Scala analysis: 516_M24
Miscellaneous tetrachord 136/133 * 133/130 * 65/51
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 136/133 38.616487 2: 68/65 78.114034 Valentine semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 65/51 419.9310 1: 136/133 38.6165 2: 133/130 39.4975 3: 65/51 419.9310
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 136/133 38.616 cents 1: 1 133/130 39.498 cents 1: 1 65/51 419.931 cents 2: 1 68/65 78.114 cents Valentine semitone 2: 1 520/399 458.547 cents 2: 1 133/102 459.429 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 : 38.6 78.1 498.0 38.6 : 39.5 459.4 498.0 78.1 : 419.9 458.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.6165 .. 419.9310 cents 8645/6936, 381.3145 cents 136/133, 38.6165 cents 2: 78.1140 .. 459.4285 cents 8645/6936, 381.3145 cents 3468/4225,-341.8169 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 136/133, 38.6165 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 65/51, 419.9310 cents Average / Smallest step : 4.299071 Largest / Average step : 2.529476 Largest / Smallest step : 10.874396 Median interval of one step : 133/130, 39.4975 cents, amount: 1 Least squares average step : 120.64140 cents, oct.: 361.92419 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2257-tone equal temperament with octave 4/3 degrees: 175 354 2257 Least number of segments generator : 1129 of 249.133 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1736 of 383.078 cents and inv. generated superset size: 45 = 42 more = 1500.000% Number of contiguous 1-step segments: 0 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 38.61649 cents Scale diversity : 0.266050 Lumma stability : 0.155072 Lumma impropriety factor : 0.686317 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 : 17689/17680, 0.8811 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% Limited inverse transpositions with margin 380.4334 cents: 2 -- Rational properties -- Prime limit : 19 Odd number limit : 399 (O: 133 U: 399) Highest odd numerator or denominator: 133 Scale harmonicity : 0.009197 Average absolute harmonicity : 0.081223 Specific harmonicity : 0.044905 Fundamental : 1/25935, -14.6626 octaves, 0.0101 Hz. Guide tone : 136, 7.0875 octaves, 35581.077 Hz. Exponens Consonantiae : 3.527160E+06, 21.75008 octaves Euler's gradus suavitatis : 62 Sum of Mann's harmonic distance : 204.5, average 68.16667 Mersenne's string divisions : 35777 Sum of van Prooijen's expressibility: 4.41389, average 1.47130 Sum of Tenney's harmonic distance : 8.98199, average 2.99400 Vogel's harmonic complexity : 45.00000 Wille's k value : 4322 Wilson's harmonic complexity : 64 Rectangular lattice diameter : 6 Triangular lattice diameter : 2 Lattice compactness : 14.81806, average 2.46968 Lattice compactness (without 2's) : 10.46410, average 1.74402 Number of different primes : 7 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 0 -0.33333 1 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 13: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <7 11 16 19 26 29 32| Scale is JI-epimorphic with val: <7 11 16 19 26 30 