Rhythm of piano songs is absorbed by practising a musical phrase in small sections. Tempo is reached incrementally by beginning very slow and gaining in pace
Rhythm, tempo, and tone are the dominant elements that occupy the mind of a piano student when practising. While subtle nuance that influence the elegance of the music produced are factored in too, we first struggle to capture the correct rhythm, render it in its appropriate tempo at the most ideal tone.
Among the three, capturing rhythm is the most vexing task. Listening to another play is one way to get to know it but the process of executing the rhythm is the best way I know on how to absorb it. I find it vexing because in the process of figuring it out I would get it wrong requiring corrections be made in every aspect of the music
The sound produced is not pleasant to hear, it is not yet music that can be enjoyed. A rough and tumble phase in learning a composition.
Depending on the difficulty level of the song and my own proficiency, with practise over time the desired rhythm gradually makes itself heard. Persistence is needed in this phase of learning a composition therefore to stay engaged, break a phrase down into smaller sections. Such as practising a group of semiquavers until its execution is decent enough before moving on to the next group of notes.
Even a group of semiquavers could be divided into shorter cells of 3 or 4 notes that are easier to practise. See Image 1 below for example. An intermediate level student could master an advanced level composition by breaking it into smaller and shorter sections when practising.
In addition to dividing a musical phrase into smaller, shorter sections during practice, they should also be practised slow. Speed is built up incrementally, only reaching the required tempo as demanded by the written score after the phrase could be executed well slow.. An accelerando should first be practised as adagio, then raised to moderato.
Usually what I would do is; regardless of whether the notes are semiquavers, quavers, or crotchets for the first few sessions of practice I would play them all as breves. And because I had divided the phrase into smaller cells of 4 notes, once I could string them together them without hesitation,
And because I had divided the phrase into smaller cells of 4 notes, once I could string them together them without hesitation, I would begin to pick-up the pace playing rhythmically according to the instructions in the written score. But still choosing to stay out of tempo on the slow side.
Two or three cells of 4 notes typically sum up into a bar. When the rhythm to the bar is being played firm and consistent, only then would I increase the tempo to moderato. The process is repeated with the next bar. After several bars, the rhythm to a complete phrase could be heard.
At this point, you can hone your skills in expression by playing with the tempo. For example, play a bar adagio then shift to moderato in the next bar, or 2 bars played as adagio followed by 2 bars as moderato. Such practise also has the extra benefit of developing your ability to control tempo. Able to change it at will should the need arises.
Break a musical phrase into smaller, shorter sections when practising to capture the rhythm. A section could be as small as a cell of 4 notes. Thereby easier played rhythmically. Put together they make a bar. Keep practising at a slow tempo until the rhythm could be executed firmly and consistently. Tempo is built up incrementally, get up to speed by practising very slowly initially from adagio increasing to moderato and climaxing in an accelerando if the composition demands it.