196.8911 cents 289/300,-64.6716 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 21/20, 84.4672 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 20/17, 281.3583 cents Average / Smallest step : 1.965438 Largest / Average step : 1.694776 Largest / Smallest step : 3.330977 Median interval of one step : 68/63, 132.2195 cents, amount: 1 Least squares average step : 165.01808 cents, oct.: 495.05425 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 64.67161 cents Scale diversity : 1.114091 Lumma stability : 0.339195 Lumma impropriety factor : 0.129851 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 : 1360/1323, 47.7523 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 : 63 (O: 21 U: 63) Highest odd numerator or denominator: 21 Scale harmonicity : 0.017814 Average absolute harmonicity : 0.094779 Specific harmonicity : 0.088221 Fundamental : 1/1020, -9.9944 octaves, 0.2565 Hz. Guide tone : 84, 6.3923 octaves, 21976.547 Hz. Exponens Consonantiae : 8.568000E+04, 16.38667 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 43.0, average 14.33333 Mersenne's string divisions : 10906 Sum of van Prooijen's expressibility: 3.12156, average 1.04052 Sum of Tenney's harmonic distance : 6.25510, average 2.08503 Vogel's harmonic complexity : 25.33333 Wille's k value : 535 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 16.91605, average 2.81934 Lattice compactness (without 2's) : 10.77729, average 1.79622 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.00000 4 3: -1 .. 1 0.33333 3 1 5: -1 .. 0 -0.33333 1 7: 0 .. 1 0.66667 2 1 17: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 15 20 29| Scale is weakly epimorphic with val: <6 10 15 20 32| Scale is weakly epimorphic with val: <6 10 15 21 28| Scale is weakly epimorphic with val: <6 10 16 21 27| Scale is weakly epimorphic with val: <6 10 16 21 30| Scale is weakly epimorphic with val: <6 10 16 21 33| Scale is weakly epimorphic with val: <6 10 16 22 29| Scale is weakly epimorphic with val: <6 10 17 20 27| Scale is weakly epimorphic with val: <6 10 17 22 28| Scale is weakly epimorphic with val: <6 10 17 22 31| Scale is weakly epimorphic with val: <6 10 18 21 28| Scale is weakly epimorphic with val: <6 10 19 22 29| Scale is weakly epimorphic with val: <6 11 15 19 28| Scale is weakly epimorphic with val: <6 11 15 19 31| Scale is weakly epimorphic with val: <6 11 15 21 29| Scale is weakly epimorphic with val: <6 11 16 19 27| Scale is weakly epimorphic with val: <6 11 16 20 29| Scale is weakly epimorphic with val: <6 11 16 20 32| Scale is weakly epimorphic with val: <6 11 16 22 30| Scale is weakly epimorphic with val: <6 11 17 20 28| Scale is weakly epimorphic with val: <6 11 17 21 27| Scale is weakly epimorphic with val: <6 11 17 21 30| Scale is weakly epimorphic with val: <6 11 17 21 33| Scale is weakly epimorphic with val: <6 11 18 21 29| Scale is weakly epimorphic with val: <6 11 18 22 28| Scale is weakly epimorphic with val: <6 11 18 22 31| Scale is weakly epimorphic with val: <6 11 19 19 27| Scale is weakly