Scala analysis: 041_H11
Hyperenharmonic tetrachord 50/49 * 49/48 * 32/25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 50/49 34.975615 Erlich's decatonic comma, tritonic diesis 2: 25/24 70.672427 classic chromatic semitone, minor chroma 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 32/25 427.3726 classic diminished fourth 1: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 2: 49/48 35.6968 slendro diesis, septimal 1/6-tone 3: 32/25 427.3726 classic diminished fourth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 1 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 1 32/25 427.373 cents classic diminished fourth 2: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 1 64/49 462.348 cents 2 septatones or septatonic major third 2: 1 98/75 463.069 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 : 35.0 70.7 498.0 35.0 : 35.7 463.1 498.0 70.7 : 427.4 462.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.9756 .. 427.3726 cents 784/625, 392.3970 cents 50/49, 34.9756 cents 2: 70.6724 .. 463.0694 cents 784/625, 392.3970 cents 625/768,-356.7001 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 50/49, 34.9756 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 32/25, 427.3726 cents Average / Smallest step : 4.746593 Largest / Average step : 2.574301 Largest / Smallest step : 12.219158 Median interval of one step : 49/48, 35.6968 cents, amount: 1 Least squares average step : 119.31825 cents, oct.: 357.95474 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1353-tone equal temperament with octave 4/3 degrees: 95 192 1353 Least number of segments generator : 677 of 249.207 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1063 of 391.295 cents and inv. generated superset size: 24 = 21 more = 800.000% 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 34.97561 cents Scale diversity : 0.211462 Lumma stability : 0.140452 Lumma impropriety factor : 0.716201 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 : 2401/2400, 0.7212 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 : 2 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 Limited inverse transpositions with margin 391.6758 cents: 2 -- Rational properties -- Prime limit : 7 Odd number limit : 75 (O: 49 U: 75) Highest odd numerator or denominator: 49 Scale harmonicity : 0.024368 Average absolute harmonicity : 0.099177 Specific harmonicity : 0.114628 Fundamental : 1/1176, -10.1997 octaves, 0.2225 Hz. Guide tone : 100, 6.6439 octaves, 26162.557 Hz. Exponens Consonantiae : 1.176000E+05, 16.84353 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 77.5, average 25.83333 Mersenne's string divisions : 4851 Sum of van Prooijen's expressibility: 3.56526, average 1.18842 Sum of Tenney's harmonic distance : 7.24650, average 2.41550 Vogel's harmonic complexity : 20.00000 Wille's k value : 612 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 22.10774, average 3.68462 Lattice compactness (without 2's) : 13.30056, average 2.21676 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 0.00000 6 3: -1 .. 0 -0.66667 2 1 5: 0 .. 2 1.33333 4 1 7: -2 .. 0 -0.66667 2 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 11 16 18| Scale is weakly epimorphic with val: <6 11 16 21| Scale is weakly epimorphic with val: <7 10 17 18| Scale is weakly epimorphic with val: <7 10 17 21| Scale is weakly epimorphic with val: <7 10 18 20| Scale is weakly epimorphic with val: <7 11 15 19| Scale is weakly epimorphic with val: <7 11 15 22| Scale is JI-epimorphic with val: <7 11 17 20| = patent Scale is weakly epimorphic with val: <7 11 18 19| Scale is weakly epimorphic with val: <7 11 18 22| Scale is weakly epimorphic with val: <7 12 17 19| Scale is weakly epimorphic with val: <7 12 18 18| Scale is weakly epimorphic with val: <7 12 18 21| Scale is weakly epimorphic with val: <8 11 19 21|
FIT/MODE
