Scala analysis: 552_M60
Miscellaneous tetrachord 180/173 * 173/159 * 53/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 180/173 68.669842 2: 60/53 214.764169 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 53/45 283.2808 1: 180/173 68.6698 2: 173/159 146.0943 3: 53/45 283.2808
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 180/173 68.670 cents 1: 1 173/159 146.094 cents 1: 1 53/45 283.281 cents 2: 1 60/53 214.764 cents 2: 1 212/173 351.951 cents 2: 1 173/135 429.375 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 : 68.7 214.8 498.0 68.7 : 146.1 429.4 498.0 214.8: 283.3 352.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 68.6698 .. 283.2808 cents 9169/8100, 214.6110 cents 180/173, 68.6698 cents 2: 214.7642 .. 429.3752 cents 9169/8100, 214.6110 cents 2700/2809,-68.5167 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 180/173, 68.6698 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 53/45, 283.2808 cents Average / Smallest step : 2.417582 Largest / Average step : 1.706357 Largest / Smallest step : 4.125258 Median interval of one step : 173/159, 146.0943 cents, amount: 1 Least squares average step : 142.30951 cents, oct.: 426.92854 cents Scale is not proper Scale has trivalence property 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 68.51666 cents Scale diversity : 1.025359 Lumma stability : 0.275758 Lumma impropriety factor : 0.137571 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 : 2809/2700, 68.5167 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 173 Odd number limit : 173 (O: 173 U: 173) Highest odd numerator or denominator: 173 Scale harmonicity : 0.060976 Fundamental : 1/27507, -14.7475 octaves, 0.0095 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 4.951260E+06, 22.23936 octaves Euler's gradus suavitatis : 237 Sum of Mann's harmonic distance : 236.5, average 78.83333 Mersenne's string divisions : 279223 Sum of van Prooijen's expressibility: 4.43944, average 1.47981 Sum of Tenney's harmonic distance : 9.07493, average 3.02498 Vogel's harmonic complexity : 161.00000 Wille's k value : 4584 Wilson's harmonic complexity : 240 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 14.08390, average 2.34732 Lattice compactness (without 2's) : 11.04863, average 1.84144 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -1 .. 2 0.66667 4 1 5: 0 .. 1 0.66667 2 53: -1 .. 