Scala analysis: 039_H10
Hyperenharmonic tetrachord 39/38 * 76/75 * 50/39
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 39/38 44.969647 2: 26/25 67.900234 tridecimal 1/3-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 50/39 430.1448 1: 39/38 44.9696 2: 76/75 22.9306 3: 50/39 430.1448
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 76/75 22.931 cents 1: 1 39/38 44.970 cents 1: 1 50/39 430.145 cents 2: 1 26/25 67.900 cents tridecimal 1/3-tone 2: 1 152/117 453.075 cents 2: 1 25/19 475.114 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 : 45.0 67.9 498.0 45.0 : 22.9 453.1 498.0 67.9 : 430.1 475.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 22.9306 .. 430.1448 cents 625/494, 407.2142 cents 76/75, 22.9306 cents 2: 67.9002 .. 475.1144 cents 625/494, 407.2142 cents 507/625,-362.2445 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 76/75, 22.9306 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 50/39, 430.1448 cents Average / Smallest step : 7.239893 Largest / Average step : 2.590999 Largest / Smallest step : 18.758558 Median interval of one step : 39/38, 44.9696 cents, amount: 1 Least squares average step : 119.63608 cents, oct.: 358.90824 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2171-tone equal temperament with octave 4/3 degrees: 196 296 2171 Least number of segments generator : 1086 of 249.137 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1875 of 430.140 cents and inv. generated superset size: 31 = 28 more = 1033.333% 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 22.93059 cents Scale diversity : 0.169906 Lumma stability : 0.092082 Lumma impropriety factor : 0.727333 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 : 2925/2888, 22.0391 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 Limited inverse transpositions with margin 407.2142 cents: 2 -- Rational properties -- Prime limit : 19 Odd number limit : 117 (O: 39 U: 117) Highest odd numerator or denominator: 39 Scale harmonicity : 0.012921 Average absolute harmonicity : 0.086262 Specific harmonicity : 0.062663 Fundamental : 1/2850, -11.4767 octaves, 0.0918 Hz. Guide tone : 156, 7.2854 octaves, 40813.588 Hz. Exponens Consonantiae : 4.446000E+05, 18.76215 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 67.5, average 22.50000 Mersenne's string divisions : 3927 Sum of van Prooijen's expressibility: 3.46613, average 1.15538 Sum of Tenney's harmonic distance : 7.06294, average 2.35431 Vogel's harmonic complexity : 32.66667 Wille's k value : 1462 Wilson's harmonic complexity : 48 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 16.36657, average 2.72776 Lattice compactness (without 2's) : 12.31659, average 2.05276 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -1 .. 1 0.00000 2 1 5: -2 .. 0 -0.66667 2 13: 0 .. 1 0.66667 2 1 19: -1 .. 