Scala analysis: 074_E7
Enharmonic tetrachord 28/27 * 135/133 * 19/15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 20/19 88.800698 small undevicesimal semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 19/15 409.2443 undevicesimal ditone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 135/133 25.8398 3: 19/15 409.2443 undevicesimal ditone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 135/133 25.840 cents 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 19/15 409.244 cents undevicesimal ditone 2: 1 20/19 88.801 cents small undevicesimal semitone 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 532/405 472.205 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 : 63.0 88.8 498.0 63.0 : 25.8 435.1 498.0 88.8 : 409.2 472.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 25.8398 .. 409.2443 cents 2527/2025, 383.4045 cents 135/133, 25.8398 cents 2: 88.8007 .. 472.2052 cents 2527/2025, 383.4045 cents 300/361,-320.4436 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 135/133, 25.8398 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 19/15, 409.2443 cents Average / Smallest step : 6.424780 Largest / Average step : 2.465104 Largest / Smallest step : 15.837754 Median interval of one step : 28/27, 62.9609 cents, amount: 1 Least squares average step : 123.90695 cents, oct.: 371.72085 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1060-tone equal temperament with octave 4/3 degrees: 134 189 1060 Least number of segments generator : 531 of 249.492 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 993 of 466.565 cents and inv. generated superset size: 16 = 13 more = 533.333% 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 25.83979 cents Scale diversity : 0.302402 Lumma stability : 0.103765 Lumma impropriety factor : 0.643403 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 : 135/133, 25.8398 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% -- Rational properties -- Prime limit : 19 Odd number limit : 405 (O: 135 U: 405) Highest odd numerator or denominator: 27 Scale harmonicity : 0.016450 Average absolute harmonicity : 0.095702 Specific harmonicity : 0.086468 Fundamental : 1/513, -9.0028 octaves, 0.5100 Hz. Guide tone : 140, 7.1293 octaves, 36627.579 Hz. Exponens Consonantiae : 7.182000E+04, 16.13210 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 50.5, average 16.83333 Mersenne's string divisions : 15015 Sum of van Prooijen's expressibility: 3.18724, average 1.06241 Sum of Tenney's harmonic distance : 6.53749, average 2.17916 Vogel's harmonic complexity : 23.66667 Wille's k value : 85 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 15.85944, average 2.64324 Lattice compactness (without 2's) : 13.00871, average 2.16812 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -3 .. 0 -1.33333 4 1 5: 0 .. 1 0.33333 1 7: 0 .. 1 0.33333 1 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 15 21 29| Scale is weakly epimorphic with val: <6 10 15 21 32| Scale is weakly epimorphic with val: <6 10 16 21 30| Scale is weakly epimorphic with val: <6 10 16 21 33| Scale is weakly epimorphic with val: <6 10 17 21 28| Scale is weakly epimorphic with val: <6 10 17 21 31| Scale is weakly epimorphic with val: <6 10 17 21 34| Scale is weakly epimorphic with val: <6 10 18 21 29| Scale is weakly epimorphic with val: <6 10 18 21 32| Scale is weakly epimorphic with val: <6 10 19 19 28| Scale is weakly epimorphic with val: <6 10 19 21 30| Scale is