Scala analysis: 352_C29
Chromatic tetrachord 45/44 * 44/39 * 52/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 45/44 38.905773 1/5-tone 2: 15/13 247.741053 tridecimal 5/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 52/45 250.3039 1: 45/44 38.9058 1/5-tone 2: 44/39 208.8353 3: 52/45 250.3039
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 45/44 38.906 cents 1/5-tone 1: 1 44/39 208.835 cents 1: 1 52/45 250.304 cents 2: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 13/11 289.210 cents tridecimal minor third 2: 1 176/135 459.139 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 : 38.9 247.7 498.0 38.9 : 208.8 459.1 498.0 247.7: 250.3 289.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.9058 .. 250.3039 cents 2288/2025, 211.3982 cents 45/44, 38.9058 cents 2: 247.7411 .. 459.1392 cents 2288/2025, 211.3982 cents 675/676,-2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 45/44, 38.9058 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 52/45, 250.3039 cents Average / Smallest step : 4.267104 Largest / Average step : 1.507719 Largest / Smallest step : 6.433594 Median interval of one step : 44/39, 208.8353 cents, amount: 1 Least squares average step : 144.89449 cents, oct.: 434.68347 cents Scale is not proper Scale has trivalence property Scale is a mode of a 973-tone equal temperament with octave 4/3 degrees: 76 484 973 Least number of segments generator : 487 of 249.278 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 636 of 325.546 cents and inv. generated superset size: 20 = 17 more = 666.667% 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 : 0.616390 Lumma stability : 0.156234 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 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 : 13 Odd number limit : 135 (O: 45 U: 135) Highest odd numerator or denominator: 45 Scale harmonicity : 0.017025 Average absolute harmonicity : 0.092549 Specific harmonicity : 0.086358 Fundamental : 1/1716, -10.7448 octaves, 0.1525 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 3.088800E+05, 18.23669 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 62.0, average 20.66667 Mersenne's string divisions : 2492 Sum of van Prooijen's expressibility: 3.30643, average 1.10214 Sum of Tenney's harmonic distance : 6.66588, average 2.22196 Vogel's harmonic complexity : 26.33333 Wille's k value : 877 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 18.13458, average 3.02243 Lattice compactness (without 2's) : 12.67971, average 2.11328 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.00000 4 3: -1 .. 2 0.66667 4 1 5: 0 .. 1 0.66667 2 11: -1 .. 0 -0.33333 1 1 13: -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 23 27| Scale is weakly epimorphic with val: <6 10 18 23 30| Scale is weakly epimorphic with val: <6 10 18 25 25| Scale is weakly epimorphic with val: <6 10 19 23 26| Scale is weakly epimorphic with val: <6 10 19 24 25| Scale is weakly epimorphic with val: <6 10 19 24 28| Scale is weakly epimorphic with val: <6 10 19 26 26| Scale is weakly epimorphic with val: <6 11 16 23 25| Scale is weakly epimorphic with val: <6 11 16 23 28| Scale is weakly epimorphic with val: <6 11 17 24 26| Scale is weakly epimorphic with val: <6 11 17 24 29| Scale is weakly epimorphic with val: <6 11 17 25 25| Scale is weakly epimorphic with val: <6 11 18 23 26| Scale is weakly epimorphic with val: <6 11 18 25 27| Scale is weakly epimorphic with val: <6 11 18 25 30| Scale is weakly epimorphic with val: <6 11 18 26 26| Scale is weakly epimorphic with val: <6 11 19 24 27| Scale is weakly epimorphic with val: <6 11 19 26 28| Scale is weakly epimorphic with val: <6 11 19 27 27| Scale is weakly epimorphic with val: <7 10 18 25 25| Scale is weakly epimorphic with val: <7 10 19 23 26| Scale is weakly epimorphic with val: <7 10 19 26 26| Scale is weakly epimorphic with val: <7 11 15 24 25| Scale is weakly epimorphic with val: <7 11 15 24 28| Scale is weakly epimorphic with val: <7 11 15 25 27| Scale is weakly epimorphic with val: <7 11 15 25 30| Scale is weakly epimorphic with val: <7 11 15 27 28| Scale is JI-epimorphic with val: <7 11 16 23 25| Scale is weakly epimorphic with val: <7 11 16 23 28| Scale is weakly epimorphic with val: <7 11 16 25 26| Scale is weakly epimorphic with val: <7 11 16 25 29| Scale is weakly epimorphic with val: <7 11 16 26 28| Scale is weakly epimorphic with val: <7 11 17 23 27| Scale is weakly epimorphic with val: <7 11 17 23 30| Scale is JI-epimorphic with val: <7 11 17 24 26| Scale is weakly epimorphic