Scala analysis: 293_C21
Chromatic tetrachord 34/31 * 31/30 * 20/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 34/31 159.919837 2: 17/15 216.686695 septendecimal whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 20/17 281.3583 septendecimal augmented second 1: 34/31 159.9198 2: 31/30 56.7669 31st-partial chroma 3: 20/17 281.3583 septendecimal augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 31/30 56.767 cents 31st-partial chroma 1: 1 34/31 159.920 cents 1: 1 20/17 281.358 cents septendecimal augmented second 2: 1 17/15 216.687 cents septendecimal whole tone 2: 1 62/51 338.125 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 : 159.9 216.7 498.0 159.9: 56.8 338.1 498.0 216.7: 281.4 441.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 56.7669 .. 281.3583 cents 600/527, 224.5914 cents 31/30, 56.7669 cents 2: 216.6867 .. 441.2781 cents 600/527, 224.5914 cents 289/300,-64.6716 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 : 20/17, 281.3583 cents Average / Smallest step : 2.924506 Largest / Average step : 1.694776 Largest / Smallest step : 4.956383 Median interval of one step : 34/31, 159.9198 cents, amount: 1 Least squares average step : 149.10202 cents, oct.: 447.30605 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1579-tone equal temperament with octave 4/3 degrees: 507 687 1579 Least number of segments generator : 790 of 249.180 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1133 of 357.369 cents and inv. generated superset size: 36 = 33 more = 1200.000% 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 : 0.921255 Lumma stability : 0.227959 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 : 31/30, 56.7669 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% -- Rational properties -- Prime limit : 31 Odd number limit : 51 (O: 31 U: 51) Highest odd numerator or denominator: 31 Scale harmonicity : 0.024281 Fundamental : 1/465, -8.8611 octaves, 0.5626 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 3.162000E+04, 14.94855 octaves Euler's gradus suavitatis : 55 Sum of Mann's harmonic distance : 52.0, average 17.33333 Mersenne's string divisions : 14560 Sum of van Prooijen's expressibility: 3.19893, average 1.06631 Sum of Tenney's harmonic distance : 6.50856, average 2.16952 Vogel's harmonic complexity : 37.33333 Wille's k value : 263 Wilson's harmonic complexity : 56 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 11.29592, average 1.88265 Lattice compactness (without 2's) : 7.97469, average 1.32912 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.00000 3 3: -1 .. 0 -0.66667 2 1 5: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 1 31: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 15 28 33| Scale is weakly epimorphic with val: <6 10 15 28 36| Scale is weakly epimorphic with val: <6 10 15 28 39| Scale is weakly epimorphic with val: <6 10 15 32 35| Scale is weakly epimorphic with val: <6 10 16 29 34| Scale is weakly epimorphic with val: <6 10 16 29 37| Scale is weakly epimorphic with val: <6 10 16 30 33| Scale is weakly epimorphic with val: <6 10 16 33 36| Scale is weakly epimorphic with val: <6 10 17 30 35| Scale is weakly epimorphic with val: <6 10 17 30 38| Scale is weakly epimorphic with val: <6 10 17 31 34| Scale is weakly epimorphic with val: <6 10 18 31 33| Scale is weakly epimorphic with val: <6 10 18 31 36| Scale is weakly epimorphic with val: <6 10 18 31 39| Scale is weakly epimorphic