Scala analysis: 509_M17
Miscellaneous tetrachord 74/73 * 73/72 * 48/37
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 74/73 23.554568 approximation to Pythagorean comma 2: 37/36 47.434037 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 48/37 450.6110 1: 74/73 23.5546 approximation to Pythagorean comma 2: 73/72 23.8795 3: 48/37 450.6110
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 74/73 23.555 cents approximation to Pythagorean comma 1: 1 73/72 23.879 cents 1: 1 48/37 450.611 cents 2: 1 37/36 47.434 cents 2: 1 96/73 474.166 cents 2: 1 146/111 474.490 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 : 23.6 47.4 498.0 23.6 : 23.9 474.5 498.0 47.4 : 450.6 474.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 23.5546 .. 450.6110 cents 1752/1369, 427.0564 cents 74/73, 23.5546 cents 2: 47.4340 .. 474.4904 cents 1752/1369, 427.0564 cents 1369/1728,-403.1769 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 74/73, 23.5546 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 48/37, 450.6110 cents Average / Smallest step : 7.048102 Largest / Average step : 2.714279 Largest / Smallest step : 19.130513 Median interval of one step : 73/72, 23.8795 cents, amount: 1 Least squares average step : 115.18269 cents, oct.: 345.54807 cents Scale is not proper Scale has trivalence property 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 23.55457 cents Scale diversity : 0.045617 Lumma stability : 0.094588 Lumma impropriety factor : 0.809519 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 : 5329/5328, 0.3249 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 426.7315 cents: 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 73 Odd number limit : 111 (O: 73 U: 111) Highest odd numerator or denominator: 73 Scale harmonicity : 0.107143 Fundamental : 1/2628, -11.3597 octaves, 0.0996 Hz. Guide tone : 148, 7.2095 octaves, 38720.584 Hz. Exponens Consonantiae : 3.889440E+05, 18.56920 octaves Euler's gradus suavitatis : 117 Sum of Mann's harmonic distance : 113.5, average 37.83333 Mersenne's string divisions : 10731 Sum of van Prooijen's expressibility: 3.90865, average 1.30288 Sum of Tenney's harmonic distance : 7.93624, average 2.64541 Vogel's harmonic complexity : 78.66667 Wille's k value : 1350 Wilson's harmonic complexity : 116 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 15.20737, average 2.53456 Lattice compactness (without 2's) : 7.00000, average 1.16667 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.33333 5 3: -2 .. 0 -1.00000 3 1 37: 0 .. 1 0.66667 2 1 73: -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 35 46| Scale is weakly epimorphic with val: <6 11 37 44| Scale is weakly epimorphic with val: <7 10 37 45| Scale is weakly epimorphic with val: <7 11 35 44| Scale is weakly epimorphic with val: <7 11 37 45| Scale is JI-epimorphic with val: <7 11 38 44| Scale is weakly epimorphic with val: <7 11 40 45| Scale is weakly epimorphic with val: <7 11 41 44| Scale is weakly epimorphic with val: <7 12 41 44| Scale is weakly epimorphic with val: <8 11 39 44| Scale is weakly epimorphic with val: <8 11 41 45| Scale is weakly epimorphic with val: <8 12 39 44|
