In a few pieces of music I have read through, I have come across double-sharps and flats.
To my understanding, they are two semitones above/below the note indicated. What is, then, the point of these notations?
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These are also known as augmented and diminished notes, respectively. Often it has to do with altering notes in a key that are already sharpened or flattened, such as a harmonic minor in a key where the 7th is a sharp. You could write F## (or Fx) as a G, but then your scale would have no F note in it but two different G's. Every time you put down an G note, you'd have to attached a sharp or natural to indicate which note is to be played. It's clearer to have an Fx and a G# than to have a G and a G#. And some will insist that every scale should have one of each letter-note. I also suspect than in just intonation there's a difference between an augmented note and what would be the equivalent note in equivalent temperament (i.e., Fx is not actually the same sound/frequency as G). This answer to another question does a good job of explaining that. |
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It's spelling. It's like "hear" vs. "here". You wouldn't write "Come over hear so I can here you better" even though it sounds the same. A major triad is spelled as if the notes are a certain distance apart. On the staff the notes will be on three lines or three spaces. In the key of C sharp minor, the tonic chord is C sharp, E, G sharp. You write it as C E G without the sharps because the sharps are already in the key signature. To turn it into a major chord you write C , E sharp, G -- not C, F natural, G. Now suppose you're in B major. The third note of the scale is D sharp. To build a minor chord on D sharp you write D, F, A (which you play as D sharp, F sharp, A sharp because of the key signature). Now to make it a major chord you write D, F double-sharp, A. There are times when you might write D sharp, G natural, A sharp when the chord has a different meaning. It has the same notes but it's functioning as something other than a major triad because of the chords that come before and after it. Again, it's like "here" vs. "hear". |
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The flat or sharp symbols (not yet considering double-sharps and double-flats, we'll get to that) are used for two purposes:
It's in the latter case you encounter double-sharps and double-flats. Consider the case of D major: F♯ and C♯ are notes in the scale (the third degree and seventh degree respectively). This is an example of the first type. But if you augmented the 5th in D major, you'd write it A♯. This is an example of the second type. NOTE that you couldn't write an augmented 5th in D major as B♭ because the fifth is an A and you're raising that one semi-tone. When you raise or lower a diatonic note, it keeps its letter name. Now say you were augmenting the third. The diatonic note is already marked with a sharp, so you have to use a double-sharp to indicate it's raised a semi-tone. Hence it becomes In B major, with its diatonic notes: B C♯ D♯ E F♯ G♯ A♯, if you needed to augment the 2nd, 3rd, 5th, 6th or 7th degrees, you'd use a double sharp. NOTE if you need to augment the B or E you write them B♯ and E♯ and NOT C or F. If the diatonic note is already flat; the diminishing by a semi-tone would require a double-flat. If a diatonically sharp note is to be diminished or a diatonically flat note to be augmented, you typically explicitly use the natural symbol ♮. For example, a diminished fifth degree in B major would be F♮. |
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(G would be incorrect as that would be a fourth in D major, not an augmented third; similarly a diminished fourth in D major would be G♭ not F♯)
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It's all about conventions. It would sound pretty awkward to say that the major key of G sharp has both natural G and G sharp, don't you think? It's also done to make obvious when there's a foreign note to the current scale (say, a natural B in a C sharp major key). It's might be used by composers to point out certain tonal (diatonic or chromatic) relationships. For example, C sharp is "closer" to E double-sharp than to F. That way, composers can make any modulation into E double-sharp and then, by enharmony go to the "distant" F. There's even some documented music theory about how to write the chromatic scale correctly based on the current key signature. |
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