In Lesson 7, we learned a short cut for creating major scales: the key signature. Key signatures replace the individual accidentals required for each of the twelve major scales, though the information associated with key signatures needs to be memorized. Besides the circle of fifths, there is another tool to help you with your key signatures; this one involves the relationship of the accidentals used and the scale degrees they alter. Let's start with the sharp key signatures. In the key of E major there are four sharps needed--F#, C#, G#, & D#. Notice that the last sharp here was the leading tone scale degree. This is true for all key signatures using sharp signs: the last accidental used will be the leading tone scale degree. Therefore, in order to know what major scale is associated with a particular key signature, find the last sharp and move up a diatonic semitone. A diatonic semitone uses two different pitch names--here D#-E--instead of the same pitch name used by the chromatic semitone (D#-Dx).
Key signatures using flats are a bit more complicated, but not terribly so. In the key of Db major, five flats are needed (Bb, Eb, Ab, Db, & Gb). Notice that the last flat used was 4 while the second to last flat was 1. This is true of all flat key signatures: the penultimate flat will be the tonic scale degree.
Let's test these new shortcuts out. What key signature is required for D major and F major? The leading tone scale degree of D major is C#, which is the second sharp; therefore, two sharps are needed for D major. The fourth scale degree in F major is Bb, which is the first flat; therefore, only one flat is needed for F major. You can also say that the second to last flat for F major is F if you wrap around the order of flats (Bb, Eb, Ab, Db, Gb, Cb, Fb) to the end.
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