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The symmetric group on a set of size n is the Galois group of the general polynomial of degree n and plays an important role in Galois theory. In invariant theory, the symmetric group acts on the variables of a multi-variate function, and the functions left invariant are the so-called symmetric functions.
In music, a music scale can have certain symmetries, namely translational symmetry and inversional or mirror symmetry. The most prominent examples are scales which equally divides the octave . [ 1 ] The concept and term appears to have been introduced by Joseph Schillinger [ 1 ] and further developed by Nicolas Slonimsky as part of his famous ...
Modes of limited transposition are musical modes or scales that fulfill specific criteria relating to their symmetry and the repetition of their interval groups. These scales may be transposed to all twelve notes of the chromatic scale, but at least two of these transpositions must result in the same pitch classes, thus their transpositions are "limited".
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In classical theory (in contrast to jazz theory), this symmetrical scale is commonly called the octatonic scale (or the octatonic collection), although there are a total of 43 enharmonically inequivalent, transpositionally inequivalent eight-note sets.
This article summarizes the classes of discrete symmetry groups of the Euclidean plane. The symmetry groups are named here by three naming schemes: International notation, orbifold notation, and Coxeter notation. There are three kinds of symmetry groups of the plane: 2 families of rosette groups – 2D point groups; 7 frieze groups – 2D line ...
The two whole-tone scales as a symmetrical partitioning of the chromatic scale; [1] if C=0 then the top stave has even (02468t) and the bottom has odd (13579e) pitches. In music, a whole-tone scale is a scale in which each note is separated from its neighbors by the interval of a whole tone.
The group order is defined as the subscript, unless the order is doubled for symbols with a plus or minus, "±", prefix, which implies a central inversion. [ 3 ] Hermann–Mauguin notation (International notation) is also given.