with val: <6 10 18 32 35| Scale is weakly epimorphic with val: <6 10 19 30 33| Scale is weakly epimorphic with val: <6 10 19 32 34| Scale is weakly epimorphic with val: <6 10 19 32 37| Scale is weakly epimorphic with val: <6 10 19 33 36| Scale is weakly epimorphic with val: <6 11 15 29 33| Scale is weakly epimorphic with val: <6 11 15 29 36| Scale is weakly epimorphic with val: <6 11 15 29 39| Scale is weakly epimorphic with val: <6 11 15 31 34| Scale is weakly epimorphic with val: <6 11 16 30 34| Scale is weakly epimorphic with val: <6 11 16 30 37| Scale is weakly epimorphic with val: <6 11 16 32 35| Scale is weakly epimorphic with val: <6 11 17 30 33| Scale is weakly epimorphic with val: <6 11 17 31 35| Scale is weakly epimorphic with val: <6 11 17 31 38| Scale is weakly epimorphic with val: <6 11 17 33 36| Scale is weakly epimorphic with val: <6 11 18 31 34| Scale is weakly epimorphic with val: <6 11 18 32 33| Scale is weakly epimorphic with val: <6 11 18 32 36| Scale is weakly epimorphic with val: <6 11 18 32 39| Scale is weakly epimorphic with val: <6 11 19 32 35| Scale is weakly epimorphic with val: <6 11 19 33 34| Scale is weakly epimorphic with val: <6 11 19 33 37| Scale is weakly epimorphic with val: <7 10 15 28 33| Scale is weakly epimorphic with val: <7 10 15 28 36| Scale is weakly epimorphic with val: <7 10 15 28 39| Scale is weakly epimorphic with val: <7 10 15 30 34| Scale is weakly epimorphic with val: <7 10 15 33 37| Scale is weakly epimorphic with val: <7 10 16 29 34| Scale is weakly epimorphic with val: <7 10 16 29 37| Scale is weakly epimorphic with val: <7 10 16 31 35| Scale is weakly epimorphic with val: <7 10 17 29 33| Scale is weakly epimorphic with val: <7 10 17 30 35| Scale is weakly epimorphic with val: <7 10 17 30 38| Scale is weakly epimorphic with val: <7 10 17 32 36| Scale is weakly epimorphic with val: <7 10 18 30 34| Scale is weakly epimorphic with val: <7 10 18 31 33| Scale is weakly epimorphic with val: <7 10 18 31 36| Scale is weakly epimorphic with val: <7 10 18 31 39| Scale is weakly epimorphic with val: <7 10 18 33 37| Scale is weakly epimorphic with val: <7 10 19 31 35| Scale is weakly epimorphic with val: <7 10 19 32 34| Scale is weakly epimorphic with val: <7 10 19 32 37| Scale is weakly epimorphic with val: <7 11 15 27 35| Scale is weakly epimorphic with val: <7 11 15 27 38| Scale is JI-epimorphic with val: <7 11 15 28 34| Scale is weakly epimorphic with val: <7 11 15 28 37| Scale is weakly epimorphic with val: <7 11 15 30 35| Scale is weakly epimorphic with val: <7 11 15 30 38| Scale is weakly epimorphic with val: <7 11 15 31 34| Scale is weakly epimorphic with val: <7 11 15 31 37| Scale is weakly epimorphic with val: <7 11 15 33 35| Scale is weakly epimorphic with val: <7 11 15 33 38| Scale is weakly epimorphic with val: <7 11 16 28 33| Scale is weakly epimorphic with val: <7 11 16 28 36| Scale is weakly epimorphic with val: <7 11 16 28 39| Scale is JI-epimorphic with val: <7 11 16 29 35| Scale is weakly epimorphic with val: <7 11 16 29 38| Scale is weakly epimorphic with val: <7 11 16 31 33| Scale is weakly epimorphic with val: <7 11 16 31 36| Scale is weakly epimorphic with val: <7 11 16 31 39| Scale is weakly epimorphic with val: <7 11 16 32 35| Scale is weakly epimorphic with val: <7 11 16 32 38| Scale is weakly epimorphic with val: <7 11 17 27 33| Scale is weakly epimorphic with val: <7 11 17 27 36| Scale is weakly