epimorphic with val: <6 11 19 22 30| Scale is weakly epimorphic with val: <7 10 15 21 28| Scale is weakly epimorphic with val: <7 10 15 22 27| Scale is weakly epimorphic with val: <7 10 15 22 30| Scale is weakly epimorphic with val: <7 10 15 22 33| Scale is weakly epimorphic with val: <7 10 16 22 29| Scale is weakly epimorphic with val: <7 10 17 20 27| Scale is weakly epimorphic with val: <7 10 18 21 28| Scale is weakly epimorphic with val: <7 10 19 22 29| Scale is JI-epimorphic with val: <7 11 15 19 28| Scale is weakly epimorphic with val: <7 11 15 19 31| Scale is weakly epimorphic with val: <7 11 15 20 27| Scale is weakly epimorphic with val: <7 11 15 20 30| Scale is weakly epimorphic with val: <7 11 15 20 33| Scale is weakly epimorphic with val: <7 11 15 22 28| Scale is weakly epimorphic with val: <7 11 15 22 31| Scale is weakly epimorphic with val: <7 11 16 18 28| Scale is weakly epimorphic with val: <7 11 16 18 31| Scale is JI-epimorphic with val: <7 11 16 20 29| Scale is weakly epimorphic with val: <7 11 16 20 32| Scale is weakly epimorphic with val: <7 11 16 21 28| Scale is weakly epimorphic with val: <7 11 16 21 31| Scale is weakly epimorphic with val: <7 11 17 18 27| Scale is weakly epimorphic with val: <7 11 17 18 30| Scale is weakly epimorphic with val: <7 11 17 18 33| Scale is weakly epimorphic with val: <7 11 17 19 29| Scale is weakly epimorphic with val: <7 11 17 19 32| Scale is weakly epimorphic with val: <7 11 17 21 27| Scale is JI-epimorphic with val: <7 11 17 21 30| Scale is weakly epimorphic with val: <7 11 17 21 33| Scale is weakly epimorphic with val: <7 11 17 22 29| Scale is weakly epimorphic with val: <7 11 17 22 32| Scale is weakly epimorphic with val: <7 11 18 19 28| Scale is weakly epimorphic with val: <7 11 18 19 31| Scale is weakly epimorphic with val: <7 11 18 20 27| Scale is weakly epimorphic with val: <7 11 18 20 30| Scale is weakly epimorphic with val: <7 11 18 20 33| Scale is weakly epimorphic with val: <7 11 18 22 28| Scale is JI-epimorphic with val: <7 11 18 22 31| Scale is weakly epimorphic with val: <7 11 19 20 29| Scale is weakly epimorphic with val: <7 11 19 20 32| Scale is weakly epimorphic with val: <7 11 19 21 28| Scale is weakly epimorphic with val: <7 11 19 21 31| Scale is weakly epimorphic with val: <7 12 15 18 27| Scale is weakly epimorphic with val: <7 12 15 20 28| Scale is weakly epimorphic with val: <7 12 15 20 31| Scale is weakly epimorphic with val: <7 12 15 21 30| Scale is weakly epimorphic with val: <7 12 16 19 28| Scale is weakly epimorphic with val: <7 12 16 21 29| Scale is weakly epimorphic with val: <7 12 16 21 32| Scale is weakly epimorphic with val: <7 12 16 22 31| Scale is weakly epimorphic with val: <7 12 17 20 29| Scale is weakly epimorphic with val: <7 12 17 22 27| Scale is weakly epimorphic with val: <7 12 17 22 30| Scale is weakly epimorphic with val: <7 12 17 22 33| Scale is weakly epimorphic with val: <7 12 18 18 27| Scale is weakly epimorphic with val: <7 12 18 21 30| Scale is weakly epimorphic with val: <7 12 19 