scales and key signatures

We have defined the concept of key signature in chapter Key signatures. In this chapter, we shall explain it further. It is important to understand that we cannot write a key signature using arbitrarily chosen accidentals. To get a valid key signature, we must start from a major scale or a natural minor scale and find the key signature such that when we write the scale in the key signature, all the notes are without accidentals. For instance, the next figure shows the key signature that must be used with the D major scale so that all the notes can be rewritten without accidentals.

Figure: The D major scale rewritten in the key signature such that all the notes are without accidentals

If we want to do the same for the B natural minor scale, we must again use the same key signature.

Figure: The B natural minor scale rewritten in the key signature such that all the notes are without accidentals

This key signature is called the D major/B minor key signature.

We can do the same for all the scales that we examined in the preceding chapters. The next figure shows the resulting key signatures and their names. From the names of the key signatures we can read the names of the related major and natural minor scales. The key signatures are shown both in the treble clef and in the bass clef. The key signatures have up to four accidentals. The accidentals of a key signature can only be all sharps or all flats. There are no key signatures with mixed sharps and flats. 

In chapter Circle of fifths, we shall learn the other key signatures that are used in music, that is, the key signatures with up to seven sharps or flats.

Figure: Key signatures with up to four accidentals

An interesting fact is that Bach wrote two sets of compositions, dedicated to those who study playing or composing keyboard music, which only uses the key signatures with up to four sharps or flats. They are known as Bach’s Two-Part Inventions and Three-part Inventions. The three-part inventions are also known as Sinfonias. Bach’s title for them is also interesting: 

“Honest method, by which the amateurs of the keyboard – especially, however, those desirous of learning – are shown a clear way not only (1) to learn to play cleanly in two parts, but also, after further progress, (2) to handle three obligate parts correctly and well; and along with this not only to obtain good inventions (ideas) but to develop the same well; above all, however, to achieve a cantabile style in playing and at the same time acquire a strong foretaste of composition.”