Scala analysis: 040_H10
Hyperenharmonic tetrachord 78/77 * 77/75 * 50/39
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 78/77 22.338814 tridecimal minor third comma 2: 26/25 67.900234 tridecimal 1/3-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 50/39 430.1448 1: 78/77 22.3388 tridecimal minor third comma 2: 77/75 45.5614 3: 50/39 430.1448
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 78/77 22.339 cents tridecimal minor third comma 1: 1 77/75 45.561 cents 1: 1 50/39 430.145 cents 2: 1 26/25 67.900 cents tridecimal 1/3-tone 2: 1 100/77 452.484 cents 2: 1 154/117 475.706 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 : 22.3 67.9 498.0 22.3 : 45.6 475.7 498.0 67.9 : 430.1 452.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 22.3388 .. 430.1448 cents 1925/1521, 407.8060 cents 78/77, 22.3388 cents 2: 67.9002 .. 475.7062 cents 1925/1521, 407.8060 cents 507/625,-362.2445 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 78/77, 22.3388 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 50/39, 430.1448 cents Average / Smallest step : 7.431684 Largest / Average step : 2.590999 Largest / Smallest step : 19.255488 Median interval of one step : 77/75, 45.5614 cents, amount: 1 Least squares average step : 118.01959 cents, oct.: 354.05877 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1115-tone equal temperament with octave 4/3 degrees: 50 152 1115 Least number of segments generator : 558 of 249.246 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 963 of 430.150 cents and inv. generated superset size: 16 = 13 more = 533.333% 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 22.33881 cents Scale diversity : 0.168382 Lumma stability : 0.089706 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 : 78/77, 22.3388 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% Limited inverse transpositions with margin 384.5833 cents: 2 -- Rational properties -- Prime limit : 13 Odd number limit : 117 (O: 77 U: 117) Highest odd numerator or denominator: 77 Scale harmonicity : 0.014133 Average absolute harmonicity : 0.086839 Specific harmonicity : 0.068254 Fundamental : 1/5775, -12.4956 octaves, 0.0453 Hz. Guide tone : 156, 7.2854 octaves, 40813.588 Hz. Exponens Consonantiae : 9.009000E+05, 19.78101 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 106.5, average 35.50000 Mersenne's string divisions : 55335 Sum of van Prooijen's expressibility: 3.76155, average 1.25385 Sum of Tenney's harmonic distance : 7.67068, average 2.55689 Vogel's harmonic complexity : 31.66667 Wille's k value : 1501 Wilson's harmonic complexity : 47 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 15.04156, average 2.50693 Lattice compactness (without 2's) : 12.97706, average 2.16284 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.33333 4 3: -1 .. 1 0.00000 2 1 5: -2 .. 0 -0.66667 2 7: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.33333 1 13: 0 .. 1 0.66667 2 2 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 16 19 25 27| Scale is weakly epimorphic with val: <7 11 16 19 26 26| Scale is JI-epimorphic with val: <7 11 16 20 24 27| Scale is weakly epimorphic with val: <7 11 16 20 25 26| Scale is weakly epimorphic with val: <7 11 16 21 24 26| Scale is weakly epimorphic with val: <7 11 16 21 26 27| Scale is weakly epimorphic with val: <7 11 17 19 24 26| Scale is weakly epimorphic with val: <7 11 17 19 25 28| Scale is weakly epimorphic with val: <7 11 17 20 24 28| Scale is weakly epimorphic with val: <7 11 17 20 26 26| Scale is weakly epimorphic with val: <7 11 17 21 25 26| Scale is weakly epimorphic with val: <7 11 17 21 26 28| Scale is weakly epimorphic with val: <7 11 18 19 24 27| Scale is weakly epimorphic with val: <7 11 18 19 