Scala analysis: 089_E10
Enharmonic tetrachord 27/26 * 52/51 * 34/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/26 65.337341 tridecimal comma 2: 18/17 98.954592 Arabic lute index finger 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 34/27 399.0904 septendecimal major third 1: 27/26 65.3373 tridecimal comma 2: 52/51 33.6173 3: 34/27 399.0904 septendecimal major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 52/51 33.617 cents 1: 1 27/26 65.337 cents tridecimal comma 1: 1 34/27 399.090 cents septendecimal major third 2: 1 18/17 98.955 cents Arabic lute index finger 2: 1 104/81 432.708 cents 2: 1 17/13 464.428 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 : 65.3 99.0 498.0 65.3 : 33.6 432.7 498.0 99.0 : 399.1 464.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.6173 .. 399.0904 cents 289/234, 365.4732 cents 52/51, 33.6173 cents 2: 98.9546 .. 464.4277 cents 289/234, 365.4732 cents 243/289,-300.1358 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 52/51, 33.6173 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 34/27, 399.0904 cents Average / Smallest step : 4.938387 Largest / Average step : 2.403942 Largest / Smallest step : 11.871595 Median interval of one step : 27/26, 65.3373 cents, amount: 1 Least squares average step : 125.52725 cents, oct.: 376.58175 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1837-tone equal temperament with octave 4/3 degrees: 241 365 1837 Least number of segments generator : 919 of 249.158 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1493 of 404.780 cents and inv. generated superset size: 48 = 45 more = 1600.000% 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 33.61725 cents Scale diversity : 0.388328 Lumma stability : 0.134997 Lumma impropriety factor : 0.602628 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 : 1377/1352, 31.7201 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 17 Odd number limit : 81 (O: 27 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.015166 Average absolute harmonicity : 0.091272 Specific harmonicity : 0.078374 Fundamental : 1/1326, -10.3729 octaves, 0.1973 Hz. Guide tone : 108, 6.7549 octaves, 28255.561 Hz. Exponens Consonantiae : 1.432080E+05, 17.12775 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 47.5, average 15.83333 Mersenne's string divisions : 1855 Sum of van Prooijen's expressibility: 3.13893, average 1.04631 Sum of Tenney's harmonic distance : 6.41124, average 2.13708 Vogel's harmonic complexity : 28.66667 Wille's k value : 688 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 19.06358, average 3.17726 Lattice compactness (without 2's) : 15.41578, average 2.56930 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -1 .. 3 1.33333 6 1 13: -1 .. 