VII. time signatures

Time signatures and bar lines are secrets told to the performer by the composer.  
 - Antal Dorati

Time signatures, like bar lines, have evolved into practical notational conventions that indicate groupings used consistently for all or significant portions of a piece of music. The time signature consists of two numbers stacked vertically. The bottom number stands for one of the binary note values: 2, 4, 8, or 16 (1 for the whole note and 32 for the thirty-second note are found rarely, if ever). The top number shows how many of the notes indicated by the lower number occur in a measure, the space between bar lines. The most common time signatures are shown in Example 23.

Ex. 23

Ex. 23 Common Time signatures.png

You may say with a great deal of confidence that “2/4 means there can be two quarter notes between bar lines,” that “6/8 means there can be six eighth notes between bar lines,” etc. Keep in mind, however, that these note values may or may not represent the pulse you choose as a beat. That choice depends primarily on the tempo of the pulse streams in the metric structure. For example, we say that in 3/4 there can be three quarter notes in a measure, and the speed of the quarter note is such that the pulse it represents may be chosen as the beat. But a slow speed for the quarter note might cause us to choose the eighth note as the beat. And if the quarter note is performed very fast, we may choose the dotted half note as the beat. Tempo is the crucial factor when deciding whether the note value shown in the time signature represents the beat.

Although some composers nowadays substitute a note value for the bottom number in a time signature:

2 over dotted quarteer.png

no consistent way of showing tuplets (see below) or dotted notes in time signatures is in common use. You will encounter scores in which time signatures change frequently (this is sometimes referred to as “mixed meter”). While mixed meters of, say, 2/4, 3/4, 5/4, 6/8, 3/8, and 4/16 in succession may present a challenge in performance, each time signature gives the same kind of information—it tells how many of what kind of note (or its equivalent) occurs in a single measure.   

What does “or its equivalent” refer to in the previous sentence? Let’s use 2/4 as an example.  2/4 means there can be two quarter notes in each measure (see Example 24). We know, however, that a half note or four eighth notes or eight sixteenth notes are equivalent to two quarter notes. The term tuplet refers to a grouping of notes that can not be expressed by the time signature. In the example below, the second line shows the standard way of notating tuplets. Here six eighth notes can be played in the time of four eighths (the natural division in 2/4) by using a slur and a number; three quarter notes can fill the time of two quarters, and six sixteenths can fill the time expressed by four sixteenths. Tuplet notation is found throughout the 18th and 19th centuries,  and we will consider it a legitimate option, especially for triple meters. So a piece may be notated with a signature of 2/4, and two three-note triplets can be used throughout to communicate triple meter. A look through Beethoven’s piano sonatas, for example, will show that he was fond of switching frequently from duple to triple divisions and back at levels faster than the beat. In Example 24, any of the groups in any combination that is equivalent to two quarter notes may appear in a measure following a time signature of 2/4.  Anything else is a mistake!!

Ex. 24 

Ex. 24 filling a bar of 2:4.png