Scala analysis: 005_H2
Hyperenharmonic tetrachord 72/71 * 71/70 * 35/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 72/71 24.213458 2: 36/35 48.770381 septimal diesis, 1/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 35/27 449.2746 septimal semi-diminished fourth, 9/4-tone 1: 72/71 24.2135 2: 71/70 24.5569 3: 35/27 449.2746 septimal semi-diminished fourth, 9/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 72/71 24.213 cents 1: 1 71/70 24.557 cents 1: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 2: 1 36/35 48.770 cents septimal diesis, 1/4-tone 2: 1 280/213 473.488 cents 2: 1 71/54 473.832 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 : 24.2 48.8 498.0 24.2 : 24.6 473.8 498.0 48.8 : 449.3 473.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 24.2135 .. 449.2746 cents 2485/1944, 425.0612 cents 72/71, 24.2135 cents 2: 48.7704 .. 473.8315 cents 2485/1944, 425.0612 cents 972/1225,-400.5042 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 72/71, 24.2135 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 35/27, 449.2746 cents Average / Smallest step : 6.856311 Largest / Average step : 2.706229 Largest / Smallest step : 18.554748 Median interval of one step : 71/70, 24.5569 cents, amount: 1 Least squares average step : 115.42066 cents, oct.: 346.26198 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1399-tone equal temperament with octave 4/3 degrees: 68 137 1399 Least number of segments generator : 700 of 249.200 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1126 of 400.857 cents and inv. generated superset size: 32 = 29 more = 1066.667% 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 24.21346 cents Scale diversity : 0.054948 Lumma stability : 0.097234 Lumma impropriety factor : 0.804153 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 : 5041/5040, 0.3435 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 424.7177 cents: 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 71 Odd number limit : 213 (O: 71 U: 213) Highest odd numerator or denominator: 71 Scale harmonicity : 0.036120 Fundamental : 1/7455, -12.8640 octaves, 0.0351 Hz. Guide tone : 72, 6.1699 octaves, 18837.041 Hz. Exponens Consonantiae : 5.367600E+05, 19.03392 octaves Euler's gradus suavitatis : 90 Sum of Mann's harmonic distance : 110.5, average 36.83333 Mersenne's string divisions : 71071 Sum of van Prooijen's expressibility: 3.87245, average 1.29082 Sum of Tenney's harmonic distance : 7.88814, average 2.62938 Vogel's harmonic complexity : 63.66667 Wille's k value : 1242 Wilson's harmonic complexity : 92 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 17.21485, average 2.86914 Lattice compactness (without 2's) : 13.18033, average 