Scala analysis: 037_H9
Hyperenharmonic tetrachord 81/80 * 40/39 * 104/81
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 81/80 21.506290 syntonic comma, Didymus comma 2: 27/26 65.337341 tridecimal comma 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 104/81 432.7077 1: 81/80 21.5063 syntonic comma, Didymus comma 2: 40/39 43.8311 tridecimal minor diesis 3: 104/81 432.7077
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 81/80 21.506 cents syntonic comma, Didymus comma 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 104/81 432.708 cents 2: 1 27/26 65.337 cents tridecimal comma 2: 1 13/10 454.214 cents tridecimal semi-diminished fourth 2: 1 320/243 476.539 cents grave fourth 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 : 21.5 65.3 498.0 21.5 : 43.8 476.5 498.0 65.3 : 432.7 454.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 432.7077 cents 8320/6561, 411.2014 cents 81/80, 21.5063 cents 2: 65.3373 .. 476.5387 cents 8320/6561, 411.2014 cents 2187/2704,-367.3703 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 81/80, 21.5063 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 104/81, 432.7077 cents Average / Smallest step : 7.719370 Largest / Average step : 2.606437 Largest / Smallest step : 20.120052 Median interval of one step : 40/39, 43.8311 cents, amount: 1 Least squares average step : 117.59400 cents, oct.: 352.78199 cents Scale is not proper Scale has trivalence property 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 21.50629 cents Scale diversity : 0.150903 Lumma stability : 0.086363 Lumma impropriety factor : 0.737625 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 : 81/80, 21.5063 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 Limited inverse transpositions with margin 388.8766 cents: 2 -- Rational properties -- Prime limit : 13 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.020882 Average absolute harmonicity : 0.097950 Specific harmonicity : 0.104807 Fundamental : 1/3120, -11.6073 octaves, 0.0839 Hz. Guide tone : 324, 8.3399 octaves, 84766.683 Hz. Exponens Consonantiae : 1.010880E+06, 19.94718 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 110.5, average 36.83333 Mersenne's string divisions : 8533 Sum of van Prooijen's expressibility: 3.81697, average 1.27232 Sum of Tenney's harmonic distance : 7.73709, average 2.57903 Vogel's harmonic complexity : 24.00000 Wille's k value : 1579 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 27.73438, average 4.62240 Lattice compactness (without 2's) : 19.23956, average 3.20659 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -1.00000 7 3: -1 .. 4 2.00000 8 1 5: -1 .. 0 -0.33333 1 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 4 / 3 = 1.33333 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <6 11 17 25| Scale is weakly epimorphic with val: <6 11 17 28| Scale is weakly epimorphic with val: <7 11 15 27| Scale is weakly epimorphic with val: <7 11 15 30| Scale is weakly epimorphic with val: <7 11 17 25| Scale is weakly epimorphic with val: <7 11 17 28| Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 12 16 26| Scale is weakly epimorphic with val: <7 12 17 25| Scale is weakly epimorphic with val: <7 12 17 28| Scale is weakly epimorphic with val: <7 12 19 26| Scale is weakly epimorphic with val: <8 12 17 25|
FIT/MODE
