Scala analysis: 128_E15
Enharmonic tetrachord 26/25 * 375/364 * 56/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 26/25 67.900234 tridecimal 1/3-tone 2: 15/14 119.442808 major diatonic semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 56/45 378.6022 septimal narrow major third 1: 26/25 67.9002 tridecimal 1/3-tone 2: 375/364 51.5426 3: 56/45 378.6022 septimal narrow major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 375/364 51.543 cents 1: 1 26/25 67.900 cents tridecimal 1/3-tone 1: 1 56/45 378.602 cents septimal narrow major third 2: 1 15/14 119.443 cents major diatonic semitone 2: 1 50/39 430.145 cents 2: 1 1456/1125 446.502 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 : 67.9 119.4 498.0 67.9 : 51.5 430.1 498.0 119.4: 378.6 446.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.5426 .. 378.6022 cents 20384/16875, 327.0596 cents 375/364, 51.5426 cents 2: 119.4428 .. 446.5024 cents 20384/16875, 327.0596 cents 675/784,-259.1594 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 375/364, 51.5426 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 56/45, 378.6022 cents Average / Smallest step : 3.220930 Largest / Average step : 2.280530 Largest / Smallest step : 7.345427 Median interval of one step : 26/25, 67.9002 cents, amount: 1 Least squares average step : 128.63720 cents, oct.: 385.91161 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1401-tone equal temperament with octave 4/3 degrees: 191 336 1401 Least number of segments generator : 701 of 249.200 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 863 of 306.790 cents and inv. generated superset size: 45 = 42 more = 1500.000% 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 51.54257 cents Scale diversity : 0.566166 Lumma stability : 0.206980 Lumma impropriety factor : 0.520353 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 : 9464/9375, 16.3577 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% Limited inverse transpositions with margin 327.0596 cents: 2 -- Rational properties -- Prime limit : 13 Odd number limit : 1125 (O: 375 U: 1125) Highest odd numerator or denominator: 25 Scale harmonicity : 0.016674 Average absolute harmonicity : 0.097077 Specific harmonicity : 0.088437 Fundamental : 1/1050, -10.0362 octaves, 0.2492 Hz. Guide tone : 780, 9.6073 octaves, 204067.941 Hz. Exponens Consonantiae : 8.190000E+05, 19.64350 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 43.5, average 14.50000 Mersenne's string divisions : 10353 Sum of van Prooijen's expressibility: 3.05115, average 1.01705 Sum of Tenney's harmonic distance : 6.21431, average 2.07144 Vogel's harmonic complexity : 22.00000 Wille's k value : 562 Wilson's harmonic complexity : 41 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 17.20429, average 2.86738 Lattice compactness (without 2's) : 13.33120, average 2.22187 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -1 .. 1 0.00000 2 1 5: -2 .. 1 -0.33333 3 7: -1 .. 0 -0.33333 1 1 13: 0 .. 