Scala analysis: 539_M47
Miscellaneous tetrachord 24/23 * 115/96 * 16/15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 24/23 73.680654 vicesimotertial minor semitone 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 24/23 73.6807 vicesimotertial minor semitone 2: 115/96 312.6331 3: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 24/23 73.681 cents vicesimotertial minor semitone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 115/96 312.633 cents 2: 1 128/115 185.412 cents 2: 1 5/4 386.314 cents major third 2: 1 23/18 424.364 cents vicesimotertial major third 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 : 73.7 386.3 498.0 73.7 : 312.6 424.4 498.0 386.3: 111.7 185.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.6807 .. 312.6331 cents 2645/2304, 238.9524 cents 24/23, 73.6807 cents 2: 185.4119 .. 424.3643 cents 2645/2304, 238.9524 cents 12288/13225,-127.2211 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 24/23, 73.6807 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 115/96, 312.6331 cents Average / Smallest step : 2.253169 Largest / Average step : 1.883162 Largest / Smallest step : 4.243082 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Least squares average step : 167.17451 cents, oct.: 501.52352 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2055-tone equal temperament with octave 4/3 degrees: 304 1594 2055 Least number of segments generator : 1028 of 249.144 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1079 of 261.504 cents and inv. generated superset size: 46 = 43 more = 1533.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 73.68065 cents Scale diversity : 0.999350 Lumma stability : 0.295880 Lumma impropriety factor : 0.255441 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 : 46/45, 38.0506 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 -- Rational properties -- Prime limit : 23 Odd number limit : 115 (O: 115 U: 115) Highest odd numerator or denominator: 23 Scale harmonicity : 0.017001 Average absolute harmonicity : 0.118091 Specific harmonicity : 0.089655 Fundamental : 1/276, -8.1085 octaves, 0.9479 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 3.312000E+04, 15.01542 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 31.5, average 10.50000 Mersenne's string divisions : 2961 Sum of van Prooijen's expressibility: 2.53782, average 0.84594 Sum of Tenney's harmonic distance : 5.12215, average 1.70738 Vogel's harmonic complexity : 23.00000 Wille's k value : 172 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 19.77239, average 3.29540 Lattice compactness (without 2's) : 8.79655, average 1.46609 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 1.00000 7 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.33333 1 1 23: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is weakly epimorphic with val: <6 10 15 30| Scale is weakly epimorphic with val: <6 10 15 33| Scale is weakly epimorphic with val: <6 10 15 36| Scale is weakly epimorphic with val: <6 11 15 30| Scale is weakly epimorphic with val: <6 11 15 33| Scale is weakly epimorphic with val: <6 11 15 36| Scale is weakly epimorphic with val: <7 10 17 32| Scale is weakly epimorphic with val: <7 10 17 35| Scale is weakly epimorphic with val: <7 11 15 30| Scale is weakly epimorphic with val: <7 11 15 33| Scale is weakly epimorphic with val: <7 11 15 36| Scale is JI-epimorphic with val: <7 11 16 31| Scale is weakly epimorphic with val: <7 11 16 34| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 11 18 33| Scale is weakly epimorphic with val: <7 11 18 36| Scale is weakly epimorphic with val: <7 11 19 31| Scale is weakly epimorphic with val: <7 11 19 34| Scale is weakly epimorphic with val: <7 12 15 30| Scale is weakly epimorphic with val: <7 12 17 32| Scale is weakly epimorphic with val: <7 12 17 35| Scale is weakly epimorphic with val: <7 12 18 30| Scale is weakly epimorphic with val: <8 11 17 32| Scale is weakly epimorphic with val: <8 11 19 31| Scale is weakly epimorphic with val: <8 11 19 34| Scale is weakly epimorphic with val: <8 12 15 33| Scale is weakly epimorphic with val: <8 12 18 33| Scale is weakly epimorphic with val: <8 12 19 31| Scale is weakly epimorphic with val: <8 12 19 34|
FIT/MODE
3: 0 2 1 N G T3 SD: 52.8380 c. M: 73.6807 c. 4: 1 2 1 P M ME I SD: 30.2604 c. M:-50.8306 c. 5: 1 3 1 N M DE I SD: 16.5250 c. M:-25.9283 c. 8: 1 5 2 N T3 SD: 9.8971 c. M: 12.7800 c. 12: 2 7 3 N T3 SD: 9.1345 c. M: 12.7800 c. 13: 2 8 3 N T3 SD: 2.5105 c. M: 3.2022 c. 27: 4 17 6 N T3 SD: 0.6118 c. M:-1.0546 c. 40: 6 25 9 N T3 SD: 0.6221 c. M:-1.0261 c. 67: 10 42 15 N T3 SD: 0.4002 c. M:-0.6544 c. 94: 14 59 21 N T3 SD: 0.3930 c. M:-0.4963 c. 129: 19 81 29 N T3 SD: 0.2307 c. M: 0.3252 c. 156: 23 98 35 N T3 SD: 0.1450 c. M: 0.2509 c. 183: 27 115 41 N T3 SD: 0.1428 c. M: 0.1986 c. 196: 29 123 44 N T3 SD: 0.0435 c. M: 0.0747 c. 223: 33 140 50 N T3 SD: 0.0378 c. M:-0.0620 c. 419: 62 263 94 N T3 SD: 0.0092 c. M:-0.0157 c. 1413: 209 887 317 N T3 SD: 0.0081 c. M: 0.0137 c. 1609: 238 1010 361 N T3 SD: 0.0092 c. M: 0.0116 c. 1636: 242 1027 367 N T3 SD: 0.0062 c. M: 0.0090 c. 1832: 271 1150 411 N T3 SD: 0.0043 c. M: 0.0070 c. 2055: 304 1290 461 N T3 SD: 0.0034 c. M:-0.0044 c. 2251: 333 1413 505 N T3 SD: 0.0021 c. M: 0.0027 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 5 x S SD: 0.0000 cents 5 x 6:7 S SD: 55.0665 cents 6 x x 8 S SD: 0.0000 cents 7 x 9 x SD: 48.7704 cents 8:9:10:11 H SD: 46.9014 cents 9:10:11:12 H SD: 38.4915 cents 10:11 x 13 SD: 50.6487 cents 11:12:14:15 S SD: 30.5669 cents 12:13:15:16 SD: 21.6307 cents 15:16:19:20 SD: 14.8086 cents 16:17:20:21 SD: 13.8301 cents 17:18:21:23 SD: 13.7328 cents 19:20:24:25 S SD: 10.9700 cents 20:21:25:27 SD: 8.0199 cents 21:22:26:28 SD: 5.9766 cents 24:25:30:32 S SD: 1.0027 cents 141:147:176:188 SD: 0.9659 cents 156:163:195:208 SD: 0.7702 cents 180:188:225:240 SD: 0.5341 cents 204:213:255:272 SD: 0.3535 cents 228:238:285:304 SD: 0.2109 cents 252:263:315:336 SD: 0.0954 cents 276:288:345:368 SD: 0.0000 cents