Scala analysis: 013_H4
Hyperenharmonic tetrachord 66/65 * 65/64 * 128/99
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 66/65 26.431568 Winmeanma 2: 33/32 53.272943 undecimal comma, al-Farabi's 1/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 128/99 444.7721 1: 66/65 26.4316 Winmeanma 2: 65/64 26.8414 13th-partial chroma 3: 128/99 444.7721
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 66/65 26.432 cents Winmeanma 1: 1 65/64 26.841 cents 13th-partial chroma 1: 1 128/99 444.772 cents 2: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 2: 1 256/195 471.204 cents 2: 1 130/99 471.613 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 : 26.4 53.3 498.0 26.4 : 26.8 471.6 498.0 53.3 : 444.8 471.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 26.4316 .. 444.7721 cents 4160/3267, 418.3405 cents 66/65, 26.4316 cents 2: 53.2729 .. 471.6134 cents 4160/3267, 418.3405 cents 3267/4096,-391.4991 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 66/65, 26.4316 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 128/99, 444.7721 cents Average / Smallest step : 6.280937 Largest / Average step : 2.679108 Largest / Smallest step : 16.827305 Median interval of one step : 65/64, 26.8414 cents, amount: 1 Least squares average step : 116.22232 cents, oct.: 348.66695 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1206-tone equal temperament with octave 4/3 degrees: 64 129 1206 Least number of segments generator : 605 of 249.848 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1079 of 445.597 cents and inv. generated superset size: 40 = 37 more = 1333.333% 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 26.43157 cents Scale diversity : 0.086577 Lumma stability : 0.106141 Lumma impropriety factor : 0.786072 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 : 4225/4224, 0.4098 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 417.9307 cents: 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 13 Odd number limit : 195 (O: 65 U: 195) Highest odd numerator or denominator: 65 Scale harmonicity : 0.016929 Average absolute harmonicity : 0.090937 Specific harmonicity : 0.080379 Fundamental : 1/6240, -12.6073 octaves, 0.0419 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 8.236800E+05, 19.65172 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 101.5, average 33.83333 Mersenne's string divisions : 59605 Sum of van Prooijen's expressibility: 3.80855, average 1.26952 Sum of Tenney's harmonic distance : 7.73530, average 2.57843 Vogel's harmonic complexity : 27.66667 Wille's k value : 3217 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 26.00960, average 4.33493 Lattice compactness (without 2's) : 10.71025, average 1.78504 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -0.66667 8 3: -1 .. 1 0.33333 3 1 5: -1 .. 0 -0.33333 1 11: 0 .. 1 0.66667 2 1 13: -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 15 23 26| Scale is weakly epimorphic with val: <6 10 15 23 29| Scale is weakly epimorphic with val: <6 10 16 23 25| Scale is weakly epimorphic with val: <6 10 16 23 28| Scale is weakly epimorphic with val: <6 10 17 23 27| Scale is weakly epimorphic with val: <6 10 17 23 30| Scale is weakly epimorphic with val: <6 10 18 23 26| Scale is weakly epimorphic with val: <6 10 18 23 29| Scale is weakly epimorphic with val: <6 10 19 23 25| Scale is weakly epimorphic with val: <6 10 19 23 28| Scale is weakly epimorphic with val: <7 11 15 23 25| Scale is weakly epimorphic with val: <7 11 15 23 28| Scale is weakly epimorphic with val: <7 11 15 25 26| Scale is weakly epimorphic with val: <7 11 15 25 