Scala analysis: 099_E12
Enharmonic tetrachord 51/50 * 25/24 * 64/51
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 51/50 34.282983 17th-partial chroma 2: 17/16 104.955410 17th harmonic 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 64/51 393.0896 1: 51/50 34.2830 17th-partial chroma 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 64/51 393.0896
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 51/50 34.283 cents 17th-partial chroma 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 64/51 393.090 cents 2: 1 17/16 104.955 cents 17th harmonic 2: 1 32/25 427.373 cents classic diminished fourth 2: 1 200/153 463.762 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 : 34.3 105.0 498.0 34.3 : 70.7 463.8 498.0 105.0: 393.1 427.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.2830 .. 393.0896 cents 3200/2601, 358.8066 cents 51/50, 34.2830 cents 2: 104.9554 .. 463.7620 cents 3200/2601, 358.8066 cents 867/1024,-288.1342 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 51/50, 34.2830 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 64/51, 393.0896 cents Average / Smallest step : 4.842490 Largest / Average step : 2.367796 Largest / Smallest step : 11.466027 Median interval of one step : 25/24, 70.6724 cents, amount: 1 Least squares average step : 124.16634 cents, oct.: 372.49903 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2368-tone equal temperament with octave 4/3 degrees: 163 499 2368 Least number of segments generator : 1185 of 249.233 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1487 of 312.750 cents and inv. generated superset size: 49 = 46 more = 1633.333% 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 34.28298 cents Scale diversity : 0.426395 Lumma stability : 0.137670 Lumma impropriety factor : 0.578530 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 : 51/50, 34.2830 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing 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 class 1 -- Rational properties -- Prime limit : 17 Odd number limit : 153 (O: 51 U: 153) Highest odd numerator or denominator: 51 Scale harmonicity : 0.018433 Average absolute harmonicity : 0.088354 Specific harmonicity : 0.082529 Fundamental : 1/1200, -10.2288 octaves, 0.2180 Hz. Guide tone : 204, 7.6724 octaves, 53371.615 Hz. Exponens Consonantiae : 2.448000E+05, 17.90124 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 70.5, average 23.50000 Mersenne's string divisions : 23331 Sum of van Prooijen's expressibility: 3.41514, average 1.13838 Sum of Tenney's harmonic distance : 6.92029, average 2.30676 Vogel's harmonic complexity : 24.00000 Wille's k value : 637 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 23.15364, average 3.85894 Lattice compactness (without 2's) : 11.09977, average 1.84996 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -1.00000 7 3: -1 .. 1 0.00000 2 1 5: -2 .. 0 -0.66667 2 17: 0 .. 