Scala analysis: 511_M19
Miscellaneous tetrachord 22/17 * 357/352 * 64/63
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 22/17 446.362533 2: 21/16 470.780907 narrow fourth 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 64/63 27.2641 septimal comma, Archytas' comma 1: 22/17 446.3625 2: 357/352 24.4184 3: 64/63 27.2641 septimal comma, Archytas' comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 357/352 24.418 cents 1: 1 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 22/17 446.363 cents 2: 1 34/33 51.682 cents 2: 1 21/16 470.781 cents narrow fourth 2: 1 1408/1071 473.627 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 : 446.4 470.8 498.0 446.4: 24.4 51.7 498.0 470.8: 27.3 473.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 24.4184 .. 446.3625 cents 7744/6069, 421.9442 cents 357/352, 24.4184 cents 2: 51.6825 .. 473.6266 cents 7744/6069, 421.9442 cents 289/363,-394.6801 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 357/352, 24.4184 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 22/17, 446.3625 cents Average / Smallest step : 6.798774 Largest / Average step : 2.688688 Largest / Smallest step : 18.279781 Median interval of one step : 64/63, 27.2641 cents, amount: 1 Least squares average step : 205.86138 cents, oct.: 617.58415 cents Scale is not proper Scale has trivalence property Scale is a mode of a 877-tone equal temperament with octave 4/3 degrees: 786 829 877 Least number of segments generator : 439 of 249.306 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 508 of 288.491 cents and inv. generated superset size: 13 = 10 more = 433.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LSM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 24.41837 cents Scale diversity : 0.073434 Lumma stability : 0.098057 Lumma impropriety factor : 0.792459 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 : 22528/22491, 2.8457 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Limited inverse transpositions with margin 421.9442 cents: 1 -- Rational properties -- Prime limit : 17 Odd number limit : 1071 (O: 357 U: 1071) Highest odd numerator or denominator: 21 Scale harmonicity : 0.014302 Average absolute harmonicity : 0.097852 Specific harmonicity : 0.075917 Fundamental : 1/816, -9.6724 octaves, 0.3206 Hz. Guide tone : 924, 9.8517 octaves, 241742.022 Hz. Exponens Consonantiae : 7.539840E+05, 19.52417 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 41.5, average 13.83333 Mersenne's string divisions : 10101 Sum of van Prooijen's expressibility: 3.02979, average 1.00993 Sum of Tenney's harmonic distance : 6.17839, average 2.05946 Vogel's harmonic complexity : 24.00000 Wille's k value : 535 Wilson's harmonic complexity : 41 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 21.99905, average 3.66651 Lattice compactness (without 2's) : 9.79655, average 1.63276 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.33333 7 3: -1 .. 1 0.00000 2 1 7: 0 .. 1 0.33333 1 1 11: 0 .. 1 0.33333 1 17: -1 .. 