Scala analysis: 204_C12
Chromatic tetrachord 33/31 * 31/30 * 40/33
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33/31 108.237371 2: 11/10 165.004228 Ptolemy's second, 4/5-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 40/33 333.0408 1: 33/31 108.2374 2: 31/30 56.7669 31st-partial chroma 3: 40/33 333.0408
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 31/30 56.767 cents 31st-partial chroma 1: 1 33/31 108.237 cents 1: 1 40/33 333.041 cents 2: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 1 124/99 389.808 cents 2: 1 40/31 441.278 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 : 108.2 165.0 498.0 108.2: 56.8 389.8 498.0 165.0: 333.0 441.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 56.7669 .. 333.0408 cents 400/341, 276.2739 cents 31/30, 56.7669 cents 2: 165.0042 .. 441.2781 cents 400/341, 276.2739 cents 363/400,-168.0365 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 31/30, 56.7669 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 40/33, 333.0408 cents Average / Smallest step : 2.924506 Largest / Average step : 2.006088 Largest / Smallest step : 5.866817 Median interval of one step : 33/31, 108.2374 cents, amount: 1 Least squares average step : 138.02720 cents, oct.: 414.08161 cents Scale is not proper Scale has trivalence property Scale is a mode of a 658-tone equal temperament with octave 4/3 degrees: 143 218 658 Least number of segments generator : 331 of 250.536 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 585 of 442.791 cents and inv. generated superset size: 30 = 27 more = 1000.000% 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 56.76686 cents Scale diversity : 0.843208 Lumma stability : 0.227959 Lumma impropriety factor : 0.337392 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 : 990/961, 51.4705 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 31 Odd number limit : 99 (O: 33 U: 99) Highest odd numerator or denominator: 33 Scale harmonicity : 0.030381 Fundamental : 1/930, -9.8611 octaves, 0.2813 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 1.227600E+05, 16.90548 octaves Euler's gradus suavitatis : 52 Sum of Mann's harmonic distance : 46.0, average 15.33333 Mersenne's string divisions : 1344 Sum of van Prooijen's expressibility: 3.03703, average 1.01234 Sum of Tenney's harmonic distance : 6.13045, average 2.04348 Vogel's harmonic complexity : 35.66667 Wille's k value : 511 Wilson's harmonic complexity : 53 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.57848, average 2.26308 Lattice compactness (without 2's) : 9.21076, average 1.53513 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -1 .. 1 0.00000 2 1 5: -1 .. 0 -0.33333 1 11: 0 .. 1 0.66667 2 1 31: -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 15 24 33| Scale is weakly epimorphic with val: <6 10 15 24 36| Scale is weakly epimorphic with val: <6 10 15 24 39| Scale is weakly epimorphic with val: <6 10 16 25 34| Scale is weakly epimorphic with val: <6 10 16 25 37| Scale is weakly epimorphic with val: <6 10 16 26 33| Scale is weakly epimorphic with val: <6 10 17 26 35| Scale is weakly epimorphic with val: <6 10 17 26 38| Scale is weakly epimorphic with val: <6 10 17 27 34| Scale is weakly epimorphic with val: <6 10 18 27 33| Scale is weakly epimorphic with val: <6 10 18 27 36| Scale is weakly epimorphic with val: <6 10 18 27 39| Scale is weakly epimorphic with val: <6 10 19 26 33| Scale is weakly epimorphic with val: <6 11 15 24 33| Scale is weakly epimorphic with val: <6 11 15 24 36| Scale is weakly epimorphic with val: <6 11 15 24 39| Scale is weakly epimorphic with val: <6 11 15 26 34| Scale is weakly epimorphic