Scala analysis: 358_C29
Chromatic tetrachord 11/10 * 150/143 * 52/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-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: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 150/143 82.7368 3: 52/45 250.3039
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 150/143 82.737 cents 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 52/45 250.304 cents 2: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 40/33 333.041 cents 2: 1 286/225 415.308 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 : 165.0 247.7 498.0 165.0: 82.7 333.0 498.0 247.7: 250.3 415.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 82.7368 .. 250.3039 cents 3718/3375, 167.5671 cents 150/143, 82.7368 cents 2: 247.7411 .. 415.3082 cents 3718/3375, 167.5671 cents 675/676,-2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 150/143, 82.7368 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 52/45, 250.3039 cents Average / Smallest step : 2.006543 Largest / Average step : 1.507719 Largest / Smallest step : 3.025303 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 153.90152 cents, oct.: 461.70457 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2131-tone equal temperament with octave 4/3 degrees: 706 1060 2131 Least number of segments generator : 1066 of 249.139 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1776 of 415.076 cents and inv. generated superset size: 34 = 31 more = 1133.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 2.56289 cents Scale diversity : 1.057835 Lumma stability : 0.332246 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 fifths form a closed circle 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 : 225 (O: 143 U: 225) Highest odd numerator or denominator: 15 Scale harmonicity : 0.016268 Average absolute harmonicity : 0.095135 Specific harmonicity : 0.086764 Fundamental : 1/390, -8.6073 octaves, 0.6708 Hz. Guide tone : 660, 9.3663 octaves, 172672.873 Hz. Exponens Consonantiae : 2.574000E+05, 17.97365 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 28.0, average 9.33333 Mersenne's string divisions : 84 Sum of van Prooijen's expressibility: 2.69461, average 0.89820 Sum of Tenney's harmonic distance : 5.41061, average 1.80354 Vogel's harmonic complexity : 21.66667 Wille's k value : 214 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 15.15498, average 2.52583 Lattice compactness (without 2's) : 10.97356, average 1.82893 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -1 .. 1 0.00000 2 1 5: -1 .. 1 0.00000 2 11: 0 .. 1 0.33333 1 1 13: -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 15 24 27| Scale is weakly epimorphic with val: <6 10 15 24 30| Scale is weakly epimorphic with val: <6 10 16 25 25| Scale is weakly epimorphic with val: <6 10 16 25 28| Scale is weakly epimorphic with val: <6 10 17 26 26| Scale is weakly epimorphic with val: <6 10 17 26 29| Scale is weakly epimorphic with val: <6 10 18 25 25| Scale is weakly epimorphic with val: <6 10 18 27 27| Scale is weakly epimorphic with val: <6 10 18 27 30| Scale is weakly epimorphic with val: <6 10 19 23 26| Scale is weakly epimorphic with val: <6 10 19 26 26| Scale is weakly epimorphic with val: <6 11 15 24 27| Scale is weakly epimorphic with val: <6 11 15 24 30| Scale is weakly epimorphic with val: <6 11 16 25 25| Scale is weakly epimorphic with val: <6 11 16 25 28| Scale is weakly epimorphic with val: <6 11 17 25 25| Scale is weakly epimorphic with val: <6 11 17 26 26| Scale is weakly epimorphic with val: <6 11 17 26 29| Scale is weakly epimorphic with val: <6 11 18 23 26| Scale is weakly epimorphic with val: <6 11 18 26 26| Scale is weakly epimorphic with val: <6 11 18 27 27| Scale is weakly epimorphic with val: <6 11 18 27 30| Scale is weakly epimorphic with val: <6 11 19 24 27| Scale is weakly epimorphic with val: <6 11 19 27 27| Scale is weakly epimorphic with val: <7 10 15 25 26| Scale is weakly epimorphic with val: <7 10 15 25 29| Scale is weakly epimorphic with val: <7 10 16 26 27| Scale is weakly epimorphic with val: <7 10 16 26 30| Scale is weakly epimorphic with val: <7 10 17 27 28| Scale is weakly epimorphic with val: <7 10 18 24 25| Scale is weakly epimorphic with val: <7 10 19 25 26| Scale is weakly epimorphic with val: <7 11 15 23 27| Scale is weakly epimorphic with val: <7 11 15 23 30| 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 26 27| Scale is weakly epimorphic with val: <7 11 15 26 30| Scale is weakly epimorphic with val: <7 11 15 27 28| Scale is JI-epimorphic with val: <7 11 16 24 25| Scale is weakly epimorphic with val: <7 11 16 24 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 27 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 25 26| Scale is weakly epimorphic with val: <7 11 17 25 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 18 23 27| Scale is weakly epimorphic with val: <7 11 18 23 30| 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 26 27| Scale is weakly epimorphic with val: <7 11 18 26 30| Scale is weakly epimorphic with val: <7 11 18 27 28| Scale is weakly epimorphic with val: <7 11 19 24 25| Scale is weakly epimorphic with val: <7 11 19 24 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 27 28| Scale is weakly epimorphic with val: <7 12 15 25 26| Scale is weakly epimorphic with val: <7 12 15 25 29| Scale is weakly epimorphic with val: <7 12 16 24 25| Scale is weakly epimorphic with val: <7 12 16 26 27| Scale is weakly epimorphic with val: <7 12 16 26 30| Scale is weakly epimorphic with val: <7 12 17 25 26| Scale is weakly epimorphic with val: <7 12 17 27 28| Scale is weakly epimorphic with val: <7 12 18 23 27| Scale is weakly epimorphic with val: <7 12 18 26 27| Scale is weakly epimorphic with val: <7 12 19 24 28| Scale is weakly epimorphic with val: <7 12 19 27 28| Scale is weakly epimorphic with val: <8 11 15 26 28| Scale is weakly epimorphic with val: <8 11 16 27 29| Scale is weakly epimorphic with val: <8 11 17 23 25| Scale is weakly epimorphic with val: <8 11 18 24 26| Scale is weakly epimorphic with val: <8 11 19 25 27| Scale is weakly epimorphic with val: <8 12 15 26 28| Scale is weakly epimorphic with val: <8 12 16 23 25| Scale is weakly epimorphic with val: <8 12 16 27 29| Scale is weakly epimorphic with val: <8 12 17 24 26| Scale is weakly epimorphic with val: <8 12 18 25 27| Scale is weakly epimorphic with val: <8 12 19 23 28| Scale is weakly epimorphic with val: <8 12 19 26 28|
FIT/MODE
