Scala analysis: 019_H6
Hyperenharmonic tetrachord 62/61 * 61/60 * 40/31
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 62/61 28.150767 2: 31/30 56.766858 31st-partial chroma 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 40/31 441.2781 1: 62/61 28.1508 2: 61/60 28.6161 3: 40/31 441.2781
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 62/61 28.151 cents 1: 1 61/60 28.616 cents 1: 1 40/31 441.278 cents 2: 1 31/30 56.767 cents 31st-partial chroma 2: 1 80/61 469.429 cents 2: 1 122/93 469.894 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 : 28.2 56.8 498.0 28.2 : 28.6 469.9 498.0 56.8 : 441.3 469.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 28.1508 .. 441.2781 cents 1220/961, 413.1274 cents 62/61, 28.1508 cents 2: 56.7669 .. 469.8942 cents 1220/961, 413.1274 cents 961/1200,-384.5113 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 62/61, 28.1508 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 40/31, 441.2781 cents Average / Smallest step : 5.897353 Largest / Average step : 2.658062 Largest / Smallest step : 15.675528 Median interval of one step : 61/60, 28.6161 cents, amount: 1 Least squares average step : 116.84425 cents, oct.: 350.53275 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1044-tone equal temperament with octave 4/3 degrees: 59 119 1044 Least number of segments generator : 523 of 249.500 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 865 of 412.652 cents and inv. generated superset size: 24 = 21 more = 800.000% 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 28.15077 cents Scale diversity : 0.111323 Lumma stability : 0.113045 Lumma impropriety factor : 0.772041 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 : 3721/3720, 0.4653 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 412.6621 cents: 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 61 Odd number limit : 93 (O: 61 U: 93) Highest odd numerator or denominator: 61 Scale harmonicity : 0.082873 Fundamental : 1/1830, -10.8376 octaves, 0.1430 Hz. Guide tone : 124, 6.9542 octaves, 32441.570 Hz. Exponens Consonantiae : 2.269200E+05, 17.79182 octaves Euler's gradus suavitatis : 100 Sum of Mann's harmonic distance : 95.5, average 31.83333 Mersenne's string divisions : 52521 Sum of van Prooijen's expressibility: 3.75381, average 1.25127 Sum of Tenney's harmonic distance : 7.62539, average 2.54180 Vogel's harmonic complexity : 67.33333 Wille's k value : 945 Wilson's harmonic complexity : 100 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 11.99410, average 1.99902 Lattice compactness (without 2's) : 5.82843, average 0.97140 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -1 .. 0 -0.66667 2 1 5: -1 .. 0 -0.33333 1 31: 0 .. 1 0.66667 2 1 61: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 15 34 42| Scale is weakly epimorphic with val: <6 10 16 35 43| Scale is weakly epimorphic with val: <6 10 16 39 42| Scale is weakly epimorphic with val: <6 10 17 36 44| Scale is weakly epimorphic with val: <6 10 18 37 42| Scale is weakly epimorphic with val: <6 10 19 38 43| Scale is weakly epimorphic with val: <6 10 19 39 42| Scale is weakly epimorphic with val: <6 11 15 35 42| Scale is weakly epimorphic with val: <6 11 16 36 43| Scale is weakly epimorphic with val: <6 11 17 37 44| Scale is weakly epimorphic with val: <6 11 17 39 42| Scale is weakly epimorphic with val: <6 11 18 38 42| Scale is weakly epimorphic with val: <6 11 19 39 43| Scale is