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There are only 12 notes in a chromatic scale, but clearly there are more notes than this within an octave when all sharps and flats are taken into account. Let's look at why this is.
Sharps and flats
The seven natural notes C to B can be modified with sharps and flats.
As you should already know well, a sharp raises a note by a semitone, and a flat lowers a note by a semitone. However, rather than producing 14 (7 x 2) new pitches, the total number of pitches only increases by 5, for a total of 12, as seen in the chromatic scale:
So what has happened to all of those extra notes?
Some natural notes, when sharpened, sound at the same pitch as the next note above flattened. For example, C sharp sounds at the same pitch as D flat. This is always the case when the interval between the two natural notes is a tone.
Here are all of the five possible cases:
Where the interval between two natural notes is just a semitone, then the sharpening the lower note produces the same pitch as higher tone (without flattening). Similarly, the upper note flattened produces the same pitch as the lower note, without sharpening the lower note.
There are just two cases of this:
These operations also work in reverse - so for example, flattening F produces the same pitch as E, and flattening C produces the same pitch as B:
Therefore, there are a total of just 12 distinct sounding pitches in our musical system, even though there are 21 different notated pitches.
When a pair of notes (for example, E flat and D sharp) are sound at the same pitch, we say that they are the enharmonic equivalent of each other.
Here is the chromatic scale again, this time showing all the 21 pitches - natural, sharp, and flat - and their equivalents, showing that there are just 12 distinct pitches in total:
Double sharps and flats
We discussed double sharps and double flats in Double sharps and flats. These notes, too, have enharmonic equivalents.
As a double sharp raises a note by two semitones, it is enharmonically equivalent to the note that is two semitones above.
For example, F double sharp is enharmonically equivalent to G natural.
Similarly, as a double flat lowers a note by two semitones, it is enharmonically equivalent to the note that is two semitones below.
For example, B double flat is enharmonically equivalent to A natural.
Entire keys can be enharmonic equivalent to each other.
For example, just as C flat is enharmonically equivalent to B natural, so C flat major is enharmonically equivalent to B major. Every degree of C flat major is the enharmonic equivalent to the corresponding degree in B major, as shown here:
Sounding and notated pitches
It is very important to realise that an enharmonic equivalent note is a different note.
Just because two enharmonically equivalent notes sound the same, they are notated differently and therefore must be treated as different notes.
One of the situations when this is of particular importance is when describing intervals. For example, try to describe the following interval. The enharmonic equivalent is shown in small notes:
Let's approach this using the method we have previously used in the "Intervals" series:
- Number: The number of the interval is 2 - there are two notes from B to C - so it is a type of 2nd.
- Quality: B natural to C is a minor 2nd, B flat to C is a major 2nd, and this is one semitone wider, so therefore it is an augmented 2nd.
This is the correct answer, but imagine if you had been confused by the B double flat, and perhaps thought of a piano keyboard, then you might have given the answer for A to C - a minor 3rd - which would be incorrect!
Both intervals sound the same, but one is an augmented 2nd, and the other is a minor 3rd: completely different when notated!
Building on the case of describing intervals, it can be easy to make mistakes with enharmonic equivalents when transposing, particularly if you need to transpose to an enharmonically equivalent key.
Here is a very tricky example. We have been given this short melody in G sharp minor to transpose up by a tone, e.g. for a trumpet in B flat:
The key is G sharp minor, and to transpose up by a tone would take us into the obscure key of A sharp minor: and no trumpet player (or indeed, any player) will thank you for giving them music in A sharp minor to play!
Therefore, it would be better to transpose the music into B flat minor, which is of course an enharmonically equivalent key to A sharp minor (A sharp and B flat are enharmonic equivalents).
We'll need to take this one step at a time:
- Write out the enharmonically equivalent version
- Transpose this version up by a tone
Firstly, let's rewrite the music in A flat minor rather than G sharp minor. Write down each note's enharmonic equivalent, taking special care over the F double sharp. We'll get rid of the key signature entirely and use only accidentals for now:
Now, be careful!
We have not yet done the transposition, even though every note looks to be one step higher, all of these notes sound at exactly the same pitch as the original!
No transposition has yet taken place!
Secondly, then, let's transpose each note up by a tone, taking special care over tricky notes like the C flat. Again, for the moment, we write in every accidental and we won't write in a key signature:
Finally, we write in the correct key signature for B flat minor. We must make sure, however, that any notes not in the key signature are given accidentals! B flat minor has 5 flats, so let's write those in, and watch out for accidentals:
In case you are wondering what the music would have looked like in A sharp minor, here it is - I think you'll agree that the B flat minor version looks much more straightforward!
Are you sure you've understood everything in this study guide? Why not try the following practice questions, just to be sure!