2.19672 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 2 1.00000 5 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 1 71: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 11 15 19 45| Scale is weakly epimorphic with val: <7 11 15 20 44| Scale is weakly epimorphic with val: <7 11 15 22 45| Scale is weakly epimorphic with val: <7 11 16 18 45| Scale is weakly epimorphic with val: <7 11 16 19 44| Scale is weakly epimorphic with val: <7 11 16 21 45| Scale is weakly epimorphic with val: <7 11 16 22 44| Scale is weakly epimorphic with val: <7 11 17 18 44| Scale is weakly epimorphic with val: <7 11 17 20 45| Scale is weakly epimorphic with val: <7 11 17 21 44| Scale is weakly epimorphic with val: <7 11 18 19 45| Scale is weakly epimorphic with val: <7 11 18 20 44| Scale is weakly epimorphic with val: <7 11 18 22 45| Scale is weakly epimorphic with val: <7 11 19 19 44| Scale is weakly epimorphic with val: <7 11 19 21 45| Scale is weakly epimorphic with val: <7 11 19 22 44| Scale is weakly epimorphic with val: <7 12 15 20 44| Scale is weakly epimorphic with val: <7 12 16 19 44| Scale is weakly epimorphic with val: <7 12 17 18 44| Scale is weakly epimorphic with val: <8 11 15 19 43| Scale is weakly epimorphic with val: <8 11 15 20 45| Scale is weakly epimorphic with val: <8 11 15 22 43| Scale is weakly epimorphic with val: <8 11 16 18 43| Scale is weakly epimorphic with val: <8 11 16 19 45| Scale is weakly epimorphic with val: <8 11 16 21 43| Scale is weakly epimorphic with val: <8 11 17 18 45| Scale is weakly epimorphic with val: <8 11 17 20 43| Scale is weakly epimorphic with val: <8 11 18 19 43| Scale is weakly epimorphic with val: <8 11 18 22 43| Scale is weakly epimorphic with val: <8 11 19 21 43| Scale is weakly epimorphic with val: <8 12 15 20 45| Scale is weakly epimorphic with val: <8 12 15 22 43| Scale is weakly epimorphic with val: <8 12 16 19 45| Scale is weakly epimorphic with val: <8 12 16 21 43| Scale is weakly epimorphic with val: <8 12 16 22 45| Scale is weakly epimorphic with val: <8 12 17 18 45| Scale is weakly epimorphic with val: <8 12 17 20 43| Scale is weakly epimorphic with val: <8 12 17 21 45| Scale is weakly epimorphic with val: <8 12 18 19 43| Scale is weakly epimorphic with val: <8 12 18 20 45| Scale is weakly epimorphic with val: <8 12 19 19 45| Scale is weakly epimorphic with val: <8 12 19 22 45|
FIT/MODE
