A. minor

A. minor may refer to:

A minor

A minor (abbreviated Am) is a minor scale based on A, consisting of the pitches A, B, C, D, E, F, and G. The harmonic minor scale raises the G to G♯. Its key signature has no flats or sharps (see below: Scales and keys).

Its relative major is C major, and its parallel major is A major.

Changes needed for the melodic and harmonic versions of the scale are written in with accidentals as necessary.

Johann Joachim Quantz considered A minor, along with C minor, much more suitable for expressing "the sad effect" than other minor keys (Versuch einer Anweisung die Flöte traversiere zu spielen).

Whereas traditionally key signatures were cancelled with naturals whenever the new key signature had fewer sharps or flats than the old key signature, or had flats instead of sharps or vice versa (so, for example, D major changing to D minor would be notated with a key signature of F♮, C♮, and B♭ at the change), in modern popular and commercial music, cancellation is only done when C major or A minor replaces another key.

A-flat minor

A-flat minor is a minor scale based on A-flat, consisting of the pitches A♭, B♭, C♭, D♭, E♭, F♭, and G♭. For the harmonic minor, the G♭ is raised to G♮. Its key signature has seven flats (see below: Scales and keys).

Its relative major is C-flat major (or, enharmonically, B major), and its parallel major is A-flat major. Its direct enharmonic equivalent is G-sharp minor.

Changes needed for the melodic and harmonic versions of the scale are written in with accidentals as necessary.

Although A-flat minor occurs in modulation in works in other keys, it is only rarely used as the principal key of a piece of music. Some well-known uses of the key in classical and romantic piano music include:

Minor

Minor may refer to:

Music theory

Mathematics

People

Places

Sports

Minor (academic)

An academic minor is a college or university student's declared secondary academic discipline during their undergraduate studies. As with an academic major, the college or university in question lays out a framework of required classes or class types a student must complete to earn the minor—although the latitude the student is given changes from college to college. Academic minors and majors differ in that the former is subordinate to the latter. To obtain an academic minor, a total of two years of study at a university in a selected subject is the usual requirement.

Some students will prepare for their intended career with their major, while pursuing personal interests with a minor. For example, some students may major in civil engineering and minor in a foreign language.

Other students may pursue a minor to provide specific specialization and thus make themselves more attractive to employers. It is not infrequent for a physics major to minor in computer science or an economics major to minor in mathematics. Engineering students frequently take a minor in mathematics, as they already have most course credits needed for the purpose.

Graph minor

In graph theory, an undirected graph H is called a minor of the graph G if H can be formed from G by deleting edges and vertices and by contracting edges.

The theory of graph minors began with Wagner's theorem that a graph is planar if and only if its minors do not include the complete graph K₅ nor the complete bipartite graph K_3,3. The Robertson–Seymour theorem implies that an analogous forbidden minor characterization exists for every property of graphs that is preserved by deletions and edge contractions. For every fixed graph H, it is possible to test whether H is a minor of an input graph G in polynomial time; together with the forbidden minor characterization this implies that every graph property preserved by deletions and contractions may be recognized in polynomial time.

Other results and conjectures involving graph minors include the graph structure theorem, according to which the graphs that do not have H as a minor may be formed by gluing together simpler pieces, and Hadwiger's conjecture relating the inability to color a graph to the existence of a large complete graph as a minor of it. Important variants of graph minors include the topological minors and immersion minors.