0 -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 18 24 27| Scale is weakly epimorphic with val: <6 10 18 25 28| Scale is weakly epimorphic with val: <6 10 18 26 29| Scale is weakly epimorphic with val: <6 10 18 27 30| Scale is weakly epimorphic with val: <6 10 21 24 27| Scale is weakly epimorphic with val: <6 10 21 25 28| Scale is weakly epimorphic with val: <6 10 21 26 29| Scale is weakly epimorphic with val: <6 10 21 27 30| Scale is weakly epimorphic with val: <6 11 18 24 27| Scale is weakly epimorphic with val: <6 11 18 25 28| Scale is weakly epimorphic with val: <6 11 18 26 29| Scale is weakly epimorphic with val: <6 11 18 27 30| Scale is weakly epimorphic with val: <6 11 21 24 27| Scale is weakly epimorphic with val: <6 11 21 25 28| Scale is weakly epimorphic with val: <6 11 21 26 29| Scale is weakly epimorphic with val: <6 11 21 27 30| Scale is weakly epimorphic with val: <7 10 20 23 27| Scale is weakly epimorphic with val: <7 10 20 24 28| Scale is weakly epimorphic with val: <7 10 20 25 29| Scale is weakly epimorphic with val: <7 10 20 26 30| Scale is weakly epimorphic with val: <7 10 20 27 31| Scale is weakly epimorphic with val: <7 10 21 23 28| Scale is weakly epimorphic with val: <7 10 21 23 31| Scale is weakly epimorphic with val: <7 10 21 24 29| Scale is weakly epimorphic with val: <7 10 21 24 32| Scale is weakly epimorphic with val: <7 10 21 25 27| Scale is weakly epimorphic with val: <7 10 21 25 30| Scale is weakly epimorphic with val: <7 10 21 25 33| Scale is weakly epimorphic with val: <7 10 21 26 28| Scale is weakly epimorphic with val: <7 10 21 26 31| Scale is weakly epimorphic with val: <7 10 21 27 29| Scale is weakly epimorphic with val: <7 10 21 27 32| Scale is weakly epimorphic with val: <7 11 18 23 28| Scale is weakly epimorphic with val: <7 11 18 23 31| Scale is weakly epimorphic with val: <7 11 18 24 29| Scale is weakly epimorphic with val: <7 11 18 24 32| Scale is weakly epimorphic with val: <7 11 18 25 27| Scale is weakly epimorphic with val: <7 11 18 25 30| Scale is weakly epimorphic with val: <7 11 18 25 33| Scale is weakly epimorphic with val: <7 11 18 26 28| Scale is weakly epimorphic with val: <7 11 18 26 31| Scale is weakly epimorphic with val: <7 11 18 27 29| Scale is weakly epimorphic with val: <7 11 18 27 32| Scale is JI-epimorphic with val: <7 11 19 23 29| Scale is weakly epimorphic with val: <7 11 19 23 32| Scale is weakly epimorphic with val: <7 11 19 24 27| Scale is JI-epimorphic with val: <7 11 19 24 30| Scale is weakly epimorphic with val: <7 11 19 24 33| Scale is weakly epimorphic with val: <7 11 19 25 28| Scale is JI-epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 26 29| Scale is JI-epimorphic with val: <7 11 19 26 32| Scale is weakly epimorphic with val: <7 11 19 27 27| Scale is weakly epimorphic with val: <7 11 19 27 30| Scale is JI-epimorphic with val: <7 11 19 27 33| Scale is weakly epimorphic with val: <7 11 21 23 28| Scale is weakly epimorphic with val: <7 11 21 23 31| Scale is weakly epimorphic with val: <7 11 21 24 29| Scale is weakly epimorphic with val: <7 11 21 