Scala analysis: 035_H9
Hyperenharmonic tetrachord 54/53 * 53/52 * 104/81
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 54/53 32.360457 2: 27/26 65.337341 tridecimal comma 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 104/81 432.7077 1: 54/53 32.3605 2: 53/52 32.9769 3: 104/81 432.7077
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 54/53 32.360 cents 1: 1 53/52 32.977 cents 1: 1 104/81 432.708 cents 2: 1 27/26 65.337 cents tridecimal comma 2: 1 208/159 465.068 cents 2: 1 106/81 465.685 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 : 32.4 65.3 498.0 32.4 : 33.0 465.7 498.0 65.3 : 432.7 465.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 32.3605 .. 432.7077 cents 2756/2187, 400.3472 cents 54/53, 32.3605 cents 2: 65.3373 .. 465.6845 cents 2756/2187, 400.3472 cents 2187/2704,-367.3703 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 54/53, 32.3605 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 104/81, 432.7077 cents Average / Smallest step : 5.130181 Largest / Average step : 2.606437 Largest / Smallest step : 13.371494 Median interval of one step : 53/52, 32.9769 cents, amount: 1 Least squares average step : 118.36930 cents, oct.: 355.10789 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1616-tone equal temperament with octave 4/3 degrees: 105 212 1616 Least number of segments generator : 809 of 249.331 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1089 of 335.626 cents and inv. generated superset size: 38 = 35 more = 1266.667% 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 32.36046 cents Scale diversity : 0.172740 Lumma stability : 0.129950 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 : 2809/2808, 0.6164 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 399.7308 cents: 2 -- Rational properties -- Prime limit : 53 Odd number limit : 159 (O: 53 U: 159) Highest odd numerator or denominator: 53 Scale harmonicity : 0.027917 Fundamental : 1/4134, -12.0133 octaves, 0.0633 Hz. Guide tone : 108, 6.7549 octaves, 28255.561 Hz. Exponens Consonantiae : 4.464720E+05, 18.76821 octaves Euler's gradus suavitatis : 76 Sum of Mann's harmonic distance : 83.5, average 27.83333 Mersenne's string divisions : 39697 Sum of van Prooijen's expressibility: 3.63276, average 1.21092 Sum of Tenney's harmonic distance : 7.38219, average 2.46073 Vogel's harmonic complexity : 53.66667 Wille's k value : 2146 Wilson's harmonic complexity : 78 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 20.17316, average 3.36219 Lattice compactness (without 2's) : 16.28538, average 2.71423 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -1 .. 3 1.66667 7 1 13: -1 .. 0 -0.33333 1 1 53: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 3 / 3 = 1.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <7 11 25 41| Scale is weakly epimorphic with val: <7 11 27 42| Scale is weakly epimorphic with val: <7 11 28 41| Scale is weakly epimorphic with val: <7 11 30 42| Scale is weakly epimorphic with val: <7 12 25 40| Scale is weakly epimorphic with val: <7 12 26 42| Scale is weakly epimorphic with val: <7 12 28 40| Scale is weakly epimorphic with val: <8 12 25 42| Scale is weakly epimorphic with val: <8 12 26 41| Scale is weakly epimorphic with val: <8 12 29 41|
