Scala analysis: 100_E12
Enharmonic tetrachord 49/48 * 51/49 * 64/51
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 49/48 35.696812 slendro diesis, septimal 1/6-tone 2: 17/16 104.955410 17th harmonic 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 64/51 393.0896 1: 49/48 35.6968 slendro diesis, septimal 1/6-tone 2: 51/49 69.2586 3: 64/51 393.0896
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 1 51/49 69.259 cents 1: 1 64/51 393.090 cents 2: 1 17/16 104.955 cents 17th harmonic 2: 1 196/153 428.786 cents 2: 1 64/49 462.348 cents 2 septatones or septatonic major third 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 : 35.7 105.0 498.0 35.7 : 69.3 462.3 498.0 105.0: 393.1 428.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 393.0896 cents 1024/833, 357.3928 cents 49/48, 35.6968 cents 2: 104.9554 .. 462.3482 cents 1024/833, 357.3928 cents 867/1024,-288.1342 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 49/48, 35.6968 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 64/51, 393.0896 cents Average / Smallest step : 4.650695 Largest / Average step : 2.367796 Largest / Smallest step : 11.011896 Median interval of one step : 51/49, 69.2586 cents, amount: 1 Least squares average step : 124.26733 cents, oct.: 372.80199 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2107-tone equal temperament with octave 4/3 degrees: 151 444 2107 Least number of segments generator : 1054 of 249.141 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1833 of 433.278 cents and inv. generated superset size: 40 = 37 more = 1333.333% 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 35.69681 cents Scale diversity : 0.431236 Lumma stability : 0.143348 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 : 2448/2401, 33.5618 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% -- Rational properties -- Prime limit : 17 Odd number limit : 153 (O: 51 U: 153) Highest odd numerator or denominator: 49 Scale harmonicity : 0.016848 Average absolute harmonicity : 0.093436 Specific harmonicity : 0.086611 Fundamental : 1/48, -5.5850 octaves, 5.4505 Hz. Guide tone : 3332, 11.7022 octaves, 871736.384 Hz. Exponens Consonantiae : 1.599360E+05, 17.28714 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 68.5, average 22.83333 Mersenne's string divisions : 22407 Sum of van Prooijen's expressibility: 3.39777, average 1.13259 Sum of Tenney's harmonic distance : 6.88519, average 2.29506 Vogel's harmonic complexity : 13.33333 Wille's k value : 25 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 25.88021, average 4.31337 Lattice compactness (without 2's) : 10.09977, average 1.68330 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -2.00000 10 3: -1 .. 0 -0.66667 2 1 7: 0 .. 2 0.66667 2 1 17: 0 .. 1 0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 19 27| Scale is weakly epimorphic with val: <6 10 22 27| Scale is weakly epimorphic with val: <6 11 19 29| Scale is weakly epimorphic with val: <6 11 19 32| Scale is weakly epimorphic with val: <6 11 20 27| Scale is weakly epimorphic with val: <7 10 20 31| Scale is weakly epimorphic with val: <7 11 19 29| Scale is weakly epimorphic with val: <7 11 19 32| Scale is weakly epimorphic with val: <7 11 20 27| Scale is JI-epimorphic with val: <7 11 20 30| = patent Scale is weakly epimorphic with val: <7 11 20 33| Scale is weakly epimorphic with val: <7 11 22 29| Scale is weakly epimorphic with val: <7 11 22 32| Scale is weakly epimorphic with val: <7 12 19 31| Scale is weakly epimorphic with val: <7 12 22 31|
FIT/MODE
3: 0 1 2 N G T3 SD: 40.8352 c. M:-61.0596 c. 4: 0 1 3 N G T3 SD: 23.4996 c. M: 35.6968 c. 5: 0 1 4 N G T3 SD: 20.8394 c. M: 35.6968 c. 6: 0 1 5 N G T3 SD: 24.1935 c. M: 35.6968 c. 9: 1 1 7 N M DE S SD: 11.8113 c. M:-19.6415 c. 10: 1 1 8 N M DE S SD: 8.7104 c. M:-14.1077 c. 13: 1 2 10 N T3 SD: 5.9553 c. M:-9.9781 c. 14: 1 2 11 N T3 SD: 1.0235 c. M:-1.7685 c. 43: 3 6 34 N T3 SD: 0.6857 c. M: 0.9495 c. 57: 4 8 45 N T3 SD: 0.4350 c. M: 0.7463 c. 71: 5 10 56 N T3 SD: 0.3911 c. M: 0.6232 c. 85: 6 12 67 N T3 SD: 0.4303 c. M: 0.5407 c. 123: 9 17 97 N T3 SD: 0.4689 c. M:-0.7455 c. 124: 9 17 98 N T3 SD: 0.4005 c. M: 0.5266 c. 128: 9 18 101 N T3 SD: 0.3958 c. M: 0.6780 c. 137: 10 19 108 N T3 SD: 0.4664 c. M:-0.6568 c. 138: 10 19 109 N T3 SD: 0.2835 c. M:-0.3934 c. 152: 11 21 120 N T3 SD: 0.2085 c. M:-0.3459 c. 166: 12 23 131 N T3 SD: 0.1797 c. M:-0.3064 c. 180: 13 25 142 N T3 SD: 0.1912 c. M:-0.2731 c. 195: 14 27 154 N T3 SD: 0.1419 c. M: 0.2383 c. 209: 15 29 165 N T3 SD: 0.0661 c. M: 0.1038 c. 223: 16 31 176 N T3 SD: 0.0230 c. M:-0.0374 c. 712: 51 99 562 N T3 SD: 0.0217 c. M: 0.0302 c. 726: 52 101 573 N T3 SD: 0.0142 c. M: 0.0242 c. 935: 67 130 738 N T3 SD: 0.0123 c. M: 0.0197 c. 949: 68 132 749 N T3 SD: 0.0068 c. M: 0.0097 c. 1158: 83 161 914 N T3 SD: 0.0077 c. M: 0.0133 c. 1172: 84 163 925 N T3 SD: 0.0046 c. M:-0.0080 c. 2107: 151 293 1663 N T3 SD: 0.0034 c. M: 0.0043 c. 2330: 167 324 1839 N T3 SD: 0.0015 c. M: 0.0026 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: 15.4189 cents 26:27:28:35 S SD: 13.7352 cents 27:28:29:36 SD: 11.0310 cents 28:29:30:37 SD: 10.9478 cents 29:30:31:39 SD: 9.7747 cents 30:31:32:40 S SD: 7.3776 cents 33:34:35:44 SD: 5.4271 cents 42:43:45:56 SD: 5.1130 cents 44:45:47:59 SD: 4.6159 cents 45:46:48:60 S SD: 2.3910 cents 48:49:51:64 SD: 0.0000 cents