Scala analysis: 016_H5
Hyperenharmonic tetrachord 64/63 * 63/62 * 31/24
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 64/63 27.264092 septimal comma, Archytas' comma 2: 32/31 54.964428 Greek enharmonic 1/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 31/24 443.0806 1: 64/63 27.2641 septimal comma, Archytas' comma 2: 63/62 27.7003 3: 31/24 443.0806
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 63/62 27.700 cents 1: 1 31/24 443.081 cents 2: 1 32/31 54.964 cents Greek enharmonic 1/4-tone 2: 1 248/189 470.345 cents 2: 1 21/16 470.781 cents narrow fourth 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 : 27.3 55.0 498.0 27.3 : 27.7 470.8 498.0 55.0 : 443.1 470.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 443.0806 cents 651/512, 415.8165 cents 64/63, 27.2641 cents 2: 54.9644 .. 470.7809 cents 651/512, 415.8165 cents 768/961,-388.1161 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 64/63, 27.2641 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 31/24, 443.0806 cents Average / Smallest step : 6.089145 Largest / Average step : 2.668919 Largest / Smallest step : 16.251433 Median interval of one step : 63/62, 27.7003 cents, amount: 1 Least squares average step : 116.52342 cents, oct.: 349.57027 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1169-tone equal temperament with octave 4/3 degrees: 64 129 1169 Least number of segments generator : 585 of 249.236 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1104 of 470.352 cents and inv. generated superset size: 18 = 15 more = 600.000% 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 27.26409 cents Scale diversity : 0.098535 Lumma stability : 0.109484 Lumma impropriety factor : 0.779279 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 : 3969/3968, 0.4362 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 415.3802 cents: 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 31 Odd number limit : 189 (O: 63 U: 189) Highest odd numerator or denominator: 63 Scale harmonicity : 0.046256 Fundamental : 1/1953, -10.9315 octaves, 0.1340 Hz. Guide tone : 64, 6.0000 octaves, 16744.036 Hz. Exponens Consonantiae : 1.249920E+05, 16.93148 octaves Euler's gradus suavitatis : 47 Sum of Mann's harmonic distance : 98.5, average 32.83333 Mersenne's string divisions : 8001 Sum of van Prooijen's expressibility: 3.76782, average 1.25594 Sum of Tenney's harmonic distance : 7.68121, average 2.56040 Vogel's harmonic complexity : 32.66667 Wille's k value : 325 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 23.49360, average 3.91560 Lattice compactness (without 2's) : 7.88635, average 1.31439 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 6 4.33333 13 3: -2 .. 0 -1.00000 3 1 7: -1 .. 