29| Scale is JI-epimorphic with val: <7 11 15 26 28| Scale is weakly epimorphic with val: <7 11 16 23 27| Scale is weakly epimorphic with val: <7 11 16 23 30| Scale is weakly epimorphic with val: <7 11 16 25 25| Scale is weakly epimorphic with val: <7 11 16 25 28| Scale is JI-epimorphic with val: <7 11 16 26 27| Scale is weakly epimorphic with val: <7 11 16 26 30| Scale is weakly epimorphic with val: <7 11 17 23 26| Scale is weakly epimorphic with val: <7 11 17 23 29| Scale is weakly epimorphic with val: <7 11 17 25 27| = patent Scale is weakly epimorphic with val: <7 11 17 25 30| Scale is JI-epimorphic with val: <7 11 17 26 26| Scale is weakly epimorphic with val: <7 11 17 26 29| Scale is weakly epimorphic with val: <7 11 18 23 25| Scale is weakly epimorphic with val: <7 11 18 23 28| Scale is weakly epimorphic with val: <7 11 18 25 26| Scale is weakly epimorphic with val: <7 11 18 25 29| Scale is weakly epimorphic with val: <7 11 18 26 28| Scale is weakly epimorphic with val: <7 11 19 23 27| Scale is weakly epimorphic with val: <7 11 19 23 30| Scale is weakly epimorphic with val: <7 11 19 25 25| Scale is weakly epimorphic with val: <7 11 19 25 28| Scale is weakly epimorphic with val: <7 11 19 26 27| Scale is weakly epimorphic with val: <7 11 19 26 30| Scale is weakly epimorphic with val: <7 12 15 24 25| Scale is weakly epimorphic with val: <7 12 15 26 26| Scale is weakly epimorphic with val: <7 12 15 26 29| Scale is weakly epimorphic with val: <7 12 15 27 28| Scale is weakly epimorphic with val: <7 12 16 26 28| Scale is weakly epimorphic with val: <7 12 16 27 27| Scale is weakly epimorphic with val: <7 12 17 26 27| Scale is weakly epimorphic with val: <7 12 17 26 30| Scale is weakly epimorphic with val: <7 12 18 26 26| Scale is weakly epimorphic with val: <7 12 18 26 29| Scale is weakly epimorphic with val: <7 12 19 26 28| Scale is weakly epimorphic with val: <8 11 15 24 25| Scale is weakly epimorphic with val: <8 11 15 27 28| Scale is weakly epimorphic with val: <8 11 16 27 27| Scale is weakly epimorphic with val: <8 12 15 24 26| Scale is weakly epimorphic with val: <8 12 15 27 29| Scale is weakly epimorphic with val: <8 12 16 24 25| Scale is weakly epimorphic with val: <8 12 16 27 28| Scale is weakly epimorphic with val: <8 12 17 27 27|
FIT/MODE
3: 0 0 3 N M DE S SD: 34.3348 c. M: 53.2729 c. 7: 0 1 6 N G T3 SD: 18.4227 c. M: 26.4316 c. 8: 0 1 7 N G T3 SD: 16.1174 c. M: 26.4316 c. 9: 0 1 8 N G T3 SD: 15.3068 c. M: 26.4316 c. 10: 0 1 9 N G T3 SD: 15.3911 c. M: 26.4316 c. 11: 0 1 10 N G T3 SD: 15.9433 c. M: 26.4316 c. 12: 0 1 11 N G T3 SD: 16.7047 c. M: 26.4316 c. 13: 1 0 12 N G T3 SD: 11.0300 c. M: 14.9618 c. 14: 1 1 12 N M DE S SD: 11.5925 c. M:-17.8763 c. 15: 1 1 13 N M DE S SD: 8.5309 c. M:-13.1331 c. 16: 1 1 14 N M DE S SD: 5.8522 c. M:-8.9827 c. 17: 1 1 15 N M DE S SD: 3.4889 c. M:-5.3206 c. 18: 1 1 16 N M DE S SD: 1.3901 c. M:-2.0654 c. 19: 1 1 17 N M DE S SD: 0.5051 c. M: 0.8472 c. 37: 2 2 33 N M DE S SD: 0.4338 c. M:-0.5698 c. 56: 3 3 50 N M DE S SD: 0.1529 c. M:-0.2494 c. 75: 4 4 67 N M DE S SD: 0.1141 c. M: 0.1481 c. 131: 7 7 117 N M DE S SD: 0.1082 c. M:-0.1815 c. 187: 10 10 167 N M DE S SD: 0.1166 c. M:-0.2019 c. 206: 11 11 184 N M DE S SD: 0.1058 c. M:-0.1631 c. 431: 23 23 385 N M DE S SD: 0.1082 c. M:-0.1462 c. 468: 25 25 418 N M DE S SD: 0.1065 c. M:-0.1734 c. 487: 26 26 435 N M DE S SD: 0.1061 c. M:-0.1581 c. 506: 27 27 452 N M DE S SD: 0.1089 c. M:-0.1440 c. 543: 29 29 485 N M DE S SD: 0.1059 c. M:-0.1675 c. 581: 31 31 519 N M DE S SD: 0.1094 c. M:-0.1423 c. 599: 32 32 535 N M DE S SD: 0.1068 c. M:-0.1752 c. 617: 33 