3: 1 0 2 N G T3 SD: 47.1882 c. M: 81.7261 c. 4: 1 1 2 P M ME S SD: 23.3903 c. M: 40.4930 c. 6: 2 1 3 P T3 SD: 0.9423 c. M:-1.2814 c. 76: 25 13 38 P T3 SD: 1.0032 c. M:-1.2814 c. 82: 27 14 41 P T3 SD: 0.9434 c. M:-1.2814 c. 88: 29 15 44 P T3 SD: 0.8961 c. M:-1.2814 c. 94: 31 16 47 P T3 SD: 0.8588 c. M:-1.2814 c. 97: 32 16 49 N T3 SD: 0.8454 c. M: 1.2858 c. 99: 33 16 50 N T3 SD: 0.9209 c. M: 1.2339 c. 100: 33 17 50 P T3 SD: 0.8294 c. M:-1.2814 c. 103: 34 17 52 N T3 SD: 0.7421 c. M: 1.1362 c. 105: 35 17 53 N T3 SD: 0.8583 c. M: 1.0902 c. 106: 35 18 53 P T3 SD: 0.8063 c. M:-1.2814 c. 109: 36 18 55 N T3 SD: 0.6503 c. M: 1.0032 c. 115: 38 19 58 N T3 SD: 0.5683 c. M: 0.8840 c. 121: 40 20 61 N T3 SD: 0.4945 c. M: 0.7766 c. 127: 42 21 64 N T3 SD: 0.4279 c. M: 0.6794 c. 133: 44 22 67 N T3 SD: 0.3677 c. M: 0.5909 c. 139: 46 23 70 N T3 SD: 0.3130 c. M: 0.5101 c. 145: 48 24 73 N T3 SD: 0.2633 c. M: 0.4359 c. 151: 50 25 76 N T3 SD: 0.2184 c. M: 0.3677 c. 157: 52 26 79 N T3 SD: 0.1780 c. M: 0.3047 c. 163: 54 27 82 N T3 SD: 0.1423 c. M: 0.2463 c. 169: 56 28 85 N T3 SD: 0.1121 c. M: 0.1921 c. 175: 58 29 88 N T3 SD: 0.0892 c. M: 0.1415 c. 181: 60 30 91 N T3 SD: 0.0767 c. M: 0.0944 c. 187: 62 31 94 N T3 SD: 0.0767 c. M:-0.1230 c. 368: 122 61 185 N T3 SD: 0.0752 c. M:-0.1085 c. 380: 126 63 191 N T3 SD: 0.0809 c. M:-0.1370 c. 537: 178 89 270 N T3 SD: 0.0795 c. M: 0.1097 c. 549: 182 91 276 N T3 SD: 0.0753 c. M:-0.1036 c. 571: 189 95 287 N T3 SD: 0.0892 c. M: 0.1522 c. 573: 190 95 288 N T3 SD: 0.0828 c. M:-0.1416 c. 577: 191 96 290 N T3 SD: 0.0813 c. M: 0.1401 c. 583: 193 97 293 N T3 SD: 0.0741 c. M: 0.1283 c. 589: 195 98 296 N T3 SD: 0.0678 c. M: 0.1167 c. 595: 197 99 299 N T3 SD: 0.0626 c. M: 0.1053 c. 601: 199 100 302 N T3 SD: 0.0587 c. M: 0.0942 c. 607: 201 101 305 N T3 SD: 0.0563 c. M: 0.0832 c. 613: 203 102 308 N T3 SD: 0.0554 c. M: 0.0725 c. 752: 249 125 378 N T3 SD: 0.0592 c. M: 0.0931 c. 758: 251 126 381 N T3 SD: 0.0522 c. M: 0.0843 c. 764: 253 127 384 N T3 SD: 0.0456 c. M: 0.0757 c. 770: 255 128 387 N T3 SD: 0.0395 c. M: 0.0672 c. 776: 257 129 390 N T3 SD: 0.0340 c. M: 0.0589 c. 782: 259 130 393 N T3 SD: 0.0296 c. M: 0.0507 c. 788: 261 131 396 N T3 SD: 0.0266 c. M: 0.0426 c. 794: 263 132 399 N T3 SD: 0.0253 c. M: 0.0347 c. 951: 315 158 478 N T3 SD: 0.0266 c. M: 0.0366 c. 957: 317 159 481 N T3 SD: 0.0207 c. M: 0.0301 c. 963: 319 160 484 N T3 SD: 0.0152 c. M: 0.0236 c. 969: 321 161 487 N T3 SD: 0.0101 c. M: 0.0172 c. 975: 323 162 490 N T3 SD: 0.0068 c. M: 0.0109 c. 1162: 385 193 584 N T3 SD: 0.0067 c. M:-0.0107 c. 1956: 648 325 983 N T3 SD: 0.0066 c. M:-0.0083 c. 2125: 704 353 1068 N T3 SD: 0.0052 c. M: 0.0076 c. 2131: 706 354 1071 N T3 SD: 0.0026 c. M: 0.0040 c. 2137: 708 355 1074 N T3 SD: 0.0005 c. M:-0.0009 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 8:9 x 11 SD: 32.9836 cents 9:10 x 12 S SD: 8.6997 cents 15 x 17:20 SD: 15.5272 cents 16:18 x 21 S SD: 23.7539 cents 17:19:20:23 SD: 16.7600 cents 18:20:21:24 S SD: 8.6197 cents 19:21:22:25 SD: 8.3724 cents 20:22:23:27 SD: 7.4232 cents 21:23:24:28 SD: 6.0633 cents 32:35:37:43 SD: 5.6941 cents 33:36:38:44 SD: 4.9292 cents 39:43:45:52 SD: 1.3436 cents 90:99:104:120 SD: 0.8543 cents 111:122:128:148 SD: 0.5863 cents 150:165:173:200 SD: 0.2565 cents 240:264:277:320 SD: 0.1603 cents 351:386:405:468 SD: 0.1495 cents 390:429:450:520 SD: 0.0000 cents