weakly epimorphic with val: <7 10 15 35 43| Scale is weakly epimorphic with val: <7 10 16 36 44| Scale is weakly epimorphic with val: <7 10 16 38 42| Scale is weakly epimorphic with val: <7 10 17 37 42| Scale is weakly epimorphic with val: <7 10 17 39 43| Scale is weakly epimorphic with val: <7 10 18 38 43| Scale is weakly epimorphic with val: <7 10 19 38 42| Scale is weakly epimorphic with val: <7 10 19 39 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 33 42| Scale is weakly epimorphic with val: <7 11 16 35 43| Scale is JI-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 16 39 42| 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 JI-epimorphic with val: <7 11 17 37 43| Scale is weakly epimorphic with val: <7 11 17 39 44| Scale is weakly 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 JI-epimorphic with val: <7 11 18 38 44| Scale is weakly epimorphic with val: <7 11 19 33 42| Scale is weakly 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 11 19 39 42| Scale is weakly epimorphic with val: <7 12 15 37 43| Scale is weakly epimorphic with val: <7 12 15 38 42| Scale is weakly epimorphic with val: <7 12 16 38 44| Scale is weakly epimorphic with val: <7 12 16 39 43| Scale is weakly epimorphic with val: <7 12 17 39 42| Scale is weakly epimorphic with val: <7 12 18 38 42| Scale is weakly epimorphic with val: <7 12 19 39 43| Scale is weakly epimorphic with val: <8 11 15 37 44| Scale is weakly epimorphic with val: <8 11 15 38 43| Scale is weakly epimorphic with val: <8 11 16 38 42| Scale is weakly epimorphic with val: <8 11 16 39 44| Scale is weakly epimorphic with val: <8 11 17 37 42| Scale is weakly epimorphic with val: <8 11 17 39 43| Scale is weakly epimorphic with val: <8 11 18 38 43| Scale is weakly epimorphic with val: <8 11 19 39 44| Scale is weakly epimorphic with val: <8 12 15 37 42| Scale is weakly epimorphic with val: <8 12 15 38 44| Scale is weakly epimorphic with val: <8 12 16 38 43| Scale is weakly epimorphic with val: <8 12 16 39 42| Scale is weakly epimorphic with val: <8 12 17 39 44| Scale is weakly epimorphic with val: <8 12 18 37 42| Scale is weakly epimorphic with val: <8 12 19 38 43|
FIT/MODE
3: 0 0 3 N M DE S SD: 36.5830 c. M: 56.7669 c. 6: 0 1 5 N G T3 SD: 22.2189 c. M: 28.1508 c. 7: 0 1 6 N G T3 SD: 18.2512 c. M: 28.1508 c. 8: 0 1 7 N G T3 SD: 16.5589 c. M: 28.1508 c. 9: 0 1 8 N G T3 SD: 16.2738 c. M: 28.1508 c. 10: 0 1 9 N G T3 SD: 16.7426 c. M: 28.1508 c. 11: 0 1 10 N G T3 SD: 17.5546 c. M: 28.1508 c. 12: 0 1 11 N G T3 SD: 18.4881 c. M: 28.1508 c. 13: 1 1 11 N M DE S SD: 12.8773 c. M:-19.8554 c. 14: 1 1 12 N M DE S SD: 9.3447 c. M:-14.3824 c. 15: 1 1 13 N M DE S SD: 6.2833 c. M:-9.6391 c. 16: 1 1 14 N M DE S SD: 3.6051 c. M:-5.4888 c. 17: 1 1 15 N M DE S SD: 1.2450 c. M:-1.8267 c. 18: 1 1 16 N M DE S SD: 0.8704 c. M: 1.4285 c. 35: 2 2 31 N M DE S SD: 0.1989 c. M:-0.3089 c. 88: 5 5 78 N M DE S SD: 0.1302 c. M: 0.1708 c. 123: 7 7 109 N M DE S SD: 0.1205 c. M:-0.1933 c. 158: 9 9 140 N M DE S SD: 0.1274 c. M:-0.2189 c. 193: 11 11 171 N M DE S SD: 0.1358 c. M:-0.2352 c. 211: 12 12 187 N M DE S SD: 0.1212 c. M:-0.1741 c. 299: 17 17 265 N M DE S SD: 0.1229 c. M:-0.1662 c. 334: 19 19 296 N M DE S SD: 0.1203 c. M:-0.1811 c. 387: 22 22 343 N M DE S SD: 0.1242 c. M:-0.1619 c. 404: 23 23 358 N M DE S SD: 0.1222 c. M:-0.2033 c. 457: 26 26 405 N M DE S SD: 0.1202 c. M:-0.1844 c. 475: 27 27 421 N M DE S SD: 0.1251 c. M:-0.1592 c. 510: 29 29 452 