Scala analysis: 009_H3
Hyperenharmonic tetrachord 68/67 * 67/66 * 22/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/67 25.648381 2: 34/33 51.682466 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 22/17 446.3625 1: 68/67 25.6484 2: 67/66 26.0341 3: 22/17 446.3625
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 68/67 25.648 cents 1: 1 67/66 26.034 cents 1: 1 22/17 446.363 cents 2: 1 34/33 51.682 cents 2: 1 88/67 472.011 cents 2: 1 67/51 472.397 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 : 25.6 51.7 498.0 25.6 : 26.0 472.4 498.0 51.7 : 446.4 472.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 25.6484 .. 446.3625 cents 737/578, 420.7142 cents 68/67, 25.6484 cents 2: 51.6825 .. 472.3966 cents 737/578, 420.7142 cents 289/363,-394.6801 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 68/67, 25.6484 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 22/17, 446.3625 cents Average / Smallest step : 6.472728 Largest / Average step : 2.688688 Largest / Smallest step : 17.403147 Median interval of one step : 67/66, 26.0341 cents, amount: 1 Least squares average step : 115.93917 cents, oct.: 347.81750 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1243-tone equal temperament with octave 4/3 degrees: 64 129 1243 Least number of segments generator : 622 of 249.223 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 785 of 314.534 cents and inv. generated superset size: 36 = 33 more = 1200.000% 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 25.64838 cents Scale diversity : 0.075371 Lumma stability : 0.102996 Lumma impropriety factor : 0.792459 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 : 4489/4488, 0.3857 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 420.3284 cents: 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 67 Odd number limit : 67 (O: 67 U: 67) Highest odd numerator or denominator: 67 Scale harmonicity : 0.018880 Fundamental : 1/2211, -11.1105 octaves, 0.1183 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 1.503480E+05, 17.19795 octaves Euler's gradus suavitatis : 97 Sum of Mann's harmonic distance : 104.5, average 34.83333 Mersenne's string divisions : 63315 Sum of van Prooijen's expressibility: 3.82171, average 1.27390 Sum of Tenney's harmonic distance : 7.78776, average 2.59592 Vogel's harmonic complexity : 66.00000 Wille's k value : 569 Wilson's harmonic complexity : 98 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 11.35045, average 1.89174 Lattice compactness (without 2's) : 7.97469, average 1.32912 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 0 -0.66667 2 1 11: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 1 67: -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 23 30 44| Scale is weakly epimorphic with val: <6 10 24 31 45| Scale is