0 -0.33333 1 1 17: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 2 / 3 = 0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is JI-epimorphic with val: <7 11 25 27| Scale is weakly epimorphic with val: <7 11 25 30| Scale is weakly epimorphic with val: <7 11 25 33| Scale is weakly epimorphic with val: <7 11 27 28| Scale is weakly epimorphic with val: <7 11 27 31| Scale is weakly epimorphic with val: <7 11 28 30| Scale is weakly epimorphic with val: <7 11 28 33| Scale is weakly epimorphic with val: <7 11 30 31| Scale is weakly epimorphic with val: <7 12 25 28| Scale is weakly epimorphic with val: <7 12 26 27| Scale is weakly epimorphic with val: <7 12 26 30| Scale is weakly epimorphic with val: <7 12 26 33| Scale is weakly epimorphic with val: <7 12 28 28| Scale is weakly epimorphic with val: <8 11 27 27| Scale is weakly epimorphic with val: <8 12 25 27| Scale is weakly epimorphic with val: <8 12 25 30| Scale is weakly epimorphic with val: <8 12 25 33| Scale is weakly epimorphic with val: <8 12 26 29| Scale is weakly epimorphic with val: <8 12 29 29|
FIT/MODE
3: 0 0 3 N M DE S SD: 68.4616 c. M: 98.9546 c. 4: 1 0 3 N G T3 SD: 37.2142 c. M:-59.1739 c. 5: 1 0 4 N G T3 SD: 19.7904 c. M:-34.2717 c. 6: 1 0 5 N G T3 SD: 13.7422 c. M:-17.6702 c. 8: 1 1 6 N M DE S SD: 14.8620 c. M:-25.5567 c. 9: 1 1 7 N M DE S SD: 8.8955 c. M:-11.7221 c. 10: 1 1 8 N M DE S SD: 8.9758 c. M: 15.5328 c. 14: 2 1 11 N T3 SD: 5.6018 c. M:-7.7693 c. 15: 2 1 12 N T3 SD: 0.7235 c. M:-1.0687 c. 61: 8 4 49 N T3 SD: 0.5651 c. M: 0.9785 c. 76: 10 5 61 N T3 SD: 0.3952 c. M: 0.6562 c. 91: 12 6 73 N T3 SD: 0.3208 c. M: 0.4402 c. 106: 14 7 85 N T3 SD: 0.3038 c. M:-0.4422 c. 121: 16 8 97 N T3 SD: 0.3156 c. M:-0.5198 c. 146: 19 10 117 N T3 SD: 0.3025 c. M: 0.5233 c. 161: 21 11 129 N T3 SD: 0.2175 c. M: 0.3749 c. 176: 23 12 141 N T3 SD: 0.1541 c. M: 0.2519 c. 191: 25 13 153 N T3 SD: 0.1149 c. M: 0.1482 c. 206: 27 14 165 N T3 SD: 0.1045 c. M:-0.1709 c. 221: 29 15 177 N T3 SD: 0.1180 c. M:-0.2037 c. 252: 33 17 202 N T3 SD: 0.1037 c. M: 0.1361 c. 267: 35 18 214 N T3 SD: 0.0605 c. M: 0.0917 c. 282: 37 19 226 N T3 SD: 0.0305 c. M: 0.0520 c. 488: 64 33 391 N T3 SD: 0.0269 c. M:-0.0421 c. 579: 76 39 464 N T3 SD: 0.0287 c. M:-0.0364 c. 740: 97 50 593 N T3 SD: 0.0325 c. M: 0.0531 c. 755: 99 51 605 N T3 SD: 0.0180 c. M: 0.0308 c. 770: 101 52 617 N T3 SD: 0.0070 c. M: 0.0094 c. 1052: 138 71 843 N T3 SD: 0.0055 c. M: 0.0084 c. 1822: 239 123 1460 N T3 SD: 0.0039 c. M: 0.0065 c. 1837: 241 124 1472 N T3 SD: 0.0025 c. M:-0.0037 c. 2119: 278 143 1698 N T3 SD: 0.0028 c. M: 0.0037 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: 83.9582 cents 7 x 8:9 S SD: 73.2224 cents 8 x 9:11 SD: 58.8508 cents 9 x 10:12 S SD: 41.7246 cents 10 x 11:13 SD: 39.6349 cents 11 x 12:15 S SD: 32.3448 cents 12 x 13:16 SD: 19.8090 cents 13 x 14:17 SD: 22.3113 cents 14 x 15:19 SD: 18.4303 cents 15 x 16:20 S SD: 6.3883 cents 16 x 17:21 SD: 13.9583 cents 17 x 18:23 SD: 12.6370 cents 18 x 19:24 SD: 2.6758 cents 19 x 20:25 S SD: 12.5391 cents 20 x 21:27 SD: 12.9654 cents 21:22 x 28 SD: 7.5998 cents 22:23 x 29 SD: 11.4726 cents 23:24 x 31 SD: 10.2458 cents 24:25 x 32 SD: 2.6675 cents 25:26 x 33 SD: 8.7936 cents 27:28:29:36 SD: 8.2905 cents 29:30:31:39 SD: 7.7271 cents 30:31:32:40 S SD: 5.1283 cents 33:34:35:44 SD: 4.6540 cents 39 x 41:52 SD: 6.1874 cents 40 x 42:53 SD: 9.0512 cents 41 x 43:55 SD: 9.7850 cents 42:44 x 56 SD: 7.5998 cents 44:46:47:59 SD: 7.1747 cents 45:47:48:60 SD: 5.3971 cents 47:49:50:63 SD: 4.6831 cents 48:50:51:64 SD: 2.6765 cents 51:53:54:68 SD: 0.4189 cents 237:246:251:316 SD: 0.3025 cents 288:299:305:384 SD: 0.1855 cents 339:352:359:452 SD: 0.1137 cents 390:405:413:520 SD: 0.0822 cents