weakly epimorphic with val: <6 10 19 21 33| Scale is weakly epimorphic with val: <6 10 19 22 28| Scale is weakly epimorphic with val: <6 11 19 20 28| Scale is weakly epimorphic with val: <7 10 15 19 30| Scale is weakly epimorphic with val: <7 10 15 19 33| Scale is weakly epimorphic with val: <7 10 16 19 28| Scale is weakly epimorphic with val: <7 10 16 19 31| Scale is weakly epimorphic with val: <7 10 16 19 34| Scale is weakly epimorphic with val: <7 10 17 18 28| Scale is weakly epimorphic with val: <7 10 17 19 29| Scale is weakly epimorphic with val: <7 10 17 19 32| Scale is weakly epimorphic with val: <7 10 17 21 28| Scale is weakly epimorphic with val: <7 10 18 18 29| Scale is weakly epimorphic with val: <7 10 18 19 30| Scale is weakly epimorphic with val: <7 10 18 19 33| Scale is weakly epimorphic with val: <7 10 18 21 29| Scale is weakly epimorphic with val: <7 10 19 19 28| Scale is weakly epimorphic with val: <7 10 19 19 31| Scale is weakly epimorphic with val: <7 10 19 19 34| Scale is weakly epimorphic with val: <7 10 19 21 30| Scale is weakly epimorphic with val: <7 11 15 18 28| Scale is weakly epimorphic with val: <7 11 15 18 31| Scale is weakly epimorphic with val: <7 11 15 18 34| Scale is weakly epimorphic with val: <7 11 15 20 30| Scale is weakly epimorphic with val: <7 11 15 20 33| Scale is weakly epimorphic with val: <7 11 15 21 28| Scale is weakly epimorphic with val: <7 11 15 21 31| Scale is weakly epimorphic with val: <7 11 15 21 34| Scale is weakly epimorphic with val: <7 11 16 18 29| Scale is weakly epimorphic with val: <7 11 16 18 32| Scale is JI-epimorphic with val: <7 11 16 20 28| Scale is weakly epimorphic with val: <7 11 16 20 31| Scale is weakly epimorphic with val: <7 11 16 20 34| Scale is weakly epimorphic with val: <7 11 16 21 29| Scale is weakly epimorphic with val: <7 11 16 21 32| Scale is weakly epimorphic with val: <7 11 17 18 30| Scale is weakly epimorphic with val: <7 11 17 18 33| Scale is JI-epimorphic with val: <7 11 17 20 29| Scale is weakly epimorphic with val: <7 11 17 20 32| Scale is weakly epimorphic with val: <7 11 17 21 30| Scale is weakly epimorphic with val: <7 11 17 21 33| Scale is weakly epimorphic with val: <7 11 18 18 28| Scale is weakly epimorphic with val: <7 11 18 18 31| Scale is weakly epimorphic with val: <7 11 18 18 34| Scale is JI-epimorphic with val: <7 11 18 20 30| Scale is weakly epimorphic with val: <7 11 18 20 33| Scale is weakly epimorphic with val: <7 11 18 21 28| Scale is weakly epimorphic with val: <7 11 18 21 31| Scale is weakly epimorphic with val: <7 11 18 21 34| Scale is weakly epimorphic with val: <7 11 19 20 28| Scale is JI-epimorphic with val: <7 11 19 20 31| Scale is weakly epimorphic with val: <7 11 19 20 34| Scale is weakly epimorphic with val: <7 11 19 21 29| Scale is weakly epimorphic with val: <7 11 19 21 32| Scale is weakly epimorphic with val: <7 12 17 20 28| Scale is weakly epimorphic with val: <7 12 18 20 29| Scale is weakly epimorphic with val: <7 12 19 20 30| Scale is weakly epimorphic with val: <8 11 15 18 28| Scale is weakly epimorphic with val: <8 11 15 20 30| Scale is weakly epimorphic with val: <8 11 15 20 33| Scale is weakly epimorphic with val: <8 11 15 21 28| Scale is weakly epimorphic with val: <8 11 16 18 29| Scale is weakly epimorphic with val: <8 11 16 20 28| Scale is weakly epimorphic with val: <8 11 16 20 31| Scale is weakly epimorphic with val: <8 11 16 20 34| Scale is weakly epimorphic with val: <8 11 