with val: <6 11 16 25 34| Scale is weakly epimorphic with val: <6 11 16 25 37| Scale is weakly epimorphic with val: <6 11 16 27 35| Scale is weakly epimorphic with val: <6 11 17 25 33| Scale is weakly epimorphic with val: <6 11 17 26 35| Scale is weakly epimorphic with val: <6 11 17 26 38| Scale is weakly epimorphic with val: <6 11 18 26 34| Scale is weakly epimorphic with val: <6 11 18 27 33| Scale is weakly epimorphic with val: <6 11 18 27 36| Scale is weakly epimorphic with val: <6 11 18 27 39| Scale is weakly epimorphic with val: <6 11 19 27 35| Scale is weakly epimorphic with val: <7 10 15 25 33| Scale is weakly epimorphic with val: <7 10 15 25 36| Scale is weakly epimorphic with val: <7 10 15 25 39| Scale is weakly epimorphic with val: <7 10 15 27 34| Scale is weakly epimorphic with val: <7 10 16 26 34| Scale is weakly epimorphic with val: <7 10 16 26 37| Scale is weakly epimorphic with val: <7 10 17 26 33| Scale is weakly epimorphic with val: <7 10 17 27 35| Scale is weakly epimorphic with val: <7 10 17 27 38| Scale is weakly epimorphic with val: <7 10 18 27 34| Scale is weakly epimorphic with val: <7 11 15 23 35| Scale is weakly epimorphic with val: <7 11 15 23 38| Scale is JI-epimorphic with val: <7 11 15 24 34| Scale is weakly epimorphic with val: <7 11 15 24 37| Scale is weakly epimorphic with val: <7 11 15 26 35| Scale is weakly epimorphic with val: <7 11 15 26 38| Scale is weakly epimorphic with val: <7 11 15 27 34| Scale is weakly epimorphic with val: <7 11 15 27 37| Scale is weakly epimorphic with val: <7 11 16 24 33| Scale is weakly epimorphic with val: <7 11 16 24 36| Scale is weakly epimorphic with val: <7 11 16 24 39| Scale is JI-epimorphic with val: <7 11 16 25 35| Scale is weakly epimorphic with val: <7 11 16 25 38| Scale is weakly epimorphic with val: <7 11 16 27 33| Scale is weakly epimorphic with val: <7 11 16 27 36| Scale is weakly epimorphic with val: <7 11 16 27 39| Scale is weakly epimorphic with val: <7 11 17 23 33| Scale is weakly epimorphic with val: <7 11 17 23 36| Scale is weakly epimorphic with val: <7 11 17 23 39| Scale is weakly epimorphic with val: <7 11 17 25 34| Scale is weakly epimorphic with val: <7 11 17 25 37| Scale is weakly epimorphic with val: <7 11 17 26 33| Scale is JI-epimorphic with val: <7 11 17 26 36| Scale is weakly epimorphic with val: <7 11 17 26 39| Scale is weakly epimorphic with val: <7 11 18 23 35| Scale is weakly epimorphic with val: <7 11 18 23 38| Scale is weakly epimorphic with val: <7 11 18 24 34| Scale is weakly epimorphic with val: <7 11 18 24 37| Scale is weakly epimorphic with val: <7 11 18 26 35| Scale is weakly epimorphic with val: <7 11 18 26 38| Scale is weakly epimorphic with val: <7 11 18 27 34| Scale is JI-epimorphic with val: <7 11 18 27 37| Scale is weakly epimorphic with val: <7 11 19 24 33| Scale is weakly epimorphic with val: <7 11 19 24 36| Scale is weakly epimorphic with val: <7 11 19 24 39| Scale is weakly epimorphic with val: <7 11 19 25 35| Scale is weakly epimorphic with val: <7 11 19 25 38| Scale is weakly epimorphic with val: <7 11 19 27 33| Scale is weakly epimorphic with val: <7 11 19 27 36| Scale is weakly epimorphic with val: <7 11 19 27 39| Scale is weakly epimorphic with val: <7 12 15 25 33| Scale is weakly epimorphic with val: <7 12 15 25 36| Scale is weakly epimorphic with val: <7 12 15 25 39| Scale is weakly epimorphic with val: <7 12 15 26 35| Scale is weakly epimorphic with val: <7 12 16 24 33| Scale is weakly epimorphic with val: <7 12 16 26 34| Scale is weakly epimorphic with val: <7 12 16 26 37| Scale is weakly epimorphic with val: <7 12 16 27 36| Scale is weakly epimorphic with