Scala analysis: 273_C19
Chromatic tetrachord 14/13 * 22/21 * 13/11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/13 128.298245 2/3-tone 2: 44/39 208.835280 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 13/11 289.2097 tridecimal minor third 1: 14/13 128.2982 2/3-tone 2: 22/21 80.5370 undecimal minor semitone 3: 13/11 289.2097 tridecimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 14/13 128.298 cents 2/3-tone 1: 1 13/11 289.210 cents tridecimal minor third 2: 1 44/39 208.835 cents 2: 1 26/21 369.747 cents 2: 1 14/11 417.508 cents undecimal diminished fourth or 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 : 128.3 208.8 498.0 128.3: 80.5 369.7 498.0 208.8: 289.2 417.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 289.2097 cents 273/242, 208.6727 cents 22/21, 80.5370 cents 2: 208.8353 .. 417.5080 cents 273/242, 208.6727 cents 484/507,-80.3744 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 13/11, 289.2097 cents Average / Smallest step : 2.061350 Largest / Average step : 1.742070 Largest / Smallest step : 3.591015 Median interval of one step : 14/13, 128.2982 cents, amount: 1 Least squares average step : 145.72170 cents, oct.: 437.16510 cents Scale is not proper Scale has trivalence property 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 80.37444 cents Scale diversity : 1.089769 Lumma stability : 0.323413 Lumma impropriety factor : 0.161380 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 : 147/143, 47.7612 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 : 39 (O: 13 U: 39) Highest odd numerator or denominator: 39 Scale harmonicity : 0.018087 Average absolute harmonicity : 0.088803 Specific harmonicity : 0.083470 Fundamental : 1/39, -5.2854 octaves, 6.7083 Hz. Guide tone : 308, 8.2668 octaves, 80580.674 Hz. Exponens Consonantiae : 1.201200E+04, 13.55219 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 58.5, average 19.50000 Mersenne's string divisions : 15687 Sum of van Prooijen's expressibility: 3.18213, average 1.06071 Sum of Tenney's harmonic distance : 6.57377, average 2.19126 Vogel's harmonic complexity : 13.00000 Wille's k value : 10 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 12.02808, average 2.00468 Lattice compactness (without 2's) : 9.02458, average 1.50410 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 0 -0.66667 2 1 7: 0 .. 1 0.33333 1 11: 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: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 22 24 25| Scale is weakly epimorphic with val: <6 11 22 23 25| Scale is weakly epimorphic with val: <7 10 18 25 26| Scale is weakly epimorphic with val: <7 10 19 26 27| Scale is weakly epimorphic with val: <7 10 20 24 25| Scale is weakly epimorphic with val: <7 10 20 27 28| Scale is weakly epimorphic with val: <7 10 21 23 25| Scale is weakly epimorphic with val: <7 10 21 25 26| Scale is weakly epimorphic with val: <7 10 22 24 26| Scale is weakly epimorphic with val: <7 10 22 26 27| 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 26| Scale is weakly epimorphic with val: <7 11 18 24 29| Scale is weakly 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 29| Scale is JI-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 27| Scale is weakly