Scala analysis: 533_M41
Miscellaneous tetrachord 360/349 * 349/327 * 109/90
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 360/349 53.723844 2: 120/109 166.447525 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 109/90 331.5975 1: 360/349 53.7238 2: 349/327 112.7237 3: 109/90 331.5975
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 360/349 53.724 cents 1: 1 349/327 112.724 cents 1: 1 109/90 331.597 cents 2: 1 120/109 166.448 cents 2: 1 436/349 385.321 cents 2: 1 349/270 444.321 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 : 53.7 166.4 498.0 53.7 : 112.7 444.3 498.0 166.4: 331.6 385.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 53.7238 .. 331.5975 cents 38041/32400, 277.8736 cents 360/349, 53.7238 cents 2: 166.4475 .. 444.3212 cents 38041/32400, 277.8736 cents 10800/11881,-165.1499 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 360/349, 53.7238 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 109/90, 331.5975 cents Average / Smallest step : 3.090155 Largest / Average step : 1.997395 Largest / Smallest step : 6.172259 Median interval of one step : 349/327, 112.7237 cents, amount: 1 Least squares average step : 134.33956 cents, oct.: 403.01869 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 53.72384 cents Scale diversity : 0.832797 Lumma stability : 0.215739 Lumma impropriety factor : 0.331596 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 : 360/349, 53.7238 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 : 349 Odd number limit : 349 (O: 349 U: 349) Highest odd numerator or denominator: 349 Scale harmonicity : 0.057471 Fundamental : 1/114123, -16.8002 octaves, 0.0023 Hz. Guide tone : 360, 8.4919 octaves, 94185.204 Hz. Exponens Consonantiae : 4.108428E+07, 25.29208 octaves Euler's gradus suavitatis : 470 Sum of Mann's harmonic distance : 472.5, average 157.50000 Mersenne's string divisions : 1136527 Sum of van Prooijen's expressibility: 5.05737, average 1.68579 Sum of Tenney's harmonic distance : 10.29492, average 3.43164 Vogel's harmonic complexity : 316.33333 Wille's k value : 19020 Wilson's harmonic complexity : 472 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 16.06046, average 2.67674 Lattice compactness (without 2's) : 11.04863, average 1.84144 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -1 .. 2 0.66667 4 1 5: 0 .. 1 0.66667 2 109: -1 .. 0 -0.33333 1 1 349: -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 11 15 48 60| Scale is weakly epimorphic with val: <7 11 15 49 62| Scale is weakly epimorphic with val: <7 11 16 49 61| Scale is weakly epimorphic with val: <7 11 16 50 60| Scale is weakly epimorphic with val: <7 11 17 48 61| Scale is weakly epimorphic with val: <7 11 17 50 62| Scale is JI-epimorphic with val: <7 11 18 48 60| Scale is weakly epimorphic with val: <7 11 18 49 62| Scale is JI-epimorphic with val: <7 11 19 49 61| Scale is weakly epimorphic with val: <7 11 19 50 60| Scale is weakly epimorphic with val: <7 12 18 48 62| Scale is weakly epimorphic with val: <7 12 18 50 60| Scale is weakly epimorphic with val: <7 12 19 48 61| Scale is weakly epimorphic with