Scala analysis: 026_H8
Hyperenharmonic tetrachord 56/55 * 55/54 * 9/7, Wilson
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 56/55 31.194250 undecimal diesis, konbini comma 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: 56/55 31.1943 undecimal diesis, konbini comma 2: 55/54 31.7667 telepathma 3: 9/7 435.0841 septimal major third, BP third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 56/55 31.194 cents undecimal diesis, konbini comma 1: 1 55/54 31.767 cents telepathma 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 72/55 466.278 cents undecimal semi-diminished fourth 2: 1 55/42 466.851 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 : 31.2 63.0 498.0 31.2 : 31.8 466.9 498.0 63.0 : 435.1 466.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.1943 .. 435.0841 cents 495/392, 403.8898 cents 56/55, 31.1943 cents 2: 62.9609 .. 466.8507 cents 495/392, 403.8898 cents 196/243,-372.1232 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 56/55, 31.1943 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/7, 435.0841 cents Average / Smallest step : 5.321974 Largest / Average step : 2.620752 Largest / Smallest step : 13.947573 Median interval of one step : 55/54, 31.7667 cents, amount: 1 Least squares average step : 117.94650 cents, oct.: 353.83951 cents Scale is not proper Scale has trivalence property Scale is a mode of a 878-tone equal temperament with octave 4/3 degrees: 55 111 878 Least number of segments generator : 441 of 250.157 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 489 of 277.385 cents and inv. generated superset size: 46 = 43 more = 1533.333% 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 31.19425 cents Scale diversity : 0.155611 Lumma stability : 0.125267 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 : 3025/3024, 0.5724 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 403.3174 cents: 2 -- Rational properties -- Prime limit : 11 Odd number limit : 55 (O: 55 U: 55) Highest odd numerator or denominator: 55 Scale harmonicity : 0.021802 Average absolute harmonicity : 0.096663 Specific harmonicity : 0.106273 Fundamental : 1/1485, -10.5362 octaves, 0.1762 Hz. Guide tone : 56, 5.8074 octaves, 14651.032 Hz. Exponens Consonantiae : 8.316000E+04, 16.34360 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 86.5, average 28.83333 Mersenne's string divisions : 42735 Sum of van Prooijen's expressibility: 3.64885, average 1.21628 Sum of Tenney's harmonic distance : 7.44625, average 2.48208 Vogel's harmonic complexity : 22.66667 Wille's k value : 247 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 17.37806, average 2.89634 Lattice compactness (without 2's) : 13.44702, average 2.24117 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -3 .. 0 -1.33333 4 1 5: -1 .. 0 -0.33333 1 7: 0 .. 