0 -0.33333 1 1 173: -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: <7 10 19 40 54| Scale is weakly epimorphic with val: <7 11 15 41 53| Scale is weakly epimorphic with val: <7 11 15 42 55| Scale is weakly epimorphic with val: <7 11 16 40 53| Scale is weakly epimorphic with val: <7 11 16 42 54| Scale is weakly epimorphic with val: <7 11 17 40 55| Scale is weakly epimorphic with val: <7 11 17 41 54| = patent Scale is JI-epimorphic with val: <7 11 18 41 53| Scale is weakly epimorphic with val: <7 11 18 42 55| Scale is weakly epimorphic with val: <7 11 19 40 53| Scale is JI-epimorphic with val: <7 11 19 42 54| Scale is weakly epimorphic with val: <7 12 17 40 54| Scale is weakly epimorphic with val: <7 12 18 40 53| Scale is weakly epimorphic with val: <7 12 18 41 55| Scale is weakly epimorphic with val: <7 12 19 41 54| Scale is weakly epimorphic with val: <7 12 19 42 53| Scale is weakly epimorphic with val: <8 11 16 40 53| Scale is weakly epimorphic with val: <8 11 17 41 54| Scale is weakly epimorphic with val: <8 11 18 41 53| Scale is weakly epimorphic with val: <8 11 18 42 55| Scale is weakly epimorphic with val: <8 11 19 42 54| Scale is weakly epimorphic with val: <8 12 15 40 53| Scale is weakly epimorphic with val: <8 12 16 41 54| Scale is weakly epimorphic with val: <8 12 16 42 53| Scale is weakly epimorphic with val: <8 12 17 40 54| Scale is weakly epimorphic with val: <8 12 17 42 55| Scale is weakly epimorphic with val: <8 12 18 41 55|
FIT/MODE
3: 0 1 2 N G T3 SD: 48.6211 c. M: 68.6698 c. 4: 1 1 2 P M ME S SD: 37.8237 c. M:-55.8414 c. 5: 1 1 3 N M DE S SD: 19.9910 c. M:-30.9392 c. 6: 1 2 3 P T3 SD: 21.4414 c. M:-34.2583 c. 7: 1 2 4 N T3 SD: 1.6207 c. M:-2.4794 c. 30: 4 9 17 N T3 SD: 1.4421 c. M: 2.2638 c. 37: 5 11 21 N T3 SD: 0.8632 c. M: 1.3665 c. 44: 6 13 25 N T3 SD: 0.4690 c. M: 0.7546 c. 51: 7 15 29 N T3 SD: 0.1851 c. M: 0.3107 c. 58: 8 17 33 N T3 SD: 0.0539 c. M: 0.0896 c. 167: 23 49 95 N T3 SD: 0.0495 c. M: 0.0768 c. 225: 31 66 128 N T3 SD: 0.0415 c. M: 0.0514 c. 283: 39 83 161 N T3 SD: 0.0396 c. M: 0.0593 c. 508: 70 149 289 N T3 SD: 0.0402 c. M: 0.0558 c. 624: 86 183 355 N T3 SD: 0.0396 c. M: 0.0621 c. 733: 101 215 417 N T3 SD: 0.0405 c. M: 0.0545 c. 740: 102 217 421 N T3 SD: 0.0401 c. M: 0.0664 c. 791: 109 232 450 N T3 SD: 0.0399 c. M: 0.0570 c. 907: 125 266 516 N T3 SD: 0.0396 c. M: 0.0612 c. 1653: 228 485 940 N T3 SD: 0.0383 c. M:-0.0610 c. 1660: 229 487 944 N T3 SD: 0.0382 c. M:-0.0552 c. 1667: 230 489 948 N T3 SD: 0.0393 c. M:-0.0495 c. 1697: 234 498 965 N T3 SD: 0.0390 c. M:-0.0673 c. 1704: 235 500 969 N T3 SD: 0.0367 c. M:-0.0616 c. 1711: 236 502 973 N T3 SD: 0.0356 c. M:-0.0559 c. 1718: 237 504 977 N T3 SD: 0.0357 c. M:-0.0504 c. 1725: 238 506 981 N T3 SD: 0.0370 c. M:-0.0459 c. 1755: 242 515 998 N T3 SD: 0.0360 c. M:-0.0621 c. 1762: 243 517 1002 N T3 SD: 0.0340 c. M:-0.0566 c. 1769: 244 519 1006 N T3 SD: 0.0331 c. M:-0.0512 c. 1776: 245 521 1010 N T3 SD: 0.0335 c. M:-0.0458 c. 1783: 246 523 1014 N T3 SD: 0.0350 c. M:-0.0453 c. 1813: 250 532 1031 N T3 SD: 0.0333 c. M:-0.0572 c. 1820: 251 