Rhythm is mostly counting by various levels of two. Below starts with an example of various lengths of note values you might see:
The first two measures (also called bars) in order: whole note, half note, quarter note, eighth note, sixteenth note, thirty-second note. In the second staff below each note is the same value rest: whole, half, quarter, etc. A rest signifies a silence of a certain duration.
A whole note is a whole measure (from vertical line to vertical line) in this very common time signature, and is four quarter notes. It has a head but no stem.
Half notes and quarter notes have stems but not flags. Stems generally go up for lower notes and down for higher ones as in measure 3.
A half note is half as long as a whole note, and twice as long as a quarter note.
This pattern continues as small as you need to go, but sixteenth as about as small as is usually needed.
Eighth, sixteenth, and smaller notes have flags to differentiate from each other. When there is a pair or more of these notes they are often (depending on meter/beat/style) beamed together, as seen in the last three bars of the example.
The 4/4 at the beginning of the example tells you the time signature. The top number says how many beats, the bottom tells what kind (so 4 – quarter, 2 – half, 8 – eighth).
Generally a beam of eighth or sixteenth notes will show the halfway point of the bar, and often the divisions between the beats (bottom number on the time signature) as well.
A dot to the right of the note head or rest means the value plus half – quarter plus eighth note and rest are shown in measure 4, and a dotted half rest in measure 5.
Measure 5 shows a different time signature, six eighth notes are the total for that bar. Therefore, the beam shows three in a group, because that makes the halfway point of the bar visually clear.
Time signature and meters are often conflated, but are not necessarily the same. There will be a couple posts on various types of meters in the future.
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