Scala analysis: 119_E14
Enharmonic tetrachord 6561/6422 * 3211/3072 * 8192/6561
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 6561/6422 37.071667 2: 2187/2048 113.685006 apotome 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 8192/6561 384.3600 Pythagorean diminished fourth 1: 6561/6422 37.0717 2: 3211/3072 76.6133 3: 8192/6561 384.3600 Pythagorean diminished fourth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 6561/6422 37.072 cents 1: 1 3211/3072 76.613 cents 1: 1 8192/6561 384.360 cents Pythagorean diminished fourth 2: 1 2187/2048 113.685 cents apotome 2: 1 4096/3211 421.432 cents 2: 1 25688/19683 460.973 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 : 37.1 113.7 498.0 37.1 : 76.6 461.0 498.0 113.7: 384.4 421.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 37.0717 .. 384.3600 cents 52609024/43046721, 347.2883 cents 6561/6422, 37.0717 cents 2: 113.6850 .. 460.9733 cents 52609024/43046721, 347.2883 cents 14348907/16777216,-270.6750 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 6561/6422, 37.0717 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 8192/6561, 384.3600 cents Average / Smallest step : 4.478218 Largest / Average step : 2.315212 Largest / Smallest step : 10.368026 Median interval of one step : 3211/3072, 76.6133 cents, amount: 1 Least squares average step : 125.61262 cents, oct.: 376.83786 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2002-tone equal temperament with octave 4/3 degrees: 149 457 2002 Least number of segments generator : 1003 of 249.520 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1051 of 261.461 cents and inv. generated superset size: 155 = 152 more = 5166.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 37.07167 cents Scale diversity : 0.487658 Lumma stability : 0.148869 Lumma impropriety factor : 0.543475 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 : 6561/6422, 37.0717 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 19 Odd number limit : 19683 (O: 6561 U: 19683) Highest odd numerator or denominator: 6561 Scale harmonicity : 0.008665 Average absolute harmonicity : 0.085973 Specific harmonicity : 0.043727 Fundamental : 1/19728384, -24.2338 octaves, 0.0000 Hz. Guide tone : 26244, 14.6797 octaves, 6866101.336 Hz. Exponens Consonantiae : 5.177517E+11, 38.91347 octaves Euler's gradus suavitatis : 74 Sum of Mann's harmonic distance : 8612.5, average 2870.83333 Mersenne's string divisions : 54983005 Sum of van Prooijen's expressibility: 7.63394, average 2.54465 Sum of Tenney's harmonic distance : 15.35500, average 5.11833 Vogel's harmonic complexity : 54.66667 Wille's k value : 10533685 Wilson's harmonic complexity : 72 Rectangular lattice diameter : 12 Triangular lattice diameter : 9 Lattice compactness : 58.94784, average 9.82464 Lattice compactness (without 2's) : 36.02973, average 6.00496 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -11 .. 2 -3.33333 14 3: -1 .. 8 4.66667 16 2 13: -2 .. 