0 -0.33333 1 1 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 15 27 30| Scale is weakly epimorphic with val: <6 10 15 27 33| Scale is weakly epimorphic with val: <6 10 15 28 29| Scale is weakly epimorphic with val: <6 10 16 27 28| Scale is weakly epimorphic with val: <6 10 16 29 29| Scale is weakly epimorphic with val: <6 10 16 29 32| Scale is weakly epimorphic with val: <6 10 16 30 31| Scale is weakly epimorphic with val: <6 10 17 29 30| Scale is weakly epimorphic with val: <6 10 18 28 29| Scale is weakly epimorphic with val: <6 10 19 27 28| Scale is weakly epimorphic with val: <6 10 19 30 31| Scale is weakly epimorphic with val: <6 11 15 26 28| Scale is weakly epimorphic with val: <6 11 15 27 30| Scale is weakly epimorphic with val: <6 11 15 27 33| Scale is weakly epimorphic with val: <6 11 15 29 31| Scale is weakly epimorphic with val: <6 11 16 28 30| Scale is weakly epimorphic with val: <6 11 16 29 29| Scale is weakly epimorphic with val: <6 11 16 29 32| Scale is weakly epimorphic with val: <6 11 17 27 29| Scale is weakly epimorphic with val: <6 11 17 30 32| Scale is weakly epimorphic with val: <6 11 18 26 28| Scale is weakly epimorphic with val: <6 11 18 29 31| Scale is weakly epimorphic with val: <6 11 19 28 30| Scale is weakly epimorphic with val: <7 10 15 26 30| Scale is weakly epimorphic with val: <7 10 15 26 33| Scale is weakly epimorphic with val: <7 10 15 28 28| Scale is weakly epimorphic with val: <7 10 16 28 29| Scale is weakly epimorphic with val: <7 10 16 28 32| Scale is weakly epimorphic with val: <7 10 16 30 30| Scale is weakly epimorphic with val: <7 10 17 29 29| Scale is weakly epimorphic with val: <7 10 17 30 31| Scale is weakly epimorphic with val: <7 10 17 30 34| Scale is weakly epimorphic with val: <7 10 18 28 28| Scale is weakly epimorphic with val: <7 10 19 30 30| Scale is JI-epimorphic with val: <7 11 15 25 28| Scale is weakly epimorphic with val: <7 11 15 25 31| Scale is weakly epimorphic with val: <7 11 15 25 34| Scale is weakly epimorphic with val: <7 11 15 27 29| Scale is weakly epimorphic with val: <7 11 15 27 32| Scale is weakly epimorphic with val: <7 11 15 28 28| Scale is weakly epimorphic with val: <7 11 15 28 31| Scale is weakly epimorphic with val: <7 11 15 28 34| Scale is weakly epimorphic with val: <7 11 15 30 32| Scale is weakly epimorphic with val: <7 11 16 26 28| Scale is weakly epimorphic with val: <7 11 16 26 31| Scale is weakly epimorphic with val: <7 11 16 26 34| Scale is JI-epimorphic with val: <7 11 16 27 30| Scale is weakly epimorphic with val: <7 11 16 27 33| Scale is weakly epimorphic with val: <7 11 16 29 31| Scale is weakly epimorphic with val: <7 11 16 29 34| Scale is weakly epimorphic with val: <7 11 16 30 30| Scale is weakly epimorphic with val: <7 11 16 30 33| Scale is weakly epimorphic with val: <7 11 17 25 30| Scale is weakly epimorphic with val: <7 11 17 25 33| Scale is weakly epimorphic with val: <7 11 17 26 29| Scale is weakly epimorphic with val: <7 11 17 26 32| Scale is weakly epimorphic with val: <7 11 17 28 30| Scale is weakly epimorphic with val: <7 11 17 28 33| Scale is weakly epimorphic with val: <7 11 17 29 29| Scale is JI-epimorphic with val: <7 11 17 29 32| Scale is weakly epimorphic with val: <7 11 18 25 28| Scale is weakly epimorphic with val: <7 11 18 25 31| Scale is weakly epimorphic with val: <7 11 18 25 34| Scale is weakly epimorphic with val: <7 11 18 27 29| Scale is weakly epimorphic with val: <7 11 18 27 32| Scale is weakly epimorphic with val: <7 11 18 28 28| Scale is weakly epimorphic with val: <7 11 18 28 31| Scale is weakly epimorphic with val: <7 11 18 28 34| Scale is weakly epimorphic with val: <7 11 18 30 32| Scale is weakly epimorphic with val: <7 11 19 26 28| Scale is weakly epimorphic with val: <7 11 19 26 