Doom is a series of first-person shootervideo games developed by id Software. The series focuses on the exploits of an unnamed space marine operating under the auspices of Union Aerospace Corporation (UAC), who fights hordes of demons and the undead in order to survive.
Doom is considered to be one of the pioneering first-person shooter games, introducing to IBM-compatible computers features such as 3D graphics, third dimension spatiality, networked multiplayer gameplay, and support for player-created modifications with the Doom WAD format. Since the release of Doom in 1993, the series has spawned numerous sequels, expansion packs, and a film.
Since its debut, over 10 million copies of games in the Doom series have been sold.
Campaign: this describes either a subset of the theatre of operation, or a more limited geographic and operational strategic commitment, such as the Battle of Britain, and need not represent total national commitment to a conflict, or have broader goals outside of the military impact.
Musical set theory provides concepts for categorizing musical objects and describing their relationships. Many of the notions were first elaborated by HowardHanson (1960) in connection with tonal music, and then mostly developed in connection with atonal music by theorists such as AllenForte (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).