Just plain Bill, CC BY-SA 3.0, via Wikimedia Commons
Simply put, harmonic mixing, or mixing in key, is a formulaic method of mixing two keys in a way that ensures a smooth sonic transition from one key to the other. The formula that ensures this smooth transition is based on a music theory concept known as “The Circle of Fifths.”
In the circle of fifths, pictured to the right, the 12 chromatic tones (i.e. all possible musical notes) are arranged in a sequence of perfect fifth intervals, meaning the second note in the sequence is five pitches ahead of the first, the third is five pitches ahead of the second, and so on and so forth.
The Camelot system and the Open Key system, seen below, add an alpha-numeric component to the circle of fifths.
Luke Collins, Harmonic Mixing for DJ's & tips for producers
In the outer part of the circle, the major keys are listed (in the Camelot system, these keys are denoted with the letter B; and in the Open Key system, they are denoted with the letter d). Major keys can be considered the “happy-sounding” keys. In the inner part of the circle, the corresponding minor keys are listed (in the Camelot system, these keys are denoted with the letter A and in the Open Key system; in the Open Key system, they are denoted with the letter m). Minor keys can be considered the “sad-sounding” keys.
In harmonic mixing, two keys mix well together if they are right next to each other on the circle of fifths, or if they are relative keys (meaning one is a major key and the other is a minor key in the same position on the circle, or vice versa; in the Camelot and Open Key systems, this means that the two keys share the same number).
You can also generally mix two “diagonal” keys, meaning they are diagonal from each other on the circle of fifths (for example, C and e, or F and g; in the Camelot system, 12B and 1A, or 11B and 10A; in the Open Key system, 12d and 1m, or 11d and 10m).
The reason that this method works is that the more notes that the scales of two keys have in common, the more seamlessly you can transition from one key to the other, and as a result, the better that transition sounds.
You can certainly try to mix two keys that do not necessarily follow the aforementioned guidelines, but your results may vary. Sometimes, you might find that the transition does indeed sound good. Other times, however, you will not yield the same success.
While there are no hard-and-fast rules in music or mixing, and other factors such as tempo (i.e. how fast or slow a song is) could be considered, harmonic mixing is generally a good technique to utilize in order to ensure a smooth transition between songs. Mixing two keys that are “incompatible” might lead to listeners thinking “wow, this song sounds kind of random coming after that last song.” The use of harmonic mixing eliminates this issue.