Scala analysis: 095_E11
Enharmonic tetrachord 30/29 * 116/113 * 113/90
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 30/29 58.691521 2: 120/113 104.053960 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 113/90 393.9910 1: 30/29 58.6915 2: 116/113 45.3624 3: 113/90 393.9910
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 116/113 45.362 cents 1: 1 30/29 58.692 cents 1: 1 113/90 393.991 cents 2: 1 120/113 104.054 cents 2: 1 58/45 439.353 cents 2: 1 113/87 452.683 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 : 58.7 104.1 498.0 58.7 : 45.4 439.4 498.0 104.1: 394.0 452.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 45.3624 .. 393.9910 cents 12769/10440, 348.6286 cents 116/113, 45.3624 cents 2: 104.0540 .. 452.6826 cents 12769/10440, 348.6286 cents 10800/12769,-289.9371 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 116/113, 45.3624 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 113/90, 393.9910 cents Average / Smallest step : 3.659746 Largest / Average step : 2.373226 Largest / Smallest step : 8.685402 Median interval of one step : 30/29, 58.6915 cents, amount: 1 Least squares average step : 125.78103 cents, oct.: 377.34309 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1570-tone equal temperament with octave 4/3 degrees: 185 328 1570 Least number of segments generator : 787 of 249.657 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1533 of 486.308 cents and inv. generated superset size: 82 = 79 more = 2733.333% 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 45.36244 cents Scale diversity : 0.451215 Lumma stability : 0.182162 Lumma impropriety factor : 0.582150 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 : 1695/1682, 13.3291 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 348.6286 cents: 2 -- Rational properties -- Prime limit : 113 Odd number limit : 113 (O: 113 U: 113) Highest odd numerator or denominator: 113 Scale harmonicity : 0.014534 Fundamental : 1/9831, -13.2631 octaves, 0.0266 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 1.179720E+06, 20.17001 octaves Euler's gradus suavitatis : 152 Sum of Mann's harmonic distance : 149.5, average 49.83333 Mersenne's string divisions : 96229 Sum of van Prooijen's expressibility: 3.99260, average 1.33087 Sum of Tenney's harmonic distance : 8.15096, average 2.71699 Vogel's harmonic complexity : 104.00000 Wille's k value : 2542 Wilson's harmonic complexity : 153 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.88400, average 2.48067 Lattice compactness (without 2's) : 9.83182, average 1.63864 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.66667 2 29: -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: <6 10 19 32 49| Scale is weakly epimorphic with val: <6 11 18 32 48| Scale is weakly epimorphic with val: <6 11 19 33 49| Scale is weakly epimorphic with val: <7 10 18 32 50| Scale is weakly epimorphic with val: <7 10 19 33 48| Scale is weakly epimorphic with val: <7 11 15 32 48| Scale is weakly epimorphic with val: <7 11 15 34 49| Scale is weakly epimorphic with val: <7 11 15 35 48| Scale is weakly epimorphic with val: <7 11 15 37 49| Scale is weakly epimorphic with val: <7 11 15 38 48| Scale is weakly epimorphic with val: <7 11 16 32 50| Scale is weakly epimorphic with val: <7 11 16 33 49| Scale is weakly epimorphic with val: <7 11 16 35 50| Scale is weakly epimorphic with val: <7 11 16 36 49| Scale is weakly epimorphic with val: <7 11 16 38 50| Scale is weakly epimorphic with val: <7 11 17 33 48| Scale is weakly epimorphic with val: <7 11 17 34 50| Scale is weakly epimorphic with val: <7 11 17 36 48| Scale is weakly epimorphic with val: <7 11 17 37 50| Scale is weakly epimorphic with val: <7 11 18 32 48| Scale is weakly epimorphic with val: <7 11 18 34 49| Scale is JI-epimorphic with val: <7 11 18 35 48| Scale is weakly epimorphic with val: <7 11 18 37 49| Scale is weakly epimorphic with val: <7 11 18 38 48| Scale is weakly