Scala analysis: 027_H8
Hyperenharmonic tetrachord 42/41 * 82/81 * 9/7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 42/41 41.718502 2: 28/27 62.960904 Archytas' 1/3-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 9/7 435.0841 septimal major third, BP third 1: 42/41 41.7185 2: 82/81 21.2424 3: 9/7 435.0841 septimal major third, BP third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 82/81 21.242 cents 1: 1 42/41 41.719 cents 1: 1 9/7 435.084 cents septimal major third, BP third 2: 1 28/27 62.961 cents Archytas' 1/3-tone 2: 1 82/63 456.326 cents 2: 1 54/41 476.803 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 : 41.7 63.0 498.0 41.7 : 21.2 456.3 498.0 63.0 : 435.1 476.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.2424 .. 435.0841 cents 729/574, 413.8417 cents 82/81, 21.2424 cents 2: 62.9609 .. 476.8026 cents 729/574, 413.8417 cents 196/243,-372.1232 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 82/81, 21.2424 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/7, 435.0841 cents Average / Smallest step : 7.815265 Largest / Average step : 2.620752 Largest / Smallest step : 20.481869 Median interval of one step : 42/41, 41.7185 cents, amount: 1 Least squares average step : 118.69824 cents, oct.: 356.09471 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1946-tone equal temperament with octave 4/3 degrees: 163 246 1946 Least number of segments generator : 975 of 249.534 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1325 of 339.111 cents and inv. generated superset size: 42 = 39 more = 1400.000% 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 21.24240 cents Scale diversity : 0.136017 Lumma stability : 0.085303 Lumma impropriety factor : 0.747168 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 : 1701/1681, 20.4761 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 413.8417 cents: 2 -- Rational properties -- Prime limit : 41 Odd number limit : 81 (O: 41 U: 81) Highest odd numerator or denominator: 41 Scale harmonicity : 0.043568 Fundamental : 1/1107, -10.1124 octaves, 0.2363 Hz. Guide tone : 84, 6.3923 octaves, 21976.547 Hz. Exponens Consonantiae : 9.298800E+04, 16.50476 octaves Euler's gradus suavitatis : 57 Sum of Mann's harmonic distance : 72.5, average 24.16667 Mersenne's string divisions : 31955 Sum of van Prooijen's expressibility: 3.52127, average 1.17376 Sum of Tenney's harmonic distance : 7.19374, average 2.39791 Vogel's harmonic complexity : 39.66667 Wille's k value : 283 Wilson's harmonic complexity : 60 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 16.51844, average 2.75307 Lattice compactness (without 2's) : 14.04863, average 2.34144 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -3 .. 1 -1.00000 5 1 7: 0 .. 1 0.66667 2 1 41: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 21 36| Scale is weakly epimorphic with val: <6 10 21 39| Scale is weakly epimorphic with val: <6 10 21 42| Scale is weakly epimorphic with val: <7 10 19 37| Scale is weakly epimorphic with val: <7 10 19 40| Scale is weakly epimorphic with val: <7 11 18 38| Scale is weakly epimorphic with val: <7 11 18 41| Scale is weakly epimorphic with val: <7 11 20 36| Scale is weakly epimorphic with val: <7 11 20 39| = patent Scale is weakly epimorphic with val: <7 11 20 42| Scale is JI-epimorphic with val: <7 11 21 38| Scale is weakly epimorphic with val: <7 11 21 41| Scale is weakly epimorphic with val: <7 12 20 36| Scale is weakly epimorphic with val: <8 11 20 38| Scale is weakly epimorphic with val: <8 11 20 41| Scale is weakly epimorphic with val: <8 11 21 37| Scale is weakly epimorphic with val: <8 12 19 36| Scale is weakly epimorphic with val: <8 12 22 39|
