Scala analysis: 349_C29
Chromatic tetrachord 24/23 * 115/104 * 52/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 24/23 73.680654 vicesimotertial minor 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: 24/23 73.6807 vicesimotertial minor semitone 2: 115/104 174.0604 3: 52/45 250.3039
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 24/23 73.681 cents vicesimotertial minor semitone 1: 1 115/104 174.060 cents 1: 1 52/45 250.304 cents 2: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 416/345 323.985 cents 2: 1 23/18 424.364 cents vicesimotertial 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 : 73.7 247.7 498.0 73.7 : 174.1 424.4 498.0 247.7: 250.3 324.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.6807 .. 250.3039 cents 299/270, 176.6233 cents 24/23, 73.6807 cents 2: 247.7411 .. 424.3643 cents 299/270, 176.6233 cents 675/676,-2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 24/23, 73.6807 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 52/45, 250.3039 cents Average / Smallest step : 2.253169 Largest / Average step : 1.507719 Largest / Smallest step : 3.397146 Median interval of one step : 115/104, 174.0604 cents, amount: 1 Least squares average step : 147.37841 cents, oct.: 442.13523 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1548-tone equal temperament with octave 4/3 degrees: 229 770 1548 Least number of segments generator : 775 of 249.344 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1159 of 372.890 cents and inv. generated superset size: 80 = 77 more = 2666.667% 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 2.56289 cents Scale diversity : 0.987569 Lumma stability : 0.295880 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 : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 23 Odd number limit : 345 (O: 115 U: 345) Highest odd numerator or denominator: 23 Scale harmonicity : 0.012662 Average absolute harmonicity : 0.089085 Specific harmonicity : 0.066228 Fundamental : 1/897, -9.8090 octaves, 0.2917 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 1.076400E+05, 16.71585 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 41.0, average 13.66667 Mersenne's string divisions : 1316 Sum of van Prooijen's expressibility: 3.01494, average 1.00498 Sum of Tenney's harmonic distance : 6.11115, average 2.03705 Vogel's harmonic complexity : 31.33333 Wille's k value : 517 Wilson's harmonic complexity : 47 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 16.36061, average 2.72677 Lattice compactness (without 2's) : 10.56387, average 1.76065 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 3 1.66667 5 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.33333 1 13: -1 .. 0 -0.33333 1 1 23: -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 18 25 30| Scale is weakly epimorphic with val: <6 10 18 25 33| Scale is weakly epimorphic with val: <6 10 18 25 36| Scale is weakly epimorphic with val: <6 10 19 26 30| Scale is weakly epimorphic with val: <6 10 19 26 33| Scale is weakly epimorphic with val: <6 10 19 26 36| Scale is weakly epimorphic with val: <6 11 17 25 30| Scale is weakly epimorphic with val: <6 11 17 25 33| Scale is weakly epimorphic with val: <6 11 17 25 36| Scale is weakly epimorphic with val: <6 11 18 26 30| Scale is weakly epimorphic with val: <6 11 18 26 33| Scale is weakly epimorphic with val: <6 11 18 26 36| Scale is weakly epimorphic with val: <6 11 19 27 30| Scale is weakly epimorphic with val: <6 11 19 27 33| Scale is weakly epimorphic with val: <6 11 19 27 36| Scale is weakly epimorphic with val: <7 10 18 25 32| Scale is weakly epimorphic with val: <7 10 18 25 35| Scale is weakly epimorphic with val: <7 10 19 26 32| Scale is weakly epimorphic with val: <7 10 19 26 35| Scale is weakly epimorphic with val: <7 11 15 25 30| Scale is weakly