Scala analysis: 555_M63
Miscellaneous tetrachord 34/29 * 58/57 * 19/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 34/29 275.378215 2: 68/57 305.487393 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 19/17 192.5576 quasi-meantone 1: 34/29 275.3782 2: 58/57 30.1092 3: 19/17 192.5576 quasi-meantone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 58/57 30.109 cents 1: 1 19/17 192.558 cents quasi-meantone 1: 1 34/29 275.378 cents 2: 1 58/51 222.667 cents 2: 1 68/57 305.487 cents 2: 1 38/29 467.936 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 : 275.4 305.5 498.0 275.4: 30.1 222.7 498.0 305.5: 192.6 467.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 30.1092 .. 275.3782 cents 969/841, 245.2690 cents 58/57, 30.1092 cents 2: 222.6668 .. 467.9358 cents 969/841, 245.2690 cents 841/867,-52.7114 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 58/57, 30.1092 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 34/29, 275.3782 cents Average / Smallest step : 5.513767 Largest / Average step : 1.658755 Largest / Smallest step : 9.145989 Median interval of one step : 19/17, 192.5576 cents, amount: 1 Least squares average step : 170.03486 cents, oct.: 510.10457 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1720-tone equal temperament with octave 4/3 degrees: 951 1055 1720 Least number of segments generator : 861 of 249.312 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 873 of 252.787 cents and inv. generated superset size: 16 = 13 more = 533.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LSM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 30.10918 cents Scale diversity : 0.612814 Lumma stability : 0.120909 Lumma impropriety factor : 0.105837 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 : 58/57, 30.1092 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 29 Odd number limit : 57 (O: 29 U: 57) Highest odd numerator or denominator: 57 Scale harmonicity : 0.008133 Average absolute harmonicity : 0.080180 Specific harmonicity : 0.039735 Fundamental : 1/1653, -10.6909 octaves, 0.1583 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 1.124040E+05, 16.77833 octaves Euler's gradus suavitatis : 67 Sum of Mann's harmonic distance : 97.5, average 32.50000 Mersenne's string divisions : 7875 Sum of van Prooijen's expressibility: 3.69539, average 1.23180 Sum of Tenney's harmonic distance : 7.66144, average 2.55381 Vogel's harmonic complexity : 46.00000 Wille's k value : 484 Wilson's harmonic complexity : 68 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 12.02808, average 2.00468 Lattice compactness (without 2's) : 9.02458, average 1.50410 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 0 -0.66667 2 1 17: 0 .. 1 0.66667 2 19: -1 .. 0 -0.33333 1 1 29: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 29 30 32| Scale is weakly epimorphic with val: <6 10 30 31 33| Scale is weakly epimorphic with val: <6 10 31 32 34| Scale is weakly epimorphic with val: <6 10 32 33 35| Scale is weakly epimorphic with val: <6 10 33 34 36| Scale is weakly epimorphic with val: <6 11 29 31 32| Scale is weakly epimorphic with val: <6 11 30 32 33| Scale is weakly epimorphic with val: <6 11 31 33 34| Scale is weakly epimorphic with val: <6 11 32 34 35| Scale is weakly epimorphic with val: <7 10 27 28 32| Scale is weakly epimorphic with val: <7 10 27 28 35| Scale is weakly epimorphic with val: <7 10 27 28 38| Scale is weakly epimorphic with val: <7 10 28 29 33| Scale is weakly epimorphic with val: <7 10 28 29 36| Scale is weakly epimorphic with val: <7 10 28 30 32| Scale is weakly epimorphic with val: <7 10 29 30 34| Scale is weakly epimorphic with val: <7 10 29 30 37| Scale is weakly epimorphic with val: <7 10 29 31 33| Scale is weakly epimorphic with val: <7 10 30 31 32| Scale is weakly epimorphic with val: <7 10 30 31 35| Scale is weakly epimorphic with val: <7 10 30 31 38| Scale is weakly epimorphic with val: <7 10 30 32 34| Scale is weakly epimorphic