Scala analysis: 298_C22
Chromatic tetrachord 276/265 * 265/243 * 27/23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 276/265 70.411089 2: 92/81 220.454344 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 27/23 277.5907 vicesimotertial minor third 1: 276/265 70.4111 2: 265/243 150.0433 3: 27/23 277.5907 vicesimotertial minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 276/265 70.411 cents 1: 1 265/243 150.043 cents 1: 1 27/23 277.591 cents vicesimotertial minor third 2: 1 92/81 220.454 cents 2: 1 324/265 348.002 cents 2: 1 265/207 427.634 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 : 70.4 220.5 498.0 70.4 : 150.0 427.6 498.0 220.5: 277.6 348.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.4111 .. 277.5907 cents 2385/2116, 207.1796 cents 276/265, 70.4111 cents 2: 220.4543 .. 427.6339 cents 2385/2116, 207.1796 cents 2116/2187,-57.1363 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 276/265, 70.4111 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 27/23, 277.5907 cents Average / Smallest step : 2.357796 Largest / Average step : 1.672082 Largest / Smallest step : 3.942428 Median interval of one step : 265/243, 150.0433 cents, amount: 1 Least squares average step : 143.24677 cents, oct.: 429.74031 cents Scale is not proper Scale has trivalence property Scale is a mode of a 863-tone equal temperament with octave 4/3 degrees: 122 382 863 Least number of segments generator : 432 of 249.311 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 695 of 401.091 cents and inv. generated superset size: 20 = 17 more = 666.667% 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 57.13631 cents Scale diversity : 1.034259 Lumma stability : 0.282750 Lumma impropriety factor : 0.114721 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 : 2187/2116, 57.1363 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 53 Odd number limit : 265 (O: 265 U: 265) Highest odd numerator or denominator: 265 Scale harmonicity : 0.015669 Fundamental : 1/21465, -14.3897 octaves, 0.0122 Hz. Guide tone : 276, 8.1085 octaves, 72208.656 Hz. Exponens Consonantiae : 5.924340E+06, 22.49822 octaves Euler's gradus suavitatis : 91 Sum of Mann's harmonic distance : 360.5, average 120.16667 Mersenne's string divisions : 655151 Sum of van Prooijen's expressibility: 4.80885, average 1.60295 Sum of Tenney's harmonic distance : 9.81561, average 3.27187 Vogel's harmonic complexity : 64.00000 Wille's k value : 3577 Wilson's harmonic complexity : 96 Rectangular lattice diameter : 8 Triangular lattice diameter : 5 Lattice compactness : 20.17518, average 3.36253 Lattice compactness (without 2's) : 17.56594, average 2.92766 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -4 .. 1 -1.33333 6 1 5: -1 .. 0 -0.33333 1 23: 0 .. 1 0.66667 2 1 53: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <6 10 15 31 40| Scale is weakly epimorphic with val: <6 10 16 31 42| Scale is weakly epimorphic with val: <6 10 17 31 41| Scale is weakly epimorphic with val: <6 10 18 31 40| Scale is weakly epimorphic with val: <6 10 19 31 42| Scale is weakly epimorphic with val: <6 11 15 35 41| Scale is weakly epimorphic with val: <6 11 16 35 40| Scale is weakly epimorphic with val: <6 11 17 35 42| Scale is weakly epimorphic with val: <6 11 18 35 41| Scale is weakly epimorphic with val: <6 11 19 35 40| Scale is weakly epimorphic with val: <7 10 15 34 40| Scale is weakly epimorphic with val: <7 11 15 31 42| Scale is JI-epimorphic with val: <7 11 15 32 41| Scale is weakly epimorphic with val: <7 11 15 34 42| Scale is weakly epimorphic with val: <7 11 15 35 41| Scale is weakly epimorphic with val: <7 11 16 31 41| Scale is JI-epimorphic with val: <7 11 16 