Operation

Operation or Operations may refer to:

Military operation

A military operation is the coordinated military actions of a state, or a non-state actor, in response to a developing situation. These actions are designed as a military plan to resolve the situation in the state's favor. Operations may be of a combat or non-combat nature and are referred to by a code name for the purpose of national security. Military operations are often known for their more generally accepted common usage names than their actual operational objectives.

Types of military operations

Military operations can be classified by the scale and scope of force employment, and their impact on the wider conflict. The scope of military operations can be:

Set theory (music)

Musical set theory provides concepts for categorizing musical objects and describing their relationships. Many of the notions were first elaborated by Howard Hanson (1960) in connection with tonal music, and then mostly developed in connection with atonal music by theorists such as Allen Forte (1973), drawing on the work in twelve-tone theory of Milton Babbitt. The concepts of set theory are very general and can be applied to tonal and atonal styles in any equally tempered tuning system, and to some extent more generally than that.

One branch of musical set theory deals with collections (sets and permutations) of pitches and pitch classes (pitch-class set theory), which may be ordered or unordered, and can be related by musical operations such as transposition, inversion, and complementation. The methods of musical set theory are sometimes applied to the analysis of rhythm as well.

Mathematical set theory versus musical set theory

Although musical set theory is often thought to involve the application of mathematical set theory to music, there are numerous differences between the methods and terminology of the two. 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 kind in some sense, they are far more involved).