Time signature

The time signature (also known as meter, metre, and measure signature) is a convention in Western music notation to specify how many of a particular note value are contained in each measure (bar). The time signature is a notational device representing the meter, an auditory feature of the music. In a music score the time signature appears at the beginning as a time symbol or stacked numerals, such as or (read common time or four-four time, respectively), immediately following the key signature (or immediately following the clef symbol if the key signature is empty). A mid-score time signature, usually immediately following a barline, indicates a change of meter. Most time signatures are either simple (the note values are grouped in pairs) or compound (grouped in threes). Less-common signatures correspond to complex, mixed, additive, and irrational meters. Most time signatures consist of two numerals, one stacked above the other: The lower numeral indicates the note value that the signature is counting. This number is always a power of 2 (unless the time signature is irrational), usually 2, 4 or 8, but less often 16 is also used, usually in Baroque music. 2 corresponds to the half note (minim), 4 to the quarter note (crotchet), 8 to the eighth note (quaver), 16 to the sixteenth note (semiquaver). The upper numeral indicates how many such note values constitute a bar. For instance, means two quarter-notes (crotchets) per bar, while means four eighth-notes (quavers) per bar. The most common time signatures are , , and . By convention, two special symbols are sometimes used for and : The symbol is sometimes used for time, also called common time or imperfect time. The symbol is typically used in place of and is called alla breve or, colloquially, cut time or cut common time. These symbols derive from Mensural time signatures, described below. Simple meters are those whose upper number is 2, 3, or 4, sometimes described as duple meter, triple meter, and quadruple meter respectively.

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Beat (music)

In music and music theory, the beat is the basic unit of time, the pulse (regularly repeating event), of the mensural level (or beat level). The beat is often defined as the rhythm listeners would tap their toes to when listening to a piece of music, or the numbers a musician counts while performing, though in practice this may be technically incorrect (often the first multiple level). In popular use, beat can refer to a variety of related concepts, including pulse, tempo, meter, specific rhythms, and groove.

Metre (music)

In music, metre (Commonwealth spelling) or meter (American spelling) refers to regularly recurring patterns and accents such as bars and beats. Unlike rhythm, metric onsets are not necessarily sounded, but are nevertheless implied by the performer (or performers) and expected by the listener. A variety of systems exist throughout the world for organising and playing metrical music, such as the Indian system of tala and similar systems in Arabic and African music.

Time signature

Inhomogeneous minima of mixed signature lattices

Eva Bayer Fluckiger, Martino Borello, Peter Simon Jossen

We establish an explicit upper bound for the Euclidean minimum of a number field which depends, in a precise manner, only on its discriminant and the number of real and complex embeddings. Such bounds were shown to exist by Davenport and Swinnerton-Dyer ([9-11]). In the case of totally real fields, an optimal bound was conjectured by Minkowski and it is proved for fields of small degree. In this note we develop methods of McMullen ([20]) in the case of mixed signature in order to get explicit bounds for the Euclidean minimum. (C) 2016 Elsevier Inc. All rights reserved.

Academic Press Inc Elsevier Science2016

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