3: 0 0 3 N M DE S SD: 31.4369 c. M: 48.7704 c. 7: 0 1 6 N G T3 SD: 19.0360 c. M: 24.2135 c. 8: 0 1 7 N G T3 SD: 16.0015 c. M: 24.2135 c. 9: 0 1 8 N G T3 SD: 14.4848 c. M: 24.2135 c. 10: 0 1 9 N G T3 SD: 13.9924 c. M: 24.2135 c. 11: 0 1 10 N G T3 SD: 14.1244 c. M: 24.2135 c. 12: 0 1 11 N G T3 SD: 14.5956 c. M: 24.2135 c. 13: 0 1 12 N G T3 SD: 15.2281 c. M: 24.2135 c. 14: 0 1 13 N G T3 SD: 15.9208 c. M: 24.2135 c. 15: 1 1 13 N M DE S SD: 11.4284 c. M:-17.6356 c. 16: 1 1 14 N M DE S SD: 8.7495 c. M:-13.4852 c. 17: 1 1 15 N M DE S SD: 6.3858 c. M:-9.8231 c. 18: 1 1 16 N M DE S SD: 4.2849 c. M:-6.5680 c. 19: 1 1 17 N M DE S SD: 2.4055 c. M:-3.6554 c. 20: 1 1 18 N M DE S SD: 0.7174 c. M:-1.0341 c. 41: 2 2 37 N M DE S SD: 0.1144 c. M: 0.1806 c. 102: 5 5 92 N M DE S SD: 0.1204 c. M:-0.2005 c. 143: 7 7 129 N M DE S SD: 0.0963 c. M:-0.1664 c. 184: 9 9 166 N M DE S SD: 0.0896 c. M:-0.1474 c. 225: 11 11 203 N M DE S SD: 0.0887 c. M:-0.1354 c. 266: 13 13 240 N M DE S SD: 0.0897 c. M:-0.1271 c. 307: 15 15 277 N M DE S SD: 0.0912 c. M:-0.1210 c. 348: 17 17 314 N M DE S SD: 0.0928 c. M:-0.1163 c. 388: 19 19 350 N M DE S SD: 0.1013 c. M:-0.1753 c. 389: 19 19 351 N M DE S SD: 0.0943 c. M: 0.1182 c. 409: 20 20 369 N M DE S SD: 0.0888 c. M:-0.1408 c. 531: 26 26 479 N M DE S SD: 0.0998 c. M:-0.1729 c. 553: 27 27 499 N M DE S SD: 0.0990 c. M: 0.1367 c. 573: 28 28 517 N M DE S SD: 0.0904 c. M:-0.1238 c. 593: 29 29 535 N M DE S SD: 0.0890 c. M:-0.1429 c. 634: 31 31 572 N M DE S SD: 0.0887 c. M:-0.1389 c. 674: 33 33 608 N M DE S SD: 0.0990 c. M:-0.1715 c. 695: 34 34 627 N M DE S SD: 0.0905 c. M:-0.1513 c. 716: 35 35 646 N M DE S SD: 0.0889 c. M:-0.1323 c. 737: 36 36 665 N M DE S SD: 0.0935 c. M: 0.1147 c. 744: 36 37 671 N T3 SD: 0.0866 c. M: 0.1145 c. 745: 36 37 672 N T3 SD: 0.0867 c. M: 0.1469 c. 765: 37 38 690 N T3 SD: 0.0795 c. M: 0.1250 c. 766: 37 38 691 N T3 SD: 0.0904 c. M: 0.1565 c. 777: 38 38 701 N M DE S SD: 0.0891 c. M:-0.1440 c. 785: 38 39 708 N T3 SD: 0.0767 c. M: 0.1043 c. 786: 38 39 709 N T3 SD: 0.0788 c. M: 0.1349 c. 805: 39 40 726 N T3 SD: 0.0783 c. M:-0.1061 c. 806: 39 40 727 N T3 SD: 0.0711 c. M: 0.1145 c. 807: 39 40 728 N T3 SD: 0.0838 c. M: 0.1444 c. 825: 40 41 744 N T3 SD: 0.0834 c. M:-0.1286 c. 826: 40 41 745 N T3 SD: 0.0679 c. M: 0.0951 c. 827: 40 41 746 N T3 SD: 0.0720 c. M: 0.1242 c. 846: 41 42 763 N T3 SD: 0.0692 c. M:-0.0922 c. 847: 41 42 764 N T3 SD: 0.0638 c. M: 0.1050 c. 867: 42 43 782 N T3 SD: 0.0601 c. M: 0.0867 c. 868: 42 43 783 N T3 SD: 0.0661 c. M: 0.1145 c. 887: 43 44 800 N T3 SD: 0.0609 c. M:-0.0796 c. 888: 43 44 801 N T3 SD: 0.0574 c. M: 0.0964 c. 908: 44 45 819 N T3 SD: 0.0531 c. M: 0.0791 c. 909: 44 45 820 N T3 SD: 0.0611 c. M: 0.1057 c. 928: 45 46 837 N T3 SD: 0.0534 c. M:-0.0681 c. 929: 45 46 838 N T3 SD: 0.0519 c. M: 0.0886 c. 949: 46 47 856 N T3 SD: 0.0468 c. M: 0.0722 c. 969: 47 48 874 N T3 SD: 0.0466 c. M:-0.0576 c. 970: 47 48 875 N T3 SD: 0.0472 c. M: 0.0814 c. 990: 48 49 893 N T3 SD: 0.0413 c. M: 0.0658 c. 1010: 49 50 911 N T3 SD: 0.0403 c. M: 0.0509 c. 1011: 49 50 912 N T3 SD: 0.0432 