0 -0.66667 2 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 11 / 3 = 3.66667 Average absolute exponent except 2's: 19 / 3 = 6.33333 Scale is weakly epimorphic with val: <6 11 25 29| Scale is weakly epimorphic with val: <7 12 26 34| Scale is weakly epimorphic with val: <7 12 27 32| Scale is weakly epimorphic with val: <7 12 28 30| Scale is weakly epimorphic with val: <8 12 26 33| Scale is weakly epimorphic with val: <8 12 27 31| Scale is weakly epimorphic with val: <8 12 28 29|
FIT/MODE
3: 0 1 2 N G T3 SD: 37.0258 c. M:-52.3300 c. 4: 0 1 3 N G T3 SD: 22.2974 c. M: 37.0717 c. 5: 0 1 4 N G T3 SD: 22.8943 c. M: 37.0717 c. 8: 1 1 6 N M DE S SD: 15.8266 c. M:-25.1840 c. 9: 1 1 7 N M DE S SD: 10.6883 c. M:-18.2667 c. 10: 1 1 8 N M DE S SD: 10.9584 c. M: 14.0760 c. 12: 1 2 9 N T3 SD: 6.7540 c. M:-10.8262 c. 13: 1 2 10 N T3 SD: 1.0157 c. M:-1.2485 c. 40: 3 6 31 N T3 SD: 0.9521 c. M: 1.6249 c. 53: 4 8 41 N T3 SD: 0.6092 c. M: 0.9201 c. 66: 5 10 51 N T3 SD: 0.4752 c. M:-0.6590 c. 79: 6 12 61 N T3 SD: 0.4516 c. M:-0.7545 c. 92: 7 14 71 N T3 SD: 0.4752 c. M:-0.8231 c. 105: 8 16 81 N T3 SD: 0.5127 c. M:-0.8746 c. 109: 8 17 84 N T3 SD: 0.4343 c. M:-0.5455 c. 122: 9 19 94 N T3 SD: 0.4059 c. M:-0.6204 c. 123: 9 19 95 N T3 SD: 0.4048 c. M: 0.6294 c. 136: 10 21 105 N T3 SD: 0.2761 c. M: 0.4507 c. 149: 11 23 115 N T3 SD: 0.1764 c. M: 0.3032 c. 162: 12 25 125 N T3 SD: 0.1104 c. M: 0.1794 c. 175: 13 27 135 N T3 SD: 0.0986 c. M:-0.1539 c. 215: 16 33 166 N T3 SD: 0.1023 c. M: 0.1771 c. 228: 17 35 176 N T3 SD: 0.0663 c. M: 0.0958 c. 377: 28 58 291 N T3 SD: 0.0631 c. M: 0.0816 c. 390: 29 60 301 N T3 SD: 0.0272 c. M: 0.0376 c. 403: 30 62 311 N T3 SD: 0.0076 c. M:-0.0126 c. 1196: 89 184 923 N T3 SD: 0.0057 c. M: 0.0098 c. 1599: 119 246 1234 N T3 SD: 0.0040 c. M: 0.0064 c. 2002: 149 308 1545 N T3 SD: 0.0037 c. M:-0.0046 c. 2230: 166 343 1721 N T3 SD: 0.0036 c. M: 0.0057 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: 76.5929 cents 7 x 8:9 S SD: 66.6479 cents 8 x 9:11 SD: 52.3893 cents 9 x 10:12 S SD: 34.3594 cents 10 x 11:13 SD: 33.7447 cents 11 x 12:15 S SD: 26.8287 cents 12 x 13:16 SD: 12.4438 cents 13 x 14:17 SD: 18.3280 cents 14 x 15:19 SD: 15.5892 cents 15 x 16:20 S SD: 0.9769 cents 16 x 17:21 SD: 14.3138 cents 17 x 18:23 SD: 14.6267 cents 18 x 19:24 SD: 10.0410 cents 19 x 20:25 S SD: 16.9192 cents 20 x 21:27 SD: 18.1397 cents 21 x 22:28 SD: 16.5740 cents 22 x 23:29 SD: 20.8594 cents 23:24:25:31 SD: 17.0979 cents 24:25:26:32 SD: 13.9380 cents 25:26:27:33 SD: 13.4802 cents 26:27:28:35 S SD: 11.9581 cents 27:28:29:36 SD: 9.2544 cents 29:30:31:39 SD: 8.7648 cents 30:31:32:40 S SD: 6.5973 cents 33:34:35:44 SD: 6.2641 cents 39:40:42:52 SD: 5.3669 cents 41:42:44:55 S SD: 4.7820 cents 42:43:45:56 SD: 2.2751 cents 45:46:48:60 S SD: 0.7284 cents 132:135:141:176 SD: 0.6340 cents 177:181:189:236 SD: 0.5404 cents 192:196:205:256 SD: 0.4667 cents 234:239:250:312 SD: 0.3145 cents 279:285:298:372 SD: 0.1467 cents 324:331:346:432 SD: 0.0276 cents