weakly epimorphic with val: <6 10 25 32 43| Scale is weakly epimorphic with val: <6 10 26 33 44| Scale is weakly epimorphic with val: <6 11 23 31 44| Scale is weakly epimorphic with val: <6 11 24 32 45| Scale is weakly epimorphic with val: <6 11 25 33 43| Scale is weakly epimorphic with val: <7 10 23 29 44| Scale is weakly epimorphic with val: <7 10 24 30 45| Scale is weakly epimorphic with val: <7 10 24 32 43| Scale is weakly epimorphic with val: <7 10 25 31 43| Scale is weakly epimorphic with val: <7 10 25 33 44| Scale is weakly epimorphic with val: <7 10 26 32 44| Scale is weakly epimorphic with val: <7 10 27 32 43| Scale is weakly epimorphic with val: <7 10 27 33 45| Scale is weakly epimorphic with val: <7 11 23 28 43| Scale is weakly epimorphic with val: <7 11 23 29 45| Scale is weakly epimorphic with val: <7 11 23 31 43| Scale is weakly epimorphic with val: <7 11 23 32 45| Scale is weakly epimorphic with val: <7 11 24 27 43| Scale is weakly epimorphic with val: <7 11 24 29 44| Scale is JI-epimorphic with val: <7 11 24 30 43| Scale is weakly epimorphic with val: <7 11 24 32 44| Scale is weakly epimorphic with val: <7 11 24 33 43| Scale is weakly epimorphic with val: <7 11 25 27 45| Scale is weakly epimorphic with val: <7 11 25 28 44| Scale is weakly epimorphic with val: <7 11 25 30 45| Scale is JI-epimorphic with val: <7 11 25 31 44| Scale is weakly epimorphic with val: <7 11 25 33 45| Scale is weakly epimorphic with val: <7 11 26 28 43| Scale is weakly epimorphic with val: <7 11 26 29 45| Scale is weakly epimorphic with val: <7 11 26 31 43| Scale is JI-epimorphic with val: <7 11 26 32 45| Scale is weakly epimorphic with val: <7 11 27 27 43| Scale is weakly epimorphic with val: <7 11 27 29 44| Scale is weakly epimorphic with val: <7 11 27 30 43| Scale is weakly epimorphic with val: <7 11 27 32 44| Scale is weakly epimorphic with val: <7 11 27 33 43| Scale is weakly epimorphic with val: <7 12 23 31 44| Scale is weakly epimorphic with val: <7 12 23 32 43| Scale is weakly epimorphic with val: <7 12 24 32 45| Scale is weakly epimorphic with val: <7 12 24 33 44| Scale is weakly epimorphic with val: <7 12 25 33 43| Scale is weakly epimorphic with val: <7 12 26 32 43| Scale is weakly epimorphic with val: <7 12 27 33 44| Scale is weakly epimorphic with val: <8 11 23 29 44| Scale is weakly epimorphic with val: <8 11 23 30 43| Scale is weakly epimorphic with val: <8 11 24 30 45| Scale is weakly epimorphic with val: <8 11 24 31 44| Scale is weakly epimorphic with val: <8 11 25 31 43| Scale is weakly epimorphic with val: <8 11 25 32 45| Scale is weakly epimorphic with val: <8 11 26 30 43| Scale is weakly epimorphic with val: <8 11 26 32 44| Scale is weakly epimorphic with val: <8 11 27 31 44| Scale is weakly epimorphic with val: <8 11 27 33 45| Scale is