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In terms of classical music theory, syncopation means a shift in the rhythmic information from a primary beat (in a 4/4 meter this would be 1 and 3) to a to a secondary beat (2 and 4). This usually creates a tension that needs to be resolved. It can be said that syncopation is a rhythmic dissonance.
Each time signature is structured by different beat weights. For example, in 4/4 time, beats 1 and 3 are considered heavy, while beats 2 and 4 are light beats. An emphasis on these beats is already a shift in emphasis, a syncopation.
A classic example of such a rhythmic shift is the melody of the medieval chorale “Es ist ein Ros entsprungen” by Michael Praetorius. The syncopation begins in the first bar on the fourth beat and resolves to the first beat of the last bar.
The concept of rhythmic shifting and off-beat-phrasing plays an important role in Afro-American musical styles. Below are some easy exercises to prepare you for using such rhythms in comping patterns and solo guitar arrangements.
Begin with these exercises in quarter notes. First, clap or tap each of the rhythms notated in the upper part. Then you should add the half notes by tapping them with your foot. Ultimately, you can follow the same path on the guitar. Here you play the treble notes with your fingers while your thumb plays the bass notes.
Now the same rhythms follow in eighth notes. The basic pulse (played by foot/thumb) changes to quarter notes. Please observe the the counting of the eighth notes (“1 and 2 and…”). The rhythms are identical to example 1.
The same rhythms are found here again, now in sixteenth notes. Many bossa nova, samba or choro songs are notated in this way. The difference to the previous examples is that the basic pulse (also marked with the foot) is still felt in quarter notes.