Scala analysis: 209_C13
Chromatic tetrachord 64/61 * 61/58 * 29/24
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 64/61 83.115195 2: 32/29 170.422806 29th subharmonic 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 29/24 327.6222 1: 64/61 83.1152 2: 61/58 87.3076 3: 29/24 327.6222
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 64/61 83.115 cents 1: 1 61/58 87.308 cents 1: 1 29/24 327.622 cents 2: 1 32/29 170.423 cents 29th subharmonic 2: 1 232/183 410.737 cents 2: 1 61/48 414.930 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 : 83.1 170.4 498.0 83.1 : 87.3 414.9 498.0 170.4: 327.6 410.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 83.1152 .. 327.6222 cents 1769/1536, 244.5070 cents 64/61, 83.1152 cents 2: 170.4228 .. 414.9298 cents 1769/1536, 244.5070 cents 768/841,-157.1994 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 64/61, 83.1152 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 29/24, 327.6222 cents Average / Smallest step : 1.997409 Largest / Average step : 1.973449 Largest / Smallest step : 3.941785 Median interval of one step : 61/58, 87.3076 cents, amount: 1 Least squares average step : 137.00684 cents, oct.: 411.02053 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1546-tone equal temperament with octave 4/3 degrees: 258 529 1546 Least number of segments generator : 775 of 249.667 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1327 of 427.494 cents and inv. generated superset size: 48 = 45 more = 1600.000% 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 83.11519 cents Scale diversity : 0.934748 Lumma stability : 0.333766 Lumma impropriety factor : 0.315633 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 : 3721/3712, 4.1924 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 240.3146 cents: 2 -- Rational properties -- Prime limit : 61 Odd number limit : 183 (O: 61 U: 183) Highest odd numerator or denominator: 61 Scale harmonicity : 0.015940 Fundamental : 1/5307, -12.3737 octaves, 0.0493 Hz. Guide tone : 64, 6.0000 octaves, 16744.036 Hz. Exponens Consonantiae : 3.396480E+05, 18.37368 octaves Euler's gradus suavitatis : 97 Sum of Mann's harmonic distance : 96.5, average 32.16667 Mersenne's string divisions : 53375 Sum of van Prooijen's expressibility: 3.72485, average 1.24162 Sum of Tenney's harmonic distance : 7.63824, average 2.54608 Vogel's harmonic complexity : 66.33333 Wille's k value : 884 Wilson's harmonic complexity : 93 Rectangular lattice diameter : 3 Triangular lattice diameter : 1 Lattice compactness : 22.18903, average 3.69817 Lattice compactness (without 2's) : 5.41421, average 0.90237 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 6 4.33333 13 3: -1 .. 0 -0.33333 1 1 29: -1 .. 0 -0.33333 1 1 61: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 3 / 3 = 1.00000 Scale is weakly epimorphic with val: <7 10 32 43| Scale is weakly epimorphic with val: <7 11 33 44| Scale is weakly epimorphic with val: <7 11 34 43| Scale is weakly epimorphic with val: <7 11 36 44| Scale is weakly epimorphic with val: <7 11 37 43| Scale is weakly epimorphic with val: <7 12 32 44| Scale is weakly epimorphic with val: <8 11 37 44| Scale is weakly epimorphic with val: <8 12 37 43|
FIT/MODE
3: 0 1 2 N G T3 SD: 48.0540 c. M: 83.1152 c. 4: 0 1 3 N G T3 SD: 54.8209 c. M: 83.1152 c. 5: 1 1 3 N M DE S SD: 19.1591 c. M:-28.7952 c. 6: 1 1 4 N M DE S SD: 2.5456 c. M: 4.4078 c. 23: 4 4 15 N M DE S SD: 2.5921 c. M:-3.5013 c. 29: 5 5 19 N M DE S SD: 1.7628 c. M:-2.7546 c. 35: 6 6 23 N M DE S SD: 1.3214 c. M:-2.2639 c. 41: 7 7 27 N M DE S SD: 1.1259 c. M:-1.9169 c. 47: 8 8 31 N M DE S SD: 1.0827 c. M:-1.6584 c. 53: 9 9 35 N M DE S SD: 1.1186 c. M:-1.4585 c. 61: 10 11 40 N T3 SD: 1.0373 c. M: 1.4685 c. 67: 11 12 44 N T3 SD: 0.8393 c. M: 1.3466 c. 73: 12 13 48 N T3 SD: 0.7232 c. M: 1.2448 c. 79: 13 14 52 N T3 SD: 0.6792 c. M: 1.1584 c. 85: 14 15 56 N T3 SD: 0.6897 c. M: 1.0843 c. 90: 15 16 59 N T3 SD: 0.6531 c. M:-1.1260 c. 91: 15 16 60 N T3 SD: 0.7340 c. M: 1.0199 c. 96: 16 17 63 N T3 SD: 0.4547 c. M:-0.7802 c. 102: 17 18 67 N T3 SD: 0.2812 c. M:-0.4750 c. 108: 18 19 71 N T3 SD: 0.1330 c. M:-0.2037 c. 114: 19 20 75 N T3 SD: 0.0661 c. M: 0.1077 c. 377: 63 66 248 N T3 SD: 0.0650 c. M:-0.1125 c. 450: 75 79 296 N T3 SD: 0.0632 c. M: 0.1077 c. 479: 80 84 315 N T3 SD: 0.0680 c. M:-0.0978 c. 485: 81 85 319 N T3 SD: 0.0440 c. M:-0.0635 c. 491: 82 86 323 N T3 SD: 0.0361 c. M:-0.0614 c. 599: 100 105 394 N T3 SD: 0.0236 c. M:-0.0309 c. 605: 101 106 398 N T3 SD: 0.0198 c. M:-0.0295 c. 713: 119 125 469 N T3 SD: 0.0106 c. M:-0.0162 c. 827: 138 145 544 N T3 SD: 0.0065 c. M:-0.0086 c. 1432: 239 251 942 N T3 SD: 0.0050 c. M:-0.0082 c. 1546: 258 271 1017 N T3 SD: 0.0029 c. M: 0.0051 c. 2259: 377 396 1486 N T3 SD: 0.0017 c. M:-0.0025 c. 2373: 396 416 1561 N T3 SD: 0.0016 c. M: 0.0028 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 x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 83.9987 cents 6 x 7:8 S SD: 48.2240 cents 7 x 8:9 S SD: 43.7458 cents 8 x 9:11 SD: 31.4619 cents 9 x 10:12 S SD: 5.9905 cents 10 x 11:13 SD: 22.0824 cents 11 x 12:15 S SD: 21.8239 cents 12 x 13:16 SD: 15.9251 cents 13 x 14:17 SD: 26.9472 cents 14:15 x 19 SD: 23.7625 cents 15:16:17:20 SD: 18.1329 cents 16:17:18:21 S SD: 16.1304 cents 17:18:19:23 SD: 12.3810 cents 18:19:20:24 S SD: 5.3076 cents 21:22:23:28 SD: 4.3946 cents 38:40:42:51 SD: 4.3371 cents 39:41:43:52 SD: 1.2441 cents 105:110:116:140 SD: 1.1000 cents 126:132:139:168 SD: 0.8712 cents 144:151:159:192 SD: 0.4890 cents 165:173:182:220 SD: 0.4407 cents 183:192:202:244 SD: 0.1971 cents 348:365:384:464 SD: 0.1814 cents 387:406:427:516 SD: 0.0659 cents 570:598:629:760 SD: 0.0447 cents