Scala analysis: 357_C29
Chromatic tetrachord 27/26 * 10/9 * 52/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/26 65.337341 tridecimal comma 2: 15/13 247.741053 tridecimal 5/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 52/45 250.3039 1: 27/26 65.3373 tridecimal comma 2: 10/9 182.4037 minor whole tone 3: 52/45 250.3039
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 27/26 65.337 cents tridecimal comma 1: 1 10/9 182.404 cents minor whole tone 1: 1 52/45 250.304 cents 2: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 6/5 315.641 cents minor third 2: 1 104/81 432.708 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 : 65.3 247.7 498.0 65.3 : 182.4 432.7 498.0 247.7: 250.3 315.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 65.3373 .. 250.3039 cents 1352/1215, 184.9666 cents 27/26, 65.3373 cents 2: 247.7411 .. 432.7077 cents 1352/1215, 184.9666 cents 675/676,-2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 27/26, 65.3373 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 52/45, 250.3039 cents Average / Smallest step : 2.540890 Largest / Average step : 1.507719 Largest / Smallest step : 3.830948 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 146.78246 cents, oct.: 440.34738 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1936-tone equal temperament with octave 4/3 degrees: 254 963 1936 Least number of segments generator : 969 of 249.280 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1735 of 446.337 cents and inv. generated superset size: 54 = 51 more = 1800.000% 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 : 0.909774 Lumma stability : 0.262375 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 13 Odd number limit : 81 (O: 27 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.023685 Average absolute harmonicity : 0.092804 Specific harmonicity : 0.105623 Fundamental : 1/78, -6.2854 octaves, 3.3542 Hz. Guide tone : 540, 9.0768 octaves, 141277.805 Hz. Exponens Consonantiae : 4.212000E+04, 15.36222 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 44.0, average 14.66667 Mersenne's string divisions : 1484 Sum of van Prooijen's expressibility: 3.08458, average 1.02819 Sum of Tenney's harmonic distance : 6.21555, average 2.07185 Vogel's harmonic complexity : 13.33333 Wille's k value : 40 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 17.99553, average 2.99926 Lattice compactness (without 2's) : 14.70299, average 2.45050 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -1 .. 3 1.00000 5 1 5: 0 .. 1 0.33333 1 13: -1 .. 0 -0.66667 2 2 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 19 26| Scale is weakly epimorphic with val: <6 11 17 25| Scale is JI-epimorphic with val: <7 11 16 25| Scale is weakly epimorphic with val: <7 11 16 28| Scale is weakly epimorphic with val: <7 11 17 27| = patent Scale is weakly epimorphic with val: <7 11 17 30| Scale is weakly epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <7 11 19 28| Scale is weakly epimorphic with val: <7 12 15 26| Scale is weakly epimorphic with val: <7 12 16 25| Scale is weakly epimorphic with val: <7 12 18 26| Scale is weakly epimorphic with val: <7 12 19 28| Scale is weakly epimorphic with val: <8 11 19 27| Scale is weakly epimorphic with val: <8 12 15 25| Scale is weakly epimorphic with val: <8 12 17 26| Scale is weakly epimorphic with val: <8 12 18 25|
FIT/MODE
3: 0 1 2 N G T3 SD: 60.4100 c. M: 81.7261 c. 4: 1 1 2 P M ME S SD: 34.1721 c. M:-59.1739 c. 6: 1 2 3 P T3 SD: 10.2287 c. M:-17.6702 c. 8: 1 3 4 P T3 SD: 1.9269 c. M: 3.0817 c. 22: 3 8 11 P T3 SD: 1.6621 c. M:-2.5779 c. 30: 4 11 15 P T3 SD: 0.9634 c. M:-1.2814 c. 38: 5 14 19 P T3 SD: 0.7484 c. M:-1.2814 c. 68: 9 25 34 P T3 SD: 0.8122 c. M:-1.2814 c. 84: 11 31 42 P T3 SD: 0.7429 c. M:-1.2814 c. 98: 13 36 49 P T3 SD: 0.8514 c. M:-1.2814 c. 99: 13 36 50 N T3 SD: 0.7133 c. M: 1.2339 c. 101: 13 37 51 N T3 SD: 0.9868 c. M: 1.2325 c. 105: 14 38 53 N T3 SD: 0.8814 c. M: 1.0902 c. 106: 14 39 53 P T3 SD: 0.7827 c. M:-1.2814 c. 107: 14 39 54 N T3 SD: 0.6120 c. M: 1.0459 c. 113: 15 41 57 N T3 SD: 0.6955 c. M: 0.9223 c. 115: 15 42 58 N T3 SD: 0.5544 c. M: 0.8840 c. 121: 16 44 61 N T3 SD: 0.5395 c. M: 0.7766 c. 123: 16 45 62 N T3 SD: 0.5341 c. M: 0.7431 c. 129: 17 47 65 N T3 SD: 0.4119 c. M: 0.6490 c. 137: 18 50 69 N T3 SD: 0.3149 c. M: 0.5362 c. 145: 19 53 73 N T3 SD: 0.2555 c. M: 0.4359 c. 153: 20 56 77 N T3 SD: 0.2410 c. M: 0.3462 c. 167: 22 61 84 N T3 SD: 0.1989 c. M:-0.2734 c. 175: 23 64 88 N T3 SD: 0.1071 c. M: 0.1415 c. 183: 24 67 92 N T3 SD: 0.0472 c. M: 0.0793 c. 396: 52 145 199 N T3 SD: 0.0386 c. M:-0.0625 c. 404: 53 148 203 N T3 SD: 0.0281 c. M:-0.0487 c. 579: 76 212 291 N T3 SD: 0.0216 c. M:-0.0364 c. 587: 77 215 295 N T3 SD: 0.0061 c. M:-0.0088 c. 1357: 178 497 682 N T3 SD: 0.0049 c. M: 0.0079 c. 1753: 230 642 881 N T3 SD: 0.0049 c. M:-0.0080 c. 1936: 254 709 973 N T3 SD: 0.0042 c. M:-0.0053 c. 2340: 307 857 1176 N T3 SD: 0.0036 c. M:-0.0045 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: 34.1717 cents 12:13:14:16 S SD: 25.2309 cents 13:14:15:17 SD: 23.7912 cents 14:15:16:19 SD: 21.4497 cents 15:16:17:20 SD: 18.6094 cents 17:18:20:23 SD: 17.9475 cents 18:19:21:24 SD: 11.3769 cents 19:20:22:25 SD: 11.1211 cents 20:21:23:27 SD: 9.7860 cents 21:22:24:28 S SD: 7.4944 cents 24:25:28:32 SD: 6.6200 cents 25:26:29:33 SD: 6.6174 cents 26:27:30:35 S SD: 5.5223 cents 27:28:31:36 SD: 2.9646 cents 51:53:59:68 SD: 1.5639 cents 78:81:90:104 SD: 0.0000 cents