Reasons for Rhythm and the Need to Know it

Music is: an art of sound in time that expresses ideas and emotions in significant forms through the elements of rhythm, melody, harmony, and color. (according to Dictionary.com)

Whether, as a performer, you're considering music of the Renaissance or modern compositions of the 21st century, there is some point where you have to consider the process of music in relation to time which loosely equates to rhythm. There are pieces of abstract music which don't apply a specific rhythm to the score, but even with these pieces, as a performer, you have to be aware of the impact the duration of the various notes play on the overall effect of the performance.
If you're playing music from the Baroque or Classical age, a more regulated rhythm might be a good choice, whereas music from the late Romantic is opt to Molto Rubato. Still, there is a sense in even the most irregular rhythmic music of how long it takes to get from one moment to the next. Understanding the effect of elongating or shortening the duration of notes is key to ensuring the proper impact on your audience. An audience listening to Bach or Mozart will appreciate the regular pulse these composers experienced when listening to music during their lifetimes. But, giving the music a more Rubato sense of expression might capture the imagination of a modern audience who is accustomed to a variety of different styles.
If the rhythm of the music is played irregular simply because the performer hasn't taken the time to practice either maintaining a strict pulse, or make appropriate decisions as to when and where a piece should speed up or slow down, the music feels uncomfortable, unpolished and ultimately unpleasant.
This is even more important when playing in an ensemble. If your sense of rhythm is different than the person next to you, the points where your notes should be simultaneous end up out of sync, creating a sense of ragged performance and completely destroying the intended effect.
The need to understand rhythm is becoming increasingly more important with modern music. No longer is there a strong sense of regular rhythm, but often intricate poly-rhythms are used to create very specific effects.
Whether the music is minimalist (Glass or Adams earlier works) with a need for steady rhythm to keep the intricate accents in their proper place, or shifting metric lines as in Ligeti's Piano Etudes where the lines are in slightly different metric lengths, rhythm is what holds the piece together. George Crumb's Black Angels expects not only an understanding of each player's rhythmic material, but how that material fits into the whole. When done right, the various poly-rhythms really make the music sing.
In one of my own works, "You Can't Catch Rabbits with Drums" the percussion section has three separate repetitive motives through the first 2/3's of the piece. These motives fall in-sync at various times which also coincide with the orchestras' accents. If these don't line up the piece sounds cacophonous with no real ebb or flow in the percussion line (the critiques of the performance bear witness to this). However, when done with precision, these accents pop out and create an interesting new element to the music, not found in any single part.
As a performer, understanding rhythm is basic to the core of the music. Composers are getting more and more adventurous with what rhythm can do, requiring performers to be even more precise with their rhythm skills.

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Thanks to Erica Sipes and her article on Baking Cakes - conquering rhythm for the inspiration for this post.