1 0.66667 2 1 11: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 15 21 23| Scale is weakly epimorphic with val: <6 10 15 21 26| Scale is weakly epimorphic with val: <6 10 16 21 25| Scale is weakly epimorphic with val: <6 10 17 21 24| Scale is weakly epimorphic with val: <6 10 17 21 27| Scale is weakly epimorphic with val: <6 10 18 21 23| Scale is weakly epimorphic with val: <6 10 18 21 26| Scale is weakly epimorphic with val: <6 10 19 21 25| Scale is weakly epimorphic with val: <7 10 15 19 23| Scale is weakly epimorphic with val: <7 10 15 19 26| Scale is weakly epimorphic with val: <7 10 15 21 24| Scale is weakly epimorphic with val: <7 10 16 19 25| Scale is weakly epimorphic with val: <7 10 16 21 23| Scale is weakly epimorphic with val: <7 10 17 19 24| Scale is weakly epimorphic with val: <7 10 17 19 27| Scale is weakly epimorphic with val: <7 10 18 19 23| Scale is weakly epimorphic with val: <7 10 18 19 26| Scale is weakly epimorphic with val: <7 10 19 19 25| Scale is weakly epimorphic with val: <7 11 15 18 23| Scale is weakly epimorphic with val: <7 11 15 18 26| Scale is weakly epimorphic with val: <7 11 15 20 24| Scale is weakly epimorphic with val: <7 11 15 20 27| Scale is weakly epimorphic with val: <7 11 15 21 23| Scale is JI-epimorphic with val: <7 11 15 21 26| Scale is weakly epimorphic with val: <7 11 16 18 25| Scale is weakly epimorphic with val: <7 11 16 20 23| Scale is weakly epimorphic with val: <7 11 16 20 26| Scale is JI-epimorphic with val: <7 11 16 21 25| Scale is weakly epimorphic with val: <7 11 17 18 24| Scale is weakly epimorphic with val: <7 11 17 18 27| Scale is weakly epimorphic with val: <7 11 17 20 25| = patent Scale is JI-epimorphic with val: <7 11 17 21 24| Scale is weakly epimorphic with val: <7 11 17 21 27| Scale is weakly epimorphic with val: <7 11 18 18 23| Scale is weakly epimorphic with val: <7 11 18 18 26| Scale is weakly epimorphic with val: <7 11 18 20 24| Scale is weakly epimorphic with val: <7 11 18 20 27| Scale is JI-epimorphic with val: <7 11 18 21 23| Scale is weakly epimorphic with val: <7 11 18 21 26| Scale is weakly epimorphic with val: <7 11 19 20 23| Scale is weakly epimorphic with val: <7 11 19 20 26| Scale is weakly epimorphic with val: <7 11 19 21 25| Scale is weakly epimorphic with val: <7 12 15 20 23| Scale is weakly epimorphic with val: <8 11 15 18 24| Scale is weakly epimorphic with val: <8 11 15 20 25| Scale is weakly epimorphic with val: <8 11 15 21 27| Scale is weakly epimorphic with val: <8 11 16 18 23| Scale is weakly epimorphic with val: <8 11 16 20 24| Scale is weakly epimorphic with val: <8 11 16 20 27| Scale is weakly epimorphic with val: <8 11 16 21 26| Scale is weakly epimorphic with val: <8 11 17 20 23| Scale is weakly epimorphic with val: <8 11 17 20 26| Scale is weakly epimorphic with val: <8 11 17 21 25| Scale is weakly epimorphic with val: <8 11 18 20 25| Scale is weakly epimorphic with val: <8 11 18 21 24| Scale is weakly epimorphic with val: <8 11 19 20 24| Scale is weakly epimorphic with val: <8 11 19 20 27| Scale is weakly epimorphic with val: <8 11 19 21 23| Scale is weakly epimorphic with val: <8 12 15 19 25| Scale is weakly epimorphic with val: <8 12 16 19 24| Scale is weakly epimorphic with val: <8 12 16 22 27| Scale is weakly epimorphic with val: <8 12 17 19 23| Scale is weakly epimorphic with val: <8 12 17 22 26| Scale is weakly epimorphic with val: <8 12 18 22 25| Scale is weakly epimorphic with val: <8 12 19 22 24|
FIT/MODE