26 28| Scale is weakly epimorphic with val: <7 11 18 20 25 28| Scale is weakly epimorphic with val: <7 11 18 20 26 27| Scale is weakly epimorphic with val: <7 11 18 21 24 28| Scale is weakly epimorphic with val: <7 11 18 21 25 27| Scale is weakly epimorphic with val: <7 12 16 19 24 28| Scale is weakly epimorphic with val: <7 12 16 20 26 28| Scale is weakly epimorphic with val: <7 12 16 21 25 28| Scale is weakly epimorphic with val: <7 12 17 19 25 28| Scale is weakly epimorphic with val: <7 12 17 20 24 28| Scale is weakly epimorphic with val: <7 12 18 19 24 27|
FIT/MODE
3: 0 0 3 N M DE S SD: 41.2693 c. M: 67.9002 c. 5: 0 1 4 N G T3 SD: 22.3940 c. M:-31.7088 c. 6: 0 1 5 N G T3 SD: 15.5698 c. M: 22.3388 c. 7: 0 1 6 N G T3 SD: 13.0330 c. M: 22.3388 c. 8: 0 1 7 N G T3 SD: 13.3027 c. M: 22.3388 c. 9: 0 1 8 N G T3 SD: 14.7967 c. M: 22.3388 c. 13: 1 1 11 N M DE S SD: 10.5070 c. M:-15.9723 c. 14: 1 1 12 N M DE S SD: 7.8686 c. M:-13.2358 c. 15: 1 1 13 N M DE S SD: 6.3315 c. M:-10.8642 c. 16: 1 1 14 N M DE S SD: 6.0307 c. M:-8.7890 c. 19: 1 2 16 N T3 SD: 6.5910 c. M:-10.7385 c. 20: 1 2 17 N T3 SD: 4.1992 c. M:-6.8065 c. 21: 1 2 18 N T3 SD: 2.0375 c. M:-3.2491 c. 22: 1 2 19 N T3 SD: 0.1732 c. M:-0.2996 c. 221: 10 20 191 N T3 SD: 0.2036 c. M: 0.2923 c. 243: 11 22 210 N T3 SD: 0.1937 c. M: 0.2645 c. 265: 12 24 229 N T3 SD: 0.1863 c. M: 0.2413 c. 271: 12 25 234 N T3 SD: 0.1742 c. M: 0.2852 c. 287: 13 26 248 N T3 SD: 0.1806 c. M: 0.2216 c. 293: 13 27 253 N T3 SD: 0.1491 c. M: 0.2413 c. 315: 14 29 272 N T3 SD: 0.1277 c. M: 0.2035 c. 337: 15 31 291 N T3 SD: 0.1093 c. M: 0.1706 c. 359: 16 33 310 N T3 SD: 0.0935 c. M: 0.1418 c. 381: 17 35 329 N T3 SD: 0.0797 c. M: 0.1163 c. 403: 18 37 348 N T3 SD: 0.0679 c. M: 0.0936 c. 425: 19 39 367 N T3 SD: 0.0578 c. M: 0.0733 c. 447: 20 41 386 N T3 SD: 0.0494 c. M:-0.0656 c. 469: 21 43 405 N T3 SD: 0.0427 c. M:-0.0633 c. 491: 22 45 424 N T3 SD: 0.0377 c. M:-0.0611 c. 513: 23 47 443 N T3 SD: 0.0346 c. M:-0.0591 c. 535: 24 49 462 N T3 SD: 0.0331 c. M:-0.0573 c. 557: 25 51 481 N T3 SD: 0.0333 c. M:-0.0556 c. 579: 26 53 500 N T3 SD: 0.0346 c. M:-0.0541 c. 601: 27 55 519 N T3 SD: 0.0368 c. M:-0.0527 c. 602: 27 55 520 N T3 SD: 0.0348 c. M: 0.0602 c. 623: 28 57 538 N T3 SD: 0.0395 c. M:-0.0513 c. 624: 28 57 539 N T3 SD: 0.0337 c. M: 0.0576 c. 690: 31 63 596 N T3 SD: 0.0362 c. M: 0.0506 c. 712: 32 65 615 N T3 SD: 0.0383 c. M: 0.0486 c. 939: 42 86 811 N T3 SD: 0.0362 c. M: 0.0620 c. 961: 43 88 830 N T3 SD: 0.0314 c. M: 0.0538 c. 983: 44 90 849 N T3 SD: 0.0269 c. M: 0.0459 c. 1005: 45 92 868 N T3 SD: 0.0225 c. M: 0.0383 c. 1027: 46 94 887 N T3 SD: 0.0184 c. M: 0.0311 c. 1049: 47 96 906 N T3 SD: 0.0144 c. M: 0.0241 c. 1071: 48 98 925 N T3 SD: 0.0107 c. M: 0.0175 c. 1093: 49 100 944 N T3 SD: 0.0072 c. M: 0.0111 c. 1115: 50 102 963 N T3 SD: 0.0042 c. M: 0.0053 c. 1137: 51 104 982 N T3 SD: 0.0029 c. M: 0.0049 c. 2252: 101 206 1945 N T3 SD: 0.0032 c. M: 0.0051 c. 2296: 103 210 1983 N T3 SD: 0.0035 c. M: 0.0047 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 x 32:41 SD: 9.5373 cents 32 x 33:43 SD: 9.9432 cents 33 x 34:44 SD: 8.1089 cents 34 x 35:45 SD: 10.9213 cents 35 x 36:47 SD: 11.3774 cents 36 x 37:48 SD: 10.2331 cents 37 x 38:49 SD: 12.3492 cents 38:39:40:51 SD: 10.9436 cents 39:40:41:52 SD: 9.4918 cents 40:41:42:53 SD: 9.4800 cents 41:42:43:55 SD: 8.8077 cents 42:43:44:56 SD: 7.4399 cents 44:45:46:59 SD: 7.0922 cents 45:46:47:60 SD: 5.7866 cents 48:49:50:64 SD: 4.5475 cents 51:52:53:68 SD: 3.7846 cents 54:55:56:72 SD: 3.5478 cents 66:67:69:88 SD: 3.2604 cents 69:70:72:92 SD: 2.1089 cents 72:73:75:96 SD: 1.0572 cents 75:76:78:100 SD: 0.1973 cents 474:480:493:632 SD: 0.1931 cents 546:553:568:728 SD: 0.1882 cents 549:556:571:732 SD: 0.1407 cents