epimorphic with val: <7 11 19 32 50| Scale is weakly epimorphic with val: <7 11 19 33 49| Scale is weakly epimorphic with val: <7 11 19 35 50| Scale is JI-epimorphic with val: <7 11 19 36 49| Scale is weakly epimorphic with val: <7 11 19 38 50| Scale is weakly epimorphic with val: <7 12 16 32 48| Scale is weakly epimorphic with val: <7 12 17 33 49| Scale is weakly epimorphic with val: <7 12 18 33 48| Scale is weakly epimorphic with val: <7 12 18 34 50| Scale is weakly epimorphic with val: <7 12 18 36 48| Scale is weakly epimorphic with val: <7 12 19 34 49| Scale is weakly epimorphic with val: <7 12 19 35 48| Scale is weakly epimorphic with val: <7 12 19 37 49| Scale is weakly epimorphic with val: <8 11 16 32 50| Scale is weakly epimorphic with val: <8 11 16 34 48| Scale is weakly epimorphic with val: <8 11 16 37 48| Scale is weakly epimorphic with val: <8 11 17 32 49| Scale is weakly epimorphic with val: <8 11 17 33 48| Scale is weakly epimorphic with val: <8 11 17 35 49| Scale is weakly epimorphic with val: <8 11 17 38 49| Scale is weakly epimorphic with val: <8 11 18 33 50| Scale is weakly epimorphic with val: <8 11 18 34 49| Scale is weakly epimorphic with val: <8 11 18 36 50| Scale is weakly epimorphic with val: <8 11 19 35 50| Scale is weakly epimorphic with val: <8 12 15 32 49| Scale is weakly epimorphic with val: <8 12 15 33 48| Scale is weakly epimorphic with val: <8 12 15 36 48| Scale is weakly epimorphic with val: <8 12 16 33 50| Scale is weakly epimorphic with val: <8 12 16 34 49| Scale is weakly epimorphic with val: <8 12 16 37 49| Scale is weakly epimorphic with val: <8 12 17 32 50| Scale is weakly epimorphic with val: <8 12 17 34 48| Scale is weakly epimorphic with val: <8 12 17 35 50| Scale is weakly epimorphic with val: <8 12 17 38 50| Scale is weakly epimorphic with val: <8 12 18 35 49| Scale is weakly epimorphic with val: <8 12 19 36 50|
FIT/MODE
3: 0 0 3 N M DE S SD: 68.9732 c. M: 104.0540 c. 4: 0 1 3 N G T3 SD: 35.8850 c. M: 58.6915 c. 5: 1 0 4 N G T3 SD: 23.7627 c. M:-40.9175 c. 6: 1 0 5 N G T3 SD: 18.5672 c. M:-24.3160 c. 8: 1 1 6 N M DE S SD: 11.9889 c. M:-20.4573 c. 9: 1 1 7 N M DE S SD: 4.2858 c. M:-6.6227 c. 19: 2 2 15 N M DE S SD: 3.6467 c. M: 6.2657 c. 23: 3 2 18 N T3 SD: 4.3629 c. M:-6.2709 c. 24: 3 2 19 N T3 SD: 2.0648 c. M:-3.5641 c. 33: 4 3 26 N T3 SD: 1.3352 c. M:-1.6776 c. 34: 4 3 27 N T3 SD: 0.8767 c. M: 1.5153 c. 43: 5 4 34 N T3 SD: 0.4628 c. M: 0.7793 c. 67: 8 6 53 N T3 SD: 0.4484 c. M:-0.7765 c. 76: 9 7 60 N T3 SD: 0.4895 c. M:-0.7976 c. 77: 9 7 61 N T3 SD: 0.4271 c. M: 0.5641 c. 101: 12 9 80 N T3 SD: 0.4010 c. M: 0.5000 c. 110: 13 10 87 N T3 SD: 0.1083 c. M:-0.1683 c. 153: 18 14 121 N T3 SD: 0.0861 c. M:-0.1123 c. 263: 31 24 208 N T3 SD: 0.0582 c. M:-0.0999 c. 297: 35 27 235 N T3 SD: 0.0491 c. M: 0.0850 c. 407: 48 37 322 N T3 SD: 0.0350 c. M:-0.0460 c. 450: 53 41 356 N T3 SD: 0.0216 c. M: 0.0329 c. 560: 66 51 443 N T3 SD: 0.0040 c. M:-0.0066 c. 1570: 185 143 1242 N T3 SD: 0.0035 c. M: 0.0047 c. 2130: 251 194 1685 N T3 SD: 0.0017 c. M: 0.0023 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: 81.4085 cents 7 x 8:9 S SD: 70.9288 cents 8 x 9:11 SD: 56.5889 cents 9 x 10:12 S SD: 39.1749 cents 10 x 11:13 SD: 37.5370 cents 11 x 12:15 S SD: 30.3465 cents 12 x 13:16 SD: 17.2594 cents 13 x 14:17 SD: 20.7238 cents 14 x 15:19 SD: 17.1446 cents 15 x 16:20 S SD: 3.8387 cents 16 x 17:21 SD: 13.6395 cents 17 x 18:23 SD: 12.8916 cents 18 x 19:24 SD: 5.2255 cents 19 x 20:25 S SD: 13.7702 cents 20 x 21:27 SD: 14.5444 cents 21:22 x 28 SD: 10.9228 cents 22:23 x 29 SD: 13.4637 cents 23:24 x 31 SD: 11.9893 cents 24:25 x 32 SD: 5.9905 cents 30:31:32:40 S SD: 2.6383 cents 33:34:35:44 SD: 2.4475 cents 63:65:67:84 SD: 1.7438 cents 81:84:86:108 SD: 1.4281 cents 111:115:118:148 SD: 1.0570 cents 114:118:121:152 SD: 0.4484 cents 144:149:153:192 SD: 0.3288 cents 258:267:274:344 SD: 0.2267 cents 291:301:309:388 SD: 0.0826 cents 435:450:462:580 SD: 0.0663 cents