3: 0 0 3 N M DE S SD: 39.7135 c. M: 65.3373 c. 5: 0 1 4 N G T3 SD: 23.3600 c. M:-34.2717 c. 6: 0 1 5 N G T3 SD: 16.0702 c. M: 21.5063 c. 7: 0 1 6 N G T3 SD: 12.8621 c. M: 21.5063 c. 8: 0 1 7 N G T3 SD: 12.5435 c. M: 21.5063 c. 9: 0 1 8 N G T3 SD: 13.6931 c. M: 21.5063 c. 14: 1 1 12 N M DE S SD: 8.7882 c. M:-14.0684 c. 15: 1 1 13 N M DE S SD: 6.7812 c. M:-11.6967 c. 16: 1 1 14 N M DE S SD: 5.8330 c. M:-9.6215 c. 17: 1 1 15 N M DE S SD: 5.9490 c. M:-7.7905 c. 20: 1 2 17 N T3 SD: 5.7538 c. M:-9.3694 c. 21: 1 2 18 N T3 SD: 3.5900 c. M:-5.8119 c. 22: 1 2 19 N T3 SD: 1.6255 c. M:-2.5779 c. 23: 1 2 20 N T3 SD: 0.2327 c. M: 0.3749 c. 114: 5 10 99 N T3 SD: 0.2252 c. M:-0.3378 c. 137: 6 12 119 N T3 SD: 0.1857 c. M:-0.3059 c. 160: 7 14 139 N T3 SD: 0.1645 c. M:-0.2832 c. 183: 8 16 159 N T3 SD: 0.1541 c. M:-0.2662 c. 206: 9 18 179 N T3 SD: 0.1500 c. M:-0.2530 c. 229: 10 20 199 N T3 SD: 0.1495 c. M:-0.2424 c. 252: 11 22 219 N T3 SD: 0.1510 c. M:-0.2338 c. 275: 12 24 239 N T3 SD: 0.1534 c. M:-0.2266 c. 297: 13 26 258 N T3 SD: 0.1733 c. M:-0.2937 c. 298: 13 26 259 N T3 SD: 0.1563 c. M:-0.2205 c. 304: 13 27 264 N T3 SD: 0.1647 c. M: 0.2083 c. 305: 13 27 265 N T3 SD: 0.1610 c. M: 0.2781 c. 321: 14 28 279 N T3 SD: 0.1593 c. M:-0.2153 c. 327: 14 29 284 N T3 SD: 0.1385 c. M: 0.1833 c. 328: 14 29 285 N T3 SD: 0.1457 c. M: 0.2483 c. 350: 15 31 304 N T3 SD: 0.1162 c. M: 0.1615 c. 351: 15 31 305 N T3 SD: 0.1340 c. M: 0.2223 c. 373: 16 33 324 N T3 SD: 0.0971 c. M: 0.1424 c. 396: 17 35 344 N T3 SD: 0.0810 c. M: 0.1256 c. 419: 18 37 364 N T3 SD: 0.0676 c. M: 0.1106 c. 442: 19 39 384 N T3 SD: 0.0569 c. M: 0.0971 c. 465: 20 41 404 N T3 SD: 0.0491 c. M: 0.0850 c. 488: 21 43 424 N T3 SD: 0.0443 c. M: 0.0740 c. 511: 22 45 444 N T3 SD: 0.0424 c. M: 0.0640 c. 533: 23 47 463 N T3 SD: 0.0424 c. M:-0.0719 c. 534: 23 47 464 N T3 SD: 0.0431 c. M: 0.0549 c. 556: 24 49 483 N T3 SD: 0.0312 c. M:-0.0535 c. 579: 25 51 503 N T3 SD: 0.0211 c. M:-0.0364 c. 602: 26 53 523 N T3 SD: 0.0122 c. M:-0.0207 c. 625: 27 55 543 N T3 SD: 0.0064 c. M:-0.0093 c. 1898: 82 167 1649 N T3 SD: 0.0064 c. M:-0.0109 c. 2340: 101 206 2033 N T3 SD: 0.0060 c. M: 0.0095 c. 2363: 102 208 2053 N T3 SD: 0.0046 c. M: 0.0079 c. 2386: 103 210 2073 N T3 SD: 0.0041 c. M: 0.0064 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: 100.7668 cents 7 x 8:9 S SD: 88.6932 cents 8 x 9:11 SD: 74.2300 cents 9 x 10:12 S SD: 58.5332 cents 10 x 11:13 SD: 54.4395 cents 11 x 12:15 S SD: 46.8767 cents 12 x 13:16 SD: 36.6177 cents 13 x 14:17 SD: 35.6868 cents 14 x 15:19 SD: 31.0900 cents 15 x 16:20 S SD: 23.1970 cents 16 x 17:21 SD: 24.0464 cents 17 x 18:23 SD: 21.0291 cents 18 x 19:24 SD: 14.1328 cents 19 x 20:25 S SD: 16.4038 cents 20 x 21:27 SD: 14.3916 cents 21 x 22:28 SD: 7.5998 cents 22 x 23:29 SD: 11.4726 cents 23 x 24:31 SD: 10.2458 cents 24 x 25:32 SD: 2.6675 cents 25 x 26:33 SD: 8.7936 cents 26 x 27:35 SD: 8.2835 cents 27 x 28:36 SD: 1.1882 cents 28 x 29:37 SD: 8.0950 cents 29 x 30:39 SD: 8.1394 cents 30 x 31:40 SD: 4.2852 cents 31 x 32:41 SD: 8.7193 cents 32 x 33:43 SD: 9.0424 cents 33 x 34:44 SD: 6.8274 cents 34 x 35:45 SD: 9.9104 cents 35 x 36:47 SD: 10.3235 cents 36 x 37:48 SD: 8.9517 cents 37 x 38:49 SD: 11.2382 cents 38 x 39:51 SD: 11.6589 cents 39 x 41:52 SD: 10.6212 cents 40:41:42:53 SD: 10.1926 cents 41:42:43:55 SD: 9.5004 cents 42:43:44:56 SD: 8.1707 cents 44:45:46:59 SD: 7.7025 cents 45:46:47:60 SD: 6.4345 cents 47:48:49:63 SD: 6.2713 cents 48:49:50:64 SD: 5.0534 cents 51:52:53:68 SD: 4.0587 cents 54:55:56:72 SD: 3.5107 cents 57:58:59:76 SD: 3.4278 cents 69:70:72:92 SD: 3.0037 cents 72:73:75:96 SD: 1.9464 cents 75:76:78:100 SD: 0.9774 cents 78:79:81:104 SD: 0.1826 cents 570:577:592:760 SD: 0.1458 cents