31| Scale is weakly epimorphic with val: <7 11 16 19 27 30 30| Scale is JI-epimorphic with val: <7 11 16 19 27 31 32| Scale is weakly epimorphic with val: <7 11 16 19 28 29 30| Scale is weakly epimorphic with val: <7 11 16 19 28 31 31| Scale is weakly epimorphic with val: <7 11 16 20 26 29 31| Scale is JI-epimorphic with val: <7 11 16 20 26 30 30| Scale is weakly epimorphic with val: <7 11 16 20 27 30 32| Scale is JI-epimorphic with val: <7 11 16 20 27 31 31| Scale is weakly epimorphic with val: <7 11 16 20 28 29 32| Scale is weakly epimorphic with val: <7 11 16 21 26 29 30| Scale is weakly epimorphic with val: <7 11 16 21 26 30 32| Scale is weakly epimorphic with val: <7 11 16 21 27 30 31| Scale is weakly epimorphic with val: <7 11 16 21 28 29 31| Scale is weakly epimorphic with val: <7 11 16 21 28 31 32| Scale is weakly epimorphic with val: <7 11 17 19 26 30 30| Scale is JI-epimorphic with val: <7 11 17 19 26 31 32| Scale is weakly epimorphic with val: <7 11 17 19 27 29 30| Scale is weakly epimorphic with val: <7 11 17 19 27 31 31| Scale is weakly epimorphic with val: <7 11 17 19 28 29 32| Scale is weakly epimorphic with val: <7 11 17 19 28 30 31| Scale is weakly epimorphic with val: <7 11 17 20 26 30 32| Scale is JI-epimorphic with val: <7 11 17 20 26 31 31| Scale is weakly epimorphic with val: <7 11 17 20 27 29 32| Scale is weakly epimorphic with val: <7 11 17 20 28 29 31| Scale is weakly epimorphic with val: <7 11 17 20 28 30 30| Scale is weakly epimorphic with val: <7 11 17 21 26 30 31| Scale is weakly epimorphic with val: <7 11 17 21 27 29 31| Scale is weakly epimorphic with val: <7 11 17 21 27 31 32| Scale is weakly epimorphic with val: <7 11 17 21 28 29 30| Scale is weakly epimorphic with val: <7 11 17 21 28 30 32| Scale is weakly epimorphic with val: <7 11 18 19 26 29 30| Scale is weakly epimorphic with val: <7 11 18 19 26 31 31| Scale is weakly epimorphic with val: <7 11 18 19 27 29 32| Scale is weakly epimorphic with val: <7 11 18 19 27 30 31| Scale is weakly epimorphic with val: <7 11 18 19 28 30 30| Scale is weakly epimorphic with val: <7 11 18 19 28 31 32| Scale is weakly epimorphic with val: <7 11 18 20 26 29 32| Scale is weakly epimorphic with val: <7 11 18 20 27 29 31| Scale is weakly epimorphic with val: <7 11 18 20 27 30 30| Scale is weakly epimorphic with val: <7 11 18 20 28 30 32| Scale is weakly epimorphic with val: <7 11 18 20 28 31 31| Scale is weakly epimorphic with val: <7 11 18 21 26 29 31| Scale is weakly epimorphic with val: <7 11 18 21 26 31 32| Scale is weakly epimorphic with val: <7 11 18 21 27 29 30| Scale is weakly epimorphic with val: <7 11 18 21 27 30 32| Scale is weakly epimorphic with val: <7 11 18 21 28 30 31| Scale is weakly epimorphic with val: <7 12 16 19 26 31 32| Scale is weakly epimorphic with val: <7 12 16 20 26 31 31|
FIT/MODE
