Music theory: Double sharps

WARNING – This post is quite technical, so please only read it if you’re really interested in why I’ve written several double-sharps towards the end of “Do you know where you’re going to?” – otherwise, feel very free to skip this one!

One of the basic building blocks of music is something called an interval – not the bit in a concert where everyone grabs a drink, but the gap between two notes. If you picture a piano keyboard, to travel from one note to the note immediately higher than it (whether white or black) is to go up one semitone. Two semitones make one tone, so to travel from a C to C# is one semitone, and from a C to a D is one tone.

The next important note regards sharps and flats. A sharp raises the pitch of a note by one semitone. A flat lowers it by one semitone. Don’t fall into the trap of thinking of sharps and flats as “the black notes on a piano” – that doesn’t always hold true, as we’ll see later. Just remember that a “something sharp” is the note one semitone higher than the “something”.

We’re going to look at what happens when we play each white note on a piano in turn, starting on C. There aren’t black notes between every white note on a piano, so travelling from each white note to the white note above it doesn’t mean you always go up by a tone. The pattern is below:

  • C to D is a tone (travelling via C# or Db)
  • D to E is a tone (travelling via D# or Eb)
  • E to F is a semitone (there’s no black note between E and F)
  • F to G is a tone (travelling via F# or Gb)
  • G to A is a tone (travelling via G# or Ab)
  • A to B is a tone (travelling via A# or Bb)
  • B to C is a semitone (there’s no black note between B and C)

So, to travel between C and C along the white notes of a piano, the pattern is tone, tone, semitone, tone, tone, tone, semitone. This pattern defines a major scale. Using this pattern starting on C, we play a C major scale.

You can have a major scale beginning on any note, and the pattern is always the same. For example, if you start on D instead of C, the notes look like this:

  • A tone up from D is E (via D# or Eb)
  • A tone up from E is F# (via F)
  • A semitone up from F# is G
  • A tone up from G is A (via G# or Ab)
  • A tone up from A is B (via A# or Bb)
  • A tone up from B is C# (via C)
  • A semitone up from C# is D

So the notes of a D major scale are D, E, F#, G, A, B, C# and D.

A scale must contain every note-name (A, B, C etc) once and only once. That is why, in the D major scale example above, the third note is F#, and not Gb. F# and Gb are the same note, but it wouldn’t make musical sense to use Gb here, because that would mean there was no F of any type, and G would be used twice (Gb and G natural). This is really important when it comes to double-sharps (and double-flats, for that matter).

Before we get to double-sharps, which are a pretty rare and extreme case, let’s look at something which is less rare, but shows an important step along the way. What happens when we start a major scale on F#?

  • We start on F#
  • A tone up from F# is G# (not Ab – it must be a G something)
  • A tone up from G# is A# (not Bb – it must be an A something)
  • A semitone up from A# is B
  • A tone up from B is C#
  • A tone up from C# is D#
  • A tone up from D# is F – but we can’t use F, as it must be an E-something. A sharp merely raises the pitch of a note by one semitone, so we use an E sharp – this is the same note as an F, but we can’t write F as the previous note was D – it has to be an E-something, so it’s an E#
  • A semitone up from E# is F#

This is really important – even though an E# is the same note as an F, we have to have every note-name used once and only once, so we can’t skip D and have two Fs, one natural and one sharp. It would break the rules of music theory.

Of course, F# and Gb are the same note. So could we get around the “problem” of using E# by calling F# Gb? Let’s go through the tone, tone, semitone, tone, tone, tone, semitone pattern and see:

  • We start on Gb
  • A tone up from Gb is Ab
  • A tone up from Ab is Bb
  • A semitone up from Bb is B – hold on, we can’t use B twice – so what do we use instead? It has to be a C-something, as that’s the next note-name up – and B is just one semitone lower than C, so we use a Cb. We’ve got the same “problem” as we have with an F major scale – we have to use a “white” note that is a sharp or a flat.
  • To finish the pattern, a tone up from Cb is Db
  • A tone up from Db is Eb
  • A tone up from Eb is F
  • And a semitone up from F is Gb

Starting on F# or Gb makes no difference – we have to use an E# or a Cb.

At the end of “Do you know where you’re going to?”, we finish in the key of D# major. (There’s a reason I use D# major and not Eb major, which I’ll explain in another blog post if anyone is interested – let me know if you are). Let’s step through the notes of a major scale beginning on D#, using the tone, tone, semitone, tone, tone, tone, semitone pattern we’ve already established.

  • We start on D#
  • A tone up from D# is F – but it has to be an E-something, so we use E#
  • A tone up from E# (or F if it helps you to think of it this way) is… what? G. But it has to be an F-something. It isn’t F#, as this is just a semitone up from E# (F), and we need to be a tone up from there. This is where the double-sharp comes in – G is a tone higher than F, a single sharp raises the pitch of F by one semitone, so a double-sharp raises it by two semitones, which equals one tone. An F double-sharp is the same note as a G.
  • A semitone up from F double-sharp is G#
  • A tone up from G# is A#
  • A tone up from A# is B# (or C, but we have to use B#)
  • A tone up from B# is… D. Again, we can’t use D as it must be a C-something, so we use C double-sharp.
  • Finally, a semitone up from C double-sharp (or D) is D#.

This is why we have some double-sharps at the end of “Do you know where you’re going to?” – we end in the key of D# major, and the notes of D# major are D#, E#, Fx (double-sharp), G#, A#, B# and Cx.

I hope that has proved useful to at least someone – I know it’s rather technical, but the question was asked and I was determined to answer it! If anyone would like more posts explaining the finer points of music theory (like why I used D# major and not Eb major, or what the pattern is for a minor key and why some minor keys are closely related to other major keys), just drop me an email and I’ll happily oblige.

Author: Tim Allen (admin)

Director of BeVox