Scala analysis: 348_C29
Chromatic tetrachord 45/43 * 43/39 * 52/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 45/43 78.706010 2: 15/13 247.741053 tridecimal 5/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 52/45 250.3039 1: 45/43 78.7060 2: 43/39 169.0350 3: 52/45 250.3039
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 45/43 78.706 cents 1: 1 43/39 169.035 cents 1: 1 52/45 250.304 cents 2: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 52/43 329.010 cents 2: 1 172/135 419.339 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 : 78.7 247.7 498.0 78.7 : 169.0 419.3 498.0 247.7: 250.3 329.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 78.7060 .. 250.3039 cents 2236/2025, 171.5979 cents 45/43, 78.7060 cents 2: 247.7411 .. 419.3390 cents 2236/2025, 171.5979 cents 675/676,-2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 45/43, 78.7060 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 52/45, 250.3039 cents Average / Smallest step : 2.109305 Largest / Average step : 1.507719 Largest / Smallest step : 3.180239 Median interval of one step : 43/39, 169.0350 cents, amount: 1 Least squares average step : 147.73737 cents, oct.: 443.21210 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2145-tone equal temperament with octave 4/3 degrees: 339 1067 2145 Least number of segments generator : 1073 of 249.139 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1706 of 396.114 cents and inv. generated superset size: 23 = 20 more = 766.667% 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 : 1.028646 Lumma stability : 0.316060 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 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 43 Odd number limit : 135 (O: 45 U: 135) Highest odd numerator or denominator: 45 Scale harmonicity : 0.025938 Fundamental : 1/1677, -10.7117 octaves, 0.1560 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 3.018600E+05, 18.20352 octaves Euler's gradus suavitatis : 67 Sum of Mann's harmonic distance : 61.5, average 20.50000 Mersenne's string divisions : 616 Sum of van Prooijen's expressibility: 3.30643, average 1.10214 Sum of Tenney's harmonic distance : 6.65590, average 2.21863 Vogel's harmonic complexity : 46.33333 Wille's k value : 967 Wilson's harmonic complexity : 70 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 14.52234, average 2.42039 Lattice compactness (without 2's) : 11.99410, average 1.99902 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -1 .. 2 0.66667 4 1 5: 0 .. 1 0.66667 2 13: -1 .. 0 -0.33333 1 1 43: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 2 / 3 = 0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 18 25 37| Scale is weakly epimorphic with val: <6 10 18 25 40| Scale is weakly epimorphic with val: <6 10 19 25 36| Scale is weakly epimorphic with val: <6 10 19 26 38| Scale is weakly epimorphic with val: <6 10 19 26 41| Scale is weakly epimorphic with val: <6 10 19 28 36| Scale is weakly epimorphic with val: <6 11 17 25 37| Scale is weakly epimorphic with val: <6 11 17 25 40| Scale is weakly epimorphic with val: <6 11 17 26 36| Scale is weakly epimorphic with val: <6 11 17 29 36| Scale is weakly epimorphic with val: <6 11 18 26 38| Scale is weakly epimorphic with val: <6 11 18 26 41| Scale is weakly epimorphic with val: <6 11 18 27 37| Scale is weakly epimorphic with val: <6 11 18 30 37| Scale is weakly epimorphic with val: <6 11 19 25 38| Scale is weakly epimorphic with val: <6 11 19 27 36| Scale is weakly epimorphic with val: <6 11 19 27 39| Scale is weakly epimorphic with val: <6 11 19 27 42| Scale is weakly epimorphic with val: <6 11 19 28 38| Scale is weakly epimorphic with val: <7 10 18 25 36| Scale is weakly epimorphic with val: <7 10 18 25 39| Scale is weakly epimorphic with val: <7 10 18 25 42| Scale is weakly epimorphic