Scala analysis: 543_M51
Miscellaneous tetrachord 15/14 * 266/255 * 68/57
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 19/17 192.557607 quasi-meantone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 68/57 305.4874 1: 15/14 119.4428 major diatonic semitone 2: 266/255 73.1148 3: 68/57 305.4874
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 266/255 73.115 cents 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 68/57 305.487 cents 2: 1 19/17 192.558 cents quasi-meantone 2: 1 56/45 378.602 cents septimal narrow major third 2: 1 170/133 424.930 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 : 119.4 192.6 498.0 119.4: 73.1 378.6 498.0 192.6: 305.5 424.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.1148 .. 305.4874 cents 2890/2527, 232.3726 cents 266/255, 73.1148 cents 2: 192.5576 .. 424.9302 cents 2890/2527, 232.3726 cents 1083/1156,-112.9298 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 266/255, 73.1148 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 68/57, 305.4874 cents Average / Smallest step : 2.270607 Largest / Average step : 1.840119 Largest / Smallest step : 4.178188 Median interval of one step : 15/14, 119.4428 cents, amount: 1 Least squares average step : 142.76379 cents, oct.: 428.29136 cents Scale is not proper Scale has trivalence property Scale is a mode of a 688-tone equal temperament with octave 4/3 degrees: 165 266 688 Least number of segments generator : 345 of 249.746 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 477 of 345.302 cents and inv. generated superset size: 10 = 7 more = 333.333% 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 73.11480 cents Scale diversity : 1.022048 Lumma stability : 0.293607 Lumma impropriety factor : 0.226746 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 : 3825/3724, 46.3280 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% -- Rational properties -- Prime limit : 19 Odd number limit : 255 (O: 133 U: 255) Highest odd numerator or denominator: 19 Scale harmonicity : 0.011205 Average absolute harmonicity : 0.092996 Specific harmonicity : 0.059762 Fundamental : 1/714, -9.4798 octaves, 0.3664 Hz. Guide tone : 1140, 10.1548 octaves, 298253.144 Hz. Exponens Consonantiae : 8.139600E+05, 19.63460 octaves Euler's gradus suavitatis : 52 Sum of Mann's harmonic distance : 36.0, average 12.00000 Mersenne's string divisions : 7308 Sum of van Prooijen's expressibility: 2.93197, average 0.97732 Sum of Tenney's harmonic distance : 5.91060, average 1.97020 Vogel's harmonic complexity : 28.33333 Wille's k value : 382 Wilson's harmonic complexity : 54 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 14.61851, average 2.43642 Lattice compactness (without 2's) : 10.56387, average 1.76065 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.33333 1 7: -1 .. 0 -0.33333 1 1 17: -1 .. 0 -0.33333 1 19: 0 .. 1 0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is JI-epimorphic with val: <7 11 16 19 29 31| Scale is JI-epimorphic with val: <7 11 16 19 30 32| Scale is weakly epimorphic with val: <7 11 16 21 29 30| Scale is weakly epimorphic with val: <7 11 16 21 30 31| Scale is weakly epimorphic with val: <7 11 16 21 31 32| Scale is weakly epimorphic with val: <7 11 17 19 29 30| Scale is weakly epimorphic with val: <7 11 17 19 30 31| Scale is weakly epimorphic with val: <7 11 17 19 31 32| Scale is JI-epimorphic with val: <7 11 17 20 29 31| Scale is JI-epimorphic with val: <7 11 17 20 30 32| Scale is weakly epimorphic with val: <7 11 18 20 29 30| Scale is weakly epimorphic with val: <7 11 18 20 30 31| Scale is weakly epimorphic with val: <7 11 18 20 31 32| Scale is JI-epimorphic with val: <7 11 18 21 29 31| Scale is JI-epimorphic with val: <7 11 18 21 30 32| Scale is weakly epimorphic with val: <7 12 16 20 29 32| Scale is weakly epimorphic with val: <7 12 17 19 29 30| Scale is weakly epimorphic with val: <7 12 17 19 30 31| Scale is weakly epimorphic with val: <7 12 17 19 31 32| Scale is weakly epimorphic with val: <7 12 17 21 29 32| Scale is weakly epimorphic with val: <7 12 18 19 29 32| Scale is weakly epimorphic with val: <7 12 18 20 29 30| Scale is weakly epimorphic with val: <7 12 18 20 30 31| Scale is weakly epimorphic with val: <7 12 18 20 31 32|
FIT/MODE
3: 1 0 2 N G T3 SD: 30.9488 c. M:-46.5722 c. 4: 1 1 2 P M ME S SD: 32.7311 c. M:-56.4649 c. 5: 1 1 3 N M DE S SD: 12.0795 c. M: 19.8338 c. 8: 2 1 5 N T3 SD: 4.4430 c. M: 5.7907 c. 13: 3 2 8 N T3 SD: 2.6670 c. M: 4.5093 c. 21: 5 3 13 N T3 SD: 1.7057 c. M: 2.8262 c. 34: 8 5 21 N T3 SD: 1.7907 c. M: 2.2557 c. 41: 10 6 25 N T3 SD: 1.5676 c. M:-2.0316 c. 46: 11 7 28 N T3 SD: 1.3597 c. M:-2.3296 c. 54: 13 8 33 N T3 SD: 0.7019 c. M:-1.1266 c. 62: 15 9 38 N T3 SD: 0.6222 c. M:-1.0519 c. 67: 16 10 41 N T3 SD: 0.5053 c. M:-0.7136 c. 75: 18 11 46 N T3 SD: 0.0521 c. M:-0.0880 c. 388: 93 57 238 N T3 SD: 0.0390 c. M: 0.0660 c. 463: 111 68 284 N T3 SD: 0.0243 c. M: 0.0411 c. 538: 129 79 330 N T3 SD: 0.0136 c. M: 0.0231 c. 613: 147 90 376 N T3 SD: 0.0056 c. M: 0.0095 c. 688: 165 101 422 N T3 SD: 0.0007 c. M:-0.0011 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: 74.6396 cents 6 x 7:8 S SD: 37.1566 cents 7 x 8:9 S SD: 36.9300 cents 8 x 9:11 SD: 27.2346 cents 9 x 10:12 S SD: 5.0769 cents 10 x 11:13 SD: 25.8860 cents 11:12 x 15 S SD: 24.9336 cents 12:13 x 16 SD: 9.5649 cents 15:16:17:20 SD: 8.4438 cents 21 x 23:28 SD: 17.5321 cents 22:24:25:29 SD: 15.6035 cents 23:25:26:31 SD: 12.2870 cents 24:26:27:32 SD: 7.4149 cents 26:28:29:35 SD: 6.3700 cents 27:29:30:36 SD: 3.6717 cents 42:45:47:56 SD: 0.7227 cents 111:119:124:148 SD: 0.4415 cents 153:164:171:204 SD: 0.2514 cents 195:209:218:260 SD: 0.2513 cents 348:373:389:464 SD: 0.2377 cents 366:392:409:488 SD: 0.2261 cents 408:437:456:544 SD: 0.1886 cents 450:482:503:600 SD: 0.1838 cents 477:511:533:636 SD: 0.1508 cents 519:556:580:692 SD: 0.0944 cents 561:601:627:748 SD: 0.0686 cents