Scala analysis: 022_H7
Hyperenharmonic tetrachord 60/59 * 59/58 * 58/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 60/59 29.097055 2: 30/29 58.691521 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 58/45 439.3535 1: 60/59 29.0971 2: 59/58 29.5945 3: 58/45 439.3535
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 60/59 29.097 cents 1: 1 59/58 29.594 cents 1: 1 58/45 439.353 cents 2: 1 30/29 58.692 cents 2: 1 232/177 468.451 cents 2: 1 59/45 468.948 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 : 29.1 58.7 498.0 29.1 : 29.6 468.9 498.0 58.7 : 439.4 468.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 29.0971 .. 439.3535 cents 1711/1350, 410.2564 cents 60/59, 29.0971 cents 2: 58.6915 .. 468.9479 cents 1711/1350, 410.2564 cents 675/841,-380.6620 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 60/59, 29.0971 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 58/45, 439.3535 cents Average / Smallest step : 5.705560 Largest / Average step : 2.646469 Largest / Smallest step : 15.099586 Median interval of one step : 59/58, 29.5945 cents, amount: 1 Least squares average step : 117.18679 cents, oct.: 351.56038 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 29.09706 cents Scale diversity : 0.125027 Lumma stability : 0.116845 Lumma impropriety factor : 0.764312 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 : 3481/3480, 0.4974 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 409.7590 cents: 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 59 Odd number limit : 177 (O: 59 U: 177) Highest odd numerator or denominator: 59 Scale harmonicity : 0.014749 Fundamental : 1/5133, -12.3256 octaves, 0.0510 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 3.079800E+05, 18.23248 octaves Euler's gradus suavitatis : 97 Sum of Mann's harmonic distance : 92.5, average 30.83333 Mersenne's string divisions : 7021 Sum of van Prooijen's expressibility: 3.71037, average 1.23679 Sum of Tenney's harmonic distance : 7.56770, average 2.52257 Vogel's harmonic complexity : 67.66667 Wille's k value : 1327 Wilson's harmonic complexity : 99 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 12.98159, average 2.16360 Lattice compactness (without 2's) : 9.83182, average 1.63864 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.66667 2 29: -1 .. 0 -0.33333 1 1 59: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 19 32 43| Scale is weakly epimorphic with val: <6 11 18 32 42| Scale is weakly epimorphic with val: <6 11 19 33 43| Scale is weakly epimorphic with val: <7 10 18 32 43| Scale is weakly epimorphic with val: <7 10 19 33 44| Scale is weakly epimorphic with val: <7 11 15 32 44| Scale is weakly epimorphic with val: <7 11 15 34 42| Scale is weakly epimorphic with val: <7 11 15 35 44| Scale is weakly epimorphic with val: <7 11 15 37 42| Scale is weakly epimorphic with val: <7 11 15 38 44| Scale is weakly epimorphic with val: <7 11 16 32 43| Scale is weakly epimorphic with val: <7 11 16 33 42| Scale is weakly epimorphic with val: <7 11 16 35 43| Scale is weakly epimorphic with val: <7 11 16 36 42| Scale is weakly epimorphic with val: <7 11 16 38 43| Scale is weakly epimorphic with val: <7 11 17 33 44| Scale is weakly epimorphic with val: <7 11 17 34 