Scala analysis: 326_C24
Chromatic tetrachord 27/25 * 7/6 * 200/189
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 2: 63/50 400.108480 quasi-equal major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 200/189 97.9365 1: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 2: 7/6 266.8709 septimal minor third 3: 200/189 97.9365
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 200/189 97.937 cents 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 100/81 364.807 cents grave major third 2: 1 63/50 400.108 cents quasi-equal 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 : 133.2 400.1 498.0 133.2: 266.9 364.8 498.0 400.1: 97.9 231.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 97.9365 .. 266.8709 cents 441/400, 168.9344 cents 200/189, 97.9365 cents 2: 231.1741 .. 400.1085 cents 441/400, 168.9344 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 200/189, 97.9365 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 1.695129 Largest / Average step : 1.607511 Largest / Smallest step : 2.724938 Median interval of one step : 27/25, 133.2376 cents, amount: 1 Least squares average step : 173.39925 cents, oct.: 520.19776 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1312-tone equal temperament with octave 4/3 degrees: 351 1054 1312 Least number of segments generator : 657 of 249.402 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 887 of 336.712 cents and inv. generated superset size: 58 = 55 more = 1933.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MLS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.152283 Lumma stability : 0.393284 Lumma impropriety factor : 0.071674 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 : 5103/5000, 35.3011 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 7 Odd number limit : 189 (O: 63 U: 189) Highest odd numerator or denominator: 63 Scale harmonicity : 0.027209 Average absolute harmonicity : 0.098784 Specific harmonicity : 0.124619 Fundamental : 1/150, -7.2288 octaves, 1.7442 Hz. Guide tone : 756, 9.5622 octaves, 197788.927 Hz. Exponens Consonantiae : 1.134000E+05, 16.79106 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 86.0, average 28.66667 Mersenne's string divisions : 41132 Sum of van Prooijen's expressibility: 3.70783, average 1.23594 Sum of Tenney's harmonic distance : 7.40680, average 2.46893 Vogel's harmonic complexity : 14.00000 Wille's k value : 94 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 20.43076, average 3.40513 Lattice compactness (without 2's) : 17.23356, average 2.87226 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -1 .. 3 1.33333 6 1 5: -2 .. 0 -1.33333 4 1 7: 0 .. 1 0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 11 / 3 = 3.66667 Scale is weakly epimorphic with val: <6 10 16 21| Scale is weakly epimorphic with val: <6 11 15 19| Scale is weakly epimorphic with val: <6 11 15 22| Scale is weakly epimorphic with val: <6 11 17 21| Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 11 16 22| Scale is weakly epimorphic with val: <7 11 17 20| = patent Scale is weakly epimorphic with val: <7 11 19 19| Scale is weakly epimorphic with val: <7 11 19 22| Scale is weakly epimorphic with val: <7 12 16 18| Scale is weakly epimorphic with val: <8 11 15 20| Scale is weakly epimorphic with val: <8 11 16 21| Scale is weakly epimorphic with val: <8 12 17 21|
