. Beating time signatures To the ear, a bar may seem like one singular beat. For example, a fast waltz, notated in time, may be described as being one in a bar. Correspondingly, at slow tempos, the beat indicated by the time signature could in actual performance be divided into smaller units. On a formal mathematical level, the time signatures of, e.g., and are interchangeable. In a sense, all simple triple time signatures, such as , , , etc.—and all compound duple times, such as , and so on, are equivalent. A piece in can be easily rewritten in , simply by halving the length of the notes. Other time signature rewritings are possible: most commonly a simple time signature with triplets translates into a compound meter. Though formally interchangeable, for a composer or performing musician, by convention, different time signatures often have different connotations. First, a smaller note value in the beat unit implies a more complex notation, which can affect ease of performance. Second, beaming affects the choice of actual beat divisions. It is, for example, more natural to use the quarter note/crotchet as a beat unit in or than the eighth note/quaver in or . Third, time signatures are traditionally associated with different music styles—it would seem strange to notate a conventional rock song in or , rather than . Characteristics The table below shows the characteristics of the most frequently used time signatures. Complex time signatures Signatures that do not fit the usual duple or triple categories are called complex, asymmetric, irregular, unusual, or odd—though these are broad terms, and usually a more specific description is appropriate. The term odd meter, however, sometimes describes time signatures in which the upper number is simply odd rather than even, including and . The irregular meters (not fitting duple or triple categories) are common in some non-Western music, but rarely appeared in formal written Western music until the 19th century. Early anomalous examples appeared in Spain between 1516 and 1520, but the Delphic Hymns to Apollo (one by Athenaeus is entirely in quintuple meter, the other by Limenius predominantly so), carved on the exterior walls of the Athenian Treasury at Delphi in 128 BC, are in the relatively common cretic meter, with five beats to a foot. The third movement of Frédéric Chopin's Piano Sonata No. 1 (1828) is an early, but by no means the earliest, example of