In order to build a strong rhythmic foundation, you first must be familiar with the various notes, rests, and their respective values. The value of a note determines how long it is held for, how many counts it receives, or to put it in musician speak, "how many beats the note gets."
Fractions, Pies, & Legos
The foundation of rhythm is basic math; in particular, fractions which means we can use pieces of a pie for an example. In this analogy, the pie is a whole note and if we cut it in half we get two pieces, in other words, two half notes.
More note values are created by dividing longer notes into halves and continuing the process to get even smaller/faster notes. Because each note created is half of the previous note's duration, this means that the new note will sound twice as fast.
If pies aren't your thing, then consider Legos. If a 2x2 brick represents a quarter note, then a 4x2 brick would be equivalent to a half note. Therefore, it would take two 2x2 bricks to equal the length of the 4x2 brick. Moreover, it would take four 2x2 bricks (or two 4x2 bricks) to equal the length of an 8x2 brick or a whole note.)
It's helpful to know how many of a specific note will fit into another note. For example, four eighth notes fit into a single half note. Practice adding and subtracting slices of the pie to see how many different combinations you can make to create longer notes.
The Beat
Most music uses the quarter note as a reference for the beat which means that for each tick of a metronome, you are hearing one quarter note. Furthermore, the whole note would then be held for four counts, a half note for two, and eighth notes would be considered half of a beat (think: twice as fast as a quarter note.)
Notice how the piano notes increase in speed every time the note value is halved:
Practice switching between clapping with the beat and then switch to clapping twice as fast. Also, try clapping half as often or on ever other beat.
Rhythm Pyramids
Running with the Lego analogy, it's helpful to visualize the note values as a pyramid beginning at the top with a whole note and halving the note as you move down to create short/faster note values.
Most musicians will only use whole, half, quarter, 8th, and 16th note values. However, if you are a drummer or percussionist, 32nd will show up in your studies, occasionally 64th, with the rare possibility of 128th.
The Outro
Here's a great reference guide to study until you have memorized all the notes and respective values. Both the names and the values are equally important to learn in order to effectively communicate with fellow musicians.
