Scala analysis: 233_C15
Chromatic tetrachord 14/13 * 26/25 * 25/21
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/13 128.298245 2/3-tone 2: 28/25 196.198479 middle second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 25/21 301.8465 BP second, quasi-equal minor third 1: 14/13 128.2982 2/3-tone 2: 26/25 67.9002 tridecimal 1/3-tone 3: 25/21 301.8465 BP second, quasi-equal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 26/25 67.900 cents tridecimal 1/3-tone 1: 1 14/13 128.298 cents 2/3-tone 1: 1 25/21 301.847 cents BP second, quasi-equal minor third 2: 1 28/25 196.198 cents middle second 2: 1 26/21 369.747 cents 2: 1 50/39 430.145 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 : 128.3 196.2 498.0 128.3: 67.9 369.7 498.0 196.2: 301.8 430.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 67.9002 .. 301.8465 cents 625/546, 233.9463 cents 26/25, 67.9002 cents 2: 196.1985 .. 430.1448 cents 625/546, 233.9463 cents 588/625,-105.6480 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 26/25, 67.9002 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 25/21, 301.8465 cents Average / Smallest step : 2.444984 Largest / Average step : 1.818188 Largest / Smallest step : 4.445442 Median interval of one step : 14/13, 128.2982 cents, amount: 1 Least squares average step : 143.91644 cents, oct.: 431.74933 cents Scale is not proper Scale has trivalence property 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 67.90023 cents Scale diversity : 1.005189 Lumma stability : 0.272667 Lumma impropriety factor : 0.212125 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 : 175/169, 60.3980 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 13 Odd number limit : 39 (O: 25 U: 39) Highest odd numerator or denominator: 25 Scale harmonicity : 0.020038 Average absolute harmonicity : 0.094684 Specific harmonicity : 0.099376 Fundamental : 1/975, -9.9293 octaves, 0.2683 Hz. Guide tone : 28, 4.8074 octaves, 7325.516 Hz. Exponens Consonantiae : 2.730000E+04, 14.73661 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 43.5, average 14.50000 Mersenne's string divisions : 10017 Sum of van Prooijen's expressibility: 2.98900, average 0.99633 Sum of Tenney's harmonic distance : 6.18435, average 2.06145 Vogel's harmonic complexity : 23.66667 Wille's k value : 262 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 13.86710, average 2.31118 Lattice compactness (without 2's) : 11.06789, average 1.84465 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 0 -0.33333 1 1 5: -2 .. 0 -0.66667 2 7: 0 .. 1 0.66667 2 1 13: -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 21 26| Scale is weakly epimorphic with val: <6 10 15 21 29| Scale is weakly epimorphic with val: <6 10 15 22 25| Scale is weakly epimorphic with val: <6 10 18 22 25| Scale is weakly epimorphic with val: <6 11 15 21 25| Scale is weakly epimorphic with val: <6 11 15 21 28| Scale is weakly epimorphic with val: <6 11 16 22 25| Scale is weakly epimorphic with val: <6 11 19 22 25| Scale is weakly epimorphic with val: <7 10 15 19 27| Scale is weakly epimorphic with val: <7 10 15 19 30| Scale is weakly epimorphic with val: <7 10 15 21 25| Scale is weakly epimorphic with val: <7 10 16 21 26| Scale is weakly epimorphic with val: <7 10 16 21 29| Scale is weakly epimorphic with val: <7 10 17 22 26| Scale is weakly epimorphic with val: <7 10 18 21 25| Scale is weakly epimorphic with val: <7 11 15 18 27| Scale is weakly epimorphic with val: <7 11 15 18 30| Scale is weakly epimorphic with val: <7 11 15 20 25| Scale is weakly epimorphic with val: <7 11 15 20 28| Scale is weakly epimorphic with val: <7 11 15 21 27| Scale is weakly epimorphic with val: <7 11 15 21 30| Scale is weakly epimorphic with val: <7 11 16 19 27| Scale is weakly epimorphic with val: <7 11 16 19 30| Scale is JI-epimorphic with val: <7 11 16 20 26| Scale is weakly epimorphic with val: <7 11 16 20 29| Scale is weakly epimorphic with val: <7 11 16 22 27| Scale is weakly epimorphic with val: <7 11 16 22 30| Scale is weakly epimorphic with val: <7 11 17 18 26| Scale is weakly epimorphic with val: <7 11 17 18 29| Scale is weakly epimorphic with val: <7 11 17 19 25| Scale is weakly epimorphic with val: <7 11 17 19 28| Scale is weakly epimorphic with val: <7 11 17 21 26| Scale is weakly epimorphic with val: <7 11 17 21 29| Scale is weakly epimorphic with val: <7 11 17 22 25| Scale is JI-epimorphic with val: <7 11 17 22 28| Scale is weakly epimorphic with val: <7 11 18 18 27| Scale is weakly epimorphic with val: <7 11 18 18 30| Scale is weakly epimorphic with val: <7 11 18 20 25| Scale is weakly epimorphic with val: <7 11 18 20 28| Scale is weakly epimorphic with val: <7 11 18 21 27| Scale is weakly epimorphic with val: <7 11 18 21 30| Scale is weakly epimorphic with val: <7 11 19 19 27| Scale is weakly epimorphic with val: <7 11 19 19 30| Scale is weakly epimorphic with val: <7 11 19 20 26| Scale is weakly epimorphic with val: <7 11 19 20 29| Scale is weakly epimorphic with val: <7 11 19 22 27| Scale is weakly epimorphic with val: <7 11 19 22 30| Scale is weakly epimorphic with val: <7 12 15 19 25| Scale is weakly epimorphic with val: <7 12 15 19 28| Scale is weakly epimorphic with val: <7 12 16 21 27| Scale is weakly epimorphic with val: <7 12 16 21 30| Scale is weakly epimorphic with val: <7 12 16 22 26| Scale is weakly epimorphic with val: <7 12 17 21 25| Scale is weakly epimorphic with val: <7 12 19 22 26| Scale is weakly epimorphic with val: <8 11 15 21 26| Scale is weakly epimorphic with val: <8 11 16 19 26| Scale is weakly epimorphic with val: <8 11 16 19 29| Scale is weakly epimorphic with val: <8 11 16 20 25| Scale is weakly epimorphic with val: <8 11 17 21 25| Scale is weakly epimorphic with val: <8 11 17 21 28| Scale is weakly epimorphic with val: <8 11 17 22 27| Scale is weakly epimorphic with val: <8 11 18 21 26| Scale is weakly epimorphic with val: <8 11 19 20 25| Scale is weakly epimorphic with val: <8 12 15 22 27| Scale is weakly epimorphic with val: <8 12 16 19 25| Scale is weakly epimorphic with val: <8 12 16 19 28| Scale is weakly epimorphic with val: <8 12 16 21 26| Scale is weakly epimorphic with val: <8 12 17 20 25| Scale is weakly epimorphic with val: <8 12 17 21 27| Scale is weakly epimorphic with val: <8 12 17 21 30| Scale is weakly epimorphic with val: <8 12 18 22 27| Scale is weakly epimorphic with val: <8 12 19 21 26|
FIT/MODE
3: 1 0 2 N G T3 SD: 27.8902 c. M:-37.7168 c. 4: 1 1 2 P M ME S SD: 30.5762 c. M:-52.8240 c. 5: 1 1 3 N M DE S SD: 16.6552 c. M: 28.6892 c. 7: 2 1 4 N T3 SD: 12.8264 c. M:-17.2494 c. 8: 2 1 5 N T3 SD: 5.8679 c. M: 9.4316 c. 15: 4 2 9 N T3 SD: 3.1354 c. M:-4.5138 c. 20: 5 3 12 N T3 SD: 2.7964 c. M: 3.7870 c. 23: 6 3 14 N T3 SD: 1.2063 c. M:-1.6265 c. 43: 11 6 26 N T3 SD: 0.6554 c. M: 0.8914 c. 66: 17 9 40 N T3 SD: 0.0081 c. M: 0.0139 c. 2069: 533 282 1254 N T3 SD: 0.0082 c. M: 0.0135 c. 2135: 550 291 1294 N T3 SD: 0.0079 c. M: 0.0131 c. 2201: 567 300 1334 N T3 SD: 0.0075 c. M: 0.0126 c. 2267: 584 309 1374 N T3 SD: 0.0072 c. M: 0.0122 c. 2333: 601 318 1414 N T3 SD: 0.0070 c. M: 0.0119 c. 2399: 618 327 1454 N T3 SD: 0.0067 c. M: 0.0115 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: 73.1459 cents 6 x 7:8 S SD: 35.3362 cents 7 x 8:9 S SD: 36.0117 cents 8 x 9:11 SD: 26.9141 cents 9 x 10:12 S SD: 6.8974 cents 10 x 11:13 SD: 26.8991 cents 11:12 x 15 S SD: 22.4315 cents 12:13 x 16 SD: 5.1372 cents 20 x 22:27 SD: 18.9447 cents 21:23:24:28 SD: 15.1864 cents 22:24:25:29 SD: 13.0003 cents 23:25:26:31 SD: 9.8082 cents 24:26:27:32 SD: 4.2821 cents 39:42:44:52 SD: 4.2123 cents 41:44:46:55 SD: 4.1681 cents 42:45:47:56 SD: 2.9924 cents 51:55:57:68 SD: 1.4578 cents 66:71:74:88 SD: 0.8832 cents 117:126:131:156 SD: 0.1762 cents 300:323:336:400 SD: 0.1374 cents 417:449:467:556 SD: 0.1105 cents 534:575:598:712 SD: 0.1092 cents 558:601:625:744 SD: 0.0826 cents