Tutorial: Music theory basics
So far we've learned how to construct major and minor scales using patterns of whole and half steps. At this point it is important to know that each of the letters A to G can and should occur only once in a scale. So we cannot have a C as well as a C♯ or decide to skip the C altogether. In the examples given so far, this works out pretty well. Unfortunately, this is not always the case and we'll need to start looking at flat notes.
Sharps and flats, for real this time
We now know which pattern of whole and half intervals we need to use to find the notes in the natural major (W W H W W W H) or natural minor scales (W H W W H W W). Let's try this once more for G minor:
G minor
G G♯ A A♯ B C C♯ D D♯ E F F♯ G
This results in the notes G, A, A♯, C, D, D♯ and F, but this clashes with the rule we've just learned. We cannot have an A as well as an A♯ in there. Nor can we have a D and a D♯. Last but not least, we're missing the B and E in this scale.
To solve this problem, instead of using sharp notes, we're going to use flat notes.
G minor
G A♭ A B♭ B C D♭ D E♭ E F G♭ G
We end up having G, A, B♭, C, D, E♭ and F. Now we're good on our rule again. What's important to note is that a single scale never mixes flats and sharps. You use either flats or sharps, never both.
How many sharps and how many flats?
In most of the examples so far we've seen the use of sharps and flats in our scales. We constructed the scales by taking half or whole steps starting at the root. There is another way to construct these scales which may be easier to memorize and quicker to apply. We now know that a scale consists of each of the A, B, C, D, E, F and G notes, some of which are sharp or flat. If, for each scale, we know which notes should be sharp or flat, we immediately know which notes belong to a scale. Take a look at the following list. It shows the relative major and minor keys on a single line (they share the same notes) followed by which notes in their natural scales are sharp or flat.
C major / A minor : no sharps/flats G major / E minor : F♯ (1 sharp) D major / B minor : F♯ C♯ (2 sharps) A major / F♯ minor : F♯ C♯ G♯ (3 sharps) E major / C♯ minor : F♯ C♯ G♯ D♯ (4 sharps) B major / G♯ minor : F♯ C♯ G♯ D♯ A♯ (5 sharps) F♯ major / D♯ minor : F♯ C♯ G♯ D♯ A♯ E♯ (6 sharps) C♯ major : F♯ C♯ G♯ D♯ A♯ E♯ B♯ (7 sharps) F major / D minor : B♭ (1 flat) Bb major / G minor : B♭ E♭ (2 flats) Eb major / C minor : B♭ E♭ A♭ (3 flats) Ab major / F minor : B♭ E♭ A♭ D♭ (4 flats) Db major / Bb minor : B♭ E♭ A♭ D♭ G♭ (5 flats) Gb major / Eb minor : B♭ E♭ A♭ D♭ G♭ C♭ (6 flats)
So basically, when we want to know the notes for, say, A major, we see that it has three sharps (F♯, C♯ and G♯). This means that the scale of A major consists of the notes A, B, C♯, D, E, F♯ and G♯. Similarly, D minor has only one flat (B♭) so the notes in D minor are: D E F, G, A, B♭ and C.
One thing we can clearly see here is that when the number of flats or sharps increase, it's the same notes that are sharp or flat but we add another note to that list. For instance, the scale of E major has the same sharp notes as A major but with an added D♯. This means that if we can memorize the scales in the order of number of sharps or flats, as well as the order in which sharps and flats themselves are added, we've memorized all of these scales. Here's some stuff to remember:
Major scales ordered by number of sharps: C G D A E B F♯ C♯ Major scales ordered by number of flats: C F B♭ E♭ A♭ D♭ G♭ Minor scales ordered by number of sharps: A E B F♯ C♯ G♯ D♯ Minor scales ordered by number of flats: A D G C F B♭ E♭ Order of adding sharps: F♯ C♯ G♯ D♯ A♯ E♯ B♯ Order of adding flats: B♭ E♭ A♭ D♭ G♭ C♭ F♭
It's quite a bit to remember but there are some mnemonics to help you remember these orders. Like "Father Charles Goes Down And Ends Battle" for the order in which sharps are added. The order for flats is the exact opposite ("Battle Ends And Down Goes Charles' Father"). Maybe you can come up with some of your own.
E♯? C♭? Say what now?
One confusing point that we need to address before continuing is the mention of the E♯, B♯, C♭ and F♭ notes. Earlier, we found that these notes do not exist. An E♯ is an E increased in pitch by a semi-tone, which makes it the same as an F. The interval between the E and F was just half a step (a semi-tone) in our chromatic 12-note scale. Similarly, the F♭ is an F decreased by a semi-tone which makes it the same as an E. The same can be said about B♯ being a C and C♭ being a B.
We have also learned that each letter (A to G) can occur only once in a scale. If you look at the scale of F♯ major, you'll notice that it has an F♯ but also an E♯. We cannot call the E♯ an F because then we'd have both the F and F♯ in our scale. The only way to get around this problem is to do a little dirty and refer to the F we want as E♯. To show you that this eventually ends up working correctly, I'll show the whole/half step pattern for F♯ major.
F♯ major
F♯ G G♯ A A♯ B C C♯ D D♯ E E♯ F♯
But what about switching to flats? That is worth a try, but because a single scale cannot mix both sharps and flats, we will be calling our scale G♭ and not F♯. Below is the scale of G♭ major:
G♭ major
G♭ G A♭ A B♭ B C D♭ D E♭ E F G♭
As you can see we run into the same problem. G♭ has both a B and a B♭ in it which is why the B in the scale of G♭ major is referred to as a C♭.
This whole thing raises another interesting question. Are F♯ major and G♭ major basically the same scale? We're playing the same notes (or rather, we're playing the same keys on the piano or the same frets on the guitar) we're just calling them slightly different. So in that sense, yes, they are the same, which is something that becomes a little clearer when we look at the Circle of Fifths.