3: 0 0 3 N M DE S SD: 50.3092 c. M: 78.1140 c. 5: 0 1 4 N G T3 SD: 25.5164 c. M: 38.6165 c. 6: 0 1 5 N G T3 SD: 22.4735 c. M: 38.6165 c. 7: 0 1 6 N G T3 SD: 22.6550 c. M: 38.6165 c. 8: 0 1 7 N G T3 SD: 24.1020 c. M: 38.6165 c. 9: 1 0 8 N G T3 SD: 16.3131 c. M: 22.7757 c. 10: 1 1 8 N M DE S SD: 13.9905 c. M:-21.4950 c. 11: 1 1 9 N M DE S SD: 8.1466 c. M:-12.4396 c. 12: 1 1 10 N M DE S SD: 3.2804 c. M:-4.8935 c. 13: 1 1 11 N M DE S SD: 0.8791 c. M: 1.4917 c. 38: 3 3 32 N M DE S SD: 0.5064 c. M:-0.7029 c. 51: 4 4 43 N M DE S SD: 0.2575 c. M:-0.4459 c. 64: 5 5 54 N M DE S SD: 0.2400 c. M: 0.2945 c. 115: 9 9 97 N M DE S SD: 0.2278 c. M:-0.3609 c. 286: 22 23 241 N T3 SD: 0.2277 c. M: 0.3053 c. 287: 22 23 242 N T3 SD: 0.2537 c. M: 0.4388 c. 294: 23 23 248 N M DE S SD: 0.2276 c. M:-0.3462 c. 299: 23 24 252 N T3 SD: 0.2029 c. M: 0.3053 c. 312: 24 25 263 N T3 SD: 0.1863 c. M: 0.3053 c. 324: 25 26 273 N T3 SD: 0.1954 c. M:-0.2819 c. 325: 25 26 274 N T3 SD: 0.1778 c. M: 0.3053 c. 337: 26 27 284 N T3 SD: 0.1656 c. M:-0.2135 c. 338: 26 27 285 N T3 SD: 0.1766 c. M: 0.3053 c. 350: 27 28 295 N T3 SD: 0.1425 c. M: 0.1959 c. 363: 28 29 306 N T3 SD: 0.1268 c. M: 0.1998 c. 376: 29 30 317 N T3 SD: 0.1193 c. M: 0.2034 c. 388: 30 31 327 N T3 SD: 0.1246 c. M:-0.1869 c. 389: 30 31 328 N T3 SD: 0.1197 c. M: 0.2068 c. 401: 31 32 338 N T3 SD: 0.1010 c. M:-0.1324 c. 414: 32 33 349 N T3 SD: 0.0839 c. M: 0.1203 c. 427: 33 34 360 N T3 SD: 0.0752 c. M: 0.1259 c. 440: 34 35 371 N T3 SD: 0.0760 c. M: 0.1312 c. 452: 35 36 381 N T3 SD: 0.0746 c. M:-0.1187 c. 453: 35 36 382 N T3 SD: 0.0846 c. M: 0.1362 c. 465: 36 37 392 N T3 SD: 0.0542 c. M:-0.0737 c. 478: 37 38 403 N T3 SD: 0.0415 c. M: 0.0649 c. 491: 38 39 414 N T3 SD: 0.0415 c. M: 0.0713 c. 516: 40 41 435 N T3 SD: 0.0392 c. M:-0.0674 c. 529: 41 42 446 N T3 SD: 0.0191 c. M:-0.0291 c. 542: 42 43 457 N T3 SD: 0.0137 c. M: 0.0226 c. 593: 46 47 500 N T3 SD: 0.0108 c. M:-0.0177 c. 1122: 87 89 946 N T3 SD: 0.0063 c. M:-0.0107 c. 1135: 88 90 957 N T3 SD: 0.0039 c. M: 0.0065 c. 1664: 129 132 1403 N T3 SD: 0.0044 c. M: 0.0060 c. 2257: 175 179 1903 N T3 SD: 0.0012 c. M:-0.0020 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 x 7 SD: 84.4672 cents 6 x 7:8 S SD: 94.3784 cents 7 x 8:9 S SD: 82.7518 cents 8 x 9:11 SD: 68.3056 cents 9 x 10:12 S SD: 52.1448 cents 10 x 11:13 SD: 48.6597 cents 11 x 12:15 S SD: 41.1499 cents 12 x 13:16 SD: 30.2293 cents 13 x 14:17 SD: 30.2017 cents 14 x 15:19 SD: 25.7245 cents 15 x 16:20 S SD: 16.8086 cents 16 x 17:21 SD: 19.1298 cents 17 x 18:23 SD: 16.3791 cents 18 x 19:24 SD: 7.7445 cents 19 x 20:25 S SD: 12.6493 cents 20 x 21:27 SD: 11.2125 cents 21 x 22:28 SD: 1.2115 cents 22 x 23:29 SD: 9.9098 cents 23 x 24:31 SD: 9.6171 cents 24 x 25:32 SD: 3.7208 cents 25 x 26:33 SD: 10.0879 cents 26 x 27:35 SD: 10.4607 cents 27 x 28:36 SD: 7.5766 cents 28 x 29:37 SD: 11.6463 cents 29 x 30:39 SD: 12.2277 cents 30:31 x 40 SD: 9.0752 cents 31:32 x 41 SD: 10.7676 cents 32:33 x 43 SD: 9.9540 cents 33:34:35:44 SD: 9.0364 cents 34:35:36:45 S SD: 9.0147 cents 35:36:37:47 SD: 8.0429 cents 36:37:38:48 SD: 5.9410 cents 38:39:40:51 SD: 5.6119 cents 39:40:41:52 SD: 3.3143 cents 42:43:44:56 SD: 1.0732 cents 45:46:47:60 SD: 0.9624 cents 87:89:91:116 SD: 0.2626 cents 495:506:518:660 SD: 0.2549 cents 537:549:562:716 SD: 0.2510 cents 540:552:565:720 SD: 0.2043 cents 582:595:609:776 SD: 0.1805 cents