1 0.66667 2 2 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 15 27| Scale is weakly epimorphic with val: <6 10 16 31| Scale is weakly epimorphic with val: <6 10 18 27| Scale is weakly epimorphic with val: <6 11 15 27| Scale is weakly epimorphic with val: <6 11 17 32| Scale is weakly epimorphic with val: <6 11 18 27| Scale is weakly epimorphic with val: <7 10 15 30| Scale is weakly epimorphic with val: <7 10 16 31| Scale is weakly epimorphic with val: <7 10 19 31| Scale is weakly epimorphic with val: <7 11 15 27| Scale is weakly epimorphic with val: <7 11 15 30| Scale is weakly epimorphic with val: <7 11 15 33| Scale is weakly epimorphic with val: <7 11 17 29| Scale is weakly epimorphic with val: <7 11 17 32| Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 11 18 33| Scale is weakly epimorphic with val: <7 12 16 31| Scale is weakly epimorphic with val: <7 12 17 32| Scale is weakly epimorphic with val: <7 12 19 31| Scale is weakly epimorphic with val: <8 11 15 30| Scale is weakly epimorphic with val: <8 12 16 31|
FIT/MODE
3: 0 1 2 N G T3 SD: 40.4293 c. M:-61.0596 c. 4: 0 1 3 N G T3 SD: 22.7871 c. M: 34.2830 c. 5: 0 1 4 N G T3 SD: 20.0325 c. M: 34.2830 c. 6: 0 1 5 N G T3 SD: 23.5020 c. M: 34.2830 c. 9: 1 1 7 N M DE S SD: 12.5971 c. M:-21.0554 c. 10: 1 1 8 N M DE S SD: 9.4781 c. M:-15.5215 c. 11: 1 1 9 N M DE S SD: 10.4606 c. M: 14.4018 c. 12: 1 2 9 N T3 SD: 12.0356 c. M:-19.5558 c. 13: 1 2 10 N T3 SD: 6.2126 c. M:-9.9781 c. 14: 1 2 11 N T3 SD: 1.2644 c. M:-1.7685 c. 29: 2 4 23 N T3 SD: 1.1043 c. M: 1.9116 c. 43: 3 6 34 N T3 SD: 0.4915 c. M: 0.7134 c. 57: 4 8 45 N T3 SD: 0.3900 c. M:-0.6675 c. 100: 7 14 79 N T3 SD: 0.3960 c. M:-0.5802 c. 118: 8 17 93 N T3 SD: 0.4412 c. M:-0.5626 c. 128: 9 18 101 N T3 SD: 0.4288 c. M:-0.7358 c. 133: 9 19 105 N T3 SD: 0.3406 c. M: 0.5807 c. 143: 10 20 113 N T3 SD: 0.4158 c. M:-0.5453 c. 147: 10 21 116 N T3 SD: 0.2363 c. M: 0.4024 c. 161: 11 23 127 N T3 SD: 0.1951 c. M: 0.2551 c. 190: 13 27 150 N T3 SD: 0.1333 c. M: 0.2062 c. 204: 14 29 161 N T3 SD: 0.0614 c. M: 0.1034 c. 247: 17 35 195 N T3 SD: 0.0600 c. M: 0.1038 c. 261: 18 37 206 N T3 SD: 0.0375 c. M:-0.0649 c. 451: 31 64 356 N T3 SD: 0.0388 c. M: 0.0493 c. 465: 32 66 367 N T3 SD: 0.0073 c. M: 0.0089 c. 1191: 82 169 940 N T3 SD: 0.0055 c. M:-0.0073 c. 1656: 114 235 1307 N T3 SD: 0.0043 c. M:-0.0070 c. 2121: 146 301 1674 N T3 SD: 0.0043 c. M:-0.0074 c. 2368: 163 336 1869 N T3 SD: 0.0024 c. M: 0.0042 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: 80.9577 cents 7 x 8:9 S SD: 70.5252 cents 8 x 9:11 SD: 56.1917 cents 9 x 10:12 S SD: 38.7242 cents 10 x 11:13 SD: 37.1720 cents 11 x 12:15 S SD: 30.0020 cents 12 x 13:16 SD: 16.8086 cents 13 x 14:17 SD: 20.4634 cents 14 x 15:19 SD: 16.9472 cents 15 x 16:20 S SD: 3.3879 cents 16 x 17:21 SD: 13.6320 cents 17 x 18:23 SD: 12.9883 cents 18 x 19:24 SD: 5.6762 cents 19 x 20:25 S SD: 14.0249 cents 20 x 21:27 SD: 14.8517 cents 21 x 22:28 SD: 12.2092 cents 22 x 23:29 SD: 17.1422 cents 23 x 24:31 SD: 18.2237 cents 24 x 26:32 SD: 16.8086 cents 25:26:27:33 SD: 15.7506 cents 26:27:28:35 S SD: 14.0781 cents 27:28:29:36 SD: 11.4224 cents 28:29:30:37 SD: 11.3114 cents 29:30:31:39 SD: 10.1485 cents 30:31:32:40 S SD: 7.8276 cents 32:33:34:43 SD: 7.7612 cents 33:34:35:44 SD: 5.8905 cents 36:37:38:48 SD: 5.7911 cents 42:43:45:56 SD: 5.2866 cents 44:45:47:59 SD: 4.7473 cents 45:46:48:60 S SD: 2.5843 cents 48:49:51:64 SD: 0.4713 cents 207:211:220:276 SD: 0.4164 cents 255:260:271:340 SD: 0.2588 cents 303:309:322:404 SD: 0.1584 cents 351:358:373:468 SD: 0.1019 cents 399:407:424:532 SD: 0.0897 cents