Scala analysis: 085_E9
Enharmonic tetrachord 57/56 * 28/27 * 24/19, Wilson
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 57/56 30.642111 Hendrix comma 2: 19/18 93.603014 undevicesimal semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 24/19 404.4420 smaller undevicesimal major third 1: 57/56 30.6421 Hendrix comma 2: 28/27 62.9609 Archytas' 1/3-tone 3: 24/19 404.4420 smaller undevicesimal major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 57/56 30.642 cents Hendrix comma 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 24/19 404.442 cents smaller undevicesimal major third 2: 1 19/18 93.603 cents undevicesimal semitone 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 224/171 467.403 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 : 30.6 93.6 498.0 30.6 : 63.0 467.4 498.0 93.6 : 404.4 435.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 30.6421 .. 404.4420 cents 448/361, 373.7999 cents 57/56, 30.6421 cents 2: 93.6030 .. 467.4029 cents 448/361, 373.7999 cents 361/432,-310.8390 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 57/56, 30.6421 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 24/19, 404.4420 cents Average / Smallest step : 5.417871 Largest / Average step : 2.436177 Largest / Smallest step : 13.198895 Median interval of one step : 28/27, 62.9609 cents, amount: 1 Least squares average step : 122.28451 cents, oct.: 366.85353 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2357-tone equal temperament with octave 4/3 degrees: 145 443 2357 Least number of segments generator : 1179 of 249.128 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1404 of 296.672 cents and inv. generated superset size: 50 = 47 more = 1666.667% 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 30.64211 cents Scale diversity : 0.346654 Lumma stability : 0.123050 Lumma impropriety factor : 0.624118 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 : 57/56, 30.6421 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 : 19 Odd number limit : 171 (O: 57 U: 171) Highest odd numerator or denominator: 57 Scale harmonicity : 0.017424 Average absolute harmonicity : 0.086330 Specific harmonicity : 0.076210 Fundamental : 1/504, -8.9773 octaves, 0.5191 Hz. Guide tone : 228, 7.8329 octaves, 59650.629 Hz. Exponens Consonantiae : 1.149120E+05, 16.81017 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 78.5, average 26.16667 Mersenne's string divisions : 29267 Sum of van Prooijen's expressibility: 3.51175, average 1.17058 Sum of Tenney's harmonic distance : 7.11727, average 2.37242 Vogel's harmonic complexity : 23.66667 Wille's k value : 256 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 20.77571, average 3.46262 Lattice compactness (without 2's) : 11.99410, average 1.99902 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.66667 6 3: -2 .. 1 -0.66667 4 1 7: -1 .. 0 -0.33333 1 19: 0 .. 1 0.66667 2 2 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 19 30| Scale is weakly epimorphic with val: <6 10 20 29| Scale is weakly epimorphic with val: <6 10 22 33| Scale is weakly epimorphic with val: <6 11 19 31| Scale is weakly epimorphic with val: <6 11 20 30| Scale is weakly epimorphic with val: <6 11 22 31| Scale is weakly epimorphic with val: <7 10 18 32| Scale is weakly epimorphic with val: <7 10 20 30| 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 11 20 28| Scale is JI-epimorphic with val: <7 11 20 31| = patent Scale is weakly epimorphic with val: <7 11 20 34| Scale is weakly epimorphic with val: <7 11 21 30| Scale is weakly epimorphic with val: <7 11 21 33| Scale is weakly epimorphic with val: <7 12 18 34| Scale is weakly epimorphic with val: <7 12 20 32| Scale is weakly epimorphic with val: <7 12 21 34| Scale is weakly epimorphic with val: <8 11 18 34| Scale is weakly epimorphic with val: <8 11 19 33| Scale is weakly epimorphic with val: <8 11 22 33| Scale is weakly epimorphic with val: <8 12 19 34|
