Audio: distant key (0:08)
distant key plays a melody on a violin. A cello plays harmony on the tonic note of each key. The distant key figure, the score, shows modulation to and from distant keys. The distant key table lists the relationships between parallel, relative, close and distant keys:
A distant key shares between two and five notes in common with another key.
There are three times as many distant keys as there are close keys. Trying to figure out how to modulate to a distant key is fun but a challenge because there are so many routes. Getting back is even more fun (trickier). Two facts help:
distant key shows how to apply this knowledge.
The first bar contains a melody using six notes in the key of C major.
In the second bar the key modulates from C major to its most distant key, F# major. The tonic notes of each key, C and F#, are a tritone apart. Modulation is achieved by pivoting the melody on the note B, which is one of the two notes that are common to both keys (the other note is F). The rest of the second bar contains three notes in the key of F# major which reinforce the key: the tonic, third and fifth degrees, F#, A# and C#.
Ten of the twelve notes in the chromatic scale have been used by the end of the second bar. The only two notes which have not been used are G# and D#. Modulation back home to C starts with an easy decision: which of these two notes will form the tonic of the next key? G# was chosen after tossing a coin.
G# phrygian emerged as an interesting choice of key after a lot of experimenting. It is a relative of E major, and the note E is the third degree in the key of C, hence the tied note between bars 3 and 4.
Et voila, home and dry.