weakly epimorphic with val: <8 12 23 30 44| Scale is weakly epimorphic with val: <8 12 23 32 45| Scale is weakly epimorphic with val: <8 12 24 30 43| Scale is weakly epimorphic with val: <8 12 24 31 45| Scale is weakly epimorphic with val: <8 12 25 31 44| Scale is weakly epimorphic with val: <8 12 25 32 43| Scale is weakly epimorphic with val: <8 12 26 32 45| Scale is weakly epimorphic with val: <8 12 26 33 44| Scale is weakly epimorphic with val: <8 12 27 30 43|
FIT/MODE
3: 0 0 3 N M DE S SD: 33.3112 c. M: 51.6825 c. 7: 0 1 6 N G T3 SD: 18.5903 c. M: 25.6484 c. 8: 0 1 7 N G T3 SD: 16.0170 c. M: 25.6484 c. 9: 0 1 8 N G T3 SD: 14.9578 c. M: 25.6484 c. 10: 0 1 9 N G T3 SD: 14.8477 c. M: 25.6484 c. 11: 0 1 10 N G T3 SD: 15.2629 c. M: 25.6484 c. 12: 0 1 11 N G T3 SD: 15.9316 c. M: 25.6484 c. 13: 1 0 12 N G T3 SD: 10.6323 c. M: 13.3713 c. 15: 1 1 13 N M DE S SD: 9.5543 c. M:-14.7235 c. 16: 1 1 14 N M DE S SD: 6.8755 c. M:-10.5732 c. 17: 1 1 15 N M DE S SD: 4.5120 c. M:-6.9111 c. 18: 1 1 16 N M DE S SD: 2.4117 c. M:-3.6559 c. 19: 1 1 17 N M DE S SD: 0.5389 c. M:-0.7433 c. 39: 2 2 35 N M DE S SD: 0.3525 c. M: 0.6009 c. 58: 3 3 52 N M DE S SD: 0.1132 c. M: 0.1606 c. 77: 4 4 69 N M DE S SD: 0.1343 c. M:-0.2241 c. 135: 7 7 121 N M DE S SD: 0.1035 c. M:-0.1762 c. 193: 10 10 173 N M DE S SD: 0.0997 c. M:-0.1571 c. 212: 11 11 190 N M DE S SD: 0.1118 c. M:-0.1936 c. 251: 13 13 225 N M DE S SD: 0.1001 c. M:-0.1468 c. 309: 16 16 277 N M DE S SD: 0.1012 c. M:-0.1404 c. 328: 17 17 294 N M DE S SD: 0.1005 c. M:-0.1649 c. 367: 19 19 329 N M DE S SD: 0.1024 c. M:-0.1360 c. 425: 22 22 381 N M DE S SD: 0.1034 c. M:-0.1328 c. 444: 23 23 398 N M DE S SD: 0.0997 c. M:-0.1512 c. 483: 25 25 433 N M DE S SD: 0.1043 c. M:-0.1303 c. 521: 27 27 467 N M DE S SD: 0.1001 c. M:-0.1620 c. 541: 28 28 485 N M DE S SD: 0.1050 c. M: 0.1288 c. 560: 29 29 502 N M DE S SD: 0.1006 c. M:-0.1432 c. 637: 33 33 571 N M DE S SD: 0.0996 c. M:-0.1530 c. 664: 34 35 595 N T3 SD: 0.0941 c. M: 0.1461 c. 665: 34 35 596 N T3 SD: 0.1065 c. M: 0.1844 c. 676: 35 35 606 N M DE S SD: 0.1018 c. M:-0.1380 c. 683: 35 36 612 N T3 SD: 0.0898 c. M: 0.1263 c. 684: 35 36 613 N T3 SD: 0.0949 c. M: 0.1636 c. 702: 36 37 629 N T3 SD: 0.0882 c. M:-0.1085 c. 703: 36 37 630 N T3 SD: 0.0855 c. M: 0.1439 c. 722: 37 38 647 N T3 SD: 0.0787 c. M: 0.1253 c. 723: 37 38 648 N T3 SD: 0.0933 c. M: 0.1606 c. 740: 38 39 663 N T3 SD: 0.0918 c. M:-0.1411 c. 741: 38 39 664 N T3 SD: 0.0745 c. M: 0.1076 c. 742: 38 39 665 N T3 SD: 0.0820 c. M: 0.1420 c. 760: 39 40 681 N T3 SD: 0.0730 c. M: 0.0908 c. 761: 39 40 682 N T3 SD: 0.0727 c. M: 0.1244 c. 780: 40 41 699 N T3 SD: 0.0658 c. M: 0.1076 c. 799: 41 42 716 N T3 SD: 0.0615 c. M: 0.0916 c. 800: 41 42 717 N T3 SD: 0.0716 c. M: 0.1236 c. 818: 42 43 733 N T3 SD: 0.0600 c. M: 0.0764 c. 819: 42 