Thursday, March 10, 2011

Quickly Determining the Key From a Key Signature

A couple of days ago a friend of mine asked me how you can determine the key of a music score by observing its "key signature". The key signature is the set of ♯ or ♭ symbols that are placed on the staff to indicate the notes that should be played one semitone higher (in the case of ♯) or lower (in the case of ♭) along the score (unless an accidental indicates otherwise). An example key signature (A major or F♯ minor) is shown below:




The key signature, despite its name, is a tool meant to reduce the number of accidentals in a score but it might not necessarily match the key of the score. Nevertheless, most of the time, it will.


The notational convention used comes from the circle of fifths:




Basically, the circle can be navigated clockwise or counter-clockwise, starting from the upper C, down to the G♭/F♯. In every "step" a symbol is added to the key signature: a ♯ if the circle is navigated clockwise or a ♭ if the circle is navigated counter-clockwise. The rule to add the symbol to the key signature is the following:

  • ♯ shall be added to the leading note for the major scale or, equivalently, to the supertonic for a minor scale.
  • ♭ shall be added to the subdominant for the major scale or, equivalently, to the submediant for a minor scale.
So far, so good, but theory would not help my friend so much, would it?

Fortunately, there's a quick mnemonic to find out the key from a key signature.
  • In the case of a key signature made up of ♯ symbols: Since, as explained earlier, the new ♯ shall be placed on the leading note (in the case of a major scale), the mnemonic is: look at the last ♯ in the signature and raise it by one semitone. That's the corresponding major key.
  • In the case of a key signature made up of ♭ symbols: Since the new ♭ shall be placed on the subdominant (in the case of a major scale), take the second last ♭: that's the corresponding major key. If the signature has got only one ♭, that's a F major (that's easy).
For example, if we look at the following signature:


The last ♯ symbol is a E♯. If we raise it one semitone we've got a F but, since the F is already marked as F♯ on the signature, the corresponding major key will be F♯.

If we look at this signature:


The second last ♭ is a C♭: the corresponding major key is, indeed, C♭.

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