Scala analysis: 346_C29
Chromatic tetrachord 15/14 * 14/13 * 52/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 15/13 247.741053 tridecimal 5/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 52/45 250.3039 1: 15/14 119.4428 major diatonic semitone 2: 14/13 128.2982 2/3-tone 3: 52/45 250.3039
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 14/13 128.298 cents 2/3-tone 1: 1 52/45 250.304 cents 2: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 26/21 369.747 cents 2: 1 56/45 378.602 cents septimal narrow major third 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 : 119.4 247.7 498.0 119.4: 128.3 378.6 498.0 247.7: 250.3 369.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 119.4428 .. 250.3039 cents 728/675, 130.8611 cents 15/14, 119.4428 cents 2: 247.7411 .. 378.6022 cents 728/675, 130.8611 cents 675/676,-2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 15/14, 119.4428 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 52/45, 250.3039 cents Average / Smallest step : 1.389912 Largest / Average step : 1.507719 Largest / Smallest step : 2.095597 Median interval of one step : 14/13, 128.2982 cents, amount: 1 Least squares average step : 150.64714 cents, oct.: 451.94141 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1743-tone equal temperament with octave 4/3 degrees: 418 867 1743 Least number of segments generator : 872 of 249.165 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1409 of 402.608 cents and inv. generated superset size: 61 = 58 more = 2033.333% 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 2.56289 cents Scale diversity : 1.119492 Lumma stability : 0.479647 Lumma impropriety factor : 0.005146 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 : 676/675, 2.5629 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 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 Limited inverse transpositions with margin 122.0057 cents: 2 -- Rational properties -- Prime limit : 13 Odd number limit : 45 (O: 15 U: 45) Highest odd numerator or denominator: 15 Scale harmonicity : 0.021199 Average absolute harmonicity : 0.098483 Specific harmonicity : 0.106252 Fundamental : 1/546, -9.0928 octaves, 0.4792 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 3.276000E+04, 14.99965 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 32.0, average 10.66667 Mersenne's string divisions : 812 Sum of van Prooijen's expressibility: 2.82930, average 0.94310 Sum of Tenney's harmonic distance : 5.69144, average 1.89715 Vogel's harmonic complexity : 22.00000 Wille's k value : 292 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.73543, average 2.45591 Lattice compactness (without 2's) : 10.77729, average 1.79622 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.66667 2 7: -1 .. 0 -0.33333 1 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 17 18 26| Scale is weakly epimorphic with val: <6 10 17 18 29| Scale is weakly epimorphic with val: <6 10 18 18 25| Scale is weakly epimorphic with val: <6 10 18 19 27| Scale is weakly epimorphic with val: <6 10 18 19 30| Scale is weakly epimorphic with val: <6 10 18 21 25| Scale is weakly epimorphic with val: <6 10 19 19 26| Scale is weakly epimorphic with val: <6 10 19 20 25| Scale is weakly epimorphic with val: <6 10 19 20 28| Scale is weakly epimorphic with