epimorphic with val: <7 11 19 25 30| Scale is weakly epimorphic with val: <7 11 19 27 28| Scale is weakly epimorphic with val: <7 11 20 23 25| Scale is weakly epimorphic with val: <7 11 20 23 28| Scale is JI-epimorphic with val: <7 11 20 25 26| Scale is weakly epimorphic with val: <7 11 20 25 29| Scale is weakly epimorphic with val: <7 11 20 26 28| Scale is weakly epimorphic with val: <7 11 21 23 27| Scale is weakly epimorphic with val: <7 11 21 23 30| Scale is weakly epimorphic with val: <7 11 21 24 26| Scale is weakly epimorphic with val: <7 11 21 24 29| Scale is JI-epimorphic with val: <7 11 21 26 27| Scale is weakly epimorphic with val: <7 11 21 26 30| Scale is weakly epimorphic with val: <7 11 21 27 29| Scale is weakly epimorphic with val: <7 11 22 24 25| Scale is weakly epimorphic with val: <7 11 22 24 28| Scale is weakly epimorphic with val: <7 11 22 25 27| Scale is weakly epimorphic with val: <7 11 22 25 30| Scale is JI-epimorphic with val: <7 11 22 27 28| Scale is weakly epimorphic with val: <7 12 21 24 25| Scale is weakly epimorphic with val: <7 12 22 25 26| Scale is weakly epimorphic with val: <8 11 18 23 25| Scale is weakly epimorphic with val: <8 11 18 26 28| Scale is weakly epimorphic with val: <8 11 19 24 26| Scale is weakly epimorphic with val: <8 11 19 27 29| Scale is weakly epimorphic with val: <8 11 20 24 25| Scale is weakly epimorphic with val: <8 11 20 25 27| Scale is weakly epimorphic with val: <8 11 21 23 25| Scale is weakly epimorphic with val: <8 11 21 25 26| Scale is weakly epimorphic with val: <8 11 21 26 28| Scale is weakly epimorphic with val: <8 11 22 23 27| Scale is weakly epimorphic with val: <8 11 22 24 26| Scale is weakly epimorphic with val: <8 11 22 26 27| Scale is weakly epimorphic with val: <8 11 22 27 29| Scale is weakly epimorphic with val: <8 12 18 26 27| Scale is weakly epimorphic with val: <8 12 19 24 25| Scale is weakly epimorphic with val: <8 12 19 27 28| Scale is weakly epimorphic with val: <8 12 20 23 25| Scale is weakly epimorphic with val: <8 12 20 25 26| Scale is weakly epimorphic with val: <8 12 21 24 26| Scale is weakly epimorphic with val: <8 12 21 26 27| Scale is weakly epimorphic with val: <8 12 22 24 25| Scale is weakly epimorphic with val: <8 12 22 25 27| Scale is weakly epimorphic with val: <8 12 22 27 28|
FIT/MODE
3: 1 0 2 N G T3 SD: 32.9451 c. M: 42.8203 c. 4: 1 1 2 P M ME S SD: 23.3049 c. M:-40.1872 c. 5: 1 1 3 N M DE S SD: 17.4696 c. M: 28.6892 c. 7: 2 1 4 N T3 SD: 8.5105 c. M:-14.0003 c. 12: 3 2 7 N T3 SD: 2.3148 c. M: 3.7870 c. Vietnamese tritonic 19: 5 3 11 N T3 SD: 1.6738 c. M:-2.7662 c. 31: 8 5 18 N T3 SD: 0.1331 c. M:-0.2295 c. 105: 27 17 61 N T3 SD: 0.1525 c. M: 0.2295 c. 136: 35 22 79 N T3 SD: 0.0909 c. M: 0.1249 c. 167: 43 27 97 N T3 SD: 0.0546 c. M: 0.0739 c. 198: 51 32 115 N T3 SD: 0.0349 c. M: 0.0588 c. 229: 59 37 133 N T3 SD: 0.0297 c. M: 0.0479 c. 260: 67 42 151 N T3 SD: 0.0342 c. M:-0.0441 c. 427: 110 69 248 N T3 SD: 0.0306 c. M: 0.0529 c. 489: 126 79 284 N T3 SD: 0.0313 c. M: 0.0434 c. 656: 169 106 381 N T3 SD: 0.0300 c. M: 0.0512 c. 749: 193 121 435 N T3 SD: 0.0321 c. M: 0.0420 c. 885: 228 143 514 N T3 SD: 0.0298 c. M: 0.0503 c. 1009: 260 163 586 N T3 SD: 0.0326 c. M: 0.0414 c. 1052: 271 170 611 