A key signature is a symbol comprised of a bank of either sharps (#) or flats (b) found at the beginning of each staff next to the clef symbol.
Why is the key signature revolutionary? Well, instead of each and every note on the page being marked with accidentals like sharps (#), flats (b), or naturals, the key signature tells us which notes are which at the beginning of each staff.
That said, sometimes composers write lines of music with notes that fall outside the key, but in these cases the rebel notes will be notated with appropriate accidentals. All in all, however, the key signature makes written music a whole lot tidier and easier to read. Also, it shows us which key a piece is in and tells us when the key of a piece changes.
There is a handy-dandy mnemonic device to help us discern which key we're in. In keys with flats, the second to last flat is the name of the major key. In keys with sharps, the name of the major key is half a step up from the final sharp. So, if there are three sharps in the key signature, you will be in the key of A major (or its "relative" minor key—more on that below).
Note: You will never see a key signature that has both sharps and flats. It is either one or the other, or none.
The sharps and flats in a key signature are always aligned in a particular order. For example, if a key signature contains three flats, the flats will always be ordered Bb, Eb, Ab. How can we remember the order? Though many musicians simply memorize the order, you can also determine the order by looking at the Circle of Fifths chart:
The names of each major key are listed in mauve (or is it berry?) around the outside of the outer circle. The number of sharps or flats in each key are listed just inside the outer circle. For example, you'll see that the key of E major has four sharps.
There's always the chance that the piece is in a minor key. Another fantastic feature of the Circle of Fifths chart is that it shows us the corresponding "relative minor" of each major key. On our Circle of Fifths chart, the name of the relative minor key to each major key is listed in green inside the inner circle.
The corresponding relative minor of a major key is a minor third (three half-steps) below the major key. For example, the relative minor of C major is A minor.
But it's still not necessary to have a photograph of page 532 of your theory textbook burned into your mind. To attempt to discover if you're in the relative minor examine the melodic arc of the piece, specifically the final note; the note on which the piece ends is usually a good indicator of the key. So, for instance, if you think you're in D major, but the last note is not a D (and especially if it's a B instead), you might want to look more closely.
See! Isn't the key signature a great invention? Now you can relax, knowing that the accidentals of the world are nestled peacefully at the beginning of each staff instead of pillaging the page. Now if only we could do something about that guy in the washing machine...
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