32 40| Scale is weakly epimorphic with val: <7 11 16 34 41| Scale is weakly epimorphic with val: <7 11 16 35 40| Scale is weakly epimorphic with val: <7 11 17 31 40| Scale is weakly epimorphic with val: <7 11 17 32 42| Scale is weakly epimorphic with val: <7 11 17 34 40| Scale is weakly epimorphic with val: <7 11 17 35 42| Scale is weakly epimorphic with val: <7 11 18 31 42| Scale is weakly epimorphic with val: <7 11 18 32 41| Scale is weakly epimorphic with val: <7 11 18 34 42| Scale is weakly epimorphic with val: <7 11 18 35 41| Scale is weakly epimorphic with val: <7 11 19 31 41| Scale is weakly epimorphic with val: <7 11 19 32 40| Scale is weakly epimorphic with val: <7 11 19 34 41| Scale is weakly epimorphic with val: <7 11 19 35 40| Scale is weakly epimorphic with val: <7 12 15 32 40| Scale is weakly epimorphic with val: <7 12 16 35 42| Scale is weakly epimorphic with val: <7 12 17 35 41| Scale is weakly epimorphic with val: <7 12 18 35 40| Scale is weakly epimorphic with val: <8 11 15 31 42| Scale is weakly epimorphic with val: <8 11 15 32 41| Scale is weakly epimorphic with val: <8 11 16 31 41| Scale is weakly epimorphic with val: <8 11 16 32 40| Scale is weakly epimorphic with val: <8 11 17 31 40| Scale is weakly epimorphic with val: <8 11 17 35 42| Scale is weakly epimorphic with val: <8 11 18 31 42| Scale is weakly epimorphic with val: <8 11 18 35 41| Scale is weakly epimorphic with val: <8 11 19 31 41| Scale is weakly epimorphic with val: <8 11 19 35 40| Scale is weakly epimorphic with val: <8 12 15 31 41| Scale is weakly epimorphic with val: <8 12 15 35 40| Scale is weakly epimorphic with val: <8 12 16 31 40| Scale is weakly epimorphic with val: <8 12 16 35 42| Scale is weakly epimorphic with val: <8 12 17 34 42| Scale is weakly epimorphic with val: <8 12 17 35 41| Scale is weakly epimorphic with val: <8 12 18 34 41| Scale is weakly epimorphic with val: <8 12 18 35 40| Scale is weakly epimorphic with val: <8 12 19 34 40| Scale is weakly epimorphic with val: <8 12 19 35 42|
FIT/MODE
3: 0 1 2 N G T3 SD: 51.3854 c. M: 70.4111 c. 4: 1 1 2 P M ME S SD: 35.3222 c. M:-54.1002 c. 5: 1 1 3 N M DE S SD: 20.8447 c. M:-29.1979 c. 6: 1 2 3 P T3 SD: 18.0260 c. M:-28.5682 c. 7: 1 2 4 N T3 SD: 4.0676 c. M: 7.0065 c. 20: 3 6 11 N T3 SD: 3.2604 c. M:-4.2957 c. 27: 4 8 15 N T3 SD: 2.0156 c. M:-3.3734 c. 29: 4 9 16 N T3 SD: 1.8993 c. M:-2.8072 c. 34: 5 10 19 N T3 SD: 1.6876 c. M:-2.8308 c. 36: 5 11 20 N T3 SD: 0.8834 c. M: 1.2382 c. 43: 6 13 24 N T3 SD: 0.5746 c. M: 0.9164 c. 63: 9 19 35 N T3 SD: 0.6716 c. M:-0.8990 c. 70: 10 21 39 N T3 SD: 0.4308 c. M:-0.7382 c. 106: 15 32 59 N T3 SD: 0.2210 c. M:-0.3769 c. 113: 16 34 63 N T3 SD: 0.0780 c. M:-0.1086 c. 262: 37 79 146 N T3 SD: 0.0541 c. M: 0.0765 c. 375: 53 113 209 N T3 SD: 0.0143 c. M: 0.0207 c. 488: 69 147 272 N T3 SD: 0.0071 c. M:-0.0092 c. 863: 122 260 481 N T3 SD: 0.0023 c. M: 0.0038 c. 1351: 191 407 753 N T3 SD: 0.0013 c. M: 0.0022 c. 2214: 313 667 1234 N T3 SD: 0.0007 c. M: 0.0009 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: 63.6303 cents 6 x 7:8 S SD: 23.2083 cents 7 x 8:9 S SD: 31.9335 cents 8 x 9:11 SD: 27.8914 cents 9 x 10:12 S SD: 19.0253 cents 10 x 11:13 SD: 35.3408 cents 11 x 13:15 SD: 39.4999 cents 12:13:14:16 S SD: 27.4884 cents 13:14:15:17 SD: 24.0961 cents 14:15:16:19 SD: 19.6015 cents 15:16:17:20 SD: 13.8305 cents 20:21:23:27 SD: 11.1685 cents 21:22:24:28 S SD: 4.9154 cents 30:31:34:40 SD: 4.7183 cents 44:46:50:59 SD: 3.9410 cents 45:47:51:60 SD: 2.0529 cents 51:53:58:68 SD: 1.4706 cents 96:100:109:128 SD: 0.2145 cents 243:253:276:324 SD: 0.1979 cents 339:353:385:452 SD: 0.1297 cents 435:453:494:580 SD: 0.1126 cents 552:575:627:736 SD: 0.0935 cents