0 -0.33333 1 1 31: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <7 10 19 33| Scale is weakly epimorphic with val: <7 10 19 36| Scale is weakly epimorphic with val: <7 10 19 39| Scale is weakly epimorphic with val: <7 11 18 34| Scale is weakly epimorphic with val: <7 11 18 37| Scale is JI-epimorphic with val: <7 11 19 33| Scale is weakly epimorphic with val: <7 11 19 36| Scale is weakly epimorphic with val: <7 11 19 39| Scale is weakly epimorphic with val: <7 11 21 34| Scale is weakly epimorphic with val: <7 11 21 37| Scale is weakly epimorphic with val: <7 11 22 33| Scale is weakly epimorphic with val: <7 11 22 36| Scale is weakly epimorphic with val: <7 11 22 39| Scale is weakly epimorphic with val: <8 11 19 37| Scale is weakly epimorphic with val: <8 11 22 37| Scale is weakly epimorphic with val: <8 12 19 37| Scale is weakly epimorphic with val: <8 12 21 35| Scale is weakly epimorphic with val: <8 12 21 38| Scale is weakly epimorphic with val: <8 12 22 37|
FIT/MODE
3: 0 0 3 N M DE S SD: 35.4232 c. M: 54.9644 c. 7: 0 1 6 N G T3 SD: 18.3056 c. M: 27.2641 c. 8: 0 1 7 N G T3 SD: 16.2941 c. M: 27.2641 c. 9: 0 1 8 N G T3 SD: 15.7424 c. M: 27.2641 c. 10: 0 1 9 N G T3 SD: 16.0204 c. M: 27.2641 c. 11: 0 1 10 N G T3 SD: 16.7051 c. M: 27.2641 c. 12: 0 1 11 N G T3 SD: 17.5549 c. M: 27.2641 c. 13: 1 0 12 N G T3 SD: 11.5379 c. M: 16.6533 c. 14: 1 1 12 N M DE S SD: 10.5042 c. M:-16.1849 c. 15: 1 1 13 N M DE S SD: 7.4427 c. M:-11.4416 c. 16: 1 1 14 N M DE S SD: 4.7641 c. M:-7.2912 c. 17: 1 1 15 N M DE S SD: 2.4015 c. M:-3.6291 c. 18: 1 1 16 N M DE S SD: 0.3183 c. M:-0.4051 c. 73: 4 4 65 N M DE S SD: 0.2223 c. M: 0.3842 c. 91: 5 5 81 N M DE S SD: 0.1473 c. M: 0.2342 c. 109: 6 6 97 N M DE S SD: 0.1166 c. M:-0.1512 c. 127: 7 7 113 N M DE S SD: 0.1138 c. M:-0.1872 c. 145: 8 8 129 N M DE S SD: 0.1238 c. M:-0.2143 c. 236: 13 13 210 N M DE S SD: 0.1128 c. M:-0.1706 c. 363: 20 20 323 N M DE S SD: 0.1127 c. M:-0.1764 c. 453: 25 25 403 N M DE S SD: 0.1281 c. M:-0.2218 c. 454: 25 25 404 N M DE S SD: 0.1139 c. M:-0.1613 c. 490: 27 27 436 N M DE S SD: 0.1128 c. M:-0.1792 c. 527: 29 29 469 N M DE S SD: 0.1199 c. M: 0.1511 c. 563: 31 31 501 N M DE S SD: 0.1143 c. M:-0.1593 c. 570: 31 32 507 N T3 SD: 0.1130 c. M: 0.1774 c. 588: 32 33 523 N T3 SD: 0.1062 c. M: 0.1596 c. 589: 32 33 524 N T3 SD: 0.1187 c. M: 0.2056 c. 599: 33 33 533 N M DE S SD: 0.1126 c. M:-0.1741 c. 606: 33 34 539 N T3 SD: 0.1006 c. M: 0.1428 c. 607: 33 34 540 N T3 SD: 0.1084 c. M: 0.1875 c. 624: 34 35 555 N T3 SD: 0.0962 c. M: 0.1270 c. 625: 34 35 556 N T3 SD: 0.0991 c. M: 0.1704 c. 642: 35 36 571 N T3 SD: 0.0929 c. M:-0.1153 c. 643: 35 36 572 N T3 SD: 0.0907 c. M: 0.1543 c. 660: 36 37 587 N T3 SD: 0.0905 c. M:-0.1224 c. 661: 36 37 588 N T3 SD: 0.0834 c. M: 0.1391 c. 679: 37 38 604 N T3 SD: 0.0771 c. M: 0.1247 c. 697: 38 39 620 N T3 SD: 0.0719 c. M: 0.1110 c. 715: 39 40 636 N T3 SD: 0.0677 c. M: 0.0980 c. 716: 39 40 637 N T3 SD: 0.0788 c. M: 0.1359 c. 733: 40 41 652 N T3 SD: 0.0646 c. M: 0.0856 c. 734: 40 41 653 N T3 