Scala analysis: 518_M26
Miscellaneous tetrachord 34/33 * 66/65 * 65/51
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 34/33 51.682466 2: 68/65 78.114034 Valentine semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 65/51 419.9310 1: 34/33 51.6825 2: 66/65 26.4316 Winmeanma 3: 65/51 419.9310
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 66/65 26.432 cents Winmeanma 1: 1 34/33 51.682 cents 1: 1 65/51 419.931 cents 2: 1 68/65 78.114 cents Valentine semitone 2: 1 22/17 446.363 cents 2: 1 130/99 471.613 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 : 51.7 78.1 498.0 51.7 : 26.4 446.4 498.0 78.1 : 419.9 471.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 26.4316 .. 419.9310 cents 4225/3366, 393.4994 cents 66/65, 26.4316 cents 2: 78.1140 .. 471.6134 cents 4225/3366, 393.4994 cents 3468/4225,-341.8169 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 66/65, 26.4316 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 65/51, 419.9310 cents Average / Smallest step : 6.280937 Largest / Average step : 2.529476 Largest / Smallest step : 15.887479 Median interval of one step : 34/33, 51.6825 cents, amount: 1 Least squares average step : 121.57468 cents, oct.: 364.72404 cents Scale is not proper Scale has trivalence property Scale is a mode of a 848-tone equal temperament with octave 4/3 degrees: 88 133 848 Least number of segments generator : 425 of 249.610 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 491 of 288.373 cents and inv. generated superset size: 25 = 22 more = 833.333% Number of contiguous 1-step segments: 0 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 26.43157 cents Scale diversity : 0.240828 Lumma stability : 0.106141 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 : 1105/1089, 25.2509 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 Limited inverse transpositions with margin 393.4994 cents: 2 -- Rational properties -- Prime limit : 17 Odd number limit : 99 (O: 65 U: 99) Highest odd numerator or denominator: 65 Scale harmonicity : 0.012267 Average absolute harmonicity : 0.083337 Specific harmonicity : 0.057482 Fundamental : 1/2145, -11.0668 octaves, 0.1220 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 1.458600E+05, 17.15422 octaves Euler's gradus suavitatis : 47 Sum of Mann's harmonic distance : 103.5, average 34.50000 Mersenne's string divisions : 8911 Sum of van Prooijen's expressibility: 3.80855, average 1.26952 Sum of Tenney's harmonic distance : 7.77460, average 2.59153 Vogel's harmonic complexity : 33.33333 Wille's k value : 552 Wilson's harmonic complexity : 49 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 12.84994, average 2.14166 Lattice compactness (without 2's) : 9.87832, average 1.64639 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 0 -0.66667 2 1 5: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.33333 1 13: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 2 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 24 27 30| Scale is weakly epimorphic with val: <7 11 16 24 28 29| Scale is JI-epimorphic with val: <7 11 16 25 26 30| Scale is weakly epimorphic with