24 32| Scale is weakly epimorphic with val: <7 11 21 25 27| Scale is weakly epimorphic with val: <7 11 21 25 30| Scale is weakly epimorphic with val: <7 11 21 25 33| Scale is weakly epimorphic with val: <7 11 21 26 28| Scale is weakly epimorphic with val: <7 11 21 26 31| Scale is weakly epimorphic with val: <7 11 21 27 29| Scale is weakly epimorphic with val: <7 11 21 27 32| Scale is weakly epimorphic with val: <7 11 22 23 29| Scale is weakly epimorphic with val: <7 11 22 23 32| Scale is weakly epimorphic with val: <7 11 22 24 27| Scale is weakly epimorphic with val: <7 11 22 24 30| Scale is weakly epimorphic with val: <7 11 22 24 33| Scale is weakly epimorphic with val: <7 11 22 25 28| Scale is weakly epimorphic with val: <7 11 22 25 31| Scale is weakly epimorphic with val: <7 11 22 26 29| Scale is weakly epimorphic with val: <7 11 22 26 32| Scale is weakly epimorphic with val: <7 11 22 27 27| Scale is weakly epimorphic with val: <7 11 22 27 30| Scale is weakly epimorphic with val: <7 11 22 27 33| Scale is weakly epimorphic with val: <7 12 19 23 29| Scale is weakly epimorphic with val: <7 12 19 23 32| Scale is weakly epimorphic with val: <7 12 19 24 27| Scale is weakly epimorphic with val: <7 12 19 24 30| Scale is weakly epimorphic with val: <7 12 19 24 33| Scale is weakly epimorphic with val: <7 12 19 25 28| Scale is weakly epimorphic with val: <7 12 19 25 31| Scale is weakly epimorphic with val: <7 12 19 26 29| Scale is weakly epimorphic with val: <7 12 19 26 32| Scale is weakly epimorphic with val: <7 12 19 27 27| Scale is weakly epimorphic with val: <7 12 19 27 30| Scale is weakly epimorphic with val: <7 12 19 27 33| Scale is weakly epimorphic with val: <7 12 20 23 27| Scale is weakly epimorphic with val: <7 12 20 24 28| Scale is weakly epimorphic with val: <7 12 20 25 29| Scale is weakly epimorphic with val: <7 12 20 26 30| Scale is weakly epimorphic with val: <7 12 20 27 31| Scale is weakly epimorphic with val: <8 11 19 23 28| Scale is weakly epimorphic with val: <8 11 19 24 29| Scale is weakly epimorphic with val: <8 11 19 25 30| Scale is weakly epimorphic with val: <8 11 19 26 31| Scale is weakly epimorphic with val: <8 11 19 27 32| Scale is weakly epimorphic with val: <8 11 22 23 28| Scale is weakly epimorphic with val: <8 11 22 24 29| Scale is weakly epimorphic with val: <8 11 22 25 30| Scale is weakly epimorphic with val: <8 11 22 26 31| Scale is weakly epimorphic with val: <8 11 22 27 32| Scale is weakly epimorphic with val: <8 12 19 23 28| Scale is weakly epimorphic with val: <8 12 19 24 29| Scale is weakly epimorphic with val: <8 12 19 25 30| Scale is weakly epimorphic with val: <8 12 19 26 31| Scale is weakly epimorphic with val: <8 12 19 27 32| Scale is weakly epimorphic with val: <8 12 22 23 28| Scale is weakly epimorphic with val: <8 12 22 24 29| Scale is weakly epimorphic with val: <8 12 22 25 30| Scale is weakly epimorphic with val: <8 12 22 26 31| Scale is weakly epimorphic with val: <8 12 22 27 32|
FIT/MODE
