Understanding key signatures
Once you have the major keys arranged in the circle of fifths, and you know why they only go around the circle seven steps either way, so they have up to seven flats or seven sharps, it’s only a small leap to understanding key signatures.
The basic concept is that if your music is in a major key, most of the notes are going to be the notes in the major scale. Suppose, for example, you have a piece in the key of D-major. Now, the D-major scale has two sharped notes, F-sharp and C-sharp. So your piece is going to have a lot of F-sharps and C-sharps and not so many F-naturals and C-naturals. So wouldn’t it be great to remove some excess clutter from your music? Why not just remind the musician at the beginning that all Fs and Cs are going to be sharped unless otherwise specified? Then you don’t have to sprinkle all those extra sharp-symbols all over your music. You’d save ink, help the environment, and contribute to saving our planet by decreasing your carbon footprint.
If you’re not a musician, this probably sounds like a huge nuisance. It would be hard enough to read those notes off the page, and now you have to keep remembering extra sharps (or flats) that aren’t written! Nevertheless, this is what musicians do. At the left of every staff there’s a key signature which reminds you of these “default” accidentals that are to be assumed unless otherwise specified.
So without further ado, here’s a circle of fifths with the key signatures included. The names of the major keys are given, and also the names of the minor keys (which we will discuss momentarily):
Some keys are more equal than others
You may wonder: what should you do in the cases where you have two possible key signatures? For example, if the key of B-major and the key of C-flat-major are composed of the same pitches written differently, if you’re writing music in this key, which key signature should be used? In theory, you could use either, but in practice, musicians often choose the one with less accidentals for convenience. So it’s common to see music notated in B-major but it’s very rare to see music in C-flat-major, and similarly it’s more common to see music written out in D-flat-major than C-sharp-major. As far as F-sharp-major and G-flat-major with six accidentals each, both are used. I think there is a bias towards F-sharp-major, however. F-sharp feels more “ordinary” because F-sharp is the very first sharp in many key signatures, while G-flat is a more “obscure” note.
Every major key has a relative minor key that starts on the sixth note of the major scale. For example, the notes in the C-major scale are C-D-E-F-G-A-B-C. And the sixth note in this scale is A, so the relative minor key of C-major is a-minor. (Often you’ll see minor keys written in lowercase letters, and major keys in capitals.) The “regular” or “natural” a-minor scale has these notes: A-B-C-D-E-F-G-A. (To keep things simple we won’t discuss the other “less natural” minor scales just yet.) Having the same notes, the minor key has the same key signature as its relative major key.
So from the key signature alone, you can’t tell whether a piece of music is in a major key or a minor key. If there are no accidentals in the key signature, it could be in C-major or in a-minor. (A musician would be able to look at the notes and chords used to determine which key the piece is in, but to keep things simple we won’t discuss the details of that just yet.)
Previously we listed the notes of all the major scales, and now that you know how to figure out the relative minor key of any major key (just take the sixth note of the major scale, or, if you’re feeling lazy, start at the top and go two notes down) and how to construct the natural minor scale (it has the same notes as its relative major, but starts on the major scale’s sixth note), you could construct all of the natural minor scales yourself if you so desired.
You could even go in reverse; if you start with the minor scale, its relative major will be its third note. For example, the third note of the a-minor scale is C, and a-minor’s relative major key is C-major.
Some minor keys are also more equal than others
As you’d expect, you rarely see music written in a-sharp-minor or in a-flat-minor; musicians would rather use five accidentals in the key signature instead of seven, and so they’d generally substitute b-flat-minor and g-sharp-minor respectively. You’d imagine that d-sharp-minor and e-flat minor would be equally common, both having six accidentals in their key signatures, but here the “feel” of the notes comes into play even more than with the relative major scales. D-sharp feels like an “obscure” note to base a scale on, while E-flat feels more ordinary. After all, E-flat is the second flat in many key signatures, and there is even a key of E-flat-major (but no key of D-sharp-major).
Now all this touchy-feely stuff about the six sharps or flats may seem a bit abstract, but yet I can cite a musical example that illustrates exactly this point. It did strike me as odd when I encountered it.
There is a particular piano piece that I have been playing which starts in a minor key and then modulates (changes keys) to the relative major key. This type of key change is not uncommon, and since you know that each major key and its relative minor key have the same key signature, you’d imagine that the key signature would stay the same. Normally you’d be right.
But here’s what happened: the piece started out in e-flat-minor, and then modulated to F-sharp-major! The composer (or whoever notated this music) may have used this logic of the “obscurity” of the notes to make such a choice. It must have seemed better to use e-flat-minor than d-sharp-minor, and similarly better to use F-sharp-major than G-flat-major. But by doing this, the key signature had to change from six flats to six sharps. Had the composer (or copyist) instead used e-flat-minor and G-flat-major, or d-sharp-minor and F-sharp-major, the key signature would not have had to change. (If you must know, the piece is Louis Moreau Gottschalk’s Souvenir de Porto Rico, Opus 31.)
Yet another example: I have the Edition Peters of J. S. Bach’s Well-Tempered Clavier, Book I, and Fugue VIII is notated in d-sharp-minor. But as an appendix, this edition includes another copy of the exact same piece notated in e-flat-minor. I suppose they thought that some people would be uncomfortable having to read music written in d-sharp-minor.