Scala analysis: 593_M101
Miscellaneous tetrachord 10/9 * 108/97 * 97/90
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 120/97 368.373304 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 97/90 129.6717 1: 10/9 182.4037 minor whole tone 2: 108/97 185.9696 3: 97/90 129.6717
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 97/90 129.672 cents 1: 1 10/9 182.404 cents minor whole tone 1: 1 108/97 185.970 cents 2: 1 97/81 312.075 cents 2: 1 6/5 315.641 cents minor third 2: 1 120/97 368.373 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 : 182.4 368.4 498.0 182.4: 186.0 315.6 498.0 368.4: 129.7 312.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 129.6717 .. 185.9696 cents 9720/9409, 56.2979 cents 97/90, 129.6717 cents 2: 312.0754 .. 368.3733 cents 9720/9409, 56.2979 cents 9409/8748, 126.1058 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 97/90, 129.6717 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 108/97, 185.9696 cents Average / Smallest step : 1.280272 Largest / Average step : 1.120198 Largest / Smallest step : 1.434157 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 172.37752 cents, oct.: 517.13257 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 699-tone equal temperament with octave 4/3 degrees: 256 517 699 Least number of segments generator : 350 of 249.379 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 635 of 452.444 cents and inv. generated superset size: 20 = 17 more = 666.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MLS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 126.10582 cents Scale diversity : 1.226902 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.773924 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 : 486/485, 3.5659 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle 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 classes 1 and 2 combined Limited inverse transpositions with margin 56.2979 cents: 2 -- Rational properties -- Prime limit : 97 Odd number limit : 97 (O: 97 U: 97) Highest odd numerator or denominator: 97 Scale harmonicity : 0.057471 Fundamental : 1/873, -9.7698 octaves, 0.2997 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 1.047600E+05, 16.67673 octaves Euler's gradus suavitatis : 110 Sum of Mann's harmonic distance : 121.5, average 40.50000 Mersenne's string divisions : 4123 Sum of van Prooijen's expressibility: 3.41814, average 1.13938 Sum of Tenney's harmonic distance : 7.09938, average 2.36646 Vogel's harmonic complexity : 74.00000 Wille's k value : 242 Wilson's harmonic complexity : 111 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 15.78927, average 2.63155 Lattice compactness (without 2's) : 11.30056, average 1.88343 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -2 .. 1 -0.66667 4 1 5: 0 .. 1 0.66667 2 1 97: -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: <6 10 17 47| Scale is weakly epimorphic with val: <6 11 19 49| Scale is weakly epimorphic with val: <7 10 16 48| Scale is weakly epimorphic with val: <7 11 16 49| Scale is weakly epimorphic with val: <7 11 17 48| = patent Scale is weakly epimorphic with val: <7 11 19 49| Scale is weakly epimorphic with val: <7 12 18 48| Scale is weakly epimorphic with val: <8 11 15 47| Scale is weakly epimorphic with val: <8 11 17 48| Scale is weakly epimorphic with val: <8 12 15 48| Scale is weakly epimorphic with val: <8 12 19 47|
FIT/MODE
3: 1 1 1 SP B ME I SD: 23.0176 c. M: 36.3433 c. 5: 2 2 1 SP M ME S SD: 19.8871 c. M:-30.0627 c. 8: 3 3 2 SP M ME S SD: 3.9016 c. M:-5.1604 c. 11: 4 4 3 SP M ME S SD: 3.6337 c. M: 6.1588 c. 19: 7 7 5 SP M DE S SD: 1.0199 c. M: 1.3928 c. 46: 17 17 12 SP M DE S SD: 0.9674 c. M:-1.6564 c. 65: 24 24 17 SP M DE S SD: 0.9243 c. M:-1.4898 c. 66: 24 25 17 SP T3 SD: 1.0963 c. M:-1.3874 c. 73: 27 27 19 SP M DE S SD: 1.0423 c. M:-1.8047 c. 77: 28 29 20 SP T3 SD: 0.7695 c. M: 1.2964 c. 85: 31 32 22 SP T3 SD: 0.6245 c. M:-0.7659 c. 96: 35 36 25 SP T3 SD: 0.4765 c. M: 0.8248 c. 104: 38 39 27 SP T3 SD: 0.3262 c. M: 0.4257 c. 115: 42 43 30 SP T3 SD: 0.3282 c. M: 0.5090 c. 123: 45 46 32 SP T3 SD: 0.1248 c. M: 0.1921 c. 142: 52 53 37 SP T3 SD: 0.0593 c. M: 0.1006 c. 265: 97 99 69 SP T3 SD: 0.0582 c. M: 0.1004 c. 292: 107 109 76 SP T3 SD: 0.0625 c. M:-0.0991 c. 407: 149 152 106 SP T3 SD: 0.0480 c. M: 0.0727 c. 415: 152 155 108 SP T3 SD: 0.0354 c. M:-0.0600 c. 434: 159 162 113 SP T3 SD: 0.0346 c. M:-0.0598 c. 549: 201 205 143 SP T3 SD: 0.0471 c. M: 0.0594 c. 557: 204 208 145 SP T3 SD: 0.0113 c. M:-0.0190 c. 699: 256 261 182 SP T3 SD: 0.0031 c. M: 0.0053 c. 1955: 716 730 509 SP T3 SD: 0.0010 c. M:-0.0017 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 6:7 x 8 S SD: 42.2336 cents 7:8 x 9 S SD: 39.8203 cents 8:9:10:11 H SD: 20.0621 cents 9:10:11:12 H SD: 6.9885 cents 26:29:32:35 SD: 6.6488 cents 30:33:37:40 SD: 6.0627 cents 33:37:41:44 SD: 5.7780 cents 34:38:42:45 SD: 5.5059 cents 37:41:46:49 SD: 5.0874 cents 38:42:47:51 SD: 4.8589 cents 42:47:52:56 SD: 4.1328 cents 45:50:56:60 SD: 3.4096 cents 54:60:67:72 SD: 1.6896 cents 63:70:78:84 SD: 0.4578 cents 135:150:167:180 SD: 0.0356 cents 468:520:579:624 SD: 0.0308 cents