FIT/MODE
3: 0 0 3 N M DE S SD: 30.5767 c. M: 47.4340 c. 7: 0 1 6 N G T3 SD: 19.2979 c. M:-23.7152 c. 8: 0 1 7 N G T3 SD: 16.0675 c. M: 23.5546 c. 9: 0 1 8 N G T3 SD: 14.3445 c. M: 23.5546 c. 10: 0 1 9 N G T3 SD: 13.6679 c. M: 23.5546 c. 11: 0 1 10 N G T3 SD: 13.6561 c. M: 23.5546 c. 12: 0 1 11 N G T3 SD: 14.0236 c. M: 23.5546 c. 13: 0 1 12 N G T3 SD: 14.5836 c. M: 23.5546 c. 14: 0 1 13 N G T3 SD: 15.2257 c. M: 23.5546 c. 15: 1 0 14 N G T3 SD: 9.9266 c. M: 14.2310 c. 16: 1 1 14 N M DE S SD: 9.6096 c. M:-14.8216 c. 17: 1 1 15 N M DE S SD: 7.2459 c. M:-11.1595 c. 18: 1 1 16 N M DE S SD: 5.1448 c. M:-7.9043 c. 19: 1 1 17 N M DE S SD: 3.2652 c. M:-4.9918 c. 20: 1 1 18 N M DE S SD: 1.5743 c. M:-2.3705 c. 21: 1 1 19 N M DE S SD: 0.0935 c. M:-0.1619 c. 316: 15 15 286 N M DE S SD: 0.1007 c. M: 0.1513 c. 337: 16 16 305 N M DE S SD: 0.0975 c. M: 0.1419 c. 358: 17 17 324 N M DE S SD: 0.0949 c. M: 0.1337 c. 379: 18 18 343 N M DE S SD: 0.0928 c. M: 0.1263 c. 400: 19 19 362 N M DE S SD: 0.0910 c. M: 0.1198 c. 421: 20 20 381 N M DE S SD: 0.0896 c. M: 0.1138 c. 442: 21 21 400 N M DE S SD: 0.0885 c. M: 0.1085 c. 463: 22 22 419 N M DE S SD: 0.0875 c. M:-0.1106 c. 484: 23 23 438 N M DE S SD: 0.0867 c. M:-0.1129 c. 505: 24 24 457 N M DE S SD: 0.0861 c. M:-0.1149 c. 526: 25 25 476 N M DE S SD: 0.0856 c. M:-0.1168 c. 547: 26 26 495 N M DE S SD: 0.0852 c. M:-0.1185 c. 568: 27 27 514 N M DE S SD: 0.0848 c. M:-0.1201 c. 589: 28 28 533 N M DE S SD: 0.0846 c. M:-0.1216 c. 610: 29 29 552 N M DE S SD: 0.0844 c. M:-0.1230 c. 631: 30 30 571 N M DE S SD: 0.0842 c. M:-0.1243 c. 652: 31 31 590 N M DE S SD: 0.0841 c. M:-0.1255 c. 673: 32 32 609 N M DE S SD: 0.0840 c. M:-0.1266 c. 694: 33 33 628 N M DE S SD: 0.0839 c. M:-0.1277 c. 715: 34 34 647 N M DE S SD: 0.0839 c. M:-0.1287 c. 736: 35 35 666 N M DE S SD: 0.0839 c. M:-0.1296 c. 786: 37 38 711 N T3 SD: 0.0817 c. M: 0.1097 c. 787: 37 38 712 N T3 SD: 0.0823 c. M: 0.1395 c. 807: 38 39 730 N T3 SD: 0.0777 c. M: 0.1026 c. 808: 38 39 731 N T3 SD: 0.0777 c. M: 0.1317 c. 828: 39 40 749 N T3 SD: 0.0739 c. M: 0.0959 c. 829: 39 40 750 N T3 SD: 0.0734 c. M: 0.1242 c. 849: 40 41 768 N T3 SD: 0.0703 c. M: 0.0896 c. 850: 40 41 769 N T3 SD: 0.0694 c. M: 0.1172 c. 870: 41 42 787 N T3 SD: 0.0670 c. M: 0.0835 c. 871: 41 42 788 N T3 SD: 0.0655 c. M: 0.1104 c. 891: 42 43 806 N T3 SD: 0.0638 c. M:-0.0787 c. 892: 42 43 807 N T3 SD: 0.0618 c. M: 0.1040 c. 912: 43 44 825 N T3 SD: 0.0609 c. M:-0.0768 c. 913: 43 44 826 N T3 SD: 0.0583 c. M: 0.0979 c. 933: 44 45 844 N T3 SD: 0.0581 c. M:-0.0751 c. 934: 44 45 845 N T3 SD: 0.0550 c. M: 0.0921 c. 954: 45 46 863 N T3 SD: 0.0554 c. M:-0.0734 c. 955: 45 46 864 N T3 SD: 0.0518 c. M: 0.0865 c. 975: 46 47 882 N T3 SD: 0.0529 c. M:-0.0718 c. 976: 46 47 883 N T3 SD: 0.0487 c. M: 0.0811 c. 996: 47 48 901 N T3 SD: 0.0506 c. M:-0.0703 c. 997: 47 48 902 N T3 SD: 0.0458 c. M: 0.0760 c. 1017: 48 49 920 N T3 SD: 0.0484 c. M:-0.0688 c. 1018: 48 49 921 N T3 SD: 0.0430 c. M: 0.0711 c. 1038: 49 50 939 N T3 SD: 0.0464 c. M:-0.0674 c. 1039: 49 50 940 N T3 SD: 0.0403 c. M: 0.0664 c. 1059: 50 51 958 N T3 SD: 0.0445 c. M:-0.0660 c. 1060: 50 51 959 N T3 SD: 