43 734 N T3 SD: 0.0623 c. M: 0.1076 c. 837: 43 44 750 N T3 SD: 0.0610 c. M:-0.0857 c. 838: 43 44 751 N T3 SD: 0.0551 c. M: 0.0924 c. 857: 44 45 768 N T3 SD: 0.0505 c. M: 0.0778 c. 876: 45 46 785 N T3 SD: 0.0487 c. M: 0.0639 c. 877: 45 46 786 N T3 SD: 0.0538 c. M: 0.0931 c. 895: 46 47 802 N T3 SD: 0.0497 c. M:-0.0697 c. 896: 46 47 803 N T3 SD: 0.0462 c. M: 0.0791 c. 915: 47 48 820 N T3 SD: 0.0411 c. M: 0.0657 c. 934: 48 49 837 N T3 SD: 0.0389 c. M: 0.0529 c. 954: 49 50 855 N T3 SD: 0.0390 c. M: 0.0675 c. 973: 50 51 872 N T3 SD: 0.0331 c. M: 0.0551 c. 992: 51 52 889 N T3 SD: 0.0303 c. M: 0.0432 c. 1012: 52 53 907 N T3 SD: 0.0333 c. M: 0.0571 c. 1031: 53 54 924 N T3 SD: 0.0266 c. M: 0.0457 c. 1050: 54 55 941 N T3 SD: 0.0229 c. M: 0.0346 c. 1069: 55 56 958 N T3 SD: 0.0232 c. M:-0.0322 c. 1089: 56 57 976 N T3 SD: 0.0216 c. M: 0.0373 c. 1108: 57 58 993 N T3 SD: 0.0166 c. M: 0.0269 c. 1127: 58 59 1010 N T3 SD: 0.0162 c. M:-0.0223 c. 1147: 59 60 1028 N T3 SD: 0.0182 c. M: 0.0297 c. 1166: 60 61 1045 N T3 SD: 0.0116 c. M: 0.0200 c. 1185: 61 62 1062 N T3 SD: 0.0098 c. M:-0.0133 c. 1224: 63 64 1097 N T3 SD: 0.0087 c. M: 0.0137 c. 1243: 64 65 1114 N T3 SD: 0.0041 c. M:-0.0052 c. 1301: 67 68 1166 N T3 SD: 0.0013 c. M: 0.0022 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: 107.5942 cents 7 x 8:9 S SD: 95.1069 cents 8 x 9:11 SD: 80.6400 cents 9 x 10:12 S SD: 65.3606 cents 10 x 11:13 SD: 60.7515 cents 11 x 12:15 S SD: 53.1641 cents 12 x 13:16 SD: 43.4451 cents 13 x 14:17 SD: 41.8333 cents 14 x 15:19 SD: 37.1833 cents 15 x 16:20 S SD: 30.0244 cents 16 x 17:21 SD: 29.9221 cents 17 x 18:23 SD: 26.8022 cents 18 x 19:24 SD: 20.9603 cents 19 x 20:25 S SD: 21.8150 cents 20 x 21:27 SD: 19.6046 cents 21 x 22:28 SD: 14.4273 cents 22 x 23:29 SD: 16.0487 cents 23 x 24:31 SD: 14.4414 cents 24 x 25:32 SD: 9.4950 cents 25 x 26:33 SD: 11.8928 cents 26 x 27:35 SD: 10.7345 cents 27 x 28:36 SD: 5.6392 cents 28 x 29:37 SD: 8.9906 cents 29 x 30:39 SD: 8.2152 cents 30 x 31:40 SD: 2.5422 cents 31 x 32:41 SD: 7.1986 cents 32 x 33:43 SD: 6.7831 cents 33 x 34:44 SD: 0.0000 cents 34 x 35:45 SD: 6.4321 cents 35 x 36:47 SD: 6.3307 cents 36 x 37:48 SD: 2.1242 cents 37 x 38:49 SD: 6.4838 cents 38 x 39:51 SD: 6.5943 cents 39 x 40:52 SD: 3.9257 cents 40 x 41:53 SD: 7.0290 cents 41 x 42:55 SD: 7.2464 cents 42 x 43:56 SD: 5.4728 cents 43 x 44:57 SD: 7.7957 cents 44 x 45:59 SD: 8.0538 cents 45:46 x 60 SD: 6.2011 cents 46:47 x 61 SD: 7.4699 cents 47:48 x 63 SD: 7.0886 cents 48:49 x 64 SD: 5.0242 cents 49:50 x 65 SD: 6.4307 cents 51:52:53:68 SD: 5.6358 cents 53:54:55:71 SD: 5.4395 cents 54:55:56:72 SD: 4.2770 cents 57:58:59:76 SD: 3.0594 cents 60:61:62:80 SD: 1.9624 cents 63:64:65:84 SD: 0.9708 cents 66:67:68:88 SD: 0.1286 cents 531:539:547:708 SD: 0.1248 cents 597:606:615:796 SD: 0.1206 cents