3: 0 0 3 N M DE S SD: 40.5675 c. M: 62.9609 c. 6: 0 1 5 N G T3 SD: 21.4083 c. M: 31.1943 c. 7: 0 1 6 N G T3 SD: 18.6202 c. M: 31.1943 c. 8: 0 1 7 N G T3 SD: 18.0146 c. M: 31.1943 c. 9: 0 1 8 N G T3 SD: 18.5399 c. M: 31.1943 c. 10: 0 1 9 N G T3 SD: 19.5463 c. M: 31.1943 c. 11: 1 0 10 N G T3 SD: 13.0518 c. M: 17.6841 c. 12: 1 1 10 N M DE S SD: 13.0148 c. M:-20.0466 c. 13: 1 1 11 N M DE S SD: 8.8935 c. M:-13.6614 c. 14: 1 1 12 N M DE S SD: 5.3615 c. M:-8.1884 c. 15: 1 1 13 N M DE S SD: 2.3024 c. M:-3.4451 c. 16: 1 1 14 N M DE S SD: 0.4090 c. M: 0.7053 c. 47: 3 3 41 N M DE S SD: 0.4962 c. M:-0.6193 c. 63: 4 4 55 N M DE S SD: 0.2960 c. M:-0.4277 c. 79: 5 5 69 N M DE S SD: 0.1951 c. M:-0.3276 c. 95: 6 6 83 N M DE S SD: 0.1536 c. M:-0.2612 c. 111: 7 7 97 N M DE S SD: 0.1491 c. M:-0.2140 c. 174: 11 11 152 N M DE S SD: 0.1683 c. M:-0.2914 c. 206: 13 13 180 N M DE S SD: 0.1481 c. M:-0.2358 c. 238: 15 15 208 N M DE S SD: 0.1541 c. M:-0.1951 c. 301: 19 19 263 N M DE S SD: 0.1490 c. M:-0.2438 c. 317: 20 20 277 N M DE S SD: 0.1478 c. M:-0.2281 c. 365: 23 23 319 N M DE S SD: 0.1564 c. M: 0.1936 c. 396: 25 25 346 N M DE S SD: 0.1498 c. M:-0.2480 c. 428: 27 27 374 N M DE S SD: 0.1479 c. M:-0.2245 c. 443: 28 28 387 N M DE S SD: 0.1645 c. M:-0.2849 c. 450: 28 29 393 N T3 SD: 0.1385 c. M: 0.2048 c. 451: 28 29 394 N T3 SD: 0.1581 c. M: 0.2735 c. 460: 29 29 402 N M DE S SD: 0.1512 c. M:-0.2042 c. 466: 29 30 407 N T3 SD: 0.1282 c. M: 0.2000 c. 482: 30 31 421 N T3 SD: 0.1199 c. M: 0.1956 c. 497: 31 32 434 N T3 SD: 0.1240 c. M:-0.1716 c. 498: 31 32 435 N T3 SD: 0.1135 c. M: 0.1914 c. 513: 32 33 448 N T3 SD: 0.1110 c. M:-0.1442 c. 514: 32 33 449 N T3 SD: 0.1090 c. M: 0.1876 c. 529: 33 34 462 N T3 SD: 0.0996 c. M: 0.1253 c. 530: 33 34 463 N T3 SD: 0.1062 c. M: 0.1839 c. 545: 34 35 476 N T3 SD: 0.0897 c. M: 0.1236 c. 546: 34 35 477 N T3 SD: 0.1049 c. M: 0.1805 c. 561: 35 36 490 N T3 SD: 0.0816 c. M: 0.1219 c. 577: 36 37 504 N T3 SD: 0.0753 c. M: 0.1204 c. 593: 37 38 518 N T3 SD: 0.0708 c. M: 0.1189 c. 608: 38 39 531 N T3 SD: 0.0761 c. M:-0.1139 c. 609: 38 39 532 N T3 SD: 0.0681 c. M: 0.1176 c. 624: 39 40 545 N T3 SD: 0.0659 c. M:-0.0929 c. 625: 39 40 546 N T3 SD: 0.0673 c. M: 0.1162 c. 640: 40 41 559 N T3 SD: 0.0570 c. M:-0.0729 c. 641: 40 41 560 N T3 SD: 0.0680 c. M: 0.1150 c. 656: 41 42 573 N T3 SD: 0.0494 c. M: 0.0664 c. 672: 42 43 587 N T3 SD: 0.0436 c. M: 0.0664 c. 688: 43 44 601 N T3 SD: 0.0398 c. M: 0.0664 c. 704: 44 45 615 N T3 SD: 0.0384 c. M: 0.0664 c. 720: 45 46 629 N T3 SD: 0.0391 c. M: 0.0664 c. 735: 46 47 642 N T3 SD: 0.0357 c. M:-0.0570 c. 736: 46 47 643 N T3 SD: 0.0418 c. M: 0.0664 c. 751: 47 48 656 N T3 SD: 0.0276 c. M:-0.0408 c. 767: 48 49 670 N T3 SD: 0.0209 c. M: 0.0259 c. 783: 49 50 684 N T3 SD: 0.0165 c. M: 0.0267 c. 799: 50 51 698 N T3 SD: 0.0160 c. M: 0.0275 c. 862: 54 55 753 N T3 SD: 0.0103 c. M:-0.0169 c. 878: 55 56 767 N T3 SD: 0.0034 c. M:-0.0045 c. 1772: 111 113 1548 N T3 SD: 0.0027 c. M:-0.0038 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 x 34:44 SD: 5.6392 cents 34 x 35:45 SD: 9.0345 cents 35 x 36:47 SD: 9.3968 cents 36 x 37:48 SD: 7.7634 cents 37:38 x 49 SD: 9.5132 cents 38:39 x 51 SD: 8.9252 cents 39:40 x 52 SD: 6.3184 cents 40:41 x 53 SD: 7.9265 cents 42:43:44:56 SD: 6.6665 cents 44:45:46:59 SD: 6.2499 cents 45:46:47:60 SD: 4.7004 cents 47:48:49:63 SD: 4.6703 cents 48:49:50:64 SD: 2.9766 cents 51:52:53:68 SD: 1.4557 cents 54:55:56:72 SD: 0.1908 cents 435:443:451:580 SD: 0.1850 cents 489:498:507:652 SD: 0.1788 cents 543:553:563:724 SD: 0.1750 cents 597:608:619:796 SD: 0.1726 cents