31| Scale is weakly epimorphic with val: <7 11 19 26 34| Scale is weakly epimorphic with val: <7 11 19 27 30| Scale is weakly epimorphic with val: <7 11 19 27 33| Scale is weakly epimorphic with val: <7 11 19 29 31| Scale is weakly epimorphic with val: <7 11 19 29 34| Scale is weakly epimorphic with val: <7 11 19 30 30| Scale is weakly epimorphic with val: <7 11 19 30 33| Scale is weakly epimorphic with val: <7 12 15 26 30| Scale is weakly epimorphic with val: <7 12 15 26 33| Scale is weakly epimorphic with val: <7 12 15 27 29| Scale is weakly epimorphic with val: <7 12 15 30 32| Scale is weakly epimorphic with val: <7 12 16 26 28| Scale is weakly epimorphic with val: <7 12 16 28 29| Scale is weakly epimorphic with val: <7 12 16 28 32| Scale is weakly epimorphic with val: <7 12 16 29 31| Scale is weakly epimorphic with val: <7 12 17 28 30| Scale is weakly epimorphic with val: <7 12 17 30 31| Scale is weakly epimorphic with val: <7 12 17 30 34| Scale is weakly epimorphic with val: <7 12 18 27 29| Scale is weakly epimorphic with val: <7 12 18 30 32| Scale is weakly epimorphic with val: <7 12 19 26 28| Scale is weakly epimorphic with val: <7 12 19 29 31| Scale is weakly epimorphic with val: <8 11 15 25 30| Scale is weakly epimorphic with val: <8 11 15 25 33| Scale is weakly epimorphic with val: <8 11 15 29 29| Scale is weakly epimorphic with val: <8 11 16 27 29| Scale is weakly epimorphic with val: <8 11 16 27 32| Scale is weakly epimorphic with val: <8 11 16 28 28| Scale is weakly epimorphic with val: <8 11 17 29 31| Scale is weakly epimorphic with val: <8 11 17 29 34| Scale is weakly epimorphic with val: <8 11 17 30 30| Scale is weakly epimorphic with val: <8 11 18 29 29| Scale is weakly epimorphic with val: <8 11 19 28 28| Scale is weakly epimorphic with val: <8 12 15 25 30| Scale is weakly epimorphic with val: <8 12 15 25 33| Scale is weakly epimorphic with val: <8 12 15 27 28| Scale is weakly epimorphic with val: <8 12 15 30 31| Scale is weakly epimorphic with val: <8 12 16 27 29| Scale is weakly epimorphic with val: <8 12 16 27 32| Scale is weakly epimorphic with val: <8 12 16 29 30| Scale is weakly epimorphic with val: <8 12 17 28 29| Scale is weakly epimorphic with val: <8 12 17 29 31| Scale is weakly epimorphic with val: <8 12 17 29 34| Scale is weakly epimorphic with val: <8 12 18 27 28| Scale is weakly epimorphic with val: <8 12 18 30 31| Scale is weakly epimorphic with val: <8 12 19 29 30|
FIT/MODE
3: 0 0 3 N M DE S SD: 47.0202 c. M: 67.9002 c. 5: 0 1 4 N G T3 SD: 31.7685 c. M: 44.9696 c. 6: 1 0 5 N G T3 SD: 23.6298 c. M:-38.0379 c. 7: 1 0 6 N G T3 SD: 15.2308 c. M:-26.1796 c. 8: 1 0 7 N G T3 SD: 10.4987 c. M:-17.2860 c. 9: 1 0 8 N G T3 SD: 9.4041 c. M: 12.5619 c. 12: 1 1 10 N M DE S SD: 8.9488 c. M:-15.1073 c. 13: 1 1 11 N M DE S SD: 6.3354 c. M:-8.7221 c. 14: 1 1 12 N M DE S SD: 5.7394 c. M: 9.3950 c. 15: 1 1 13 N M DE S SD: 6.8480 c. M: 11.7666 c. 19: 2 1 16 N T3 SD: 7.5478 c. M:-10.7385 c. 20: 2 1 17 N T3 SD: 4.8203 c. M:-6.8065 c. 21: 2 1 18 N T3 SD: 2.3540 c. M:-3.2491 c. 22: 2 1 19 N T3 SD: 0.1776 c. M:-0.3072 c. 221: 20 10 191 N T3 SD: 0.1788 c. M: 0.2923 c. 234: 21 11 202 N T3 SD: 0.1985 c. M: 0.2733 c. 243: 22 11 210 N T3 SD: 0.1679 c. M: 0.2645 c. 256: 23 12 221 N T3 SD: 0.1700 c. M: 0.2234 c. 265: 24 12 229 N T3 SD: 0.1600 