43| Scale is weakly epimorphic with val: <7 11 17 36 44| Scale is weakly epimorphic with val: <7 11 17 37 43| Scale is weakly epimorphic with val: <7 11 18 32 44| Scale is JI-epimorphic with val: <7 11 18 34 42| Scale is weakly epimorphic with val: <7 11 18 35 44| Scale is weakly epimorphic with val: <7 11 18 37 42| Scale is weakly epimorphic with val: <7 11 18 38 44| Scale is weakly epimorphic with val: <7 11 19 32 43| Scale is weakly epimorphic with val: <7 11 19 33 42| Scale is JI-epimorphic with val: <7 11 19 35 43| Scale is weakly epimorphic with val: <7 11 19 36 42| Scale is weakly epimorphic with val: <7 11 19 38 43| Scale is weakly epimorphic with val: <7 12 16 32 44| Scale is weakly epimorphic with val: <7 12 17 33 42| Scale is weakly epimorphic with val: <7 12 18 34 43| Scale is weakly epimorphic with val: <7 12 19 34 42| Scale is weakly epimorphic with val: <7 12 19 35 44| Scale is weakly epimorphic with val: <7 12 19 37 42| Scale is weakly epimorphic with val: <8 11 16 32 42| Scale is weakly epimorphic with val: <8 11 17 33 43| Scale is weakly epimorphic with val: <8 11 18 33 42| Scale is weakly epimorphic with val: <8 11 18 34 44| Scale is weakly epimorphic with val: <8 11 18 36 42| Scale is weakly epimorphic with val: <8 11 19 34 43| Scale is weakly epimorphic with val: <8 11 19 35 42| Scale is weakly epimorphic with val: <8 11 19 37 43| Scale is weakly epimorphic with val: <8 12 15 32 44| Scale is weakly epimorphic with val: <8 12 16 33 42| Scale is weakly epimorphic with val: <8 12 17 32 42| Scale is weakly epimorphic with val: <8 12 17 34 43| Scale is weakly epimorphic with val: <8 12 17 35 42| Scale is weakly epimorphic with val: <8 12 17 38 42| Scale is weakly epimorphic with val: <8 12 18 33 43| Scale is weakly epimorphic with val: <8 12 18 35 44| Scale is weakly epimorphic with val: <8 12 18 36 43| Scale is weakly epimorphic with val: <8 12 19 34 44| Scale is weakly epimorphic with val: <8 12 19 36 42| Scale is weakly epimorphic with val: <8 12 19 37 44|
FIT/MODE
3: 0 0 3 N M DE S SD: 37.8212 c. M: 58.6915 c. 6: 0 1 5 N G T3 SD: 21.8930 c. M: 29.0971 c. 7: 0 1 6 N G T3 SD: 18.2742 c. M: 29.0971 c. 8: 0 1 7 N G T3 SD: 16.9247 c. M: 29.0971 c. 9: 0 1 8 N G T3 SD: 16.9104 c. M: 29.0971 c. 10: 0 1 9 N G T3 SD: 17.5653 c. M: 29.0971 c. 11: 0 1 10 N G T3 SD: 18.4986 c. M: 29.0971 c. 12: 1 0 11 N G T3 SD: 12.2385 c. M: 17.1878 c. 13: 1 1 11 N M DE S SD: 11.6392 c. M:-17.9308 c. 14: 1 1 12 N M DE S SD: 8.1067 c. M:-12.4578 c. 15: 1 1 13 N M DE S SD: 5.0455 c. M:-7.7145 c. 16: 1 1 14 N M DE S SD: 2.3683 c. M:-3.5641 c. 17: 1 1 15 N M DE S SD: 0.1284 c. M:-0.1997 c. 458: 27 27 404 N M DE S SD: 0.1532 c. M:-0.2637 c. 460: 27 27 406 N M DE S SD: 0.1520 c. M: 0.2254 c. 466: 27 28 411 N T3 SD: 0.1483 c. M: 0.2404 c. 475: 28 28 419 N M DE S SD: 0.1516 c. M:-0.2614 c. 477: 28 28 421 N M DE S SD: 0.1504 c. M: 0.2208 c. 483: 28 29 426 N T3 SD: 0.1386 c. M: 0.2249 c. 492: 29 29 434 N M DE S SD: 0.1502 c. M:-0.2593 c. 494: 29 29 436 N M DE S SD: 0.1490 c. M: 0.2166 c. 499: 29 30 440 N T3 SD: 0.1432 c. M:-0.1956 c. 500: 29 30 441 N T3 SD: 0.1295 c. M: 0.2104 c. 509: 30 30 449 N M DE S SD: 0.1489 c. M:-0.2573 c. 511: 30 30 451 N M DE S SD: 0.1478 c. M: 0.2127 c. 516: 30 31 455 N T3 SD: 