epimorphic with val: <7 11 15 25 33| Scale is weakly epimorphic with val: <7 11 15 25 36| Scale is weakly epimorphic with val: <7 11 15 27 31| Scale is weakly epimorphic with val: <7 11 15 27 34| Scale is weakly epimorphic with val: <7 11 15 28 30| Scale is weakly epimorphic with val: <7 11 15 28 33| Scale is weakly epimorphic with val: <7 11 15 28 36| Scale is weakly epimorphic with val: <7 11 15 30 31| Scale is weakly epimorphic with val: <7 11 15 30 34| Scale is JI-epimorphic with val: <7 11 16 25 31| Scale is weakly epimorphic with val: <7 11 16 25 34| Scale is weakly epimorphic with val: <7 11 16 26 30| Scale is weakly epimorphic with val: <7 11 16 26 33| Scale is weakly epimorphic with val: <7 11 16 26 36| Scale is weakly epimorphic with val: <7 11 16 28 31| Scale is weakly epimorphic with val: <7 11 16 28 34| Scale is weakly epimorphic with val: <7 11 16 29 30| Scale is weakly epimorphic with val: <7 11 16 29 33| Scale is weakly epimorphic with val: <7 11 16 29 36| Scale is JI-epimorphic with val: <7 11 17 26 31| Scale is weakly epimorphic with val: <7 11 17 26 34| Scale is weakly epimorphic with val: <7 11 17 27 30| Scale is weakly epimorphic with val: <7 11 17 27 33| = patent Scale is weakly epimorphic with val: <7 11 17 27 36| Scale is weakly epimorphic with val: <7 11 17 29 31| Scale is weakly epimorphic with val: <7 11 17 29 34| Scale is weakly epimorphic with val: <7 11 17 30 30| Scale is weakly epimorphic with val: <7 11 17 30 33| Scale is weakly epimorphic with val: <7 11 17 30 36| Scale is weakly epimorphic with val: <7 11 18 25 30| Scale is weakly epimorphic with val: <7 11 18 25 33| Scale is weakly epimorphic with val: <7 11 18 25 36| Scale is JI-epimorphic with val: <7 11 18 27 31| Scale is weakly epimorphic with val: <7 11 18 27 34| Scale is weakly epimorphic with val: <7 11 18 28 30| Scale is weakly epimorphic with val: <7 11 18 28 33| Scale is weakly epimorphic with val: <7 11 18 28 36| Scale is weakly epimorphic with val: <7 11 18 30 31| Scale is weakly epimorphic with val: <7 11 18 30 34| Scale is weakly epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 25 34| Scale is weakly epimorphic with val: <7 11 19 26 30| Scale is weakly epimorphic with val: <7 11 19 26 33| Scale is weakly epimorphic with val: <7 11 19 26 36| Scale is JI-epimorphic with val: <7 11 19 28 31| Scale is weakly epimorphic with val: <7 11 19 28 34| Scale is weakly epimorphic with val: <7 11 19 29 30| Scale is weakly epimorphic with val: <7 11 19 29 33| Scale is weakly epimorphic with val: <7 11 19 29 36| Scale is weakly epimorphic with val: <7 12 15 26 30| Scale is weakly epimorphic with val: <7 12 15 29 30| Scale is weakly epimorphic with val: <7 12 16 25 32| Scale is weakly epimorphic with val: <7 12 16 25 35| Scale is weakly epimorphic with val: <7 12 16 27 30| Scale is weakly epimorphic with val: <7 12 16 30 30| Scale is weakly epimorphic with val: <7 12 17 25 30| Scale is weakly epimorphic with val: <7 12 17 26 32| Scale is weakly epimorphic with val: <7 12 17 26 35| Scale is weakly epimorphic with val: <7 12 17 28 30| Scale is weakly epimorphic with val: <7 12 18 26 30| Scale is weakly epimorphic with val: <7 12 18 27 32| Scale is weakly epimorphic with val: <7 12 18 27 35| Scale is weakly epimorphic with val: <7 12 18 29 30| Scale is weakly epimorphic with val: <7 12 19 27 30| Scale is weakly epimorphic with val: <7 12 19 28 32| Scale is weakly epimorphic with val: <7 12 19 28 35| Scale is weakly epimorphic with val: <7 12 19 30 30| Scale is weakly epimorphic with val: <8 11 15 25 32| Scale is weakly epimorphic with val: <8 11 15 28 32| Scale is weakly epimorphic with val: <8 11 16 26 32| Scale is weakly epimorphic with val: <8 11 16 29 32| Scale is weakly epimorphic with val: <8 11 17 25 31| Scale is weakly epimorphic with val: <8 11 17 25 