epimorphic with val: <7 11 17 27 39| Scale is weakly epimorphic with val: <7 11 17 29 34| Scale is weakly epimorphic with val: <7 11 17 29 37| Scale is weakly epimorphic with val: <7 11 17 30 33| Scale is JI-epimorphic with val: <7 11 17 30 36| = patent Scale is weakly epimorphic with val: <7 11 17 30 39| Scale is weakly epimorphic with val: <7 11 17 32 34| Scale is weakly epimorphic with val: <7 11 17 32 37| Scale is weakly epimorphic with val: <7 11 17 33 33| Scale is weakly epimorphic with val: <7 11 17 33 36| Scale is weakly epimorphic with val: <7 11 17 33 39| Scale is weakly epimorphic with val: <7 11 18 27 35| Scale is weakly epimorphic with val: <7 11 18 27 38| Scale is weakly epimorphic with val: <7 11 18 28 34| Scale is weakly epimorphic with val: <7 11 18 28 37| Scale is weakly epimorphic with val: <7 11 18 30 35| Scale is weakly epimorphic with val: <7 11 18 30 38| Scale is weakly epimorphic with val: <7 11 18 31 34| Scale is JI-epimorphic with val: <7 11 18 31 37| Scale is weakly epimorphic with val: <7 11 18 33 35| Scale is weakly epimorphic with val: <7 11 18 33 38| Scale is weakly epimorphic with val: <7 11 19 28 33| Scale is weakly epimorphic with val: <7 11 19 28 36| Scale is weakly epimorphic with val: <7 11 19 28 39| Scale is weakly epimorphic with val: <7 11 19 29 35| Scale is weakly epimorphic with val: <7 11 19 29 38| Scale is weakly epimorphic with val: <7 11 19 31 33| Scale is weakly epimorphic with val: <7 11 19 31 36| Scale is weakly epimorphic with val: <7 11 19 31 39| Scale is weakly epimorphic with val: <7 11 19 32 35| Scale is JI-epimorphic with val: <7 11 19 32 38| Scale is weakly epimorphic with val: <7 12 15 30 33| Scale is weakly epimorphic with val: <7 12 15 30 36| Scale is weakly epimorphic with val: <7 12 15 30 39| Scale is weakly epimorphic with val: <7 12 15 31 35| Scale is weakly epimorphic with val: <7 12 16 29 33| Scale is weakly epimorphic with val: <7 12 16 31 34| Scale is weakly epimorphic with val: <7 12 16 31 37| Scale is weakly epimorphic with val: <7 12 16 32 36| Scale is weakly epimorphic with val: <7 12 17 30 34| Scale is weakly epimorphic with val: <7 12 17 32 35| Scale is weakly epimorphic with val: <7 12 17 32 38| Scale is weakly epimorphic with val: <7 12 17 33 37| Scale is weakly epimorphic with val: <7 12 18 31 35| Scale is weakly epimorphic with val: <7 12 18 33 33| Scale is weakly epimorphic with val: <7 12 18 33 36| Scale is weakly epimorphic with val: <7 12 18 33 39| Scale is weakly epimorphic with val: <7 12 19 29 33| Scale is weakly epimorphic with val: <7 12 19 32 36| Scale is weakly epimorphic with val: <8 11 15 29 33| Scale is weakly epimorphic with val: <8 11 15 29 36| Scale is weakly epimorphic with val: <8 11 15 29 39| Scale is weakly epimorphic with val: <8 11 15 30 35| Scale is weakly epimorphic with val: <8 11 15 33 38| Scale is weakly epimorphic with val: <8 11 16 28 33| Scale is weakly epimorphic with val: <8 11 16 30 34| Scale is weakly epimorphic with val: <8 11 16 30 37| Scale is weakly epimorphic with val: <8 11 16 31 36| Scale is weakly epimorphic with val: <8 11 17 29 34| Scale is weakly epimorphic with val: <8 11 17 31 35| Scale is weakly epimorphic with val: <8 11 17 31 38| Scale is weakly epimorphic with val: <8 11 17 32 37| Scale is weakly epimorphic with val: <8 11 18 30 35| Scale is weakly epimorphic with val: <8 11 18 32 33| Scale is weakly epimorphic with val: <8 11 18 32 36| Scale