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This question is simple to answer; yet very complex when it is explored.

The quick answer is that a composition is a piece of music written for a specific instrument or group of instruments.

An arrangement is a piece of music originally written for one instrument or group of instruments and then re-written for a different instrument or group of instruments.

Why is this important?

When approaching a composition or an arrangement there is a big difference in how you learn and play the music.

Generally speaking, when it comes to compositions you will probably want to learn what's written and play the piece exactly as written; because every note matters.

When it comes to an arrangement the approach is much different. Many times there are going to be multiple different arrangements of the same piece of music. One is not necessarily better than another but there could be large differences between them.

Usually when it comes to arrangements you are free to experiment a bit with the music. Now that's not to say that you will want to drastically alter what's written, but there are many times where an arrangement is written and is pretty much impossible to play. Especially when it comes to the piano, many times pieces of music created on other instruments and arranged for piano will include too many notes making it next to impossible to perform as written. In cases like this it is up to you play what notes you feel represent the piece best.

When it comes to an arrangement I believe you have a certain level of freedom to simplify it or even embellish it. This is because there simply isn't one way to adapt a piece of music -- especially a whole symphony. I like to think of arrangements as more of a guide or a starting point.

Now there are some arrangements that are actually intended to be played exactly as written -- they are called transcriptions.

This question pops up all the time when it comes to performing. I've been asked a number of times if I could play Beethoven's Fifth Symphony. I kindly respond by telling that it's actually a piece of music written for an entire orchestra and proceed to play Beethoven's 5th Symphony by ear! In fact, Liszt wrote 4 hand arrangements of all the Beethoven Symphonies.

For beginning students I find it's much better to have them practice compositions -- there are even compositions from Bach, Mozart, Beethoven, and Schumann that are great for a beginning level. It's much more beneficial to have them learning and playing something as written rather than playing a watered down version of an entire orchestral work.

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