with val: <7 10 31 32 33| Scale is weakly epimorphic with val: <7 10 31 32 36| Scale is weakly epimorphic with val: <7 10 31 33 35| Scale is weakly epimorphic with val: <7 10 32 33 34| Scale is weakly epimorphic with val: <7 10 32 33 37| Scale is weakly epimorphic with val: <7 10 32 34 36| Scale is weakly epimorphic with val: <7 10 33 34 35| Scale is weakly epimorphic with val: <7 10 33 34 38| Scale is JI-epimorphic with val: <7 11 27 28 33| Scale is weakly epimorphic with val: <7 11 27 28 36| Scale is weakly epimorphic with val: <7 11 27 29 32| Scale is weakly epimorphic with val: <7 11 27 29 35| Scale is weakly epimorphic with val: <7 11 27 29 38| Scale is weakly epimorphic with val: <7 11 27 31 33| Scale is weakly epimorphic with val: <7 11 27 31 36| Scale is weakly epimorphic with val: <7 11 27 32 32| Scale is weakly epimorphic with val: <7 11 27 32 35| Scale is weakly epimorphic with val: <7 11 27 32 38| Scale is weakly epimorphic with val: <7 11 27 34 36| Scale is JI-epimorphic with val: <7 11 28 29 34| Scale is weakly epimorphic with val: <7 11 28 29 37| Scale is weakly epimorphic with val: <7 11 28 30 33| Scale is weakly epimorphic with val: <7 11 28 30 36| Scale is weakly epimorphic with val: <7 11 28 32 34| Scale is weakly epimorphic with val: <7 11 28 32 37| Scale is weakly epimorphic with val: <7 11 28 33 33| Scale is weakly epimorphic with val: <7 11 28 33 36| Scale is weakly epimorphic with val: <7 11 29 30 32| Scale is JI-epimorphic with val: <7 11 29 30 35| Scale is weakly epimorphic with val: <7 11 29 30 38| Scale is weakly epimorphic with val: <7 11 29 31 34| Scale is weakly epimorphic with val: <7 11 29 31 37| Scale is weakly epimorphic with val: <7 11 29 33 35| Scale is weakly epimorphic with val: <7 11 29 33 38| Scale is weakly epimorphic with val: <7 11 29 34 34| Scale is weakly epimorphic with val: <7 11 29 34 37| Scale is weakly epimorphic with val: <7 11 30 31 33| Scale is JI-epimorphic with val: <7 11 30 31 36| Scale is weakly epimorphic with val: <7 11 30 32 32| Scale is weakly epimorphic with val: <7 11 30 32 35| Scale is weakly epimorphic with val: <7 11 30 32 38| Scale is weakly epimorphic with val: <7 11 30 34 36| Scale is weakly epimorphic with val: <7 11 31 32 34| Scale is JI-epimorphic with val: <7 11 31 32 37| Scale is weakly epimorphic with val: <7 11 31 33 33| Scale is weakly epimorphic with val: <7 11 31 33 36| Scale is weakly epimorphic with val: <7 11 32 33 35| Scale is JI-epimorphic with val: <7 11 32 33 38| Scale is weakly epimorphic with val: <7 11 32 34 34| Scale is weakly epimorphic with val: <7 11 32 34 37| Scale is weakly epimorphic with val: <7 11 33 34 36| Scale is weakly epimorphic with val: <7 12 28 29 32| Scale is weakly epimorphic with val: <7 12 28 32 32| Scale is weakly epimorphic with val: <7 12 29 30 33| Scale is weakly epimorphic with val: <7 12 29 33 33| Scale is weakly epimorphic with val: <7 12 30 31 34| Scale is weakly epimorphic with val: <7 12 30 34 34| Scale is weakly epimorphic with val: <7 12 31 32 35| Scale is weakly epimorphic with val: <7 12 32 33 36| Scale is weakly epimorphic with val: <7 12 33 34 37| Scale is weakly epimorphic with val: <8 11 27 28 32| Scale is weakly epimorphic with val: <8 11 27 29 34| Scale is weakly epimorphic with val: <8 11 27 29 37| Scale is weakly epimorphic with val: <8 11 27 31 32| Scale is weakly epimorphic with val: <8 11 28 29 33| Scale is weakly epimorphic with val: <8 11 28 30 32| Scale is weakly epimorphic with val: <8 11 28 30 35| Scale is weakly epimorphic with val: <8 11 28 30 38| Scale is weakly epimorphic with val: <8 11 28 32 33| Scale is weakly epimorphic with val: <8 11 29 30 34| Scale is weakly epimorphic with val: <8 11 29 31 33| Scale is weakly epimorphic with val: <8 11 29 31 36| Scale is weakly epimorphic with val: <8 11 29 33 34| Scale is weakly epimorphic with val: <8 11 30 31 35| Scale is weakly epimorphic with val: <8 11 30 32 34| Scale is weakly epimorphic