Scala analysis: 537_M45
Miscellaneous tetrachord 15/14 * 36/35 * 98/81
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: 54/49 168.213190 Zalzal's mujannab 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 98/81 329.8318 1: 15/14 119.4428 major diatonic semitone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 98/81 329.8318
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 98/81 329.832 cents 2: 1 54/49 168.213 cents Zalzal's mujannab 2: 1 56/45 378.602 cents septimal narrow major third 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 : 119.4 168.2 498.0 119.4: 48.8 378.6 498.0 168.2: 329.8 449.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 329.8318 cents 1715/1458, 281.0614 cents 36/35, 48.7704 cents 2: 168.2132 .. 449.2746 cents 1715/1458, 281.0614 cents 2187/2401,-161.6186 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 : 98/81, 329.8318 cents Average / Smallest step : 3.404013 Largest / Average step : 1.986759 Largest / Smallest step : 6.762953 Median interval of one step : 15/14, 119.4428 cents, amount: 1 Least squares average step : 139.28601 cents, oct.: 417.85804 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2114-tone equal temperament with octave 4/3 degrees: 507 714 2114 Least number of segments generator : 1059 of 249.494 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1107 of 260.802 cents and inv. generated superset size: 29 = 26 more = 966.667% 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 : 0.808135 Lumma stability : 0.195847 Lumma impropriety factor : 0.324506 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 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 : 7 Odd number limit : 81 (O: 49 U: 81) Highest odd numerator or denominator: 49 Scale harmonicity : 0.024607 Average absolute harmonicity : 0.099078 Specific harmonicity : 0.117762 Fundamental : 1/294, -8.1997 octaves, 0.8899 Hz. Guide tone : 540, 9.0768 octaves, 141277.805 Hz. Exponens Consonantiae : 1.587600E+05, 17.27649 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 69.5, average 23.16667 Mersenne's string divisions : 20909 Sum of van Prooijen's expressibility: 3.34341, average 1.11447 Sum of Tenney's harmonic distance : 6.82399, average 2.27466 Vogel's harmonic complexity : 16.33333 Wille's k value : 157 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 19.59556, average 3.26593 Lattice compactness (without 2's) : 15.70872, average 2.61812 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -1 .. 3 1.00000 5 1 5: 0 .. 1 0.33333 1 7: -2 .. 0 -1.00000 3 2 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 18 19| Scale is weakly epimorphic with val: <6 11 15 18| Scale is weakly epimorphic with val: <6 11 18 18| Scale is weakly epimorphic with val: <6 11 18 20| Scale is weakly epimorphic with val: <7 10 19 19| Scale is weakly epimorphic with val: <7 11 16 18| Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 11 16 21| Scale is weakly epimorphic with val: <7 11 16 22| Scale is weakly epimorphic with val: <7 11 19 19| Scale is weakly epimorphic with val: <7 11 19 21| Scale is weakly epimorphic with val: <7 11 19 22| Scale is weakly epimorphic with val: <7 12 16 18| Scale is weakly epimorphic with val: <7 12 16 20| Scale is weakly epimorphic with val: <7 12 19 20| Scale is weakly epimorphic with val: <7 12 19 21| Scale is weakly epimorphic with val: <8 11 17 19| Scale is weakly epimorphic with val: <8 12 17 18|
FIT/MODE
3: 1 0 2 N G T3 SD: 26.9184 c. M:-46.5722 c. 4: 1 0 3 N G T3 SD: 25.4005 c. M: 43.7019 c. 5: 1 1 3 N M DE S SD: 21.2499 c. M:-31.0048 c. 6: 1 1 4 N M DE S SD: 21.0742 c. M: 36.4353 c. 8: 2 1 5 N T3 SD: 11.1045 c. M:-18.5537 c. 9: 2 1 6 N T3 SD: 5.2178 c. M: 8.7661 c. 12: 3 1 8 N T3 SD: 3.1896 c. M:-5.0684 c. 21: 5 2 14 N T3 SD: 1.3629 c. M: 2.1982 c. 38: 9 4 25 N T3 SD: 1.5184 c. M:-2.1706 c. 41: 10 4 27 N T3 SD: 1.5868 c. M:-2.0316 c. 50: 12 5 33 N T3 SD: 0.6498 c. M:-1.1221 c. 62: 15 6 41 N T3 SD: 0.6675 c. M:-1.0519 c. 71: 17 7 47 N T3 SD: 0.1375 c. M: 0.1926 c. 154: 37 15 102 N T3 SD: 0.1278 c. M:-0.2174 c. 225: 54 22 149 N T3 SD: 0.0516 c. M:-0.0880 c. 296: 71 29 196 N T3 SD: 0.0287 c. M:-0.0453 c. 613: 147 60 406 N T3 SD: 0.0191 c. M: 0.0316 c. 684: 164 67 453 N T3 SD: 0.0183 c. M: 0.0285 c. 838: 201 82 555 N T3 SD: 0.0146 c. M: 0.0190 c. 909: 218 89 602 N T3 SD: 0.0038 c. M: 0.0066 c. 1205: 289 118 798 N T3 SD: 0.0047 c. M:-0.0062 c. 1889: 453 185 1251 N T3 SD: 0.0040 c. M: 0.0069 c. 2114: 507 207 1400 N T3 SD: 0.0019 c. M:-0.0032 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: 84.9555 cents 6 x 7:8 S SD: 49.3289 cents 7 x 8:9 S SD: 44.5201 cents 8 x 9:11 SD: 32.0635 cents 9 x 10:12 S SD: 7.0953 cents 10 x 11:13 SD: 21.9742 cents 11 x 12:15 S SD: 21.3458 cents 12:13 x 16 SD: 9.5649 cents 13:14 x 17 SD: 17.3820 cents 14:15 x 19 SD: 15.3211 cents 17:18:19:23 SD: 13.5449 cents 18:19:20:24 S SD: 9.8266 cents 21 x 23:28 SD: 5.3599 cents 22 x 24:29 SD: 13.2325 cents 23 x 25:31 SD: 15.1625 cents 24:26 x 32 SD: 9.5649 cents 26:28:29:35 SD: 9.3514 cents 27:29:30:36 SD: 4.9396 cents 30:32:33:40 SD: 2.7842 cents 57:61:63:76 SD: 1.8152 cents 69:74:76:92 SD: 0.6376 cents 126:135:139:168 SD: 0.5934 cents 156:167:172:208 SD: 0.5644 cents 168:180:185:224 SD: 0.4454 cents 195:209:215:260 SD: 0.3376 cents 225:241:248:300 SD: 0.1956 cents 294:315:324:392 SD: 0.0000 cents