16 21 29| Scale is weakly epimorphic with val: <8 11 17 18 30| Scale is weakly epimorphic with val: <8 11 17 20 29| Scale is weakly epimorphic with val: <8 11 17 20 32| Scale is weakly epimorphic with val: <8 11 17 21 30| Scale is weakly epimorphic with val: <8 11 18 18 31| Scale is weakly epimorphic with val: <8 11 18 20 30| Scale is weakly epimorphic with val: <8 11 18 20 33| Scale is weakly epimorphic with val: <8 11 18 21 31| Scale is weakly epimorphic with val: <8 11 19 20 28| Scale is weakly epimorphic with val: <8 11 19 20 31| Scale is weakly epimorphic with val: <8 11 19 20 34| Scale is weakly epimorphic with val: <8 11 19 21 32| Scale is weakly epimorphic with val: <8 12 15 19 28| Scale is weakly epimorphic with val: <8 12 15 22 28| Scale is weakly epimorphic with val: <8 12 16 19 29| Scale is weakly epimorphic with val: <8 12 16 22 29| Scale is weakly epimorphic with val: <8 12 17 19 30| Scale is weakly epimorphic with val: <8 12 17 22 30| Scale is weakly epimorphic with val: <8 12 18 19 31| Scale is weakly epimorphic with val: <8 12 18 22 31| Scale is weakly epimorphic with val: <8 12 19 19 32| Scale is weakly epimorphic with val: <8 12 19 22 32|
FIT/MODE
3: 0 0 3 N M DE S SD: 62.8481 c. M: 88.8007 c. 5: 1 0 4 N G T3 SD: 22.0598 c. M:-36.6481 c. 6: 1 0 5 N G T3 SD: 12.0475 c. M:-20.0466 c. 7: 1 0 6 N G T3 SD: 11.2342 c. M: 17.6514 c. 10: 1 1 8 N M DE S SD: 9.8304 c. M: 13.1564 c. 11: 1 1 9 N M DE S SD: 10.2599 c. M: 17.6841 c. 15: 2 1 12 N T3 SD: 6.5495 c. M:-10.8083 c. 16: 2 1 13 N T3 SD: 2.6770 c. M:-4.5827 c. 17: 2 1 14 N T3 SD: 2.5757 c. M: 4.3674 c. 23: 3 1 19 N T3 SD: 1.7104 c. M: 2.1842 c. 39: 5 2 32 N T3 SD: 0.6176 c. M:-0.8910 c. 56: 7 3 46 N T3 SD: 0.4147 c. M: 0.7053 c. 79: 10 4 65 N T3 SD: 0.3152 c. M: 0.5396 c. 95: 12 5 78 N T3 SD: 0.1888 c. M:-0.3231 c. 135: 17 7 111 N T3 SD: 0.2056 c. M: 0.2594 c. 174: 22 9 143 N T3 SD: 0.0400 c. M: 0.0685 c. 443: 56 23 364 N T3 SD: 0.0090 c. M:-0.0155 c. 617: 78 32 507 N T3 SD: 0.0048 c. M: 0.0082 c. 1060: 134 55 871 N T3 SD: 0.0010 c. M:-0.0017 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: 89.0351 cents 7 x 8:9 S SD: 77.8368 cents 8 x 9:11 SD: 63.4196 cents 9 x 10:12 S SD: 46.8015 cents 10 x 11:13 SD: 43.9549 cents 11 x 12:15 S SD: 36.5287 cents 12 x 13:16 SD: 24.8860 cents 13 x 14:17 SD: 25.9335 cents 14 x 15:19 SD: 21.6672 cents 15 x 16:20 S SD: 11.4653 cents 16 x 17:21 SD: 15.8454 cents 17 x 18:23 SD: 13.6187 cents 18 x 19:24 SD: 2.4012 cents 19 x 20:25 S SD: 11.4653 cents 20 x 21:27 SD: 10.9693 cents 21 x 22:28 SD: 4.1318 cents 22 x 23:29 SD: 11.5300 cents 23:24 x 31 SD: 10.7844 cents 24:25 x 32 SD: 3.8558 cents 25:26 x 33 SD: 9.0435 cents 26:27 x 35 SD: 8.3683 cents 27:28 x 36 SD: 0.0000 cents 28:29 x 37 SD: 7.8417 cents 32:33:34:43 SD: 7.7197 cents 33:34:35:44 SD: 5.7535 cents 36:37:38:48 SD: 5.4175 cents 41 x 43:55 SD: 6.1446 cents 42 x 44:56 SD: 4.1318 cents 43 x 45:57 SD: 7.1380 cents 44 x 46:59 SD: 7.6892 cents 45:47 x 60 SD: 6.1610 cents 46:48 x 61 SD: 7.1401 cents 47:49 x 63 SD: 6.4943 cents 48:50:51:64 SD: 5.9670 cents 49:51:52:65 SD: 5.9272 cents 50:52:53:67 SD: 5.2153 cents 51:53:54:68 SD: 3.5948 cents 53:55:56:71 SD: 3.5000 cents 54:56:57:72 SD: 1.6008 cents 57:59:60:76 SD: 1.0858 cents 78:81:82:104 SD: 1.0842 cents 111:115:117:148 SD: 0.9581 cents 132:137:139:176 SD: 0.5167 cents 135:140:142:180 SD: 0.4276 cents 189:196:199:252 SD: 0.1526 cents 324:336:341:432 SD: 0.0891 cents 513:532:540:684 SD: 0.0000 cents