534 1035 N T3 SD: 0.0315 c. M:-0.0519 c. 1827: 252 536 1039 N T3 SD: 0.0309 c. M:-0.0467 c. 1834: 253 538 1043 N T3 SD: 0.0315 c. M:-0.0415 c. 1871: 258 549 1064 N T3 SD: 0.0307 c. M:-0.0527 c. 1878: 259 551 1068 N T3 SD: 0.0291 c. M:-0.0476 c. 1885: 260 553 1072 N T3 SD: 0.0288 c. M:-0.0425 c. 1892: 261 555 1076 N T3 SD: 0.0296 c. M:-0.0375 c. 1929: 266 566 1097 N T3 SD: 0.0283 c. M:-0.0484 c. 1936: 267 568 1101 N T3 SD: 0.0270 c. M:-0.0435 c. 1943: 268 570 1105 N T3 SD: 0.0269 c. M:-0.0386 c. 1950: 269 572 1109 N T3 SD: 0.0280 c. M:-0.0348 c. 1987: 274 583 1130 N T3 SD: 0.0261 c. M:-0.0444 c. 1994: 275 585 1134 N T3 SD: 0.0250 c. M:-0.0396 c. 2001: 276 587 1138 N T3 SD: 0.0251 c. M:-0.0348 c. 2008: 277 589 1142 N T3 SD: 0.0265 c. M:-0.0346 c. 2038: 281 598 1159 N T3 SD: 0.0261 c. M:-0.0452 c. 2045: 282 600 1163 N T3 SD: 0.0240 c. M:-0.0406 c. 2052: 283 602 1167 N T3 SD: 0.0231 c. M:-0.0359 c. 2059: 284 604 1171 N T3 SD: 0.0235 c. M:-0.0313 c. 2103: 290 617 1196 N T3 SD: 0.0221 c. M:-0.0370 c. 2110: 291 619 1200 N T3 SD: 0.0214 c. M:-0.0325 c. 2117: 292 621 1204 N T3 SD: 0.0221 c. M:-0.0280 c. 2154: 297 632 1225 N T3 SD: 0.0220 c. M:-0.0380 c. 2161: 298 634 1229 N T3 SD: 0.0203 c. M:-0.0336 c. 2168: 299 636 1233 N T3 SD: 0.0198 c. M:-0.0292 c. 2175: 300 638 1237 N T3 SD: 0.0208 c. M:-0.0260 c. 2212: 305 649 1258 N T3 SD: 0.0201 c. M:-0.0346 c. 2219: 306 651 1262 N T3 SD: 0.0186 c. M:-0.0304 c. 2226: 307 653 1266 N T3 SD: 0.0184 c. M:-0.0261 c. 2270: 313 666 1291 N T3 SD: 0.0183 c. M:-0.0314 c. 2277: 314 668 1295 N T3 SD: 0.0170 c. M:-0.0273 c. 2284: 315 670 1299 N T3 SD: 0.0171 c. M:-0.0232 c. 2328: 321 683 1324 N T3 SD: 0.0166 c. M:-0.0284 c. 2335: 322 685 1328 N T3 SD: 0.0155 c. M:-0.0244 c. 2342: 323 687 1332 N T3 SD: 0.0160 c. M:-0.0204 c. 2386: 329 700 1357 N T3 SD: 0.0150 c. M:-0.0256 c. 2393: 330 702 1361 N T3 SD: 0.0142 c. M:-0.0216 c. 2400: 331 704 1365 N T3 SD: 0.0149 c. M:-0.0189 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: 65.7854 cents 6 x 7:8 S SD: 26.0534 cents 7 x 8:9 S SD: 32.5321 cents 8 x 9:11 SD: 27.1837 cents 9 x 10:12 S SD: 16.1802 cents 10 x 11:13 SD: 33.1557 cents 11 x 12:15 S SD: 37.5032 cents 12:13:14:16 S SD: 29.0622 cents 13:14:15:17 SD: 25.3271 cents 14:15:16:19 SD: 20.5105 cents 15:16:17:20 SD: 14.3681 cents 18:19:20:24 S SD: 13.6172 cents 20:21:23:27 SD: 12.7005 cents 21:22:24:28 S SD: 6.7504 cents 23:24:26:31 SD: 6.5125 cents 24:25:27:32 SD: 3.6791 cents 45:47:51:60 SD: 2.2956 cents 54:56:61:72 SD: 2.2758 cents 69:72:78:92 SD: 1.8682 cents 75:78:85:100 SD: 0.6903 cents 99:103:112:132 SD: 0.3901 cents 174:181:197:232 SD: 0.1403 cents 447:465:506:596 SD: 0.1159 cents 492:512:557:656 SD: 0.1061 cents 591:615:669:788 SD: 0.0949 cents