is weakly epimorphic with val: <8 11 18 32 39| Scale is weakly epimorphic with val: <8 11 18 33 38| Scale is weakly epimorphic with val: <8 11 19 28 33| Scale is weakly epimorphic with val: <8 11 19 31 36| Scale is weakly epimorphic with val: <8 11 19 33 34| Scale is weakly epimorphic with val: <8 11 19 33 37| Scale is weakly epimorphic with val: <8 12 15 29 34| Scale is weakly epimorphic with val: <8 12 15 30 33| Scale is weakly epimorphic with val: <8 12 15 30 36| Scale is weakly epimorphic with val: <8 12 15 30 39| Scale is weakly epimorphic with val: <8 12 15 32 37| Scale is weakly epimorphic with val: <8 12 16 30 35| Scale is weakly epimorphic with val: <8 12 16 31 34| Scale is weakly epimorphic with val: <8 12 16 31 37| Scale is weakly epimorphic with val: <8 12 16 33 38| Scale is weakly epimorphic with val: <8 12 17 28 33| Scale is weakly epimorphic with val: <8 12 17 31 36| Scale is weakly epimorphic with val: <8 12 17 32 35| Scale is weakly epimorphic with val: <8 12 17 32 38| Scale is weakly epimorphic with val: <8 12 18 29 34| Scale is weakly epimorphic with val: <8 12 18 32 37| Scale is weakly epimorphic with val: <8 12 18 33 33| Scale is weakly epimorphic with val: <8 12 18 33 36| Scale is weakly epimorphic with val: <8 12 18 33 39| Scale is weakly epimorphic with val: <8 12 19 30 35| Scale is weakly epimorphic with val: <8 12 19 33 38|
FIT/MODE
3: 1 0 2 N G T3 SD: 29.4662 c. M: 50.6717 c. 4: 1 1 2 P M ME S SD: 27.6850 c. M: 35.4086 c. 5: 2 0 3 N G T3 SD: 24.8294 c. M:-39.2982 c. 6: 2 1 3 P T3 SD: 18.9979 c. M:-32.3358 c. 7: 2 1 4 N T3 SD: 10.3441 c. M: 17.6213 c. 9: 3 1 5 N T3 SD: 4.4320 c. M:-6.0952 c. 16: 5 2 9 N T3 SD: 2.5680 c. M: 4.2808 c. 25: 8 3 14 N T3 SD: 1.4509 c. M:-2.4531 c. 37: 12 4 21 N T3 SD: 1.1997 c. M:-1.6083 c. 44: 14 5 25 N T3 SD: 1.2564 c. M: 1.6218 c. 53: 17 6 30 N T3 SD: 0.3345 c. M: 0.5540 c. 78: 25 9 44 N T3 SD: 0.2899 c. M:-0.4098 c. 115: 37 13 65 N T3 SD: 0.2033 c. M:-0.3207 c. 131: 42 15 74 N T3 SD: 0.1398 c. M: 0.2413 c. 184: 59 21 104 N T3 SD: 0.1525 c. M: 0.2206 c. 193: 62 22 109 N T3 SD: 0.0625 c. M:-0.0790 c. 246: 79 28 139 N T3 SD: 0.0354 c. M: 0.0574 c. 324: 104 37 183 N T3 SD: 0.0444 c. M:-0.0551 c. 377: 121 43 213 N T3 SD: 0.0440 c. M: 0.0699 c. 439: 141 50 248 N T3 SD: 0.0257 c. M:-0.0445 c. 570: 183 65 322 N T3 SD: 0.0128 c. M: 0.0212 c. 763: 245 87 431 N T3 SD: 0.0145 c. M:-0.0249 c. 816: 262 93 461 N T3 SD: 0.0088 c. M: 0.0127 c. 1009: 324 115 570 N T3 SD: 0.0051 c. M:-0.0074 c. 1579: 507 180 892 N T3 SD: 0.0036 c. M:-0.0055 c. 1825: 586 208 1031 N T3 SD: 0.0017 c. M: 0.0030 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: 65.0514 cents 6 x 7:8 S SD: 25.0921 cents 7 x 8:9 S SD: 32.3031 cents 8 x 9:11 SD: 27.3918 cents 9:10 x 12 S SD: 11.2419 cents 10:11 x 13 SD: 22.0625 cents 11:12 x 15 S SD: 19.9989 cents 12:13:14:16 S SD: 18.1786 cents 14:15:16:19 SD: 17.5980 cents 15:16:17:20 SD: 16.0629 cents 16 x 18:21 S SD: 15.0547 cents 17 x 19:23 SD: 17.4713 cents 18:20 x 24 S SD: 11.2419 cents 20:22:23:27 SD: 11.1910 cents 21:23:24:28 SD: 4.8964 cents 26 x 29:35 SD: 16.1112 cents 27:30:31:36 SD: 10.5990 cents 28:31:32:37 SD: 8.9214 cents 29:32:33:39 SD: 6.5002 cents 30:33:34:40 SD: 1.6948 cents 81:89:92:108 SD: 1.6349 cents 84:92:95:112 SD: 1.4584 cents 105:115:119:140 SD: 0.8088 cents 135:148:153:180 SD: 0.2515 cents 165:181:187:220 SD: 0.1029 cents 300:329:340:400 SD: 0.0566 cents 465:510:527:620 SD: 0.0000 cents