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