FIT/MODE
3: 0 0 3 N M DE S SD: 42.0958 c. M: 65.3373 c. 6: 0 1 5 N G T3 SD: 21.2872 c. M: 32.3605 c. 7: 0 1 6 N G T3 SD: 18.9823 c. M: 32.3605 c. 8: 0 1 7 N G T3 SD: 18.7678 c. M: 32.3605 c. 9: 0 1 8 N G T3 SD: 19.5549 c. M: 32.3605 c. 10: 0 1 9 N G T3 SD: 20.7241 c. M: 32.3605 c. 11: 1 0 10 N G T3 SD: 13.7751 c. M: 20.0605 c. 12: 1 1 10 N M DE S SD: 11.4867 c. M:-17.6702 c. 13: 1 1 11 N M DE S SD: 7.3657 c. M:-11.2850 c. 14: 1 1 12 N M DE S SD: 3.8345 c. M:-5.8119 c. 15: 1 1 13 N M DE S SD: 0.7857 c. M:-1.0687 c. 31: 2 2 27 N M DE S SD: 0.6337 c. M: 1.0735 c. 46: 3 3 40 N M DE S SD: 0.2274 c. M: 0.3749 c. 61: 4 4 53 N M DE S SD: 0.1726 c. M:-0.2982 c. 107: 7 7 93 N M DE S SD: 0.1623 c. M:-0.2219 c. 168: 11 11 146 N M DE S SD: 0.1592 c. M:-0.2496 c. 260: 17 17 226 N M DE S SD: 0.1684 c. M: 0.2084 c. 275: 18 18 239 N M DE S SD: 0.1595 c. M:-0.2389 c. 404: 26 27 351 N T3 SD: 0.1779 c. M: 0.3081 c. 412: 27 27 358 N M DE S SD: 0.1644 c. M:-0.2784 c. 418: 27 28 363 N T3 SD: 0.1572 c. M:-0.1949 c. 419: 27 28 364 N T3 SD: 0.1557 c. M: 0.2669 c. 434: 28 29 377 N T3 SD: 0.1387 c. M: 0.2285 c. 449: 29 30 390 N T3 SD: 0.1274 c. M: 0.1927 c. 464: 30 31 403 N T3 SD: 0.1218 c. M: 0.1593 c. 465: 30 31 404 N T3 SD: 0.1319 c. M: 0.2285 c. 479: 31 32 416 N T3 SD: 0.1217 c. M:-0.1675 c. 480: 31 32 417 N T3 SD: 0.1140 c. M: 0.1951 c. 495: 32 33 430 N T3 SD: 0.1011 c. M: 0.1636 c. 510: 33 34 443 N T3 SD: 0.0939 c. M: 0.1340 c. 525: 34 35 456 N T3 SD: 0.0925 c. M:-0.1200 c. 526: 34 35 457 N T3 SD: 0.0967 c. M: 0.1674 c. 540: 35 36 469 N T3 SD: 0.0962 c. M:-0.1464 c. 541: 35 36 470 N T3 SD: 0.0818 c. M: 0.1394 c. 556: 36 37 483 N T3 SD: 0.0721 c. M: 0.1129 c. 571: 37 38 496 N T3 SD: 0.0686 c. M: 0.0878 c. 587: 38 39 510 N T3 SD: 0.0688 c. M: 0.1190 c. 602: 39 40 523 N T3 SD: 0.0562 c. M: 0.0951 c. 617: 40 41 536 N T3 SD: 0.0495 c. M: 0.0723 c. 632: 41 42 549 N T3 SD: 0.0501 c. M:-0.0705 c. 648: 42 43 563 N T3 SD: 0.0462 c. M: 0.0798 c. 663: 43 44 576 N T3 SD: 0.0354 c. M: 0.0589 c. 678: 44 45 589 N T3 SD: 0.0323 c. M:-0.0402 c. 709: 46 47 616 N T3 SD: 0.0277 c. M: 0.0472 c. 724: 47 48 629 N T3 SD: 0.0185 c. M: 0.0288 c. 770: 50 51 669 N T3 SD: 0.0127 c. M: 0.0199 c. 785: 51 52 682 N T3 SD: 0.0068 c. M:-0.0112 c. 831: 54 55 722 N T3 SD: 0.0062 c. M: 0.0101 c. 1555: 101 103 1351 N T3 SD: 0.0067 c. M: 0.0116 c. 1601: 104 106 1391 N T3 SD: 0.0072 c. M: 0.0098 c. 1616: 105 107 1404 N T3 SD: 0.0002 c. M:-0.0002 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 35:36 x 47 SD: 10.2606 cents 36:37 x 48 SD: 7.5368 cents 37:38 x 49 SD: 9.0614 cents 38:39 x 51 SD: 8.4833 cents 39:40:41:52 SD: 8.0472 cents 41:42:43:55 SD: 7.3889 cents 42:43:44:56 SD: 5.7850 cents 44:45:46:59 SD: 5.5182 cents 45:46:47:60 SD: 3.8194 cents 48:49:50:64 SD: 2.0975 cents 51:52:53:68 SD: 0.5925 cents 105:107:109:140 SD: 0.2276 cents 156:159:162:208 SD: 0.2055 cents 261:266:271:348 SD: 0.1831 cents