with val: <7 10 19 26 37| Scale is weakly epimorphic with val: <7 10 19 26 40| Scale is weakly epimorphic with val: <7 10 19 27 36| Scale is weakly epimorphic with val: <7 10 19 30 36| Scale is weakly epimorphic with val: <7 11 15 25 38| Scale is weakly epimorphic with val: <7 11 15 25 41| Scale is weakly epimorphic with val: <7 11 15 27 36| Scale is weakly epimorphic with val: <7 11 15 27 39| Scale is weakly epimorphic with val: <7 11 15 27 42| Scale is weakly epimorphic with val: <7 11 15 28 38| Scale is weakly epimorphic with val: <7 11 15 28 41| Scale is weakly epimorphic with val: <7 11 15 30 36| Scale is weakly epimorphic with val: <7 11 15 30 39| Scale is weakly epimorphic with val: <7 11 15 30 42| Scale is JI-epimorphic with val: <7 11 16 25 37| Scale is weakly epimorphic with val: <7 11 16 25 40| Scale is weakly epimorphic with val: <7 11 16 26 36| Scale is weakly epimorphic with val: <7 11 16 26 39| Scale is weakly epimorphic with val: <7 11 16 26 42| Scale is weakly epimorphic with val: <7 11 16 28 37| Scale is weakly epimorphic with val: <7 11 16 28 40| Scale is weakly epimorphic with val: <7 11 16 29 36| Scale is weakly epimorphic with val: <7 11 16 29 39| Scale is weakly epimorphic with val: <7 11 16 29 42| Scale is JI-epimorphic with val: <7 11 17 26 38| Scale is weakly epimorphic with val: <7 11 17 26 41| Scale is weakly epimorphic with val: <7 11 17 27 37| Scale is weakly epimorphic with val: <7 11 17 27 40| Scale is weakly epimorphic with val: <7 11 17 29 38| Scale is weakly epimorphic with val: <7 11 17 29 41| Scale is weakly epimorphic with val: <7 11 17 30 37| Scale is weakly epimorphic with val: <7 11 17 30 40| Scale is weakly epimorphic with val: <7 11 18 25 38| Scale is weakly epimorphic with val: <7 11 18 25 41| Scale is weakly epimorphic with val: <7 11 18 27 36| Scale is JI-epimorphic with val: <7 11 18 27 39| Scale is weakly epimorphic with val: <7 11 18 27 42| Scale is weakly epimorphic with val: <7 11 18 28 38| Scale is weakly epimorphic with val: <7 11 18 28 41| Scale is weakly epimorphic with val: <7 11 18 30 36| Scale is weakly epimorphic with val: <7 11 18 30 39| Scale is weakly epimorphic with val: <7 11 18 30 42| Scale is weakly epimorphic with val: <7 11 19 25 37| Scale is weakly epimorphic with val: <7 11 19 25 40| Scale is weakly epimorphic with val: <7 11 19 26 36| Scale is weakly epimorphic with val: <7 11 19 26 39| Scale is weakly epimorphic with val: <7 11 19 26 42| Scale is weakly epimorphic with val: <7 11 19 28 37| Scale is JI-epimorphic with val: <7 11 19 28 40| Scale is weakly epimorphic with val: <7 11 19 29 36| Scale is weakly epimorphic with val: <7 11 19 29 39| Scale is weakly epimorphic with val: <7 11 19 29 42| Scale is weakly epimorphic with val: <7 12 15 26 36| Scale is weakly epimorphic with val: <7 12 15 29 36| Scale is weakly epimorphic with val: <7 12 16 25 36| Scale is weakly epimorphic with val: <7 12 16 25 39| Scale is weakly epimorphic with val: <7 12 16 25 42| Scale is weakly epimorphic with val: <7 12 16 27 37| Scale is weakly epimorphic with val: <7 12 16 30 37| Scale is weakly epimorphic with val: <7 12 17 25 38| Scale is weakly epimorphic with val: <7 12 17 26 37| Scale is weakly epimorphic with val: <7 12 17 26 40| Scale is weakly epimorphic with val: <7 12 17 28 38| Scale is weakly epimorphic with val: <7 12 18 26 39| Scale is weakly epimorphic with val: <7 12 18 27 38| Scale is weakly epimorphic with val: <7 12 18 27 41| Scale is weakly epimorphic with val: <7 12 18 29 39| Scale is weakly epimorphic with val: <7 12 19 27 40| Scale is weakly epimorphic with val: <7 12 19 28 36| Scale is weakly epimorphic with val: <7 12 19 28 39| Scale is weakly epimorphic with val: <7 12 19 28 42| Scale is weakly epimorphic with val: <7 12 19 30 40| Scale is weakly epimorphic with val: <8 11 17 25 38| Scale is weakly epimorphic with val: <8 11 17 25 41| Scale is weakly epimorphic with val: <8 11 17 27 36| Scale is weakly epimorphic with val: <8 11 17 30 36| Scale is weakly epimorphic with val: <8 11 18 25 37| Scale is weakly epimorphic with val: <8 11 18 26 36| Scale is weakly epimorphic with val: <8 11 18 26 39| Scale is weakly epimorphic with val: <8 11 18 26 42| Scale is weakly epimorphic with val: <8 11 18 28 37| Scale is weakly epimorphic with val: <8 11 19 26 38| Scale is weakly epimorphic with val: <8 11 19 27 37| Scale is weakly epimorphic with val: <8 11 19 27 40| Scale is weakly epimorphic with val: <8 11 19 29 38| Scale is weakly epimorphic with val: <8 12 15 25 36| Scale is weakly epimorphic with val: <8 12 15 28 36| Scale is weakly epimorphic with val: <8 12 16 25 38| Scale is weakly epimorphic with val: <8 12 16 25 41| Scale is weakly epimorphic with val: <8 12 16 26 37| Scale is weakly epimorphic with val: <8 12 16 29 37| Scale is weakly epimorphic with val: <8 12 17 26 36| Scale is weakly epimorphic with val: <8 12 17 26 39| Scale is weakly epimorphic with val: <8 12 17 26 42| Scale is weakly epimorphic with val: <8 12 17 27 38| Scale is weakly epimorphic with val: <8 12 17 30 38| Scale is weakly epimorphic with val: <8 12 18 25 39| Scale is weakly epimorphic with val: <8 12 18 27 37| Scale is weakly epimorphic with val: <8 12 18 27 40| Scale is weakly epimorphic with val: <8 12 18 28 39| Scale is weakly epimorphic with val: <8 12 19 26 40| Scale is weakly epimorphic with val: <8 12 19 28 38| Scale is weakly epimorphic with val: <8 12 19 28 41| Scale is weakly epimorphic with val: <8 12 19 29 40|
FIT/MODE
3: 0 1 2 N G T3 SD: 65.5077 c. M: 81.7261 c. 4: 1 1 2 P M ME S SD: 26.4560 c. M:-45.8052 c. 6: 1 2 3 P T3 SD: 2.5913 c. M:-4.3015 c. 20: 3 7 10 P T3 SD: 2.4246 c. M: 3.9993 c. 26: 4 9 13 P T3 SD: 1.4123 c. M: 2.0837 c. 32: 5 11 16 P T3 SD: 0.8996 c. M:-1.2814 c. 38: 6 13 19 P T3 SD: 0.7409 c. M:-1.2814 c. 44: 7 15 22 P T3 SD: 0.8003 c. M:-1.2814 c. 70: 11 24 35 P T3 SD: 0.7826 c. M:-1.2814 c. 82: 13 28 41 P T3 SD: 0.7541 c. M:-1.2814 c. 101: 16 34 51 N T3 SD: 0.6926 c. M: 1.1841 c. 107: 17 36 54 N T3 SD: 0.6513 c. M: 1.0459 c. 109: 17 37 55 N T3 SD: 0.8298 c. M: 1.0293 c. 113: 18 38 57 N T3 SD: 0.6444 c. M: 0.9223 c. 115: 18 39 58 N T3 SD: 0.6697 c. M: 0.8840 c. 119: 19 40 60 N T3 SD: 0.6634 c. M:-0.8138 c. 121: 19 41 61 N T3 SD: 0.5334 c. M: 0.7766 c. 127: 20 43 64 N T3 SD: 0.4229 c. M: 0.6794 c. 133: 21 45 67 N T3 SD: 0.3434 c. M: 0.5909 c. 139: 22 47 70 N T3 SD: 0.3027 c. M: 0.5101 c. 145: 23 49 73 N T3 SD: 0.3037 c. M: 0.4359 c. 159: 25 54 80 N T3 SD: 0.2821 c. M: 0.3970 c. 165: 26 56 83 N T3 SD: 0.1853 c. M: 0.2278 c. 171: 27 58 86 N T3 SD: 0.1082 c. M: 0.1748 c. 177: 28 60 89 N T3 SD: 0.0861 c. M: 0.1255 c. 209: 33 71 105 N T3 SD: 0.0649 c. M:-0.0900 c. 215: 34 73 108 N T3 SD: 0.0778 c. M:-0.1232 c. 380: 60 129 191 N T3 SD: 0.0424 c. M: 0.0673 c. 386: 61 131 194 N T3 SD: 0.0051 c. M: 0.0088 c. 1753: 277 595 881 N T3 SD: 0.0047 c. M: 0.0075 c. 1759: 278 597 884 N T3 SD: 0.0059 c. M:-0.0073 c. 2139: 338 726 1075 N T3 SD: 0.0035 c. M: 0.0061 c. 2145: 339 728 1078 N T3 SD: 0.0043 c. M:-0.0060 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: 30.5639 cents 12:13:14:16 S SD: 20.9496 cents 13:14:15:17 SD: 19.9708 cents 14:15:16:19 SD: 17.8664 cents 15:16:17:20 SD: 15.1109 cents 18:19:21:24 SD: 8.0820 cents 20:21:23:27 SD: 7.6676 cents 21:22:24:28 S SD: 5.5559 cents 38:40:44:51 SD: 5.4523 cents 39:41:45:52 SD: 2.6246 cents 45:47:52:60 SD: 1.4254 cents 66:69:76:88 SD: 1.3046 cents 84:88:97:112 SD: 0.7630 cents 129:135:149:172 SD: 0.5962 cents 150:157:173:200 SD: 0.2704 cents 195:204:225:260 SD: 0.1973 cents 279:292:322:372 SD: 0.1453 cents 345:361:398:460 SD: 0.1340 cents 429:449:495:572 SD: 0.0598 cents