with val: <8 11 30 32 37| Scale is weakly epimorphic with val: <8 11 30 34 35| Scale is weakly epimorphic with val: <8 11 31 32 36| Scale is weakly epimorphic with val: <8 11 31 33 35| Scale is weakly epimorphic with val: <8 11 31 33 38| Scale is weakly epimorphic with val: <8 11 32 33 37| Scale is weakly epimorphic with val: <8 11 32 34 36| Scale is weakly epimorphic with val: <8 11 33 34 38| Scale is weakly epimorphic with val: <8 12 27 28 33| Scale is weakly epimorphic with val: <8 12 27 28 36| Scale is weakly epimorphic with val: <8 12 27 29 32| Scale is weakly epimorphic with val: <8 12 27 32 32| Scale is weakly epimorphic with val: <8 12 28 29 34| Scale is weakly epimorphic with val: <8 12 28 29 37| Scale is weakly epimorphic with val: <8 12 28 30 33| Scale is weakly epimorphic with val: <8 12 28 33 33| Scale is weakly epimorphic with val: <8 12 29 30 32| Scale is weakly epimorphic with val: <8 12 29 30 35| Scale is weakly epimorphic with val: <8 12 29 30 38| Scale is weakly epimorphic with val: <8 12 29 31 34| Scale is weakly epimorphic with val: <8 12 29 34 34| Scale is weakly epimorphic with val: <8 12 30 31 33| Scale is weakly epimorphic with val: <8 12 30 31 36| Scale is weakly epimorphic with val: <8 12 30 32 35| Scale is weakly epimorphic with val: <8 12 31 32 34| Scale is weakly epimorphic with val: <8 12 31 32 37| Scale is weakly epimorphic with val: <8 12 31 33 36| Scale is weakly epimorphic with val: <8 12 32 33 35| Scale is weakly epimorphic with val: <8 12 32 33 38| Scale is weakly epimorphic with val: <8 12 32 34 37| Scale is weakly epimorphic with val: <8 12 33 34 36|
FIT/MODE
3: 2 0 1 N G T3 SD: 36.1199 c. M:-56.6518 c. 4: 2 0 2 P M DE I SD: 35.9764 c. M: 56.4649 c. 5: 3 0 2 N G T3 SD: 14.0737 c. M:-23.4488 c. 7: 4 0 3 N G T3 SD: 13.1832 c. M: 20.8903 c. 9: 5 1 3 N T3 SD: 15.3431 c. M:-26.5426 c. 10: 5 1 4 P T3 SD: 15.6948 c. M: 26.3557 c. 11: 6 1 4 N T3 SD: 6.9505 c. M:-11.4503 c. 13: 7 1 5 N T3 SD: 4.1970 c. M: 7.2001 c. 16: 9 1 6 N T3 SD: 4.3323 c. M:-5.7907 c. 18: 10 1 7 N T3 SD: 0.9990 c. M:-1.3135 c. 47: 26 3 18 N T3 SD: 1.0520 c. M:-1.8170 c. 49: 27 3 19 N T3 SD: 0.6349 c. M: 0.9453 c. 67: 37 4 26 N T3 SD: 0.4560 c. M: 0.7136 c. 83: 46 5 32 N T3 SD: 0.4865 c. M:-0.6467 c. 85: 47 5 33 N T3 SD: 0.4625 c. M: 0.8010 c. 96: 53 6 37 N T3 SD: 0.4228 c. M:-0.6028 c. 114: 63 7 44 N T3 SD: 0.2075 c. M:-0.3297 c. 132: 73 8 51 N T3 SD: 0.0823 c. M:-0.1311 c. 313: 173 19 121 N T3 SD: 0.0597 c. M: 0.1009 c. 331: 183 20 128 N T3 SD: 0.0269 c. M: 0.0399 c. 463: 256 28 179 N T3 SD: 0.0052 c. M:-0.0089 c. 1257: 695 76 486 N T3 SD: 0.0048 c. M: 0.0073 c. 1720: 951 104 665 N T3 SD: 0.0033 c. M: 0.0057 c. 2183: 1207 132 844 N T3 SD: 0.0029 c. M: 0.0047 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: 80.8263 cents 5 x 6:7 S SD: 42.5377 cents 6:7 x 8 S SD: 4.2537 cents 7:8 x 9 S SD: 38.4645 cents 9 x 11:12 SD: 20.9603 cents 10 x 12:13 S SD: 22.4959 cents 11:13 x 15 SD: 20.6456 cents 12:14 x 16 S SD: 4.2537 cents 15 x 18:20 S SD: 5.0769 cents 16 x 19:21 SD: 14.2032 cents 17:20 x 23 SD: 12.9859 cents 18:21 x 24 S SD: 4.2537 cents 21 x 25:28 SD: 1.8204 cents 22:26 x 29 SD: 12.0705 cents 23:27 x 31 SD: 9.4233 cents 24:28:29:32 SD: 7.9045 cents 27 x 32:36 SD: 5.6762 cents 28:33 x 37 SD: 8.9906 cents 29:34:35:39 SD: 8.3256 cents 30:35:36:40 S SD: 4.4156 cents 32 x 38:43 SD: 7.8279 cents 33:39 x 44 SD: 6.9158 cents 35:41:42:47 SD: 5.3443 cents 36:42:43:48 SD: 2.9225 cents 38 x 45:51 SD: 8.5458 cents 39:46:47:52 SD: 6.7985 cents 40:47:48:53 SD: 5.1150 cents 41:48:49:55 SD: 3.7500 cents 42:49:50:56 SD: 3.0846 cents 44:52 x 59 SD: 8.4782 cents 45:53:54:60 SD: 4.2889 cents 46:54:55:61 SD: 3.4782 cents 47:55:56:63 SD: 3.3272 cents 51:60:61:68 SD: 2.4921 cents 57:67:68:76 SD: 1.4869 cents 87:102:104:116 SD: 1.1694 cents 93:109:111:124 SD: 0.3290 cents 192:225:229:256 SD: 0.2966 cents 243:285:290:324 SD: 0.2963 cents 249:292:297:332 SD: 0.1704 cents 342:401:408:456 SD: 0.0496 cents