3: 0 0 3 N M DE S SD: 45.5261 c. M: 70.6724 c. 5: 0 1 4 N G T3 SD: 26.2083 c. M: 34.9756 c. 6: 0 1 5 N G T3 SD: 21.4122 c. M: 34.9756 c. 7: 0 1 6 N G T3 SD: 20.1951 c. M: 34.9756 c. 8: 0 1 7 N G T3 SD: 20.7697 c. M: 34.9756 c. 9: 0 1 8 N G T3 SD: 22.0486 c. M: 34.9756 c. 10: 1 0 9 N G T3 SD: 14.7802 c. M: 20.8679 c. 11: 1 1 9 N M DE S SD: 12.9277 c. M:-19.8812 c. 12: 1 1 10 N M DE S SD: 8.0575 c. M:-12.3351 c. 13: 1 1 11 N M DE S SD: 3.9381 c. M:-5.9499 c. 14: 1 1 12 N M DE S SD: 0.4421 c. M:-0.5990 c. 71: 5 5 61 N M DE S SD: 0.3085 c. M: 0.5252 c. 85: 6 6 73 N M DE S SD: 0.2326 c. M: 0.3602 c. 99: 7 7 85 N M DE S SD: 0.1966 c. M: 0.2418 c. 113: 8 8 97 N M DE S SD: 0.1863 c. M:-0.2842 c. 127: 9 9 109 N M DE S SD: 0.1903 c. M:-0.3189 c. 141: 10 10 121 N M DE S SD: 0.2008 c. M:-0.3467 c. 155: 11 11 133 N M DE S SD: 0.2136 c. M:-0.3695 c. 184: 13 13 158 N M DE S SD: 0.2106 c. M: 0.2965 c. 212: 15 15 182 N M DE S SD: 0.1890 c. M:-0.2634 c. 240: 17 17 206 N M DE S SD: 0.1871 c. M:-0.3026 c. 296: 21 21 254 N M DE S SD: 0.2071 c. M:-0.3587 c. 311: 22 22 267 N M DE S SD: 0.1909 c. M:-0.2559 c. 325: 23 23 279 N M DE S SD: 0.1876 c. M:-0.2706 c. 353: 25 25 303 N M DE S SD: 0.1865 c. M:-0.2967 c. 359: 25 26 308 N T3 SD: 0.1753 c. M: 0.2928 c. 373: 26 27 320 N T3 SD: 0.1595 c. M: 0.2593 c. 387: 27 28 332 N T3 SD: 0.1461 c. M: 0.2283 c. 401: 28 29 344 N T3 SD: 0.1350 c. M: 0.1994 c. 415: 29 30 356 N T3 SD: 0.1261 c. M: 0.1725 c. 416: 29 30 357 N T3 SD: 0.1494 c. M: 0.2561 c. 429: 30 31 368 N T3 SD: 0.1194 c. M: 0.1473 c. 430: 30 31 369 N T3 SD: 0.1323 c. M: 0.2283 c. 443: 31 32 380 N T3 SD: 0.1148 c. M:-0.1556 c. 444: 31 32 381 N T3 SD: 0.1168 c. M: 0.2022 c. 457: 32 33 392 N T3 SD: 0.1121 c. M:-0.1655 c. 458: 32 33 393 N T3 SD: 0.1028 c. M: 0.1777 c. 472: 33 34 405 N T3 SD: 0.0904 c. M: 0.1547 c. 486: 34 35 417 N T3 SD: 0.0798 c. M: 0.1330 c. 500: 35 36 429 N T3 SD: 0.0711 c. M: 0.1125 c. 514: 36 37 441 N T3 SD: 0.0644 c. M: 0.0931 c. 528: 37 38 453 N T3 SD: 0.0602 c. M: 0.0747 c. 542: 38 39 465 N T3 SD: 0.0583 c. M:-0.0830 c. 557: 39 40 478 N T3 SD: 0.0629 c. M: 0.1035 c. 570: 40 41 489 N T3 SD: 0.0609 c. M:-0.1024 c. 571: 40 41 490 N T3 SD: 0.0514 c. M: 0.0863 c. 585: 41 42 502 N T3 SD: 0.0407 c. M: 0.0699 c. 599: 42 43 514 N T3 SD: 0.0313 c. M: 0.0543 c. 613: 43 44 526 N T3 SD: 0.0238 c. M: 0.0393 c. 627: 44 45 538 N T3 SD: 0.0196 c. M: 0.0251 c. 641: 45 46 550 N T3 SD: 0.0201 c. M:-0.0329 c. 698: 49 50 599 N T3 SD: 0.0203 c. M: 0.0328 c. 712: 50 51 611 N T3 SD: 0.0132 c. M: 0.0228 c. 726: 51 52 623 N T3 SD: 0.0099 c. M: 0.0132 c. 1325: 93 95 1137 N T3 SD: 0.0113 c. M: 0.0185 c. 1339: 94 96 1149 N T3 SD: 0.0070 c. M: 0.0120 c. 1353: 95 97 1161 N T3 SD: 0.0039 c. M: 0.0057 c. 2065: 145 148 1772 N T3 SD: 0.0039 c. M: 0.0055 c. 2079: 146 149 1784 N T3 SD: 0.0013 c. M: 0.0023 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: 98.0992 cents 7 x 8:9 S SD: 86.2045 cents 8 x 9:11 SD: 71.7465 cents 9 x 10:12 S SD: 55.8656 cents 10 x 11:13 SD: 52.0088 cents 11 x 12:15 S SD: 44.4635 cents 12 x 13:16 SD: 33.9501 cents 13 x 14:17 SD: 33.3574 cents 14 x 15:19 SD: 28.7988 cents 15 x 16:20 S SD: 20.5294 cents 16 x 17:21 SD: 21.9012 cents 17 x 18:23 SD: 18.9648 cents 18 x 19:24 SD: 11.4653 cents 19 x 20:25 S SD: 14.6155 cents 20 x 21:27 SD: 12.7751 cents 21 x 22:28 SD: 4.9323 cents 22 x 23:29 SD: 10.3798 cents 23 x 24:31 SD: 9.4782 cents 24 x 25:32 SD: 0.0000 cents 25 x 26:33 SD: 8.8095 cents 26 x 27:35 SD: 8.7024 cents 27 x 28:36 SD: 3.8558 cents 28 x 29:37 SD: 9.2129 cents 29 x 30:39 SD: 9.5443 cents 30 x 31:40 SD: 6.9528 cents 31 x 32:41 SD: 10.5268 cents 32 x 33:43 SD: 11.0029 cents 33:34 x 44 SD: 8.3534 cents 34:35 x 45 SD: 9.9316 cents 35:36 x 47 SD: 9.2483 cents 36:37:38:48 SD: 8.6988 cents 38:39:40:51 SD: 7.8697 cents 39:40:41:52 SD: 6.0687 cents 41:42:43:55 SD: 5.7258 cents 42:43:44:56 SD: 3.8079 cents 45:46:47:60 SD: 1.8473 cents 48:49:50:64 SD: 0.2404 cents 387:395:403:516 SD: 0.2329 cents 435:444:453:580 SD: 0.2251 cents 483:493:503:644 SD: 0.2203 cents 531:542:553:708 SD: 0.2173 cents 579:591:603:772 SD: 0.2156 cents 597:609:622:796 SD: 0.2091 cents