19 28| Scale is weakly epimorphic with val: <7 12 19 22 31| Scale is weakly epimorphic with val: <8 11 15 21 29| Scale is weakly epimorphic with val: <8 11 16 19 27| Scale is weakly epimorphic with val: <8 11 16 22 30| Scale is weakly epimorphic with val: <8 11 17 20 28| Scale is weakly epimorphic with val: <8 11 18 21 29| Scale is weakly epimorphic with val: <8 11 19 19 27| Scale is weakly epimorphic with val: <8 11 19 22 30| Scale is weakly epimorphic with val: <8 12 15 18 27| Scale is weakly epimorphic with val: <8 12 15 21 30| Scale is weakly epimorphic with val: <8 12 15 22 29| Scale is weakly epimorphic with val: <8 12 15 22 32| Scale is weakly epimorphic with val: <8 12 16 19 28| Scale is weakly epimorphic with val: <8 12 16 22 31| Scale is weakly epimorphic with val: <8 12 17 20 29| Scale is weakly epimorphic with val: <8 12 18 18 27| Scale is weakly epimorphic with val: <8 12 18 21 30| Scale is weakly epimorphic with val: <8 12 19 19 28| Scale is weakly epimorphic with val: <8 12 19 22 31|
FIT/MODE
3: 0 2 1 N G T3 SD: 52.5257 c. M: 84.4672 c. 4: 1 2 1 P M ME I SD: 23.5439 c. M:-40.0441 c. 5: 1 3 1 N M DE I SD: 20.7583 c. M:-32.6105 c. 6: 1 3 2 P T3 SD: 19.5300 c. M: 33.7955 c. 7: 1 4 2 N T3 SD: 9.6429 c. M: 13.3179 c. 11: 2 6 3 N T3 SD: 4.0859 c. M:-6.0864 c. 18: 3 10 5 N T3 SD: 3.6361 c. M: 6.1263 c. 19: 3 11 5 N T3 SD: 3.4305 c. M: 5.8285 c. 23: 4 13 6 N T3 SD: 1.8152 c. M:-2.2947 c. 30: 5 17 8 N T3 SD: 0.9095 c. M: 1.4597 c. 41: 7 23 11 N T3 SD: 0.8729 c. M: 1.4023 c. 53: 9 30 14 N T3 SD: 0.3862 c. M:-0.6604 c. 83: 14 47 22 N T3 SD: 0.2912 c. M: 0.4596 c. 94: 16 53 25 N T3 SD: 0.2245 c. M:-0.3064 c. 124: 21 70 33 N T3 SD: 0.2000 c. M: 0.3247 c. 147: 25 83 39 N T3 SD: 0.1439 c. M:-0.2343 c. 177: 30 100 47 N T3 SD: 0.0350 c. M: 0.0528 c. 501: 85 283 133 N T3 SD: 0.0183 c. M:-0.0315 c. 678: 115 383 180 N T3 SD: 0.0061 c. M:-0.0095 c. 855: 145 483 227 N T3 SD: 0.0061 c. M: 0.0100 c. 1533: 260 866 407 N T3 SD: 0.0046 c. M: 0.0077 c. 1940: 329 1096 515 N T3 SD: 0.0047 c. M:-0.0065 c. 2211: 375 1249 587 N T3 SD: 0.0047 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: 20.4882 cents 5 x 6:7 S SD: 49.1253 cents 6 x 7:8 S SD: 49.4773 cents 7 x x 9 SD: 62.9609 cents 8:9:10:11 H SD: 44.1265 cents 9:10:11:12 H SD: 33.2177 cents 11:12:14:15 S SD: 30.8458 cents 12:13:15:16 SD: 19.2849 cents 13:14:16:17 S SD: 18.5342 cents 14:15:17:19 SD: 18.3911 cents 15:16:19:20 SD: 17.0897 cents 16:17:20:21 SD: 13.2617 cents 17:18:21:23 SD: 9.7106 cents 18:19:22:24 SD: 6.8530 cents 21:22:26:28 SD: 1.8506 cents 60:63:74:80 SD: 0.9167 cents 81:85:100:108 SD: 0.4799 cents 183:192:226:244 SD: 0.4750 cents 264:277:326:352 SD: 0.4657 cents 276:290:341:368 SD: 0.4104 cents 297:312:367:396 SD: 0.3335 cents 318:334:393:424 SD: 0.3115 cents 357:375:441:476 SD: 0.2309 cents 378:397:467:504 SD: 0.1625 cents 399:419:493:532 SD: 0.1540 cents 438:460:541:584 SD: 0.1403 cents 459:482:567:612 SD: 0.0599 cents 480:504:593:640 SD: 0.0572 cents 540:567:667:720 SD: 0.0509 cents 561:589:693:748 SD: 0.0490 cents