Scala analysis: 548_M56
Miscellaneous tetrachord 7168/6561 * 36/35 * 1215/1024
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7168/6561 153.185900 2: 4096/3645 201.956281 narrow diminished third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 1215/1024 296.0887 wide augmented second 1: 7168/6561 153.1859 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 1215/1024 296.0887 wide augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 7168/6561 153.186 cents 1: 1 1215/1024 296.089 cents wide augmented second 2: 1 4096/3645 201.956 cents narrow diminished third 2: 1 2187/1792 344.859 cents 2: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 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 : 153.2 202.0 498.0 153.2: 48.8 344.9 498.0 202.0: 296.1 449.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 296.0887 cents 4725/4096, 247.3183 cents 36/35, 48.7704 cents 2: 201.9563 .. 449.2746 cents 4725/4096, 247.3183 cents 4194304/4428675,-94.1324 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 1215/1024, 296.0887 cents Average / Smallest step : 3.404013 Largest / Average step : 1.783506 Largest / Smallest step : 6.071077 Median interval of one step : 7168/6561, 153.1859 cents, amount: 1 Least squares average step : 146.51668 cents, oct.: 439.55003 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1307-tone equal temperament with octave 4/3 degrees: 402 530 1307 Least number of segments generator : 654 of 249.213 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 914 of 348.289 cents and inv. generated superset size: 12 = 9 more = 400.000% 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 48.77038 cents Scale diversity : 0.858015 Lumma stability : 0.195847 Lumma impropriety factor : 0.189004 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 : 36/35, 48.7704 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 : 7 Odd number limit : 6561 (O: 2187 U: 6561) Highest odd numerator or denominator: 6561 Scale harmonicity : 0.019992 Average absolute harmonicity : 0.089127 Specific harmonicity : 0.093354 Fundamental : 1/32805, -15.0016 octaves, 0.0080 Hz. Guide tone : 28672, 14.8074 octaves, 7501328.208 Hz. Exponens Consonantiae : 9.405850E+08, 29.80898 octaves Euler's gradus suavitatis : 39 Sum of Mann's harmonic distance : 10738.5, average 3579.50000 Mersenne's string divisions : 743933323 Sum of van Prooijen's expressibility: 7.85579, average 2.61860 Sum of Tenney's harmonic distance : 15.92561, average 5.30854 Vogel's harmonic complexity : 22.66667 Wille's k value : 5467 Wilson's harmonic complexity : 36 Rectangular lattice diameter : 10 Triangular lattice diameter : 7 Lattice compactness : 53.59925, average 8.93321 Lattice compactness (without 2's) : 29.76460, average 4.96077 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 12 8.00000 24 3: -8 ..-1 -5.00000 15 1 5: -1 .. 0 -0.33333 1 1 7: 0 .. 1 0.33333 1 1 Average exponent except 2's :-15 / 3 =-5.00000 Average absolute exponent except 2's: 17 / 3 = 5.66667 Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 11 16 22| Scale is weakly epimorphic with val: <7 11 17 20| = patent Scale is weakly epimorphic with val: <7 11 19 19| Scale is weakly epimorphic with val: <7 11 19 22| Scale is weakly epimorphic with val: <8 12 16 19| Scale is weakly epimorphic with val: <8 12 19 19|
FIT/MODE
3: 1 0 2 N G T3 SD: 22.0330 c. M: 35.9413 c. 7: 2 1 4 N T3 SD: 9.1395 c. M:-11.4916 c. 10: 3 1 6 N T3 SD: 2.6913 c. M: 3.7724 c. 29: 9 3 17 N T3 SD: 2.5147 c. M:-4.1313 c. 32: 10 3 19 N T3 SD: 1.4327 c. M:-2.4532 c. 39: 12 4 23 N T3 SD: 1.3687 c. M:-2.3699 c. 42: 13 4 25 N T3 SD: 0.5992 c. M:-0.9709 c. 52: 16 5 31 N T3 SD: 0.4762 c. M: 0.8227 c. 91: 28 9 54 N T3 SD: 0.3168 c. M:-0.5455 c. 101: 31 10 60 N T3 SD: 0.2246 c. M: 0.3206 c. 133: 41 13 79 N T3 SD: 0.2494 c. M:-0.3468 c. 143: 44 14 85 N T3 SD: 0.0438 c. M:-0.0587 c. 439: 135 43 261 N T3 SD: 0.0188 c. M: 0.0286 c. 582: 179 57 346 N T3 SD: 0.0041 c. M: 0.0071 c. 1307: 402 128 777 N T3 SD: 0.0031 c. M:-0.0053 c. 1889: 581 185 1123 N T3 SD: 0.0025 c. M:-0.0037 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: 70.8149 cents 6 x 7:8 S SD: 32.4573 cents 7 x 8:9 S SD: 34.7050 cents 8 x 9:11 SD: 26.6544 cents 9 x 10:12 S SD: 9.7763 cents 10:11 x 13 SD: 22.6982 cents 11:12 x 15 S SD: 19.4946 cents 12:13 x 16 SD: 7.3066 cents 17 x 19:23 SD: 13.4825 cents 18 x 20:24 S SD: 9.7763 cents 19:21 x 25 SD: 15.2406 cents 20:22 x 27 SD: 12.2698 cents 21:23:24:28 SD: 9.8445 cents 22:24:25:29 SD: 9.2647 cents 23:25:26:31 SD: 7.7053 cents 24:26:27:32 SD: 4.9144 cents 27 x 30:36 S SD: 9.7763 cents 28:31 x 37 SD: 13.8850 cents 29:32:33:39 SD: 10.4910 cents 30:33:34:40 SD: 6.2951 cents 31:34:35:41 SD: 5.8523 cents 32:35:36:43 SD: 4.5844 cents 33:36:37:44 SD: 1.5489 cents 87:95:98:116 SD: 1.4192 cents 96:105:108:128 SD: 0.9210 cents 120:131:135:160 SD: 0.7910 cents 129:141:145:172 SD: 0.3088 cents 162:177:182:216 SD: 0.1465 cents 291:318:327:388 SD: 0.1414 cents 444:485:499:592 SD: 0.1176 cents 573:626:644:764 SD: 0.0921 cents