SD: 0.0708 c. M: 0.1227 c. 751: 41 42 668 N T3 SD: 0.0625 c. M:-0.0792 c. 752: 41 42 669 N T3 SD: 0.0636 c. M: 0.1100 c. 769: 42 43 684 N T3 SD: 0.0615 c. M:-0.0861 c. 770: 42 43 685 N T3 SD: 0.0572 c. M: 0.0980 c. 788: 43 44 701 N T3 SD: 0.0516 c. M: 0.0865 c. 806: 44 45 717 N T3 SD: 0.0471 c. M: 0.0755 c. 824: 45 46 733 N T3 SD: 0.0435 c. M: 0.0650 c. 842: 46 47 749 N T3 SD: 0.0411 c. M: 0.0550 c. 860: 47 48 765 N T3 SD: 0.0399 c. M:-0.0522 c. 861: 47 48 766 N T3 SD: 0.0449 c. M: 0.0770 c. 878: 48 49 781 N T3 SD: 0.0398 c. M:-0.0588 c. 879: 48 49 782 N T3 SD: 0.0388 c. M: 0.0671 c. 897: 49 50 798 N T3 SD: 0.0333 c. M: 0.0576 c. 915: 50 51 814 N T3 SD: 0.0287 c. M: 0.0485 c. 933: 51 52 830 N T3 SD: 0.0252 c. M: 0.0398 c. 951: 52 53 846 N T3 SD: 0.0231 c. M: 0.0313 c. 969: 53 54 862 N T3 SD: 0.0225 c. M:-0.0313 c. 988: 54 55 879 N T3 SD: 0.0270 c. M: 0.0430 c. 1005: 55 56 894 N T3 SD: 0.0255 c. M:-0.0435 c. 1006: 55 56 895 N T3 SD: 0.0212 c. M: 0.0350 c. 1024: 56 57 911 N T3 SD: 0.0159 c. M: 0.0273 c. 1042: 57 58 927 N T3 SD: 0.0115 c. M: 0.0198 c. 1060: 58 59 943 N T3 SD: 0.0088 c. M: 0.0126 c. 1078: 59 60 959 N T3 SD: 0.0090 c. M:-0.0146 c. 1151: 63 64 1024 N T3 SD: 0.0065 c. M: 0.0107 c. 1169: 64 65 1040 N T3 SD: 0.0032 c. M: 0.0048 c. 2229: 122 124 1983 N T3 SD: 0.0028 c. M: 0.0046 c. 2247: 123 125 1999 N T3 SD: 0.0027 c. M:-0.0045 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: 105.9532 cents 7 x 8:9 S SD: 93.5600 cents 8 x 9:11 SD: 79.0930 cents 9 x 10:12 S SD: 63.7196 cents 10 x 11:13 SD: 59.2240 cents 11 x 12:15 S SD: 51.6404 cents 12 x 13:16 SD: 41.8041 cents 13 x 14:17 SD: 40.3360 cents 14 x 15:19 SD: 35.6945 cents 15 x 16:20 S SD: 28.3834 cents 16 x 17:21 SD: 28.4712 cents 17 x 18:23 SD: 25.3668 cents 18 x 19:24 SD: 19.3193 cents 19 x 20:25 S SD: 20.4371 cents 20 x 21:27 SD: 18.2547 cents 21 x 22:28 SD: 12.7863 cents 22 x 23:29 SD: 14.7912 cents 23 x 24:31 SD: 13.2344 cents 24 x 25:32 SD: 7.8540 cents 25 x 26:33 SD: 10.8406 cents 26 x 27:35 SD: 9.7732 cents 27 x 28:36 SD: 3.9982 cents 28 x 29:37 SD: 8.2851 cents 29 x 30:39 SD: 7.6604 cents 30 x 31:40 SD: 0.9012 cents 31 x 32:41 SD: 7.0091 cents 32 x 33:43 SD: 6.7892 cents 33 x 34:44 SD: 1.6410 cents 34 x 35:45 SD: 6.8208 cents 35 x 36:47 SD: 6.8956 cents 36 x 37:48 SD: 3.7652 cents 37 x 38:49 SD: 7.3335 cents 38 x 39:51 SD: 7.5626 cents 39 x 40:52 SD: 5.5667 cents 40 x 41:53 SD: 8.1706 cents 41 x 42:55 SD: 8.4589 cents 42:43 x 56 SD: 6.7364 cents 43:44 x 57 SD: 8.0476 cents 44:45 x 59 SD: 7.6115 cents 45:46 x 60 SD: 5.3933 cents 46:47 x 61 SD: 6.8625 cents 48:49:50:64 SD: 5.9428 cents 50:51:52:67 SD: 5.6878 cents 51:52:53:68 SD: 4.4173 cents 54:55:56:72 SD: 3.0590 cents 57:58:59:76 SD: 1.8425 cents 60:61:62:80 SD: 0.7510 cents 63:64:65:84 SD: 0.2863 cents 123:125:127:164 SD: 0.2643 cents 186:189:192:248 SD: 0.1454 cents 249:253:257:332 SD: 0.1306 cents