Nearly all rhythms are built in groups of either two or three beats. A large amount of old classical music is in twos, waltzes are in threes and most pop music is in fours (two groups of two). Other rhythms of sixes and eights can usually be considered groups of threes and twos, respectively.
If you don't understand any of the following terms, you can scroll down to have a look at the notation.
Music is written on a staff (the five horizontal lines), which is normally divided into measures (groups of beats) by a series of vertical bar lines. The rhythm is represented by two numbers that look like a fraction and usually appear at the beginning of the staff. This symbol is called a time signature. The top number indicates the number of beats in each measure. For example, a 3/4 time signature means that there are three beats to each measure. The bottom number indicates what kind of note is used in the transcription to represent one beat. For example, a 3/4 time signature means that there are three beats to each measure and each beat is represented by a quarter note, and a 6/8 time signature means that there are six beats to each measure and each beat is represented by an eighth note. In most kinds of music, time signatures are nearly always 3/4, 4/4 or 3/8.
Now that we know how to interpret the transcribed rhythm, we have to understand how to interpret time values (the duration of the notes). In most kinds of music, notes that last two or more beats appear on the staff as hollow circles, notes that last one beat appear as solid circles and notes that last less than one beat appear as solid circles grouped under horizontal lines called beams. Beams are usually single or double.
Let's see for ourselves how this works in a 4/4 time signature. Clapping, counting, tapping your foot or similar, try to project a steady rhythm of four perfectly separated beats. Now count over that rhythm: "One, two, three, four." In the example below, each beat appears as a quarter note (crotchet in UK), which is a single solid note head with a stem. Each note is separate and not connected to another.
The staff or bar above is divided into measures by the bar lines. The 4/4 time signature at the beginning indicates that there are four beats in each measure and that each beat is represented by a quarter note, which is a solid stemmed circle. This is a simple example of a transcription in 4/4. We're going to use 4/4 for now, but we'll see some different time signatures toward the end of this document.
In the example above, each beat contains one note. When there are several notes within a beat, horizontal lines called beams connect the notes, as seen in the example below. Two equally spaced notes per beat are called eighth notes (quavers in UK). The notes appear on the staff with a beam that joins the stems to form one beat. If there is half of a beat of silence (a rest), and therefore only one note, the beam trails off, hanging over (or under) the single note. This is called a hook or a flag. Go back to your four-beat counting and put an "and" squarely between the beats (think marching-band rhythm, not swing rhythm).
Now go back and try to feel a swing rhythm, in which the "and" is closer to the next beat (it's really the "uh" of the triplet rhythm, as seen below) and is no longer perfectly between the two. Different styles of music normally use only one of the two eighth-note rhythms. I refer to these rhythms as "straight time" and "swing time."
The symbol 
or something similar is sometimes used at the beginning of a score to indicate a triplet feel. It shows that all the eighth notes of the piece should be interpreted as the first and third notes of a triplet.
Dividing each beat into three equal parts offers a different feel, but it's still written with the same single beam. A small number three should be written over each beam to indicate a triplet, although it's often not necessary because we can see the groupings of four beats to a measure (sometimes the three is necessary, but we'll see that later). The syllables for the counting could be, "one-and-uh, two-and-uh,..." Remember to keep the syllables equally spaced. There are several ways to divide a single beat into three parts, but only one produces perfect thirds. The syllables below should flow out in a steady stream.
Four-note divisions of a single beat are written with two beams connecting the notes, as seen below. These divisions are called sixteenth notes (semiquavers in UK):
Five-note divisions, called quintuplets, are common in flamenco but seldom heard elsewhere and are written as five double-beamed notes. Six-note divisions or sextuplets are much more common and are also double beamed. When written out, both of these values should include the little number over the beams to indicate the number of divisions. Septuplets, which are very rare, follow the same rule.
When we divide a beat into eight equal parts, and that's pretty darn fast, a triple beam is used to join the thirty-second notes (demisemiquavers in UK). This time value isn't used very often, but sometimes quick slurs (fretting-hand articulation) can be noted this way.
Up to this point, we've looked at notes that last one beat or less. Notes that are held held over several beats are represented in a different way. A hollow circle is used instead of the solid note head. A note that lasts four beats is called a whole note (semibreve in UK) and is represented by a stemless hollow circle, and a note that lasts two beats is called a half note (minim in UK) and is written as a stemmed hollow circle. A dot next to a note increases its value by one-and-a-half times. This is often used to transcribe notes that last three beats. Look at this:
We've already seen quite a lot. Here's a summary of the symbols presented so far. The name is how we refer to the note, and the number or fraction represents how many beats that note is worth in 4/4 time. You'll have to memorize all the note shapes and values, from the whole note (stemless hollow circle, 4 beats) to the thirty-second note (triple beam or flag, 1/8 of a beat).