1 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 15 18 27| Scale is weakly epimorphic with val: <6 10 15 21 27| Scale is weakly epimorphic with val: <6 10 16 19 29| Scale is weakly epimorphic with val: <6 10 16 22 29| Scale is weakly epimorphic with val: <6 10 17 18 26| Scale is weakly epimorphic with val: <6 10 17 18 29| Scale is weakly epimorphic with val: <6 10 18 19 25| Scale is weakly epimorphic with val: <6 10 18 19 28| Scale is weakly epimorphic with val: <6 10 19 20 27| Scale is weakly epimorphic with val: <6 10 19 20 30| Scale is weakly epimorphic with val: <6 11 15 18 27| Scale is weakly epimorphic with val: <6 11 15 21 27| Scale is weakly epimorphic with val: <6 11 16 18 25| Scale is weakly epimorphic with val: <6 11 16 18 28| Scale is weakly epimorphic with val: <6 11 16 19 29| Scale is weakly epimorphic with val: <6 11 16 22 29| Scale is weakly epimorphic with val: <6 11 17 19 27| Scale is weakly epimorphic with val: <6 11 17 19 30| Scale is weakly epimorphic with val: <6 11 18 20 26| Scale is weakly epimorphic with val: <6 11 18 20 29| Scale is weakly epimorphic with val: <6 11 19 21 25| Scale is weakly epimorphic with val: <6 11 19 21 28| Scale is weakly epimorphic with val: <7 10 15 19 26| Scale is weakly epimorphic with val: <7 10 15 22 26| Scale is weakly epimorphic with val: <7 10 16 20 28| Scale is weakly epimorphic with val: <7 10 17 18 30| Scale is weakly epimorphic with val: <7 10 17 21 30| Scale is weakly epimorphic with val: <7 10 18 18 25| Scale is weakly epimorphic with val: <7 10 18 18 28| Scale is weakly epimorphic with val: <7 10 19 19 27| Scale is weakly epimorphic with val: <7 10 19 19 30| Scale is weakly epimorphic with val: <7 11 15 18 25| Scale is weakly epimorphic with val: <7 11 15 18 28| Scale is weakly epimorphic with val: <7 11 15 20 27| Scale is weakly epimorphic with val: <7 11 15 20 30| Scale is weakly epimorphic with val: <7 11 15 21 25| Scale is weakly epimorphic with val: <7 11 15 21 28| Scale is JI-epimorphic with val: <7 11 16 18 26| Scale is weakly epimorphic with val: <7 11 16 18 29| Scale is weakly epimorphic with val: <7 11 16 19 27| Scale is weakly epimorphic with val: <7 11 16 19 30| Scale is weakly epimorphic with val: <7 11 16 21 26| Scale is weakly epimorphic with val: <7 11 16 21 29| Scale is weakly epimorphic with val: <7 11 16 22 27| Scale is weakly epimorphic with val: <7 11 16 22 30| Scale is weakly epimorphic with val: <7 11 17 19 25| Scale is JI-epimorphic with val: <7 11 17 19 28| Scale is weakly epimorphic with val: <7 11 17 20 26| Scale is weakly epimorphic with val: <7 11 17 20 29| Scale is weakly epimorphic with val: <7 11 17 22 25| Scale is weakly epimorphic with val: <7 11 17 22 28| Scale is weakly epimorphic with val: <7 11 18 18 25| Scale is weakly epimorphic with val: <7 11 18 18 28| Scale is weakly epimorphic with val: <7 11 18 20 27| Scale is JI-epimorphic with val: <7 11 18 20 30| Scale is weakly epimorphic with val: <7 11 18 21 25| Scale is weakly epimorphic with val: <7 11 18 21 28| Scale is weakly epimorphic with val: <7 11 19 19 27| Scale is weakly epimorphic with val: <7 11 19 19 30| Scale is weakly epimorphic with val: <7 11 19 21 26| Scale is weakly epimorphic with val: <7 11 19 21 29| Scale is weakly epimorphic with val: <7 11 19 22 27| Scale is weakly epimorphic with val: <7 11 19 22 30| Scale is weakly epimorphic with val: <7 12 15 19 26| Scale is weakly epimorphic with val: <7 12 15 22 26| Scale is weakly epimorphic with val: <7 12 16 18 26| Scale is weakly epimorphic with val: <7 12 16 18 29| Scale is weakly epimorphic with val: <7 12 16 20 28| Scale is weakly epimorphic with val: <7 12 17 18 30| Scale is weakly epimorphic with val: <7 12 