c. M: 0.0748 c. 1031: 50 51 930 N T3 SD: 0.0364 c. M: 0.0600 c. 1051: 51 52 948 N T3 SD: 0.0347 c. M: 0.0457 c. 1052: 51 52 949 N T3 SD: 0.0399 c. M: 0.0687 c. 1071: 52 53 966 N T3 SD: 0.0380 c. M:-0.0576 c. 1072: 52 53 967 N T3 SD: 0.0323 c. M: 0.0546 c. 1092: 53 54 985 N T3 SD: 0.0296 c. M: 0.0409 c. 1113: 54 55 1004 N T3 SD: 0.0287 c. M: 0.0496 c. 1133: 55 56 1022 N T3 SD: 0.0249 c. M: 0.0365 c. 1154: 56 57 1041 N T3 SD: 0.0259 c. M: 0.0449 c. 1174: 57 58 1059 N T3 SD: 0.0209 c. M: 0.0324 c. 1195: 58 59 1078 N T3 SD: 0.0238 c. M: 0.0406 c. 1215: 59 60 1096 N T3 SD: 0.0173 c. M: 0.0286 c. 1235: 60 61 1114 N T3 SD: 0.0179 c. M:-0.0259 c. 1256: 61 62 1133 N T3 SD: 0.0145 c. M: 0.0250 c. 1276: 62 63 1151 N T3 SD: 0.0137 c. M:-0.0193 c. 1297: 63 64 1170 N T3 SD: 0.0126 c. M: 0.0216 c. 1317: 64 65 1188 N T3 SD: 0.0098 c. M:-0.0131 c. 1338: 65 66 1207 N T3 SD: 0.0116 c. M: 0.0184 c. 1358: 66 67 1225 N T3 SD: 0.0062 c. M: 0.0080 c. 1399: 68 69 1262 N T3 SD: 0.0033 c. M: 0.0054 c. 1440: 70 71 1299 N T3 SD: 0.0026 c. M: 0.0035 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: 109.0503 cents 7 x 8:9 S SD: 96.4821 cents 8 x 9:11 SD: 82.0157 cents 9 x 10:12 S SD: 66.8167 cents 10 x 11:13 SD: 62.1117 cents 11 x 12:15 S SD: 54.5217 cents 12 x 13:16 SD: 44.9011 cents 13 x 14:17 SD: 43.1706 cents 14 x 15:19 SD: 38.5147 cents 15 x 16:20 S SD: 31.4805 cents 16 x 17:21 SD: 31.2253 cents 17 x 18:23 SD: 28.0946 cents 18 x 19:24 SD: 22.4163 cents 19 x 20:25 S SD: 23.0664 cents 20 x 21:27 SD: 20.8374 cents 21 x 22:28 SD: 15.8833 cents 22 x 23:29 SD: 17.2187 cents 23 x 24:31 SD: 15.5790 cents 24 x 25:32 SD: 10.9510 cents 25 x 26:33 SD: 12.9296 cents 26 x 27:35 SD: 11.7146 cents 27 x 28:36 SD: 7.0953 cents 28 x 29:37 SD: 9.8059 cents 29 x 30:39 SD: 8.9340 cents 30 x 31:40 SD: 3.9982 cents 31 x 32:41 SD: 7.6628 cents 32 x 33:43 SD: 7.1026 cents 33 x 34:44 SD: 1.4560 cents 34 x 35:45 SD: 6.4273 cents 35 x 36:47 SD: 6.1610 cents 36 x 37:48 SD: 0.6682 cents 37 x 38:49 SD: 6.0110 cents 38 x 39:51 SD: 5.9859 cents 39 x 40:52 SD: 2.4697 cents 40 x 41:53 SD: 6.2063 cents 41 x 42:55 SD: 6.3342 cents 42 x 43:56 SD: 4.0168 cents 43 x 44:57 SD: 6.7522 cents 44 x 45:59 SD: 6.9556 cents 45 x 46:60 SD: 5.3599 cents 46 x 47:61 SD: 7.4522 cents 47:48 x 63 SD: 7.6493 cents 48:49 x 64 SD: 5.7417 cents 49:50 x 65 SD: 6.9686 cents 50:51 x 67 SD: 6.6323 cents 51:52 x 68 SD: 4.7019 cents 52:53 x 69 SD: 6.0500 cents 54:55:56:72 SD: 5.3585 cents 56:57:58:75 SD: 5.2104 cents 57:58:59:76 SD: 4.1405 cents 60:61:62:80 SD: 3.0428 cents 63:64:65:84 SD: 2.0486 cents 66:67:68:88 SD: 1.1448 cents 69:70:71:92 SD: 0.3285 cents 141:143:145:188 SD: 0.1271 cents 210:213:216:280 SD: 0.1145 cents 351:356:361:468 SD: 0.1021 cents