val: <7 12 17 25 34| Scale is weakly epimorphic with val: <7 12 17 27 35| Scale is weakly epimorphic with val: <7 12 17 27 38| Scale is weakly epimorphic with val: <7 12 18 26 35| Scale is weakly epimorphic with val: <7 12 19 24 33| Scale is weakly epimorphic with val: <7 12 19 27 36| Scale is weakly epimorphic with val: <8 11 15 26 33| Scale is weakly epimorphic with val: <8 11 15 26 36| Scale is weakly epimorphic with val: <8 11 15 26 39| Scale is weakly epimorphic with val: <8 11 15 27 35| Scale is weakly epimorphic with val: <8 11 16 25 33| Scale is weakly epimorphic with val: <8 11 16 27 34| Scale is weakly epimorphic with val: <8 11 16 27 37| Scale is weakly epimorphic with val: <8 11 17 26 34| Scale is weakly epimorphic with val: <8 11 18 27 35| Scale is weakly epimorphic with val: <8 11 19 25 33| Scale is weakly epimorphic with val: <8 12 15 25 34| Scale is weakly epimorphic with val: <8 12 15 26 33| Scale is weakly epimorphic with val: <8 12 15 26 36| Scale is weakly epimorphic with val: <8 12 15 26 39| Scale is weakly epimorphic with val: <8 12 16 26 35| Scale is weakly epimorphic with val: <8 12 16 27 34| Scale is weakly epimorphic with val: <8 12 16 27 37| Scale is weakly epimorphic with val: <8 12 17 24 33| Scale is weakly epimorphic with val: <8 12 17 27 36| Scale is weakly epimorphic with val: <8 12 18 25 34| Scale is weakly epimorphic with val: <8 12 19 26 35|
FIT/MODE
3: 1 0 2 N G T3 SD: 33.3630 c. M:-57.7776 c. 4: 1 0 3 N G T3 SD: 25.1960 c. M: 40.4930 c. 5: 1 1 3 N M DE S SD: 20.3718 c. M:-34.2138 c. 6: 1 1 4 N M DE S SD: 14.5782 c. M: 25.2299 c. 8: 2 1 5 N T3 SD: 15.6892 c. M:-21.7626 c. 9: 2 1 6 N T3 SD: 1.5244 c. M:-2.4393 c. 42: 9 5 28 N T3 SD: 1.0507 c. M: 1.5134 c. 51: 11 6 34 N T3 SD: 0.7500 c. M:-1.0108 c. 60: 13 7 40 N T3 SD: 0.6135 c. M:-1.0108 c. 69: 15 8 46 N T3 SD: 0.5839 c. M:-1.0108 c. 78: 17 9 52 N T3 SD: 0.6106 c. M:-1.0108 c. 87: 19 10 58 N T3 SD: 0.6592 c. M:-1.0108 c. 88: 19 10 59 N T3 SD: 0.6491 c. M: 0.8758 c. 97: 21 11 65 N T3 SD: 0.4697 c. M: 0.7007 c. 106: 23 12 71 N T3 SD: 0.3355 c. M: 0.5554 c. 115: 25 13 77 N T3 SD: 0.2506 c. M: 0.4328 c. 124: 27 14 83 N T3 SD: 0.2242 c. M: 0.3281 c. 157: 34 18 105 N T3 SD: 0.2213 c. M: 0.3805 c. 166: 36 19 111 N T3 SD: 0.1316 c. M: 0.2276 c. 175: 38 20 117 N T3 SD: 0.0634 c. M: 0.0905 c. 184: 40 21 123 N T3 SD: 0.0655 c. M:-0.1085 c. 299: 65 34 200 N T3 SD: 0.0607 c. M: 0.0997 c. 359: 78 41 240 N T3 SD: 0.0520 c. M:-0.0859 c. 465: 101 53 311 N T3 SD: 0.0491 c. M: 0.0603 c. 474: 103 54 317 N T3 SD: 0.0242 c. M: 0.0400 c. 483: 105 55 323 N T3 SD: 0.0225 c. M:-0.0333 c. 649: 141 74 434 N T3 SD: 0.0206 c. M: 0.0334 c. 658: 143 75 440 N T3 SD: 0.0009 c. M:-0.0016 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: 86.3514 cents 6 x 7:8 S SD: 50.9333 cents 7 x 8:9 S SD: 45.6687 cents 8 x 9:11 SD: 32.9836 cents 9 x 10:12 S SD: 8.6997 cents 10 x 11:13 SD: 21.9155 cents 11 x 12:15 S SD: 20.7369 cents 12 x 13:16 SD: 13.2158 cents 13:14 x 17 SD: 19.5740 cents 14:15 x 19 SD: 16.3133 cents 16:17:18:21 S SD: 15.8737 cents 17:18:19:23 SD: 12.8415 cents 18:19:20:24 S SD: 7.5785 cents 24 x 26:32 SD: 13.2158 cents 26:28:29:35 SD: 11.8090 cents 27:29:30:36 SD: 7.7618 cents 28:30:31:37 SD: 7.3952 cents 29:31:32:39 SD: 5.7960 cents 30:32:33:40 SD: 1.1646 cents 108:115:119:144 SD: 0.9841 cents 111:118:122:148 SD: 0.9192 cents 138:147:152:184 SD: 0.8496 cents 141:150:155:188 SD: 0.5264 cents 171:182:188:228 SD: 0.3235 cents 201:214:221:268 SD: 0.2752 cents 249:265:274:332 SD: 0.2532 cents 279:297:307:372 SD: 0.1880 cents 420:447:462:560 SD: 0.1249 cents 450:479:495:600 SD: 0.0389 cents 480:511:528:640 SD: 0.0364 cents