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==Variants== Some composers have used fractional beats: for example, the time signature {{music|time|{{frac|2|1|2}}|4}} appears in [[Carlos Chávez]]'s Piano Sonata No. 3 (1928) IV, m. 1. Both {{music|time|{{frac|2|1|2}}|4}} and {{music|time|{{frac|1|1|2}}|4}} appear in the fifth movement of [[Percy Grainger|Percy Grainger's]] [[Lincolnshire Posy]]. [[File:Orff time signatures.gif|frame|right|Example of Orff's time signatures (traditionally, these would be notated {{music|time|3|8}} and {{music|time|6|8}} respectively)]] Music educator [[Carl Orff]] proposed replacing the lower number of the time signature with an actual note image, as shown at right. This system eliminates the need for compound time signatures, which are confusing to beginners. While this notation has not been adopted by music publishers generally (except in Orff's own compositions), it is used extensively in music education textbooks. Similarly, American composers [[George Crumb]] and [[Joseph Schwantner]], among others, have used this system in many of their works. [[Émile Jaques-Dalcroze]] proposed this in his 1920 collection, ''Le Rythme, la musique et l'éducation''.<ref>{{cite book|last=Jaques-Dalcroze|first=Émile|author-link=Émile Jaques-Dalcroze|title=Rhythm, Music and Education|translator=Harold F. Rubenstein|location=London|publisher=Dalcroze Society|year=1967|page=84, and Appendix, example 2}} – [https://archive.org/details/lerythmelamusiqu00jaqu/page/210/mode/2up Page 210] in the French original</ref> Another possibility is to extend the barline where a time change is to take place above the top instrument's line in a score and to write the time signature there, and there only, saving the ink and effort that would have been spent writing it in each instrument's staff. [[Henryk Górecki]]'s ''Beatus Vir'' is an example of this. Alternatively, music in a large score sometimes has time signatures written as very long, thin numbers covering the whole height of the score rather than replicating it on each staff; this is an aid to the conductor, who can see signature changes more easily.
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