In order to mix harmonically you must understand a bit of music theory and know the keys of the songs you are mixing. Taking the time to do this will improve the quality of your mixing by allowing you to combine melodies and harmonies without clashing. It will also help you learn to play along with your music if you have any instruments.
Sounds are classified into pitch groups described as notes. There are 12 notes which repeat themselves (A, A#/Bb, B, C, C#/Db, D, D#/Eb, E, F, F#/Gb, G, G#/Ab). The keyboard is a good visualization:
The notes can continue in either direction. Due to the layout of the traditional keyboard, the black notes are named relative to adjacent white notes (which is why there are 2 names for each black note). Sharp (#) means above while flat (b) means below.
Each of the 12 notes is related in frequency in that they are all multiples in powers of 2. Every 12th repeating note up on the keyboard doubles in frequency. All adjacent notes are evenly spaced intervals called half-steps. The interval of 12 half-steps (for example, from a C note to the next C note) is known as an octave.
As a DJ, you must understand that most songs have a key, or tonal center. Keys are based on scales, and are usually major or minor (see more scales in advanced theory). Scales essentially describe subsets of notes that go well together. The 1st note of the scale is the tonal center, known as the tonic or root note. The 4th and 5th notes of a scale are known as the subdominant and dominant notes, also referred to as perfect 4ths and 5ths. Whether the scale is major or minor, subdominant and dominant notes are always 5 and 7 half-steps up from the tonic note, respectively.
It is important to be able to determine the notes of a key. The easiest way is to remember the pattern of intervals that form major and minor scales. Although there are multiple minor scales, we will simply refer to the natural minor. Knowing that a half-step (H) is the interval between 2 adjacent notes and a whole-step (W) is 2 half-steps, the scale patterns are:
Tip: If you forget these patterns you can refer to the keyboard. The major pattern uses all white notes from any C note to the next C. Similarly, the minor pattern uses all white notes from any A note to the next A. The fact that C major and A minor share the same notes is because they are relative keys. Every major key has a relative minor, and every minor key has a relative major.
Practice: To make sure you understand, the notes of the C minor scale are shown below. Songs in C minor would generally use these notes, with C being the tonal center.
Playing any notes in succession forms melodies, while playing them at the same time forms chords, which are the basis of harmony. There are many types of chords. Common major and minor chords use the 1st, 3rd and 5th notes of the scale. So, the patterns of intervals to form a major or minor chord from any note are:
Practice: To make sure you understand, a G major chord would consist of G-B-D. A G minor chord would consist of G-A#/Bb-D.