FIT/MODE
3: 0 0 3 N M DE S SD: 43.6062 c. M: 62.9609 c. 5: 0 1 4 N G T3 SD: 32.0599 c. M: 41.7185 c. 7: 1 0 6 N G T3 SD: 17.6373 c. M:-29.4308 c. 8: 1 0 7 N G T3 SD: 11.8641 c. M:-20.5371 c. 9: 1 0 8 N G T3 SD: 9.0112 c. M:-13.6198 c. 10: 1 0 9 N G T3 SD: 8.9158 c. M: 13.1564 c. 13: 1 1 11 N M DE S SD: 8.1290 c. M:-13.6614 c. 14: 1 1 12 N M DE S SD: 5.9103 c. M:-8.1884 c. 15: 1 1 13 N M DE S SD: 5.3035 c. M: 8.5155 c. 16: 1 1 14 N M DE S SD: 6.1281 c. M: 10.5907 c. 21: 2 1 18 N T3 SD: 5.7649 c. M:-8.1884 c. 22: 2 1 19 N T3 SD: 3.5217 c. M:-4.9543 c. 23: 2 1 20 N T3 SD: 1.4757 c. M:-2.0015 c. 24: 2 1 21 N T3 SD: 0.4257 c. M: 0.7053 c. 47: 4 2 41 N T3 SD: 0.5260 c. M:-0.6683 c. 71: 6 3 62 N T3 SD: 0.2354 c. M:-0.3698 c. 95: 8 4 83 N T3 SD: 0.1314 c. M:-0.2221 c. 119: 10 5 104 N T3 SD: 0.1305 c. M: 0.1821 c. 214: 18 9 187 N T3 SD: 0.1228 c. M:-0.1731 c. 333: 28 14 291 N T3 SD: 0.1241 c. M:-0.1592 c. 347: 29 15 303 N T3 SD: 0.1236 c. M:-0.1918 c. 348: 29 15 304 N T3 SD: 0.1241 c. M: 0.2148 c. 371: 31 16 324 N T3 SD: 0.0974 c. M:-0.1337 c. 395: 33 17 345 N T3 SD: 0.0793 c. M: 0.1097 c. 419: 35 18 366 N T3 SD: 0.0702 c. M: 0.1157 c. 443: 37 19 387 N T3 SD: 0.0699 c. M: 0.1211 c. 466: 39 20 407 N T3 SD: 0.0595 c. M:-0.0963 c. 490: 41 21 428 N T3 SD: 0.0421 c. M:-0.0570 c. 514: 43 22 449 N T3 SD: 0.0331 c. M: 0.0533 c. 538: 45 23 470 N T3 SD: 0.0355 c. M: 0.0605 c. 585: 49 25 511 N T3 SD: 0.0229 c. M:-0.0397 c. 609: 51 26 532 N T3 SD: 0.0084 c. M:-0.0103 c. 1242: 104 53 1085 N T3 SD: 0.0085 c. M: 0.0143 c. 1313: 110 56 1147 N T3 SD: 0.0051 c. M:-0.0065 c. 1337: 112 57 1168 N T3 SD: 0.0042 c. M: 0.0068 c. 1946: 163 83 1700 N T3 SD: 0.0012 c. M: 0.0015 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: 101.9550 cents 7 x 8:9 S SD: 89.8050 cents 8 x 9:11 SD: 75.3403 cents 9 x 10:12 S SD: 59.7214 cents 10 x 11:13 SD: 55.5293 cents 11 x 12:15 S SD: 47.9603 cents 12 x 13:16 SD: 37.8059 cents 13 x 14:17 SD: 36.7392 cents 14 x 15:19 SD: 32.1292 cents 15 x 16:20 S SD: 24.3852 cents 16 x 17:21 SD: 25.0343 cents 17 x 18:23 SD: 21.9904 cents 18 x 19:24 SD: 15.3211 cents 19 x 20:25 S SD: 17.2736 cents 20 x 21:27 SD: 15.2072 cents 21 x 22:28 SD: 8.7881 cents 22 x 23:29 SD: 12.1177 cents 23 x 24:31 SD: 10.7844 cents 24 x 25:32 SD: 3.8558 cents 25 x 26:33 SD: 9.0435 cents 26 x 27:35 SD: 8.3683 cents 27 x 28:36 SD: 0.0000 cents 28 x 29:37 SD: 7.8417 cents 29 x 30:39 SD: 7.7308 cents 30 x 31:40 SD: 3.0970 cents 31 x 32:41 SD: 8.0693 cents 32 x 33:43 SD: 8.2971 cents 33:34 x 44 SD: 4.9820 cents 34:35 x 45 SD: 7.6634 cents 35:36 x 47 SD: 7.0986 cents 36:37 x 48 SD: 2.8578 cents 37:38 x 49 SD: 6.2763 cents 38:39 x 51 SD: 5.9044 cents 39:40 x 52 SD: 1.0563 cents 40:41 x 53 SD: 5.4515 cents 45:46:47:60 SD: 4.2854 cents 48:49:50:64 SD: 3.2614 cents 51:52:53:68 SD: 2.9596 cents 62 x 64:83 SD: 5.3028 cents 63 x 65:84 SD: 4.4277 cents 64 x 66:85 SD: 5.9112 cents 65 x 67:87 SD: 6.2112 cents 66:68 x 88 SD: 4.9820 cents 67:69 x 89 SD: 5.6257 cents 68:70:71:91 SD: 5.2789 cents 69:71:72:92 SD: 4.4090 cents 71:73:74:95 SD: 4.1247 cents 72:74:75:96 SD: 3.1996 cents 74:76:77:99 SD: 3.1268 cents 75:77:78:100 SD: 2.0861 cents 78:80:81:104 SD: 1.0599 cents 81:83:84:108 SD: 0.1696 cents 408:418:423:544 SD: 0.1659 cents 489:501:507:652 SD: 0.1520 cents 570:584:591:760 SD: 0.1451 cents