FIT/MODE
3: 1 1 1 SP B ME I SD: 43.6235 c. M: 68.0785 c. 4: 1 2 1 P M ME I SD: 16.1489 c. M: 26.5747 c. 9: 2 5 2 N M DE I SD: 14.9589 c. M: 22.5609 c. 10: 3 5 2 P T3 SD: 9.3890 c. M:-16.1759 c. 11: 3 6 2 N T3 SD: 4.5177 c. M:-7.3829 c. 15: 4 8 3 N T3 SD: 0.9964 c. M: 1.6725 c. 41: 11 22 8 N T3 SD: 0.4901 c. M:-0.7570 c. 56: 15 30 11 N T3 SD: 0.1144 c. M:-0.1673 c. 127: 34 68 25 N T3 SD: 0.0822 c. M: 0.1038 c. 183: 49 98 36 N T3 SD: 0.0723 c. M:-0.1187 c. 239: 64 128 47 N T3 SD: 0.0752 c. M:-0.1301 c. 295: 79 158 58 N T3 SD: 0.0797 c. M:-0.1372 c. 310: 83 166 61 N T3 SD: 0.0740 c. M:-0.1100 c. 351: 94 188 69 N T3 SD: 0.0838 c. M:-0.1420 c. 422: 113 226 83 N T3 SD: 0.0732 c. M:-0.1252 c. 493: 132 264 97 N T3 SD: 0.0730 c. M:-0.1132 c. 605: 162 324 119 N T3 SD: 0.0727 c. M:-0.1232 c. 636: 170 341 125 N T3 SD: 0.0711 c. M: 0.1123 c. 651: 174 349 128 N T3 SD: 0.0693 c. M: 0.1196 c. 666: 178 357 131 N T3 SD: 0.0747 c. M: 0.1264 c. 676: 181 362 133 N T3 SD: 0.0726 c. M:-0.1147 c. 677: 181 363 133 N T3 SD: 0.0717 c. M:-0.0931 c. 681: 182 365 134 N T3 SD: 0.0851 c. M: 0.1330 c. 691: 185 370 136 N T3 SD: 0.0778 c. M:-0.1030 c. 692: 185 371 136 N T3 SD: 0.0607 c. M: 0.0897 c. 707: 189 379 139 N T3 SD: 0.0569 c. M: 0.0968 c. 722: 193 387 142 N T3 SD: 0.0606 c. M: 0.1037 c. 737: 197 395 145 N T3 SD: 0.0700 c. M: 0.1102 c. 748: 200 401 147 N T3 SD: 0.0529 c. M: 0.0705 c. 763: 204 409 150 N T3 SD: 0.0469 c. M: 0.0774 c. 778: 208 417 153 N T3 SD: 0.0488 c. M: 0.0842 c. 793: 212 425 156 N T3 SD: 0.0571 c. M: 0.0906 c. 804: 215 431 158 N T3 SD: 0.0474 c. M:-0.0620 c. 819: 219 439 161 N T3 SD: 0.0392 c. M: 0.0607 c. 834: 223 447 164 N T3 SD: 0.0388 c. M: 0.0673 c. 849: 227 455 167 N T3 SD: 0.0459 c. M: 0.0736 c. 860: 230 461 169 N T3 SD: 0.0439 c. M:-0.0649 c. 875: 234 469 172 N T3 SD: 0.0335 c. M: 0.0461 c. 890: 238 477 175 N T3 SD: 0.0305 c. M: 0.0525 c. 905: 242 485 178 N T3 SD: 0.0361 c. M: 0.0587 c. 931: 249 499 183 N T3 SD: 0.0298 c. M:-0.0394 c. 946: 253 507 186 N T3 SD: 0.0239 c. M: 0.0395 c. 961: 257 515 189 N T3 SD: 0.0275 c. M: 0.0455 c. 1002: 268 537 197 N T3 SD: 0.0190 c. M: 0.0279 c. 1017: 272 545 200 N T3 SD: 0.0200 c. M: 0.0338 c. 1058: 283 567 208 N T3 SD: 0.0164 c. M:-0.0222 c. 1073: 287 575 211 N T3 SD: 0.0135 c. M: 0.0233 c. 1129: 302 605 222 N T3 SD: 0.0083 c. M: 0.0138 c. 1185: 317 635 233 N T3 SD: 0.0059 c. M:-0.0087 c. 1256: 336 673 247 N T3 SD: 0.0043 c. M: 0.0070 c. 1312: 351 703 258 N T3 SD: 0.0030 c. M:-0.0046 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 5 x S SD: 13.7948 cents 5 x 6:7 S SD: 59.7273 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 51.9972 cents 8:9:10:11 H SD: 29.8569 cents 9:10:11:12 H SD: 24.0247 cents 10:11 x 13 SD: 27.0660 cents 11:12:14:15 S SD: 15.3447 cents 12:13:15:16 SD: 4.9302 cents 27:29:34:36 SD: 3.1932 cents 39:42:49:52 SD: 2.3284 cents 73:79:92:97 SD: 2.3030 cents 77:83:97:103 SD: 2.1791 cents 84:91:106:112 SD: 1.9805 cents 88:95:111:117 SD: 1.7731 cents 99:107:125:132 SD: 1.2767 cents 111:120:140:148 SD: 0.8165 cents 123:133:155:164 SD: 0.6986 cents 138:149:174:184 SD: 0.4272 cents 150:162:189:200 SD: 0.0000 cents