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For example, for ranges 10–14, 25–37, the inversion list would be: 10 15 25 38 To search whether an item belongs to any of the ranges, a binary search is made. If the search ends in a "first" element, the searched item is in the set. If the search ends in an "after" element, or outside the array, the searched item is not in the set.
An interval is inverted by raising or lowering either of the notes by one or more octaves so that the higher note becomes the lower note and vice versa. For example, the inversion of an interval consisting of a C with an E above it (the third measure below) is an E with a C above it – to work this out, the C may be moved up, the E may be lowered, or both may be moved.
The body of the tables contain the characters in the respective irreducible representations for each respective symmetry operation, or set of symmetry operations. The symbol i used in the body of the table denotes the imaginary unit: i 2 = −1. Used in a column heading, it denotes the operation of inversion.
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The inversion number [10] of a sequence = , …, , is the cardinality of the inversion set. It is a common measure of sortedness (sometimes called presortedness) of a permutation [ 5 ] or sequence. [ 9 ]
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It is an instance of a scheme for numbering permutations and is an example of an inversion table. The Lehmer code is named in reference to D. H. Lehmer , [ 1 ] but the code had been known since 1888 at least.
For example, musicians use the terms transposition and inversion where mathematicians would use translation and reflection. Furthermore, where musical set theory refers to ordered sets, mathematics would normally refer to tuples or sequences (though mathematics does speak of ordered sets , and although these can be seen to include the musical ...
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