c. M: 0.2413 c. 278: 25 13 240 N T3 SD: 0.1467 c. M: 0.1814 c. 300: 27 14 259 N T3 SD: 0.1274 c. M:-0.1659 c. 322: 29 15 278 N T3 SD: 0.1116 c. M:-0.1556 c. 344: 31 16 297 N T3 SD: 0.0986 c. M:-0.1466 c. 366: 33 17 316 N T3 SD: 0.0882 c. M:-0.1387 c. 388: 35 18 335 N T3 SD: 0.0800 c. M:-0.1317 c. 389: 35 18 336 N T3 SD: 0.0948 c. M: 0.1584 c. 410: 37 19 354 N T3 SD: 0.0737 c. M:-0.1254 c. 411: 37 19 355 N T3 SD: 0.0805 c. M: 0.1335 c. 432: 39 20 373 N T3 SD: 0.0693 c. M:-0.1198 c. 433: 39 20 374 N T3 SD: 0.0677 c. M: 0.1111 c. 454: 41 21 392 N T3 SD: 0.0664 c. M:-0.1147 c. 455: 41 21 393 N T3 SD: 0.0562 c. M: 0.0909 c. 477: 43 22 412 N T3 SD: 0.0459 c. M: 0.0725 c. 499: 45 23 431 N T3 SD: 0.0367 c. M: 0.0558 c. 521: 47 24 450 N T3 SD: 0.0286 c. M: 0.0404 c. 543: 49 25 469 N T3 SD: 0.0217 c. M: 0.0267 c. 565: 51 26 488 N T3 SD: 0.0164 c. M: 0.0251 c. 587: 53 27 507 N T3 SD: 0.0136 c. M: 0.0236 c. 609: 55 28 526 N T3 SD: 0.0140 c. M: 0.0222 c. 631: 57 29 545 N T3 SD: 0.0168 c. M: 0.0209 c. 1152: 104 53 995 N T3 SD: 0.0146 c. M: 0.0243 c. 1196: 108 55 1033 N T3 SD: 0.0134 c. M: 0.0229 c. 1540: 139 71 1330 N T3 SD: 0.0128 c. M: 0.0162 c. 1562: 141 72 1349 N T3 SD: 0.0110 c. M:-0.0150 c. 1584: 143 73 1368 N T3 SD: 0.0096 c. M:-0.0150 c. 1606: 145 74 1387 N T3 SD: 0.0088 c. M:-0.0150 c. 1628: 147 75 1406 N T3 SD: 0.0087 c. M:-0.0150 c. 1650: 149 76 1425 N T3 SD: 0.0092 c. M:-0.0150 c. 1672: 151 77 1444 N T3 SD: 0.0102 c. M:-0.0150 c. 2105: 190 97 1818 N T3 SD: 0.0093 c. M: 0.0155 c. 2127: 192 98 1837 N T3 SD: 0.0074 c. M: 0.0121 c. 2149: 194 99 1856 N T3 SD: 0.0057 c. M: 0.0089 c. 2171: 196 100 1875 N T3 SD: 0.0042 c. M: 0.0057 c. 2193: 198 101 1894 N T3 SD: 0.0031 c. M:-0.0047 c. 2215: 200 102 1913 N T3 SD: 0.0028 c. M:-0.0048 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: 99.4853 cents 7 x 8:9 S SD: 87.4963 cents 8 x 9:11 SD: 73.0354 cents 9 x 10:12 S SD: 57.2517 cents 10 x 11:13 SD: 53.2690 cents 11 x 12:15 S SD: 45.7139 cents 12 x 13:16 SD: 35.3362 cents 13 x 14:17 SD: 34.5617 cents 14 x 15:19 SD: 29.9816 cents 15 x 16:20 S SD: 21.9155 cents 16 x 17:21 SD: 23.0023 cents 17 x 18:23 SD: 20.0196 cents 18 x 19:24 SD: 12.8514 cents 19 x 20:25 S SD: 15.5132 cents 20 x 21:27 SD: 13.5737 cents 21 x 22:28 SD: 6.3184 cents 22 x 23:29 SD: 10.8799 cents 23 x 24:31 SD: 9.7943 cents 24 x 25:32 SD: 1.3861 cents 25 x 26:33 SD: 8.6997 cents 26 x 27:35 SD: 8.3820 cents 27 x 28:36 SD: 2.4697 cents 28 x 29:37 SD: 8.5468 cents 29 x 30:39 SD: 8.7412 cents 30 x 31:40 SD: 5.5667 cents 31:32 x 41 SD: 8.6082 cents 32:33 x 43 SD: 7.9129 cents 33:34 x 44 SD: 3.3564 cents 34:35 x 45 SD: 6.8999 cents 35:36 x 47 SD: 6.4474 cents 36:37 x 48 SD: 1.2322 cents 37:38 x 49 SD: 5.8992 cents 42:43:44:56 SD: 4.4423 cents 45:46:47:60 SD: 3.3727 cents 48:49:50:64 SD: 3.2261 cents 57 x 59:76 SD: 4.0983 cents 58 x 60:77 SD: 5.9314 cents 59 x 61:79 SD: 6.2722 cents 60 x 62:80 SD: 5.5667 cents 61:63 x 81 SD: 6.4991 cents 62:64 x 83 SD: 6.0916 cents 63:65:66:84 SD: 5.1978 cents 65:67:68:87 SD: 4.7689 cents 66:68:69:88 SD: 3.7576 cents 68:70:71:91 SD: 3.5645 cents 69:71:72:92 SD: 2.4413 cents 72:74:75:96 SD: 1.2364 cents 75:77:78:100 SD: 0.1973 cents 378:388:393:504 SD: 0.1928 cents 453:465:471:604 SD: 0.1767 cents 498:511:518:664 SD: 0.1486 cents 573:588:596:764 SD: 0.1096 cents