17 19 25| Scale is weakly epimorphic with val: <7 12 17 19 28| Scale is weakly epimorphic with val: <7 12 17 21 30| Scale is weakly epimorphic with val: <7 12 18 20 27| Scale is weakly epimorphic with val: <7 12 18 20 30| Scale is weakly epimorphic with val: <7 12 19 21 26| Scale is weakly epimorphic with val: <7 12 19 21 29| Scale is weakly epimorphic with val: <8 11 15 20 25| Scale is weakly epimorphic with val: <8 11 16 18 27| Scale is weakly epimorphic with val: <8 11 16 21 27| Scale is weakly epimorphic with val: <8 11 17 19 29| Scale is weakly epimorphic with val: <8 11 17 22 29| Scale is weakly epimorphic with val: <8 11 18 18 26| Scale is weakly epimorphic with val: <8 11 18 18 29| Scale is weakly epimorphic with val: <8 11 19 19 25| Scale is weakly epimorphic with val: <8 11 19 19 28| Scale is weakly epimorphic with val: <8 12 15 20 25| Scale is weakly epimorphic with val: <8 12 16 18 27| Scale is weakly epimorphic with val: <8 12 16 21 27| Scale is weakly epimorphic with val: <8 12 17 18 25| Scale is weakly epimorphic with val: <8 12 17 18 28| Scale is weakly epimorphic with val: <8 12 17 19 29| Scale is weakly epimorphic with val: <8 12 17 22 29| Scale is weakly epimorphic with val: <8 12 18 19 27| Scale is weakly epimorphic with val: <8 12 18 19 30| Scale is weakly epimorphic with val: <8 12 19 20 26| Scale is weakly epimorphic with val: <8 12 19 20 29|
FIT/MODE
3: 0 1 2 N G T3 SD: 47.5374 c. M: 67.9002 c. 4: 1 0 3 N G T3 SD: 32.8151 c. M:-56.6110 c. 5: 1 0 4 N G T3 SD: 21.5934 c. M:-31.7088 c. 7: 1 1 5 N M DE S SD: 13.3284 c. M:-22.8558 c. 8: 1 1 6 N M DE S SD: 4.3799 c. M: 5.6446 c. 20: 3 2 15 N T3 SD: 4.8996 c. M:-6.8065 c. 21: 3 2 16 N T3 SD: 1.9405 c. M:-3.2491 c. 29: 4 3 22 N T3 SD: 0.6412 c. M:-0.7956 c. 88: 12 9 67 N T3 SD: 0.3414 c. M: 0.5912 c. 96: 13 10 73 N T3 SD: 0.2725 c. M: 0.4566 c. 117: 16 12 89 N T3 SD: 0.1891 c. M: 0.2526 c. 125: 17 13 95 N T3 SD: 0.1085 c. M: 0.1661 c. 154: 21 16 117 N T3 SD: 0.1258 c. M:-0.2174 c. 213: 29 22 162 N T3 SD: 0.1231 c. M: 0.1926 c. 242: 33 25 184 N T3 SD: 0.0451 c. M: 0.0767 c. 367: 50 38 279 N T3 SD: 0.0295 c. M: 0.0467 c. 396: 54 41 301 N T3 SD: 0.0234 c. M:-0.0377 c. 638: 87 66 485 N T3 SD: 0.0093 c. M:-0.0150 c. 763: 104 79 580 N T3 SD: 0.0101 c. M: 0.0147 c. 1005: 137 104 764 N T3 SD: 0.0078 c. M: 0.0111 c. 1401: 191 145 1065 N T3 SD: 0.0017 c. M:-0.0027 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 x 7 SD: 84.4672 cents 6 x 7:8 S SD: 73.7140 cents 7 x 8:9 S SD: 64.1248 cents 8 x 9:11 SD: 49.9317 cents 9 x 10:12 S SD: 31.4805 cents 10 x 11:13 SD: 31.6109 cents 11 x 12:15 S SD: 24.9336 cents 12 x 13:16 SD: 9.5649 cents 13 x 14:17 SD: 17.3820 cents 14 x 15:19 SD: 15.3211 cents 15 x 16:20 S SD: 3.8558 cents 16 x 17:21 SD: 15.4371 cents 17 x 18:23 SD: 16.2676 cents 18:19 x 24 SD: 12.8514 cents 19:20 x 25 S SD: 15.5132 cents 20:21 x 27 SD: 13.5737 cents 21:22:23:28 SD: 13.3647 cents 22:23:24:29 SD: 12.6779 cents 23:24:25:31 SD: 10.5632 cents 24:25:26:32 SD: 6.4432 cents 26:27:28:35 S SD: 6.3197 cents 27:28:29:36 SD: 2.1763 cents 69:72:74:92 SD: 2.0058 cents 72:75:77:96 SD: 1.4135 cents 96:100:103:128 SD: 1.2229 cents 99:103:106:132 SD: 0.4487 cents 126:131:135:168 SD: 0.1762 cents 225:234:241:300 SD: 0.1710 cents 351:365:376:468 SD: 0.1265 cents 477:496:511:636 SD: 0.1232 cents 573:596:614:764 SD: 0.1025 cents