val: <6 10 19 22 26| Scale is weakly epimorphic with val: <6 11 16 18 25| Scale is weakly epimorphic with val: <6 11 16 18 28| Scale is weakly epimorphic with val: <6 11 17 19 26| Scale is weakly epimorphic with val: <6 11 17 19 29| Scale is weakly epimorphic with val: <6 11 17 20 25| Scale is weakly epimorphic with val: <6 11 18 18 26| Scale is weakly epimorphic with val: <6 11 18 20 27| Scale is weakly epimorphic with val: <6 11 18 20 30| Scale is weakly epimorphic with val: <6 11 18 21 26| Scale is weakly epimorphic with val: <6 11 19 19 27| Scale is weakly epimorphic with val: <6 11 19 21 25| Scale is weakly epimorphic with val: <6 11 19 21 28| Scale is weakly epimorphic with val: <6 11 19 22 27| Scale is weakly epimorphic with val: <7 10 18 18 26| Scale is weakly epimorphic with val: <7 10 18 18 29| Scale is weakly epimorphic with val: <7 10 18 19 25| Scale is weakly epimorphic with val: <7 10 18 22 25| Scale is weakly epimorphic with val: <7 10 19 19 27| Scale is weakly epimorphic with val: <7 10 19 19 30| Scale is weakly epimorphic with val: <7 10 19 20 26| 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 18 26| Scale is weakly epimorphic with val: <7 11 16 18 29| Scale is JI-epimorphic with val: <7 11 16 19 25| Scale is weakly epimorphic with val: <7 11 16 19 28| Scale is weakly epimorphic with val: <7 11 16 21 26| Scale is weakly epimorphic with val: <7 11 16 21 29| Scale is weakly epimorphic with val: <7 11 16 22 25| Scale is weakly epimorphic with val: <7 11 16 22 28| Scale is weakly epimorphic with val: <7 11 17 19 27| Scale is weakly epimorphic with val: <7 11 17 19 30| Scale is JI-epimorphic with val: <7 11 17 20 26| Scale is weakly epimorphic with val: <7 11 17 20 29| Scale is weakly epimorphic with val: <7 11 17 22 27| Scale is weakly epimorphic with val: <7 11 17 22 30| 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 JI-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 25| Scale is weakly epimorphic with val: <7 11 19 19 28| Scale is weakly epimorphic with val: <7 11 19 21 26| Scale is weakly epimorphic with val: <7 11 19 21 29| Scale is weakly epimorphic with val: <7 11 19 22 25| Scale is JI-epimorphic with val: <7 11 19 22 28| Scale is weakly epimorphic with val: <7 12 16 18 27| Scale is weakly epimorphic with val: <7 12 16 18 30| Scale is weakly epimorphic with val: <7 12 16 20 25| Scale is weakly epimorphic with val: <7 12 17 18 26| Scale is weakly epimorphic with val: <7 12 17 19 25| Scale is weakly epimorphic with val: <7 12 17 19 28| Scale is weakly epimorphic with val: <7 12 17 21 26| Scale is weakly epimorphic with val: <7 12 18 19 27| Scale is weakly epimorphic with val: <7 12 18 20 26| Scale is weakly epimorphic with val: <7 12 18 20 29| Scale is weakly epimorphic with val: <7 12 18 22 27| Scale is weakly epimorphic with val: <7 12 19 20 28| Scale is weakly epimorphic with val: <7 12 19 21 27| Scale is weakly epimorphic with val: <7 12 19 21 30| Scale is weakly epimorphic with val: <8 11 17 19 25| Scale is weakly epimorphic with val: <8 11 17 22 25| Scale is weakly epimorphic with val: <8 11 18 18 25| Scale is weakly epimorphic with val: <8 11 18 18 28| Scale is weakly epimorphic with val: <8 11 18 20 26| Scale is weakly epimorphic with val: <8 11 19 19 26| Scale is weakly epimorphic with val: <8 11 19 19 