A chord is a group of 3 or more notes played simultaneously. Different types of chords can be formed by using different combinations of notes. The most basic type of chord contains three different notes and is called a triad. The most common triad is the major chord. All major chords contain three notes taken from the major scale of the same letter name. These three notes are the 1 (first), 3 (third) and 5 (fifth) degrees of the major scale, so the chord formula for the major chord is:
The C major chord is constructed from the C major scale. Using the above chord formula on the C major scale below, it can be seen that the C major chord contains the notes C, E and G.
Once you have the correct notes for a C chord they can be arranged in any order. As long as the notes are still C, E and G, you still have a C chord. E.g. a C chord could be played C E G, or E G C, or G C E, or even G E C. These various arrangements of the notes within a chord are called inversions.
Chords can be played more easily on some instruments than others. Two of the most common instruments used for chord playing are the guitar and the keyboard. It is possible to double (or even triple) the notes of a chord on these instruments. It is not possible to play chords on the saxophone, but they can be played as arpeggios. It is worth learning all inversions of each arpeggio, as this enables you to identify all the degrees of the chord (called chord tones) more easily, which means you can respond quickly to what is being played by other musicians you are playing with regardless of the harmony. If you know the notes and inversions of chords well, it also makes it a lot easier to play in a horn section where a chord is made up of individual notes played by different instruments. It is also recommended that you learn at least a bit of basic keyboard so you get used to hearing the sound of all of the notes of chords together instead of one at a time. Most of the great horn players also have an excellent knowledge of keyboard harmony.