val: <7 12 19 49 60| Scale is weakly epimorphic with val: <8 11 16 48 61| Scale is weakly epimorphic with val: <8 11 17 48 60| Scale is weakly epimorphic with val: <8 11 17 49 62| Scale is weakly epimorphic with val: <8 11 18 49 61| Scale is weakly epimorphic with val: <8 11 18 50 60| Scale is weakly epimorphic with val: <8 11 19 50 62| Scale is weakly epimorphic with val: <8 12 15 48 61| Scale is weakly epimorphic with val: <8 12 15 49 60| Scale is weakly epimorphic with val: <8 12 16 49 62| Scale is weakly epimorphic with val: <8 12 16 50 61| Scale is weakly epimorphic with val: <8 12 17 48 62| Scale is weakly epimorphic with val: <8 12 17 50 60|
FIT/MODE
3: 0 1 2 N G T3 SD: 31.0185 c. M: 53.7238 c. 6: 1 1 4 N M DE S SD: 16.9088 c. M:-29.2837 c. 7: 1 1 5 N M DE S SD: 17.1932 c. M: 24.1490 c. 8: 1 2 5 N T3 SD: 12.7236 c. M:-20.3193 c. 9: 1 2 6 N T3 SD: 0.9650 c. M:-1.6145 c. 48: 5 11 32 N T3 SD: 1.0936 c. M: 1.8442 c. 57: 6 13 38 N T3 SD: 0.7899 c. M: 1.2981 c. 66: 7 15 44 N T3 SD: 0.5770 c. M: 0.9009 c. 75: 8 17 50 N T3 SD: 0.4266 c. M: 0.5990 c. 84: 9 19 56 N T3 SD: 0.3256 c. M: 0.4325 c. 93: 10 21 62 N T3 SD: 0.2684 c. M: 0.4325 c. 102: 11 23 68 N T3 SD: 0.2498 c. M: 0.4325 c. 177: 19 40 118 N T3 SD: 0.2918 c. M: 0.4325 c. 185: 20 42 123 N T3 SD: 0.2770 c. M:-0.4649 c. 194: 21 44 129 N T3 SD: 0.2674 c. M:-0.4232 c. 195: 21 44 130 N T3 SD: 0.2549 c. M: 0.4325 c. 203: 22 46 135 N T3 SD: 0.2656 c. M:-0.3853 c. 212: 23 48 141 N T3 SD: 0.2699 c. M:-0.3506 c. 213: 23 48 142 N T3 SD: 0.2518 c. M: 0.4325 c. 233: 25 53 155 N T3 SD: 0.2309 c. M: 0.2855 c. 242: 26 55 161 N T3 SD: 0.1919 c. M:-0.2535 c. 251: 27 57 167 N T3 SD: 0.1578 c. M:-0.2289 c. 260: 28 59 173 N T3 SD: 0.1294 c. M:-0.2060 c. 269: 29 61 179 N T3 SD: 0.1081 c. M:-0.1846 c. 278: 30 63 185 N T3 SD: 0.0959 c. M:-0.1647 c. 287: 31 65 191 N T3 SD: 0.0939 c. M:-0.1459 c. 296: 32 67 197 N T3 SD: 0.1010 c. M:-0.1283 c. 344: 37 78 229 N T3 SD: 0.0941 c. M: 0.1551 c. 353: 38 80 235 N T3 SD: 0.0671 c. M: 0.1099 c. 362: 39 82 241 N T3 SD: 0.0415 c. M: 0.0671 c. 371: 40 84 247 N T3 SD: 0.0175 c. M: 0.0263 c. 380: 41 86 253 N T3 SD: 0.0077 c. M:-0.0126 c. 751: 81 170 500 N T3 SD: 0.0067 c. M:-0.0096 c. 1131: 122 256 753 N T3 SD: 0.0045 c. M:-0.0078 c. 1511: 163 342 1006 N T3 SD: 0.0044 c. M:-0.0070 c. 1891: 204 428 1259 N T3 SD: 0.0047 c. M:-0.0064 c. 2271: 245 514 1512 N T3 SD: 0.0050 c. M:-0.0062 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: 85.7226 cents 6 x 7:8 S SD: 50.2117 cents 7 x 8:9 S SD: 45.1487 cents 8 x 9:11 SD: 32.5632 cents 9 x 10:12 S SD: 7.9781 cents 10 x 11:13 SD: 21.9274 cents 11 x 12:15 S SD: 20.9978 cents 12 x 13:16 SD: 13.9374 cents 13 x 14:17 SD: 25.4238 cents 14 x 15:19 SD: 28.0552 cents 15 x 17:20 SD: 25.1196 cents 16:17:18:21 S SD: 23.0252 cents 17:18:19:23 SD: 19.3400 cents 18:19:20:24 S SD: 14.3176 cents 19:20:21:25 SD: 14.1528 cents 20:21:22:27 SD: 12.5156 cents 21:22:23:28 SD: 9.4229 cents 27:28:30:36 S SD: 6.1457 cents 29:30:32:39 SD: 5.3884 cents 30:31:33:40 SD: 1.1226 cents 99:102:109:132 SD: 0.6822 cents 129:133:142:172 SD: 0.2954 cents 159:164:175:212 SD: 0.1565 cents