All of these examples are written in 4/4, which is so common that it often appears as a large capital "C", instead of the time signature (it doesn't stand for "common," but let's leave that for another day). Other time signatures are sometimes used. Waltzes, for example, have three beats per measure and are often written in 3/4. The same rhythm could also be written in 3/8, although the notation would look a little different, because every eighth note would indicate one beat. The two examples below would sound identical:
Different time signatures can simplify the notation. An example of this is the 12/8 signature, which is sometimes used to write blues and shuffle rhythms with a strong triplet feel.
In the 12/8 time signature, the top number indicates twelve beats per measure and the bottom number indicates that each beat is represented by an eighth note. In the example above, you can see that there are twelve eighth notes altogether, and that it looks just like a measure of 4/4 in triplets. It's a different way of writing the same idea, and in this case it would avoid having to include the little number three that should appear over each beam. In 4/4 time, in a piece where everything or nearly everything appears in triplets, the use of 12/8 time would be an alternative. However, in other pieces it's often necessary to include the number three, in order to make it clear that a grouping of three notes is a triplet, because beams can link more than one beat. In the section on eighth-notes, I said that beams join stems to form one beat, but this isn't always the case. Look at these two examples:
Here the 4/4 time signature is clearly represented by the beamed groups of notes. The symbol at "two and" is an eighth rest like the one we saw earlier, which indicates a half beat of silence. The third beat has three beamed notes that should be played like a triplet (three-and-uh).
But this same idea could also be written this way:
Notice how the first three eighth notes are beamed, but the last of them starts beat two, like the first example. The notes in the third beat look the same as those in the first beat but should be played differently, which is made clear by the little number three over the notes. Under 2/4, 3/4 and 4/4 time signatures, the same rule is applied to sixteenths, quintuplets, sextuplets and septuplets, as they are all written with a double beam.
There are only a few more symbols to learn for this brief overview of noted rhythm. When a note is held, allowing it to ring out, it may be transcribed in two ways. The first is a curved line called a tie that joins shorter notes together into one long one, and the second is a single note value that is equal to several tied notes. This might involve dotted notes, which equal one-and-a-half times the note without the dot (the dot adds 50% more value).
In the first measure of the example above, we can see that the third note is held. The curved line is a tie, which indicates that the note is sustained (only the first of the tied notes is played and the rest are the result of the note ringing out). The second and third measures show more logical ways of noting the idea. In the third measure, the tie is no longer necessary, as the value of the sustain is now represented by a single dotted note (quarter note equals two eighths and the dot equals half that for a total of three eighths). In guitar transcriptions, ties are also used to indicate slurs (hammer-ons and pull-offs).
Moments of silence, called rests, are written with other symbols, as seen below at the end of each measure. Notice that eighth, sixteenth and thirty-second rests use something similar to the single, double or triple hooks of their audible counterparts (notes). The notation before each rest is what's left of the four beats after subtracting the value of the rest. Remember that each measure has to contain four beats. There's a bit of math involved in reading notation: not complicated formulas, but adding up whole numbers and fractions until you come up with the number of beats per measure. For example, the last measure seen below would be "two + one and a half + three eighths + one eighth = four." Pay attention to whether or not the notes are dotted.
The examples below compare similar ways of dividing one beat. On the left, the divisions are made up of evenly spaced notes, and, on the right, the same amounts of notes are distributed in different (uneven) patterns. It is very important for any musician or dancer to be able to distinguish between even and uneven patterns. Of course, it's an entirely intuitive matter, but here's a cerebral approach, if you're interested. About the syllables, bear in mind that the "and" and "uh" in triplets and sextuplets do not coincide with their counterparts in eighths and sixteenths. This is because triplets consist of units of 33.3% and sixteenths of units of 25% (the difference between ternary and binary). The syllables span a single beat and may be repeated to generate a rhythm. If you count the patterns out loud, you should feel the syllables in parentheses without pronouncing them. All of these examples are written for the time signatures 2/4, 3/4 and 4/4, in which the lower 4 indicates that a quarter note represents one beat.