3: 3 0 0 N M DE S SD: 33.7363 c. M:-51.6825 c. 4: 4 0 0 N M DE S SD: 33.7363 c. M:-51.6825 c. 5: 5 0 0 N M DE S SD: 33.7363 c. M:-51.6825 c. 7: 6 0 1 N G T3 SD: 27.7180 c. M: 43.8852 c. 8: 7 0 1 N G T3 SD: 21.1045 c. M: 34.9915 c. 9: 8 0 1 N G T3 SD: 16.3455 c. M: 28.0742 c. 10: 9 0 1 N G T3 SD: 13.0588 c. M: 22.5404 c. 11: 10 0 1 N G T3 SD: 11.0377 c. M: 18.0127 c. 12: 11 0 1 N G T3 SD: 10.1057 c. M: 14.2397 c. 13: 12 0 1 N G T3 SD: 10.0138 c. M:-13.3713 c. 15: 13 1 1 N M DE S SD: 9.1661 c. M: 14.7235 c. 16: 14 1 1 N M DE S SD: 6.4992 c. M: 10.5732 c. 17: 15 1 1 N M DE S SD: 4.1591 c. M: 6.9111 c. 18: 16 1 1 N M DE S SD: 2.1236 c. M: 3.6559 c. 19: 17 1 1 N M DE S SD: 0.7433 c. M:-1.0512 c. 58: 52 3 3 N M DE S SD: 0.8728 c. M:-1.5031 c. 77: 69 4 4 N M DE S SD: 0.8043 c. M:-1.3916 c. 87: 78 4 5 N T3 SD: 0.7902 c. M: 1.3592 c. 88: 79 4 5 N T3 SD: 0.7361 c. M: 1.0339 c. 105: 94 5 6 N T3 SD: 0.7468 c. M: 1.1956 c. 106: 95 5 6 N T3 SD: 0.5353 c. M: 0.9271 c. 107: 96 5 6 N T3 SD: 0.4734 c. M: 0.6637 c. 125: 112 6 7 N T3 SD: 0.3676 c. M: 0.6264 c. 126: 113 6 7 N T3 SD: 0.2900 c. M: 0.4051 c. 144: 129 7 8 N T3 SD: 0.2601 c. M: 0.4051 c. 145: 130 7 8 N T3 SD: 0.1546 c. M: 0.2143 c. 164: 147 8 9 N T3 SD: 0.0506 c. M: 0.0676 c. 183: 164 9 10 N T3 SD: 0.0321 c. M:-0.0485 c. 347: 311 17 19 N T3 SD: 0.0079 c. M:-0.0121 c. 530: 475 26 29 N T3 SD: 0.0073 c. M:-0.0126 c. 877: 786 43 48 N T3 SD: 0.0037 c. M:-0.0051 c. 2101: 1883 103 115 N T3 SD: 0.0035 c. M:-0.0053 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 4:5 x x S SD: 60.0488 cents 5:6 x 7 S SD: 77.8183 cents 6 x x 8 S SD: 0.0000 cents 7:9 x x SD: 11.2784 cents 8:10 x 11 S SD: 40.1369 cents 9 x x 12 S SD: 0.0000 cents 10:13 x x SD: 7.8514 cents 11:14 x 15 SD: 24.2190 cents 12 x x 16 S SD: 0.0000 cents 13 x 17 x SD: 6.3532 cents 14:18 x 19 SD: 16.3259 cents 15:19 x 20 SD: 18.5591 cents 16 x 21 x SD: 0.0000 cents 17:22 x 23 SD: 12.6370 cents 18:23 x 24 SD: 10.9991 cents 19 x 25 x SD: 4.3335 cents 20:26 x 27 SD: 11.4473 cents 21:27 x 28 SD: 5.6392 cents 22:28:29 x SD: 14.9040 cents 23 x 30:31 SD: 10.8010 cents 24:31 x 32 SD: 1.6410 cents 25:32:33 x SD: 10.6996 cents 26 x 34:35 SD: 8.8717 cents 27:35 x 36 SD: 1.4560 cents 28:36:37 x SD: 8.1389 cents 29 x 38:39 SD: 7.5652 cents 30:39 x 40 SD: 3.9257 cents 31:40:41 x SD: 7.0941 cents 33:43 x 44 SD: 5.9411 cents 34:44 x 45 SD: 6.3883 cents 35:45:46:47 SD: 5.6231 cents 36 x 47:48 SD: 4.5921 cents 37:48 x 49 SD: 6.2412 cents 38:49:50:51 SD: 4.5508 cents 40:52 x 53 SD: 6.6981 cents 41:53:54:55 SD: 4.0921 cents 42:54:55:56 SD: 3.9812 cents 43:56 x 57 SD: 7.4450 cents 44:57:58:59 SD: 4.1544 cents 45:58:59:60 SD: 2.4149 cents 46 x 60:61 SD: 7.1652 cents 47:61:62:63 SD: 4.5465 cents 48:62:63:64 SD: 1.0940 cents 51:66:67:68 SD: 0.5386 cents 150:194:197:200 SD: 0.5065 cents 201:260:264:268 SD: 0.4861 cents 231:299:303:308 SD: 0.3746 cents 279:361:366:372 SD: 0.3102 cents 282:365:370:376 SD: 0.2160 cents 330:427:433:440 SD: 0.1846 cents 333:431:437:444 SD: 0.1141 cents 381:493:500:508 SD: 0.0997 cents 384:497:504:512 SD: 0.0683 cents 432:559:567:576 SD: 0.0607 cents