FIT/MODE
3: 0 0 3 N M DE S SD: 56.8638 c. M: 93.6030 c. 4: 0 1 3 N G T3 SD: 25.1281 c. M:-30.9082 c. 5: 0 1 4 N G T3 SD: 18.0279 c. M: 30.6421 c. 6: 0 1 5 N G T3 SD: 18.7190 c. M: 30.6421 c. 10: 1 1 8 N M DE S SD: 11.5941 c. M:-19.1624 c. 11: 1 1 9 N M DE S SD: 8.6308 c. M:-14.6347 c. 12: 1 1 10 N M DE S SD: 8.7605 c. M:-10.8616 c. 14: 1 2 11 N T3 SD: 8.0930 c. M:-13.1209 c. 15: 1 2 12 N T3 SD: 3.7696 c. M:-6.0060 c. 16: 1 2 13 N T3 SD: 0.3077 c. M:-0.4857 c. 149: 9 19 121 N T3 SD: 0.3227 c. M: 0.5589 c. 165: 10 21 134 N T3 SD: 0.2648 c. M: 0.4576 c. 181: 11 23 147 N T3 SD: 0.2178 c. M: 0.3742 c. 197: 12 25 160 N T3 SD: 0.1793 c. M: 0.3043 c. 213: 13 27 173 N T3 SD: 0.1477 c. M: 0.2450 c. 229: 14 29 186 N T3 SD: 0.1219 c. M: 0.1939 c. 245: 15 31 199 N T3 SD: 0.1015 c. M: 0.1496 c. 261: 16 33 212 N T3 SD: 0.0862 c. M: 0.1106 c. 277: 17 35 225 N T3 SD: 0.0759 c. M: 0.1072 c. 293: 18 37 238 N T3 SD: 0.0705 c. M: 0.1133 c. 309: 19 39 251 N T3 SD: 0.0694 c. M: 0.1188 c. 489: 30 62 397 N T3 SD: 0.0760 c. M:-0.0987 c. 505: 31 64 410 N T3 SD: 0.0649 c. M:-0.0886 c. 521: 32 66 423 N T3 SD: 0.0547 c. M:-0.0792 c. 537: 33 68 436 N T3 SD: 0.0456 c. M:-0.0703 c. 553: 34 70 449 N T3 SD: 0.0377 c. M:-0.0619 c. 569: 35 72 462 N T3 SD: 0.0314 c. M:-0.0540 c. 585: 36 74 475 N T3 SD: 0.0271 c. M:-0.0465 c. 601: 37 76 488 N T3 SD: 0.0254 c. M:-0.0394 c. 617: 38 78 501 N T3 SD: 0.0263 c. M:-0.0327 c. 830: 51 105 674 N T3 SD: 0.0229 c. M: 0.0393 c. 846: 52 107 687 N T3 SD: 0.0170 c. M: 0.0294 c. 862: 53 109 700 N T3 SD: 0.0116 c. M: 0.0199 c. 878: 54 111 713 N T3 SD: 0.0073 c. M: 0.0106 c. 894: 55 113 726 N T3 SD: 0.0062 c. M: 0.0107 c. 1495: 92 189 1214 N T3 SD: 0.0067 c. M:-0.0095 c. 1772: 109 224 1439 N T3 SD: 0.0062 c. M: 0.0088 c. 2341: 144 296 1901 N T3 SD: 0.0052 c. M:-0.0065 c. 2357: 145 298 1914 N T3 SD: 0.0033 c. M:-0.0049 c. 2373: 146 300 1927 N T3 SD: 0.0020 c. M:-0.0034 c. 2389: 147 302 1940 N T3 SD: 0.0024 c. M:-0.0036 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: 86.6339 cents 7 x 8:9 S SD: 75.6470 cents 8 x 9:11 SD: 61.2488 cents 9 x 10:12 S SD: 44.4003 cents 10 x 11:13 SD: 41.8906 cents 11 x 12:15 S SD: 34.5201 cents 12 x 13:16 SD: 22.4848 cents 13 x 14:17 SD: 24.1551 cents 14 x 15:19 SD: 20.0414 cents 15 x 16:20 S SD: 9.0641 cents 16 x 17:21 SD: 14.7666 cents 17 x 18:23 SD: 12.9172 cents 18 x 19:24 SD: 0.0000 cents 19 x 20:25 S SD: 11.7140 cents 20 x 21:27 SD: 11.6831 cents 21 x 22:28 SD: 6.5330 cents 22 x 23:29 SD: 12.9285 cents 23 x 24:31 SD: 13.6675 cents 24 x 25:32 SD: 11.4653 cents 25 x 26:33 SD: 15.5191 cents 26 x 27:35 SD: 16.3815 cents 27 x 29:36 SD: 15.0546 cents 28:29:30:37 SD: 14.2023 cents 29:30:31:39 SD: 12.8464 cents 30:31:32:40 S SD: 10.5995 cents 31:32:33:41 SD: 10.5528 cents 32:33:34:43 SD: 9.5600 cents 33:34:35:44 SD: 7.5350 cents 35:36:37:47 SD: 7.3578 cents 36:37:38:48 SD: 5.5973 cents 39:40:41:52 SD: 4.9808 cents 48:49:51:64 SD: 4.1423 cents 50:51:53:67 SD: 3.9543 cents 51:52:54:68 SD: 2.0410 cents 54:55:57:72 SD: 0.3748 cents 285:290:301:380 SD: 0.3657 cents 288:293:304:384 SD: 0.2813 cents 342:348:361:456 SD: 0.1776 cents 396:403:418:528 SD: 0.1023 cents 450:458:475:600 SD: 0.0450 cents 504:513:532:672 SD: 0.0000 cents