Of the many debated aspects of any piece of classical piano music, none is more disagreed upon than tempo. Choosing one pace for a piece might seem correct for one composer, while another pianist might disapprove completely. Any kind of music can be transposed into a different tempo and, while the score may be correctly translated into a different speed of playing, this can totally change the mood of the song. The chosen pace can just be the player taking on liberties of expression, as Moonlight Sonata by Beethoven has been played in different tempos by several different pianists over time.
Any music must have rhythm; without it there is no pulse or flow. There would be no pattern for the brain to follow and the sounds would not make sense. Tempo is one part of the rhythm, as all of the notes have to occur at a set rate. So is meter, the rate at which stronger and weaker pulses, or notes, are set in the music, as well as the phrasing of the melody, where distinguishable sequences of notes are heard within the general piece of music.
How do you go about choosing the right tempo? Piano music is made of a conglomeration of things, and choosing the speed at which to play is sometimes the last bit of information to include, after each note has been written. Even great composers like Beethoven change their mind about tempo, because even the great composer played compositions differently from the original markings found on his original scores of music. Many choices go into writing a new composition or song, and it is often hard to judge which exact tempo might strategically suit the entire piece.
For classical music, the rate at which the notes come into play tends to become faster later in a composition. A particular speed seems fine in the beginning, but can be too fast later on when there are more notes to play. This can lead the pianist to play the original phrases too fast when they come back toward the end of the composition, but it’s an ongoing debate as to how to solve this problem. It is not good practice to decide on a change of tempo in mid-song, but more subtle nuances such as rubato, accellerandi, and ritardandi give the performer some leeway of expression by making small tempo changes in the piece.
The most standard tempo in popular music and many other forms is 4/4 time. For classical music, this can sound too much like a march; so many pieces are played in 3/4. It’s possible to vary the notes between each hand, even change the pulse of the notes being played, without changing the basic tempo. The mood of the piece can change significantly when doing this, but it is not musically incorrect as the tempo remains steady throughout.
As to how to choose the right time signature of the piano music, you can always look to the written composition for guidance. If you are skilled enough, you could experiment at different speeds and see what works, and whether you can come up with a different interpretation. This can also work as a training exercise for beginners to help them learn the music, as playing the notes in different tempos will help them memorize the piece not by the pace at which it flows. The notes themselves can be rooted in their memory instead.
Piano music , no matter how complicated it can be, is always open to interpretation. Choosing the right tempo is often a matter of personal choice, even for the most well-known composers in history.