29| Scale is weakly epimorphic with val: <8 11 19 21 27| Scale is weakly epimorphic with val: <8 12 16 18 25| Scale is weakly epimorphic with val: <8 12 16 21 25| Scale is weakly epimorphic with val: <8 12 17 18 27| Scale is weakly epimorphic with val: <8 12 17 18 30| Scale is weakly epimorphic with val: <8 12 17 19 26| Scale is weakly epimorphic with val: <8 12 17 22 26| Scale is weakly epimorphic with val: <8 12 18 19 25| Scale is weakly epimorphic with val: <8 12 18 19 28| Scale is weakly epimorphic with val: <8 12 18 20 27| Scale is weakly epimorphic with val: <8 12 19 20 26| Scale is weakly epimorphic with val: <8 12 19 20 29| Scale is weakly epimorphic with val: <8 12 19 21 28|
FIT/MODE
3: 1 1 1 SP B ME I SD: 55.5985 c. M:-84.2889 c. 4: 1 1 2 P M ME S SD: 3.0183 c. M:-5.0684 c. 26: 6 7 13 P T3 SD: 2.7066 c. M: 4.5093 c. 30: 7 8 15 P T3 SD: 2.0075 c. M: 3.2323 c. 34: 8 9 17 P T3 SD: 1.4978 c. M: 2.2557 c. 38: 9 10 19 P T3 SD: 1.1324 c. M: 1.4848 c. 42: 10 11 21 P T3 SD: 0.8912 c. M:-1.2814 c. 46: 11 12 23 P T3 SD: 0.7662 c. M:-1.2814 c. 50: 12 13 25 P T3 SD: 0.7416 c. M:-1.2814 c. 54: 13 14 27 P T3 SD: 0.7855 c. M:-1.2814 c. 58: 14 15 29 P T3 SD: 0.8646 c. M:-1.2814 c. 80: 19 21 40 P T3 SD: 0.9968 c. M:-1.2814 c. 88: 21 23 44 P T3 SD: 0.8148 c. M:-1.2814 c. 96: 23 25 48 P T3 SD: 0.7431 c. M:-1.2814 c. 101: 24 26 51 N T3 SD: 0.9313 c. M: 1.1841 c. 104: 25 27 52 P T3 SD: 0.7572 c. M:-1.2814 c. 105: 25 27 53 N T3 SD: 0.8019 c. M: 1.0902 c. 109: 26 28 55 N T3 SD: 0.6880 c. M: 1.0032 c. 113: 27 29 57 N T3 SD: 0.5902 c. M: 0.9223 c. 117: 28 30 59 N T3 SD: 0.5103 c. M: 0.8470 c. 121: 29 31 61 N T3 SD: 0.4505 c. M: 0.7766 c. 125: 30 32 63 N T3 SD: 0.4135 c. M: 0.7107 c. 129: 31 33 65 N T3 SD: 0.4000 c. M: 0.6490 c. 133: 32 34 67 N T3 SD: 0.4080 c. M: 0.5909 c. 137: 33 35 69 N T3 SD: 0.4330 c. M: 0.5362 c. 151: 36 39 76 N T3 SD: 0.4584 c. M: 0.7036 c. 155: 37 40 78 N T3 SD: 0.3712 c. M: 0.5546 c. 159: 38 41 80 N T3 SD: 0.2897 c. M: 0.4132 c. 163: 39 42 82 N T3 SD: 0.2147 c. M: 0.2787 c. 167: 40 43 84 N T3 SD: 0.1491 c. M: 0.2097 c. 171: 41 44 86 N T3 SD: 0.1023 c. M: 0.1748 c. 175: 42 45 88 N T3 SD: 0.0962 c. M: 0.1415 c. 217: 52 56 109 N T3 SD: 0.0950 c. M:-0.1339 c. 221: 53 57 111 N T3 SD: 0.0893 c. M:-0.1546 c. 384: 92 99 193 N T3 SD: 0.0696 c. M: 0.1195 c. 388: 93 100 195 N T3 SD: 0.0382 c. M: 0.0660 c. 392: 94 101 197 N T3 SD: 0.0101 c. M: 0.0137 c. 1180: 283 304 593 N T3 SD: 0.0090 c. M:-0.0152 c. 1351: 324 348 679 N T3 SD: 0.0051 c. M: 0.0088 c. 1743: 418 449 876 N T3 SD: 0.0032 c. M: 0.0044 c. 2135: 512 550 1073 N T3 SD: 0.0032 c. M: 0.0053 c. 2139: 513 551 1075 N T3 SD: 0.0025 c. M:-0.0042 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: 54.1875 cents 6 x 7:8 S SD: 9.5649 cents 7 x 8:9 S SD: 32.5520 cents 8 x 9:11 SD: 34.4934 cents 9:10 x 12 S SD: 31.4805 cents 10:11:12:13 H SD: 30.9254 cents 11:12:13:15 SD: 21.6189 cents 12:13:14:16 S SD: 9.0179 cents 25:27:29:33 SD: 8.0128 cents 26:28:30:35 S SD: 6.2617 cents 27:29:31:36 SD: 3.1917 cents 39:42:45:52 SD: 2.9518 cents 45:48:52:60 SD: 2.7088 cents 57:61:66:76 SD: 2.1311 cents 72:77:83:96 SD: 1.1958 cents 84:90:97:112 SD: 0.4578 cents 195:209:225:260 SD: 0.1973 cents 279:299:322:372 SD: 0.1950 cents 351:376:405:468 SD: 0.1096 cents 462:495:533:616 SD: 0.0833 cents 546:585:630:728 SD: 0.0000 cents