Look at this piano keyboard. We’ve written the note names on the white keys. Do you notice how the note names repeat as you go up and down the keyboard?

Have you ever wondered:

Why do the names of notes A, B, C, D, E, F and G repeat?

How can 2 different notes be called the same? Isn’t that a bit confusing?

Why do we have just 7 note names A, B, C, D, E, F and G?

These are all very good questions. The answer is down to mathematics and physics!

So let’s explore these questions further and find out all about musical intervals and scales.

The reason why the note names repeat is that there is a very close harmony between notes with the same name.

For example the note produced by pressing the middle A on the keyboard above is vibrating twice as fast as the note produced from the A on the left. We call this interval an octave. See our page on Musical intervals.

The note produced by pressing the A on the right of keyboard above is vibrating twice as fast as the note produced from the A in the middle and 4 times as fast as the produced by pressing the middle A on the keyboard above is vibrating twice as fast as the note produced from the A on the left.

See our page on Harmonics for more on this.

So why are there 7 notes?

Well, in fact if you look at a piano keyboard there are more than 7 notes.

There are the 7 white notes: A, B, C, D, E, F and G, but there are also 5 black notes between the white ones.

The black notes are named after the white notes either side of them, but with the word “sharp” or “flat” added. For example, the black note between A and B is called either “A sharp” (written A#) or “B flat” (written B♭). This is because it is a little higher in pitch, or sharper, than A, and a little lower in pitch, or flatter, than B.

Altogether there are 12 different notes that repeat as you travel along the keyboard and get higher in pitch (count them!).

But why these 12 notes? Why not more than 12, or less?

Well, there is a very good reason, and it isn’t just because some ancient musician thought 12 was a good number!

It turns out the 12 notes are all related to one another! Let’s see how…

We now know that the note A and the A an octave higher are related because the higher one is vibrating twice as fast as the lower one, but are there any mathematical relationships between the notes in between?

Well, yes there are!

Musical notes sound good together if their vibrations are closely matched, like the low A and the higher A, where the mathematical ratio between them is 2:1 (2 to 1). The next best ratio is 3:2 (3 to 2) where every 3 vibrations of the higher note last as long as 2 vibrations of the lower note, i.e. the higher note is vibrating 1.5 (one and a half) times as fast.

If our lower note is A, and we play a note that vibrates 1.5 times as fast, we get the note E, which is the fifth note in the musical scale of A!

So it turns out that the notes A and E are mathematically related by the ratio 3:2. This close mathematical relationship makes the 2 notes sound pleasant when played together. They are “in harmony” – see also our page on Harmonics.

What about the other notes?

Well we started with the note A and we found that a note vibrating 3/2 times as fast is an E.

If we start with E, then the note vibrating 3/2 times as fast is B. If we continue with this we will find all 12 notes before we get back to A.

Now read our page on The Circle of Fifths

Return to Introduction to Music

Return to An Introduction to Brass Music