34| Scale is weakly epimorphic with val: <8 11 17 27 32| Scale is weakly epimorphic with val: <8 11 17 30 32| Scale is weakly epimorphic with val: <8 11 18 25 32| Scale is weakly epimorphic with val: <8 11 18 26 31| Scale is weakly epimorphic with val: <8 11 18 26 34| Scale is weakly epimorphic with val: <8 11 18 28 32| Scale is weakly epimorphic with val: <8 11 19 26 32| Scale is weakly epimorphic with val: <8 11 19 27 31| Scale is weakly epimorphic with val: <8 11 19 27 34| Scale is weakly epimorphic with val: <8 11 19 29 32| Scale is weakly epimorphic with val: <8 12 15 25 33| Scale is weakly epimorphic with val: <8 12 15 28 33| Scale is weakly epimorphic with val: <8 12 16 25 31| Scale is weakly epimorphic with val: <8 12 16 25 34| Scale is weakly epimorphic with val: <8 12 16 26 33| Scale is weakly epimorphic with val: <8 12 16 29 33| Scale is weakly epimorphic with val: <8 12 17 26 31| Scale is weakly epimorphic with val: <8 12 17 26 34| Scale is weakly epimorphic with val: <8 12 17 27 33| Scale is weakly epimorphic with val: <8 12 17 30 33| Scale is weakly epimorphic with val: <8 12 18 25 33| Scale is weakly epimorphic with val: <8 12 18 27 31| Scale is weakly epimorphic with val: <8 12 18 27 34| Scale is weakly epimorphic with val: <8 12 18 28 33| Scale is weakly epimorphic with val: <8 12 19 26 33| Scale is weakly epimorphic with val: <8 12 19 28 31| Scale is weakly epimorphic with val: <8 12 19 28 34| Scale is weakly epimorphic with val: <8 12 19 29 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 63.5295 c. M: 81.7261 c. 4: 1 1 2 P M ME S SD: 29.3564 c. M:-50.8306 c. 6: 1 2 3 P T3 SD: 5.4354 c. M:-9.3268 c. 14: 2 5 7 P T3 SD: 1.6381 c. M: 2.5314 c. 20: 3 7 10 P T3 SD: 0.9478 c. M:-1.2814 c. 34: 5 12 17 P T3 SD: 0.7820 c. M:-1.2814 c. 54: 8 19 27 P T3 SD: 0.7423 c. M:-1.2814 c. 74: 11 26 37 P T3 SD: 0.7674 c. M:-1.2814 c. 88: 13 31 44 P T3 SD: 0.7424 c. M:-1.2814 c. 94: 14 33 47 P T3 SD: 0.7934 c. M:-1.2814 c. 95: 14 33 48 N T3 SD: 0.7908 c. M: 1.3398 c. 101: 15 35 51 N T3 SD: 0.7034 c. M: 1.1841 c. 103: 15 36 52 N T3 SD: 0.9333 c. M: 1.1498 c. 107: 16 37 54 N T3 SD: 0.7579 c. M: 1.0459 c. 109: 16 38 55 N T3 SD: 0.6670 c. M: 1.0032 c. 115: 17 40 58 N T3 SD: 0.5114 c. M: 0.8840 c. 121: 18 42 61 N T3 SD: 0.5067 c. M: 0.7766 c. 129: 19 45 65 N T3 SD: 0.4191 c. M: 0.6490 c. 135: 20 47 68 N T3 SD: 0.3306 c. M: 0.5632 c. 141: 21 49 71 N T3 SD: 0.4005 c. M:-0.4963 c. 143: 21 50 72 N T3 SD: 0.4101 c. M: 0.5412 c. 149: 22 52 75 N T3 SD: 0.2399 c. M: 0.3898 c. 155: 23 54 78 N T3 SD: 0.2276 c. M: 0.3252 c. 163: 24 57 82 N T3 SD: 0.2466 c. M: 0.3489 c. 169: 25 59 85 N T3 SD: 0.1109 c. M: 0.1921 c. 183: 27 64 92 N T3 SD: 0.1235 c. M: 0.1986 c. 189: 28 66 95 N T3 SD: 0.0635 c. M:-0.1038 c. 203: 30 71 102 N T3 SD: 0.0550 c. M: 0.0779 c. 372: 55 130 187 N T3 SD: 0.0421 c. M: 0.0574 c. 392: 58 137 197 N T3 SD: 0.0084 c. M:-0.0109 c. 1156: 171 404 581 N T3 SD: 0.0078 c. M: 0.0111 c. 1548: 229 541 778 N T3 SD: 0.0037 c. M: 0.0055 c. 1940: 287 678 975 N T3 SD: 0.0013 c. M: 0.0022 c. 2332: 345 815 1172 N T3 SD: 0.0006 c. M:-0.0010 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 x 10:12 S SD: 32.6687 cents 10 x 12:13 S SD: 40.4092 cents 11:12:13:15 SD: 31.8950 cents 12:13:14:16 S SD: 22.5510 cents 13:14:15:17 SD: 21.3781 cents 14:15:16:19 SD: 19.1705 cents 15:16:17:20 SD: 16.3715 cents 17:18:20:23 SD: 16.3560 cents 18:19:21:24 SD: 9.2066 cents 20:21:23:27 SD: 8.2481 cents 21:22:24:28 S SD: 5.9766 cents 27:28:31:36 SD: 4.5749 cents 39:41:45:52 SD: 4.2997 cents 45:47:52:60 SD: 1.0075 cents 111:116:128:148 SD: 0.9327 cents 117:122:135:156 SD: 0.4112 cents 162:169:187:216 SD: 0.2800 cents 228:238:263:304 SD: 0.2701 cents 273:285:315:364 SD: 0.2642 cents 345:360:398:460 SD: 0.1115 cents 390:407:450:520 SD: 0.0617 cents 507:529:585:676 SD: 0.0474 cents