33 551 N M DE S SD: 0.1190 c. M:-0.2062 c. 625: 33 34 558 N T3 SD: 0.1032 c. M: 0.1348 c. 626: 33 34 559 N T3 SD: 0.1038 c. M: 0.1768 c. 644: 34 35 575 N T3 SD: 0.0945 c. M: 0.1373 c. 645: 34 35 576 N T3 SD: 0.1029 c. M: 0.1780 c. 662: 35 36 591 N T3 SD: 0.1006 c. M:-0.1428 c. 663: 35 36 592 N T3 SD: 0.0882 c. M: 0.1396 c. 664: 35 36 593 N T3 SD: 0.1040 c. M: 0.1792 c. 681: 36 37 608 N T3 SD: 0.0893 c. M:-0.1151 c. 682: 36 37 609 N T3 SD: 0.0846 c. M: 0.1418 c. 700: 37 38 625 N T3 SD: 0.0801 c. M: 0.1063 c. 701: 37 38 626 N T3 SD: 0.0834 c. M: 0.1439 c. 719: 38 39 642 N T3 SD: 0.0732 c. M: 0.1093 c. 720: 38 39 643 N T3 SD: 0.0844 c. M: 0.1459 c. 737: 39 40 658 N T3 SD: 0.0788 c. M:-0.1132 c. 738: 39 40 659 N T3 SD: 0.0689 c. M: 0.1121 c. 756: 40 41 675 N T3 SD: 0.0691 c. M:-0.0890 c. 757: 40 41 676 N T3 SD: 0.0671 c. M: 0.1148 c. 775: 41 42 692 N T3 SD: 0.0614 c. M: 0.0834 c. 776: 41 42 693 N T3 SD: 0.0678 c. M: 0.1173 c. 794: 42 43 709 N T3 SD: 0.0561 c. M: 0.0866 c. 813: 43 44 726 N T3 SD: 0.0535 c. M: 0.0897 c. 831: 44 45 742 N T3 SD: 0.0526 c. M:-0.0676 c. 832: 44 45 743 N T3 SD: 0.0535 c. M: 0.0926 c. 850: 45 46 759 N T3 SD: 0.0461 c. M: 0.0645 c. 869: 46 47 776 N T3 SD: 0.0423 c. M: 0.0679 c. 888: 47 48 793 N T3 SD: 0.0414 c. M: 0.0711 c. 906: 48 49 809 N T3 SD: 0.0388 c. M:-0.0498 c. 907: 48 49 810 N T3 SD: 0.0431 c. M: 0.0742 c. 925: 49 50 826 N T3 SD: 0.0334 c. M: 0.0486 c. 944: 50 51 843 N T3 SD: 0.0311 c. M: 0.0521 c. 963: 51 52 860 N T3 SD: 0.0320 c. M: 0.0554 c. 981: 52 53 876 N T3 SD: 0.0271 c. M:-0.0346 c. 1000: 53 54 893 N T3 SD: 0.0228 c. M: 0.0352 c. 1019: 54 55 910 N T3 SD: 0.0223 c. M: 0.0386 c. 1038: 55 56 927 N T3 SD: 0.0255 c. M: 0.0419 c. 1056: 56 57 943 N T3 SD: 0.0171 c. M:-0.0216 c. 1075: 57 58 960 N T3 SD: 0.0141 c. M: 0.0236 c. 1094: 58 59 977 N T3 SD: 0.0163 c. M: 0.0270 c. 1112: 59 60 993 N T3 SD: 0.0149 c. M:-0.0250 c. 1131: 60 61 1010 N T3 SD: 0.0084 c. M:-0.0104 c. 1150: 61 62 1027 N T3 SD: 0.0081 c. M: 0.0135 c. 1206: 64 65 1077 N T3 SD: 0.0008 c. M: 0.0013 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: 106.7990 cents 7 x 8:9 S SD: 94.3569 cents 8 x 9:11 SD: 79.8898 cents 9 x 10:12 S SD: 64.5654 cents 10 x 11:13 SD: 60.0105 cents 11 x 12:15 S SD: 52.4248 cents 12 x 13:16 SD: 42.6499 cents 13 x 14:17 SD: 41.1063 cents 14 x 15:19 SD: 36.4602 cents 15 x 16:20 S SD: 29.2292 cents 16 x 17:21 SD: 29.2165 cents 17 x 18:23 SD: 26.1036 cents 18 x 19:24 SD: 20.1650 cents 19 x 20:25 S SD: 21.1426 cents 20 x 21:27 SD: 18.9447 cents 21 x 22:28 SD: 13.6320 cents 22 x 23:29 SD: 15.4303 cents 23 x 24:31 SD: 13.8453 cents 24 x 25:32 SD: 8.6997 cents 25 x 26:33 SD: 11.3655 cents 26 x 27:35 SD: 10.2471 cents 27 x 28:36 SD: 4.8440 cents 28 x 29:37 SD: 8.6170 cents 29 x 30:39 SD: 7.9088 cents 30 x 31:40 SD: 1.7470 cents 31 x 32:41 SD: 7.0599 cents 32 x 33:43 SD: 6.7364 cents 33 x 34:44 SD: 0.7952 cents 34 x 35:45 SD: 6.5724 cents 35 x 36:47 SD: 6.5594 cents 36 x 37:48 SD: 2.9195 cents 37 x 38:49 SD: 6.8598 cents 38 x 39:51 SD: 7.0325 cents 39 x 40:52 SD: 4.7209 cents 40 x 41:53 SD: 7.5593 cents 41 x 42:55 SD: 7.8145 cents 42 x 43:56 SD: 6.2681 cents 43:44 x 57 SD: 8.3759 cents 44:45 x 59 SD: 7.9344 cents 45:46 x 60 SD: 5.8095 cents 46:47 x 61 SD: 7.1705 cents 47:48 x 63 SD: 6.7950 cents 48:49:50:64 SD: 6.5709 cents 50:51:52:67 SD: 6.2375 cents 51:52:53:68 SD: 5.0452 cents 53:54:55:71 SD: 4.9367 cents 54:55:56:72 SD: 3.6866 cents 57:58:59:76 SD: 2.4693 cents 60:61:62:80 SD: 1.3735 cents 63:64:65:84 SD: 0.3925 cents 129:131:133:172 SD: 0.1516 cents 192:195:198:256 SD: 0.1366 cents 321:326:331:428 SD: 0.1218 cents