val: <7 11 16 25 28 31| Scale is weakly epimorphic with val: <7 11 16 26 26 29| Scale is JI-epimorphic with val: <7 11 16 26 27 31| Scale is weakly epimorphic with val: <7 11 17 24 26 30| Scale is weakly epimorphic with val: <7 11 17 24 27 29| Scale is weakly epimorphic with val: <7 11 17 25 27 31| Scale is weakly epimorphic with val: <7 11 17 25 28 30| Scale is JI-epimorphic with val: <7 11 17 26 26 31| Scale is weakly epimorphic with val: <7 11 17 26 28 29| Scale is weakly epimorphic with val: <7 11 18 24 26 29| Scale is weakly epimorphic with val: <7 11 18 24 28 30| Scale is weakly epimorphic with val: <7 11 18 25 26 31| Scale is weakly epimorphic with val: <7 11 18 25 27 30| Scale is weakly epimorphic with val: <7 11 18 26 27 29| Scale is weakly epimorphic with val: <7 11 18 26 28 31| Scale is weakly epimorphic with val: <7 12 16 25 26 31|
FIT/MODE
3: 0 0 3 N M DE S SD: 54.0767 c. M: 78.1140 c. 4: 0 1 3 N G T3 SD: 40.0990 c. M: 51.6825 c. 5: 1 0 4 N G T3 SD: 30.3259 c. M:-47.9265 c. 6: 1 0 5 N G T3 SD: 18.3049 c. M:-31.3250 c. 7: 1 0 6 N G T3 SD: 11.9368 c. M:-19.4668 c. 8: 1 0 7 N G T3 SD: 11.0043 c. M: 15.8584 c. 10: 1 1 8 N M DE S SD: 12.4574 c. M:-21.4950 c. 11: 1 1 9 N M DE S SD: 8.0783 c. M:-12.4396 c. 12: 1 1 10 N M DE S SD: 6.5205 c. M: 10.1787 c. 13: 1 1 11 N M DE S SD: 7.7678 c. M: 13.3713 c. 17: 2 1 14 N T3 SD: 6.9123 c. M:-9.7763 c. 18: 2 1 15 N T3 SD: 3.5266 c. M:-4.8935 c. 19: 2 1 16 N T3 SD: 0.5253 c. M:-0.7433 c. 58: 6 3 49 N T3 SD: 0.4888 c. M: 0.8312 c. 77: 8 4 65 N T3 SD: 0.2890 c. M: 0.4966 c. 96: 10 5 81 N T3 SD: 0.2046 c. M: 0.2945 c. 115: 12 6 97 N T3 SD: 0.1897 c. M:-0.2874 c. 134: 14 7 113 N T3 SD: 0.2064 c. M:-0.3521 c. 211: 22 11 178 N T3 SD: 0.1910 c. M:-0.2464 c. 223: 23 12 188 N T3 SD: 0.1843 c. M: 0.3146 c. 242: 25 13 204 N T3 SD: 0.1437 c. M: 0.2315 c. 261: 27 14 220 N T3 SD: 0.1168 c. M: 0.1606 c. 280: 29 15 236 N T3 SD: 0.1039 c. M:-0.1502 c. 299: 31 16 252 N T3 SD: 0.1039 c. M:-0.1740 c. 319: 33 17 269 N T3 SD: 0.0972 c. M: 0.1606 c. 338: 35 18 285 N T3 SD: 0.0642 c. M: 0.1098 c. 357: 37 19 301 N T3 SD: 0.0377 c. M: 0.0644 c. 376: 39 20 317 N T3 SD: 0.0251 c. M:-0.0366 c. 472: 49 25 398 N T3 SD: 0.0216 c. M: 0.0307 c. 810: 84 43 683 N T3 SD: 0.0242 c. M: 0.0334 c. 829: 86 44 699 N T3 SD: 0.0117 c. M: 0.0156 c. 848: 88 45 715 N T3 SD: 0.0010 c. M:-0.0014 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 27:28 x 36 SD: 5.6392 cents 28:29 x 37 SD: 8.9906 cents 29:30 x 39 SD: 8.2152 cents 30:31 x 40 SD: 2.5422 cents 31:32 x 41 SD: 7.1986 cents 32:33 x 43 SD: 6.7831 cents 36:37:38:48 SD: 5.3537 cents 39:40:41:52 SD: 3.8487 cents 42:43:44:56 SD: 3.7369 cents 50 x 52:67 SD: 6.6873 cents 51 x 53:68 SD: 5.7599 cents 52 x 54:69 SD: 7.6298 cents 53:55 x 71 SD: 7.4371 cents 54:56 x 72 SD: 5.6392 cents 57:59:60:76 SD: 4.4540 cents 59:61:62:79 SD: 4.0827 cents 60:62:63:80 SD: 2.7124 cents 63:65:66:84 SD: 1.1422 cents 66:68:69:88 SD: 0.3859 cents 195:201:204:260 SD: 0.2611 cents 261:269:273:348 SD: 0.2181 cents 366:377:383:488 SD: 0.2138 cents 432:445:452:576 SD: 0.1417 cents 498:513:521:664 SD: 0.1037 cents 564:581:590:752 SD: 0.0952 cents