Scala analysis: 557_M65
Miscellaneous tetrachord 120/113 * 113/97 * 97/90
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 120/113 104.053960 2: 120/97 368.373304 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 97/90 129.6717 1: 120/113 104.0540 2: 113/97 264.3193 3: 97/90 129.6717
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 120/113 104.054 cents 1: 1 97/90 129.672 cents 1: 1 113/97 264.319 cents 2: 1 388/339 233.726 cents 2: 1 120/97 368.373 cents 2: 1 113/90 393.991 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 : 104.1 368.4 498.0 104.1: 264.3 394.0 498.0 368.4: 129.7 233.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 104.0540 .. 264.3193 cents 12769/11640, 160.2654 cents 120/113, 104.0540 cents 2: 233.7257 .. 393.9910 cents 12769/11640, 160.2654 cents 37636/38307,-30.5937 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 120/113, 104.0540 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 113/97, 264.3193 cents Average / Smallest step : 1.595470 Largest / Average step : 1.592141 Largest / Smallest step : 2.540214 Median interval of one step : 97/90, 129.6717 cents, amount: 1 Least squares average step : 166.78111 cents, oct.: 500.34334 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1905-tone equal temperament with octave 4/3 degrees: 398 1409 1905 Least number of segments generator : 953 of 249.153 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1568 of 409.939 cents and inv. generated superset size: 62 = 59 more = 2066.667% 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 30.59369 cents Scale diversity : 1.154106 Lumma stability : 0.417850 Lumma impropriety factor : 0.061428 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 : 10961/10800, 25.6177 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 : 113 Odd number limit : 339 (O: 113 U: 339) Highest odd numerator or denominator: 113 Scale harmonicity : 0.067873 Fundamental : 1/32883, -15.0051 octaves, 0.0080 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 3.945960E+06, 21.91194 octaves Euler's gradus suavitatis : 220 Sum of Mann's harmonic distance : 228.5, average 76.16667 Mersenne's string divisions : 50561 Sum of van Prooijen's expressibility: 4.51697, average 1.50566 Sum of Tenney's harmonic distance : 9.27739, average 3.09246 Vogel's harmonic complexity : 150.00000 Wille's k value : 5480 Wilson's harmonic complexity : 221 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.76830, average 2.29472 Lattice compactness (without 2's) : 8.30056, average 1.38343 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.66667 2 97: -1 .. 0 -0.33333 1 1 113: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <7 10 19 47 48| Scale is weakly epimorphic with val: <7 11 15 48 49| Scale is weakly epimorphic with val: <7 11 16 47 49| Scale is weakly epimorphic with val: <7 11 16 49 50| Scale is JI-epimorphic with val: <7 11 17 47 48| Scale is weakly epimorphic with val: <7 11 17 48 50| Scale is JI-epimorphic with val: <7 11 18 48 49| Scale is weakly epimorphic with val: <7 11 19 47 49| Scale is JI-epimorphic with val: <7 11 19 49 50| Scale is weakly epimorphic with val: <7 12 17 47 49| Scale is weakly epimorphic with val: <7 12 18 47 48| Scale is weakly epimorphic with val: <7 12 18 48 50| Scale is weakly epimorphic with val: <7 12 19 48 49| Scale is weakly epimorphic with val: <8 11 15 47 49| Scale is weakly epimorphic with val: <8 11 16 47 48| Scale is weakly epimorphic with val: <8 11 16 48 50| Scale is weakly epimorphic with val: <8 11 17 48 49| Scale is weakly epimorphic with val: <8 11 18 49 50| Scale is weakly epimorphic with val: <8 12 15 48 49| Scale is weakly epimorphic with val: <8 12 16 47 49| Scale is weakly epimorphic with val: <8 12 16 49 50| Scale is weakly epimorphic with val: <8 12 17 48 50|
FIT/MODE
3: 1 1 1 SP B ME I SD: 41.4729 c. M:-61.9610 c. 4: 1 2 1 P M ME I SD: 12.1810 c. M:-20.4573 c. 9: 2 5 2 N M DE I SD: 11.6142 c. M:-18.9950 c. 11: 2 6 3 N T3 SD: 8.5672 c. M: 13.5003 c. 14: 3 7 4 P T3 SD: 7.4513 c. M: 12.6269 c. 15: 3 8 4 N T3 SD: 3.1421 c. M: 4.4450 c. 19: 4 10 5 N T3 SD: 0.9266 c. M: 1.3928 c. 58: 12 31 15 N T3 SD: 0.7686 c. M: 1.0102 c. 62: 13 33 16 N T3 SD: 0.6950 c. M:-1.1440 c. 77: 16 41 20 N T3 SD: 0.3714 c. M: 0.5641 c. 81: 17 43 21 N T3 SD: 0.4187 c. M:-0.5489 c. 96: 20 51 25 N T3 SD: 0.1708 c. M: 0.2946 c. 115: 24 61 30 N T3 SD: 0.1603 c. M: 0.2531 c. 177: 37 94 46 N T3 SD: 0.1403 c. M:-0.2363 c. 196: 41 104 51 N T3 SD: 0.0871 c. M:-0.1289 c. 292: 61 155 76 N T3 SD: 0.0258 c. M:-0.0435 c. 407: 85 216 106 N T3 SD: 0.0326 c. M: 0.0403 c. 603: 126 320 157 N T3 SD: 0.0088 c. M:-0.0151 c. 895: 187 475 233 N T3 SD: 0.0085 c. M:-0.0131 c. 1302: 272 691 339 N T3 SD: 0.0049 c. M: 0.0077 c. 1905: 398 1011 496 N T3 SD: 0.0018 c. M: 0.0030 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: 17.9404 cents 5 x 6:7 S SD: 49.7880 cents 6 x 7:8 S SD: 50.7512 cents 7:8 x 9 S SD: 70.9288 cents 8:9:10:11 H SD: 38.1970 cents 9:10:11:12 H SD: 27.0354 cents 11:12:14:15 S SD: 26.0296 cents 12:13:15:16 SD: 12.9675 cents 16:17:20:21 SD: 10.8832 cents 17:18:21:23 SD: 8.6363 cents 18:19:22:24 SD: 7.8086 cents 29:31:36:39 SD: 6.5524 cents 30:32:37:40 SD: 3.1093 cents 33:35:41:44 SD: 2.5773 cents 51:54:63:68 SD: 1.9001 cents 63:67:78:84 SD: 0.9558 cents 114:121:141:152 SD: 0.3213 cents 177:188:219:236 SD: 0.1358 cents 291:309:360:388 SD: 0.0496 cents 468:497:579:624 SD: 0.0325 cents