with val: <7 11 17 24 29| Scale is weakly epimorphic with val: <7 11 17 26 27| Scale is weakly epimorphic with val: <7 11 17 26 30| Scale is weakly epimorphic with val: <7 11 17 27 29| Scale is weakly epimorphic with val: <7 11 18 24 25| Scale is weakly epimorphic with val: <7 11 18 24 28| Scale is JI-epimorphic with val: <7 11 18 25 27| Scale is weakly epimorphic with val: <7 11 18 25 30| Scale is weakly epimorphic with val: <7 11 18 27 28| Scale is weakly epimorphic with val: <7 11 19 23 25| Scale is weakly epimorphic with val: <7 11 19 23 28| Scale is weakly epimorphic with val: <7 11 19 25 26| Scale is weakly epimorphic with val: <7 11 19 25 29| Scale is JI-epimorphic with val: <7 11 19 26 28| Scale is weakly epimorphic with val: <7 12 16 23 27| Scale is weakly epimorphic with val: <7 12 16 23 30| Scale is weakly epimorphic with val: <7 12 16 25 25| Scale is weakly epimorphic with val: <7 12 17 23 26| Scale is weakly epimorphic with val: <7 12 17 24 25| Scale is weakly epimorphic with val: <7 12 17 24 28| Scale is weakly epimorphic with val: <7 12 17 26 26| Scale is weakly epimorphic with val: <7 12 18 24 27| Scale is weakly epimorphic with val: <7 12 18 25 26| Scale is weakly epimorphic with val: <7 12 18 25 29| Scale is weakly epimorphic with val: <7 12 18 27 27| Scale is weakly epimorphic with val: <7 12 19 25 28| Scale is weakly epimorphic with val: <7 12 19 26 27| Scale is weakly epimorphic with val: <7 12 19 26 30| Scale is weakly epimorphic with val: <8 11 17 25 25| Scale is weakly epimorphic with val: <8 11 18 23 26| Scale is weakly epimorphic with val: <8 11 18 26 26| Scale is weakly epimorphic with val: <8 11 19 24 27| Scale is weakly epimorphic with val: <8 11 19 27 27| Scale is weakly epimorphic with val: <8 12 16 25 25| Scale is weakly epimorphic with val: <8 12 17 23 26| Scale is weakly epimorphic with val: <8 12 17 26 26| Scale is weakly epimorphic with val: <8 12 18 23 25| Scale is weakly epimorphic with val: <8 12 18 23 28| Scale is weakly epimorphic with val: <8 12 18 24 27| Scale is weakly epimorphic with val: <8 12 18 27 27| Scale is weakly epimorphic with val: <8 12 19 24 26| Scale is weakly epimorphic with val: <8 12 19 24 29| Scale is weakly epimorphic with val: <8 12 19 25 28|
FIT/MODE
3: 0 1 2 N G T3 SD: 52.2584 c. M: 81.7261 c. 4: 0 2 2 P M DE S SD: 22.4744 c. M: 38.9058 c. 8: 1 3 4 P T3 SD: 13.5013 c. M:-23.3499 c. 10: 1 4 5 P T3 SD: 6.3357 c. M:-10.8987 c. 12: 1 5 6 P T3 SD: 1.6725 c. M:-2.5980 c. 26: 2 11 13 P T3 SD: 0.8156 c. M:-1.2814 c. 38: 3 16 19 P T3 SD: 0.7774 c. M:-1.2814 c. 64: 5 27 32 P T3 SD: 0.7398 c. M:-1.2814 c. 88: 7 37 44 P T3 SD: 0.8462 c. M:-1.2814 c. 90: 7 38 45 P T3 SD: 0.7462 c. M:-1.2814 c. 101: 8 42 51 N T3 SD: 0.7522 c. M: 1.1841 c. 102: 8 43 51 P T3 SD: 0.7453 c. M:-1.2814 c. 103: 8 43 52 N T3 SD: 0.6685 c. M: 1.1362 c. 105: 8 44 53 N T3 SD: 0.8385 c. M: 1.0902 c. 113: 9 47 57 N T3 SD: 0.6905 c. M: 0.9223 c. 115: 9 48 58 N T3 SD: 0.5120 c. M: 0.8840 c. 117: 9 49 59 N T3 SD: 0.5975 c. M: 0.8470 c. 127: 10 53 64 N T3 SD: 0.4312 c. M: 0.6794 c. 129: 10 54 65 N T3 SD: 0.4122 c. M: 0.6490 c. 139: 11 58 70 N T3 SD: 0.4156 c. M: 0.5101 c. 141: 11 59 71 N T3 SD: 0.2814 c. M: 0.4847 c. 153: 12 64 77 N T3 SD: 0.2193 c. M: 0.3462 c. 165: 13 69 83 N T3 SD: 0.2335 c. M:-0.3341 c. 167: 13 70 84 N T3 SD: 0.1442 c. M: 0.2097 c. 179: 14 75 90 N T3 SD: 0.0690 c. M: 0.1097 c. 205: 16 86 103 N T3 SD: 0.0432 c. M:-0.0667 c. 384: 30 161 193 N T3 SD: 0.0093 c. M: 0.0155 c. 589: 46 247 296 N T3 SD: 0.0092 c. M:-0.0131 c. 973: 76 408 489 N T3 SD: 0.0025 c. M: 0.0040 c. 1357: 106 569 682 N T3 SD: 0.0021 c. M: 0.0031 c. 2330: 182 977 1171 N T3 SD: 0.0017 c. M: 0.0027 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 x 13:15 SD: 28.4311 cents 15:16:17:20 SD: 26.3901 cents 17:18:20:23 SD: 24.4376 cents 18:19:21:24 SD: 19.3153 cents 19:20:22:25 SD: 18.4152 cents 20:21:23:27 SD: 16.9042 cents 21:22:24:28 S SD: 14.9355 cents 24:25:28:32 SD: 12.3607 cents 25:26:29:33 SD: 11.6820 cents 26:27:30:35 S SD: 10.3981 cents 27:28:31:36 SD: 8.5121 cents 31:32:36:41 SD: 8.0162 cents 32:33:37:43 SD: 6.6743 cents 33:34:38:44 SD: 4.4159 cents 39:40:45:52 SD: 1.6418 cents 45:46:52:60 SD: 0.9006 cents 84:86:97:112 SD: 0.7630 cents 129:132:149:172 SD: 0.6666 cents 177:181:204:236 SD: 0.6564 cents 183:187:211:244 SD: 0.6463 cents 216:221:249:288 SD: 0.5849 cents 222:227:256:296 SD: 0.3654 cents 261:267:301:348 SD: 0.3297 cents 267:273:308:356 SD: 0.2038 cents 306:313:353:408 SD: 0.1511 cents 351:359:405:468 SD: 0.0365 cents