0.0378 c. M: 0.0619 c. 1081: 51 52 978 N T3 SD: 0.0353 c. M: 0.0575 c. 1102: 52 53 997 N T3 SD: 0.0330 c. M: 0.0534 c. 1123: 53 54 1016 N T3 SD: 0.0307 c. M: 0.0493 c. 1144: 54 55 1035 N T3 SD: 0.0286 c. M: 0.0455 c. 1165: 55 56 1054 N T3 SD: 0.0265 c. M: 0.0417 c. 1186: 56 57 1073 N T3 SD: 0.0245 c. M: 0.0381 c. 1207: 57 58 1092 N T3 SD: 0.0227 c. M: 0.0346 c. 1228: 58 59 1111 N T3 SD: 0.0209 c. M: 0.0313 c. 1249: 59 60 1130 N T3 SD: 0.0192 c. M: 0.0280 c. 1270: 60 61 1149 N T3 SD: 0.0176 c. M: 0.0249 c. 1291: 61 62 1168 N T3 SD: 0.0160 c. M: 0.0218 c. 1312: 62 63 1187 N T3 SD: 0.0146 c. M: 0.0189 c. 1333: 63 64 1206 N T3 SD: 0.0133 c. M:-0.0166 c. 1354: 64 65 1225 N T3 SD: 0.0122 c. M:-0.0163 c. 1375: 65 66 1244 N T3 SD: 0.0111 c. M:-0.0161 c. 1396: 66 67 1263 N T3 SD: 0.0102 c. M:-0.0158 c. 1417: 67 68 1282 N T3 SD: 0.0095 c. M:-0.0156 c. 1438: 68 69 1301 N T3 SD: 0.0090 c. M:-0.0153 c. 1459: 69 70 1320 N T3 SD: 0.0087 c. M:-0.0151 c. 1480: 70 71 1339 N T3 SD: 0.0086 c. M:-0.0148 c. 1501: 71 72 1358 N T3 SD: 0.0087 c. M:-0.0146 c. 1522: 72 73 1377 N T3 SD: 0.0090 c. M:-0.0144 c. 1543: 73 74 1396 N T3 SD: 0.0094 c. M:-0.0142 c. 1564: 74 75 1415 N T3 SD: 0.0100 c. M:-0.0140 c. 1565: 74 75 1416 N T3 SD: 0.0098 c. M: 0.0163 c. 1585: 75 76 1434 N T3 SD: 0.0106 c. M:-0.0138 c. 1586: 75 76 1435 N T3 SD: 0.0094 c. M: 0.0161 c. 1607: 76 77 1454 N T3 SD: 0.0092 c. M: 0.0159 c. 1628: 77 78 1473 N T3 SD: 0.0091 c. M: 0.0157 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: 109.7184 cents 7 x 8:9 S SD: 97.1140 cents 8 x 9:11 SD: 82.6479 cents 9 x 10:12 S SD: 67.4848 cents 10 x 11:13 SD: 62.7374 cents 11 x 12:15 S SD: 55.1464 cents 12 x 13:16 SD: 45.5693 cents 13 x 14:17 SD: 43.7868 cents 14 x 15:19 SD: 39.1286 cents 15 x 16:20 S SD: 32.1486 cents 16 x 17:21 SD: 31.8278 cents 17 x 18:23 SD: 28.6929 cents 18 x 19:24 SD: 23.0845 cents 19 x 20:25 S SD: 23.6485 cents 20 x 21:27 SD: 21.4125 cents 21 x 22:28 SD: 16.5515 cents 22 x 23:29 SD: 17.7697 cents 23 x 24:31 SD: 16.1182 cents 24 x 25:32 SD: 11.6192 cents 25 x 26:33 SD: 13.4314 cents 26 x 27:35 SD: 12.1962 cents 27 x 28:36 SD: 7.7634 cents 28 x 29:37 SD: 10.2278 cents 29 x 30:39 SD: 9.3215 cents 30 x 31:40 SD: 4.6664 cents 31 x 32:41 SD: 7.9564 cents 32 x 33:43 SD: 7.3418 cents 33 x 34:44 SD: 2.1242 cents 34 x 35:45 SD: 6.5347 cents 35 x 36:47 SD: 6.1971 cents 36 x 37:48 SD: 0.0000 cents 37 x 38:49 SD: 5.9026 cents 38 x 39:51 SD: 5.8084 cents 39 x 40:52 SD: 1.8015 cents 40 x 41:53 SD: 5.9111 cents 41 x 42:55 SD: 5.9881 cents 42 x 43:56 SD: 3.3486 cents 43 x 44:57 SD: 6.3281 cents 44 x 45:59 SD: 6.4989 cents 45 x 46:60 SD: 4.6917 cents 46 x 47:61 SD: 6.9478 cents 47 x 48:63 SD: 7.1595 cents 48 x 49:64 SD: 5.8686 cents 49:50 x 65 SD: 7.2260 cents 50:51 x 67 SD: 6.8858 cents 51:52 x 68 SD: 5.0313 cents 52:53 x 69 SD: 6.2927 cents 53:54 x 71 SD: 5.9983 cents 54:55:56:72 SD: 5.8549 cents 56:57:58:75 SD: 5.6475 cents 57:58:59:76 SD: 4.6369 cents 59:60:61:79 SD: 4.5943 cents 60:61:62:80 SD: 3.5390 cents 63:64:65:84 SD: 2.5445 cents 66:67:68:88 SD: 1.6397 cents 69:70:71:92 SD: 0.8146 cents 72:73:74:96 SD: 0.1083 cents 579:587:595:772 SD: 0.1052 cents