0.1347 c. M:-0.1859 c. 517: 30 31 456 N T3 SD: 0.1211 c. M: 0.1970 c. 533: 31 32 470 N T3 SD: 0.1267 c. M:-0.1768 c. 534: 31 32 471 N T3 SD: 0.1132 c. M: 0.1843 c. 550: 32 33 485 N T3 SD: 0.1193 c. M:-0.1683 c. 551: 32 33 486 N T3 SD: 0.1057 c. M: 0.1725 c. 567: 33 34 500 N T3 SD: 0.1124 c. M:-0.1604 c. 568: 33 34 501 N T3 SD: 0.0987 c. M: 0.1613 c. 584: 34 35 515 N T3 SD: 0.1059 c. M:-0.1528 c. 585: 34 35 516 N T3 SD: 0.0922 c. M: 0.1509 c. 601: 35 36 530 N T3 SD: 0.0997 c. M:-0.1457 c. 602: 35 36 531 N T3 SD: 0.0860 c. M: 0.1410 c. 618: 36 37 545 N T3 SD: 0.0940 c. M:-0.1390 c. 619: 36 37 546 N T3 SD: 0.0801 c. M: 0.1316 c. 636: 37 38 561 N T3 SD: 0.0746 c. M: 0.1227 c. 653: 38 39 576 N T3 SD: 0.0693 c. M: 0.1143 c. 670: 39 40 591 N T3 SD: 0.0643 c. M: 0.1064 c. 687: 40 41 606 N T3 SD: 0.0596 c. M: 0.0988 c. 704: 41 42 621 N T3 SD: 0.0551 c. M: 0.0916 c. 721: 42 43 636 N T3 SD: 0.0508 c. M: 0.0847 c. 738: 43 44 651 N T3 SD: 0.0467 c. M: 0.0782 c. 755: 44 45 666 N T3 SD: 0.0429 c. M: 0.0719 c. 772: 45 46 681 N T3 SD: 0.0392 c. M: 0.0659 c. 789: 46 47 696 N T3 SD: 0.0356 c. M: 0.0602 c. 806: 47 48 711 N T3 SD: 0.0322 c. M: 0.0547 c. 823: 48 49 726 N T3 SD: 0.0290 c. M: 0.0495 c. 840: 49 50 741 N T3 SD: 0.0259 c. M: 0.0444 c. 857: 50 51 756 N T3 SD: 0.0230 c. M: 0.0396 c. 874: 51 52 771 N T3 SD: 0.0202 c. M: 0.0349 c. 891: 52 53 786 N T3 SD: 0.0176 c. M: 0.0305 c. 908: 53 54 801 N T3 SD: 0.0151 c. M: 0.0261 c. 925: 54 55 816 N T3 SD: 0.0128 c. M: 0.0220 c. 942: 55 56 831 N T3 SD: 0.0107 c. M: 0.0180 c. 959: 56 57 846 N T3 SD: 0.0089 c. M: 0.0141 c. 976: 57 58 861 N T3 SD: 0.0076 c. M: 0.0104 c. 993: 58 59 876 N T3 SD: 0.0067 c. M: 0.0095 c. 1010: 59 60 891 N T3 SD: 0.0066 c. M: 0.0110 c. 1969: 115 117 1737 N T3 SD: 0.0071 c. M: 0.0087 c. 2003: 117 119 1767 N T3 SD: 0.0066 c. M: 0.0102 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: 104.0897 cents 7 x 8:9 S SD: 91.8073 cents 8 x 9:11 SD: 77.3408 cents 9 x 10:12 S SD: 61.8561 cents 10 x 11:13 SD: 57.4969 cents 11 x 12:15 S SD: 49.9190 cents 12 x 13:16 SD: 39.9406 cents 13 x 14:17 SD: 38.6498 cents 14 x 15:19 SD: 34.0208 cents 15 x 16:20 S SD: 26.5199 cents 16 x 17:21 SD: 26.8499 cents 17 x 18:23 SD: 23.7691 cents 18 x 19:24 SD: 17.4557 cents 19 x 20:25 S SD: 18.9234 cents 20 x 21:27 SD: 16.7847 cents 21 x 22:28 SD: 10.9228 cents 22 x 23:29 SD: 13.4637 cents 23 x 24:31 SD: 11.9893 cents 24 x 25:32 SD: 5.9905 cents 25 x 26:33 SD: 9.8430 cents 26 x 27:35 SD: 8.9251 cents 27 x 28:36 SD: 2.1347 cents 28 x 29:37 SD: 7.8314 cents 29 x 30:39 SD: 7.4302 cents 30 x 31:40 SD: 0.9623 cents 31 x 32:41 SD: 7.2526 cents 32 x 33:43 SD: 7.2608 cents 33 x 34:44 SD: 3.5045 cents 34 x 35:45 SD: 7.6749 cents 35 x 36:47 SD: 7.9098 cents 36 x 37:48 SD: 5.6287 cents 37 x 38:49 SD: 8.5816 cents 38 x 39:51 SD: 8.9046 cents 39:40 x 52 SD: 7.3670 cents 40:41 x 53 SD: 8.7204 cents 41:42 x 55 SD: 8.2168 cents 42:43 x 56 SD: 5.8199 cents 43:44 x 57 SD: 7.3563 cents 45:46:47:60 SD: 6.2844 cents 47:48:49:63 SD: 5.9572 cents 48:49:50:64 SD: 4.5595 cents 50:51:52:67 SD: 4.5491 cents 51:52:53:68 SD: 3.0347 cents 54:55:56:72 SD: 1.6784 cents 57:58:59:76 SD: 0.4771 cents 117:119:121:156 SD: 0.1838 cents 174:177:180:232 SD: 0.1658 cents 291:296:301:388 SD: 0.1478 cents