N T3 SD: 0.0312 c. M: 0.0541 c. 1083: 279 175 629 N T3 SD: 0.0302 c. M: 0.0519 c. 1114: 287 180 647 N T3 SD: 0.0297 c. M: 0.0498 c. 1269: 327 205 737 N T3 SD: 0.0329 c. M: 0.0410 c. 1343: 346 217 780 N T3 SD: 0.0297 c. M: 0.0495 c. 1529: 394 247 888 N T3 SD: 0.0331 c. M: 0.0407 c. 1541: 397 249 895 N T3 SD: 0.0299 c. M: 0.0507 c. 1545: 398 250 897 N T3 SD: 0.0309 c. M:-0.0535 c. 1557: 401 252 904 N T3 SD: 0.0297 c. M:-0.0429 c. 1572: 405 254 913 N T3 SD: 0.0297 c. M: 0.0492 c. 1576: 406 255 915 N T3 SD: 0.0307 c. M:-0.0529 c. 1588: 409 257 922 N T3 SD: 0.0280 c. M:-0.0425 c. 1607: 414 260 933 N T3 SD: 0.0307 c. M:-0.0523 c. 1619: 417 262 940 N T3 SD: 0.0266 c. M:-0.0421 c. 1638: 422 265 951 N T3 SD: 0.0309 c. M:-0.0517 c. 1650: 425 267 958 N T3 SD: 0.0254 c. M:-0.0418 c. 1681: 433 272 976 N T3 SD: 0.0245 c. M:-0.0414 c. 1693: 436 274 983 N T3 SD: 0.0278 c. M: 0.0362 c. 1700: 438 275 987 N T3 SD: 0.0318 c. M:-0.0507 c. 1712: 441 277 994 N T3 SD: 0.0239 c. M:-0.0411 c. 1724: 444 279 1001 N T3 SD: 0.0257 c. M:-0.0316 c. 1743: 449 282 1012 N T3 SD: 0.0235 c. M:-0.0407 c. 1755: 452 284 1019 N T3 SD: 0.0239 c. M:-0.0315 c. 1774: 457 287 1030 N T3 SD: 0.0234 c. M:-0.0404 c. 1786: 460 289 1037 N T3 SD: 0.0222 c. M:-0.0313 c. 1805: 465 292 1048 N T3 SD: 0.0235 c. M:-0.0401 c. 1817: 468 294 1055 N T3 SD: 0.0208 c. M:-0.0311 c. 1836: 473 297 1066 N T3 SD: 0.0238 c. M:-0.0398 c. 1848: 476 299 1073 N T3 SD: 0.0196 c. M:-0.0310 c. 1879: 484 304 1091 N T3 SD: 0.0187 c. M:-0.0309 c. 1910: 492 309 1109 N T3 SD: 0.0181 c. M:-0.0307 c. 1922: 495 311 1116 N T3 SD: 0.0214 c. M: 0.0296 c. 1929: 497 312 1120 N T3 SD: 0.0256 c. M:-0.0390 c. 1941: 500 314 1127 N T3 SD: 0.0177 c. M:-0.0306 c. 1953: 503 316 1134 N T3 SD: 0.0196 c. M: 0.0255 c. 1972: 508 319 1145 N T3 SD: 0.0176 c. M:-0.0304 c. 1984: 511 321 1152 N T3 SD: 0.0179 c. M:-0.0223 c. 2003: 516 324 1163 N T3 SD: 0.0177 c. M:-0.0303 c. 2015: 519 326 1170 N T3 SD: 0.0164 c. M:-0.0223 c. 2034: 524 329 1181 N T3 SD: 0.0181 c. M:-0.0302 c. 2046: 527 331 1188 N T3 SD: 0.0152 c. M:-0.0223 c. 2077: 535 336 1206 N T3 SD: 0.0142 c. M:-0.0223 c. 2108: 543 341 1224 N T3 SD: 0.0135 c. M:-0.0223 c. 2139: 551 346 1242 N T3 SD: 0.0130 c. M:-0.0223 c. 2170: 559 351 1260 N T3 SD: 0.0129 c. M:-0.0223 c. 2182: 562 353 1267 N T3 SD: 0.0148 c. M: 0.0208 c. 2201: 567 356 1278 N T3 SD: 0.0130 c. M:-0.0223 c. 2213: 570 358 1285 N T3 SD: 0.0133 c. M: 0.0173 c. 2232: 575 361 1296 N T3 SD: 0.0134 c. M:-0.0223 c. 2244: 578 363 1303 N T3 SD: 0.0119 c. M:-0.0151 c. 2263: 583 366 1314 N T3 SD: 0.0140 c. M:-0.0223 c. 2275: 586 368 1321 N T3 SD: 0.0107 c. M:-0.0152 c. 2306: 594 373 1339 N T3 SD: 0.0098 c. M:-0.0153 c. 2337: 602 378 1357 N T3 SD: 0.0092 c. M:-0.0154 c. 2368: 610 383 1375 N T3 SD: 0.0090 c. M:-0.0155 c. 2399: 618 388 1393 N T3 SD: 0.0091 c. M:-0.0156 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: 68.0849 cents 6 x 7:8 S SD: 29.0178 cents 7 x 8:9 S SD: 33.4032 cents 8 x 9:11 SD: 26.7501 cents 9 x 10:12 S SD: 13.2158 cents 10:11 x 13 SD: 28.5854 cents 11:12 x 15 S SD: 22.4315 cents 12:13:14:16 S SD: 19.6460 cents 13:14:15:17 SD: 17.1392 cents 14:15:16:19 SD: 12.9802 cents 15:16:17:20 SD: 6.1111 cents 24:26:27:32 SD: 3.7980 cents 39:42:44:52 SD: 0.0000 cents