N M DE S SD: 0.1221 c. M:-0.1694 c. 527: 30 30 467 N M DE S SD: 0.1217 c. M:-0.2009 c. 544: 31 31 482 N M DE S SD: 0.1331 c. M:-0.2305 c. 545: 31 31 483 N M DE S SD: 0.1206 c. M:-0.1784 c. 552: 31 32 489 N T3 SD: 0.1131 c. M: 0.1808 c. 553: 31 32 490 N T3 SD: 0.1346 c. M: 0.2314 c. 563: 32 32 499 N M DE S SD: 0.1258 c. M:-0.1573 c. 569: 32 33 504 N T3 SD: 0.1099 c. M: 0.1412 c. 570: 32 33 505 N T3 SD: 0.1111 c. M: 0.1903 c. 587: 33 34 520 N T3 SD: 0.0989 c. M: 0.1516 c. 588: 33 34 521 N T3 SD: 0.1155 c. M: 0.1993 c. 604: 34 35 535 N T3 SD: 0.0998 c. M:-0.1290 c. 605: 34 35 536 N T3 SD: 0.0954 c. M: 0.1615 c. 622: 35 36 551 N T3 SD: 0.0873 c. M: 0.1257 c. 623: 35 36 552 N T3 SD: 0.0987 c. M: 0.1707 c. 639: 36 37 566 N T3 SD: 0.0921 c. M:-0.1303 c. 640: 36 37 567 N T3 SD: 0.0819 c. M: 0.1357 c. 657: 37 38 582 N T3 SD: 0.0779 c. M: 0.1026 c. 658: 37 38 583 N T3 SD: 0.0838 c. M: 0.1452 c. 675: 38 39 598 N T3 SD: 0.0705 c. M: 0.1127 c. 692: 39 40 613 N T3 SD: 0.0706 c. M:-0.0909 c. 693: 39 40 614 N T3 SD: 0.0708 c. M: 0.1223 c. 710: 40 41 629 N T3 SD: 0.0611 c. M: 0.0919 c. 728: 41 42 645 N T3 SD: 0.0593 c. M: 0.1015 c. 745: 42 43 660 N T3 SD: 0.0535 c. M: 0.0731 c. 763: 43 44 676 N T3 SD: 0.0494 c. M: 0.0827 c. 780: 44 45 691 N T3 SD: 0.0479 c. M:-0.0614 c. 781: 44 45 692 N T3 SD: 0.0535 c. M: 0.0919 c. 798: 45 46 707 N T3 SD: 0.0411 c. M: 0.0655 c. 816: 46 47 723 N T3 SD: 0.0432 c. M: 0.0747 c. 833: 47 48 738 N T3 SD: 0.0345 c. M: 0.0498 c. 851: 48 49 754 N T3 SD: 0.0340 c. M: 0.0589 c. 868: 49 50 769 N T3 SD: 0.0299 c. M:-0.0378 c. 886: 50 51 785 N T3 SD: 0.0260 c. M: 0.0444 c. 921: 52 53 816 N T3 SD: 0.0195 c. M: 0.0310 c. 956: 54 55 847 N T3 SD: 0.0152 c. M:-0.0186 c. 974: 55 56 863 N T3 SD: 0.0163 c. M: 0.0271 c. 991: 56 57 878 N T3 SD: 0.0141 c. M:-0.0233 c. 1009: 57 58 894 N T3 SD: 0.0090 c. M: 0.0154 c. 1044: 59 60 925 N T3 SD: 0.0030 c. M: 0.0045 c. 2123: 120 122 1881 N T3 SD: 0.0030 c. M:-0.0051 c. 2176: 123 125 1928 N T3 SD: 0.0027 c. M: 0.0044 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: 105.0520 cents 7 x 8:9 S SD: 92.7119 cents 8 x 9:11 SD: 78.2450 cents 9 x 10:12 S SD: 62.8184 cents 10 x 11:13 SD: 58.3877 cents 11 x 12:15 S SD: 50.8067 cents 12 x 13:16 SD: 40.9029 cents 13 x 14:17 SD: 39.5185 cents 14 x 15:19 SD: 34.8827 cents 15 x 16:20 S SD: 27.4822 cents 16 x 17:21 SD: 27.6833 cents 17 x 18:23 SD: 24.5895 cents 18 x 19:24 SD: 18.4181 cents 19 x 20:25 S SD: 19.6976 cents 20 x 21:27 SD: 17.5345 cents 21 x 22:28 SD: 11.8851 cents 22 x 23:29 SD: 14.1341 cents 23 x 24:31 SD: 12.6132 cents 24 x 25:32 SD: 6.9528 cents 25 x 26:33 SD: 10.3283 cents 26 x 27:35 SD: 9.3263 cents 27 x 28:36 SD: 3.0970 cents 28 x 29:37 SD: 8.0150 cents 29 x 30:39 SD: 7.4923 cents 30 x 31:40 SD: 0.0000 cents 31 x 32:41 SD: 7.0668 cents 32 x 33:43 SD: 6.9592 cents 33 x 34:44 SD: 2.5422 cents 34 x 35:45 SD: 7.1864 cents 35 x 36:47 SD: 7.3446 cents 36 x 37:48 SD: 4.6664 cents 37 x 38:49 SD: 7.9069 cents 38 x 39:51 SD: 8.1861 cents 39 x 40:52 SD: 6.4679 cents 40 x 41:53 SD: 8.8646 cents 41:42 x 55 SD: 8.5855 cents 42:43 x 56 SD: 6.2930 cents 43:44 x 57 SD: 7.7073 cents 44:45 x 59 SD: 7.2781 cents 45:46:47:60 SD: 6.9988 cents 47:48:49:63 SD: 6.5802 cents 48:49:50:64 SD: 5.2737 cents 50:51:52:67 SD: 5.1220 cents 51:52:53:68 SD: 3.7484 cents 54:55:56:72 SD: 2.3907 cents 57:58:59:76 SD: 1.1766 cents 60:61:62:80 SD: 0.1551 cents 483:491:499:644 SD: 0.1505 cents 543:552:561:724 SD: 0.1454 cents