What is an octave?

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Why are different frequencies treated the same?

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They aren’t treated the same. An octave relationship is a very simple doubling of the frequency. To our ears, notes with simple multiples 2x, 3x, 4x etc share a similar tonal quality.

This is because many thing that vibrates to produce sounds (musical instruments etc) will make the loudest sounds at their resonant frequency and simple multiples of that resonant frequency. Our ears are “trained” to hear them as similar and in music we name this relationship as octave relationships.

In short, the idea of an octave comes from how humans perceive (natural) sounds. The sound came first, then our ideas behind naming it second.

An octave is a range of frequencies that span exactly one doubling of the frequency. In western musical notation it is divided into 12 semi-tones.

In practice this means that for example every 12th key on a piano keyboard represent the same tone just shifted up or down one or more octaves

Because of the way our brains and ears work were perceive these different sounds as being somehow the same.

If you double the frequency and move up an octave, you half the wavelength and get exactly two waves in the same space as the lower frequency one.

A wave with twice the frequency but in synch with a lower one will hit all the same peaks as the lower frequency waves making it sound to out ears and interpreted by our brains as being sort of the same.

I feel like an idiot, but isn’t an octave 8 notes? Or is this something else? Be gentle with me.

The reason they’re treated the same is because they generally affect our ears in a very similar way.

Most things that make sounds don’t make a single note, but a series of them. When you play middle C on the piano, the string vibrates in a complicated way that produces a series of notes at different frequencies. These extra notes, called overtones, have frequencies that are multiples of the original. So we get a note that is double the frequency, triple the frequency, four times, five times, etc. The exact amount of these extra notes is what gives the piano a particular tone. Different instruments have different balances of these extra frequencies blending together, which is why a piano and a saxophone sound totally different. It’s the same with vowels: we can tell the difference between an Aaaaah, and an Eeeeee because they have different amounts of overtones.

Now, an octave is just the name we give to a note that has double the frequency. The reason we use the same letter name is because it can be tricky to tell them apart. If you play middle C and C one octave up, it can be really difficult to notice the higher note. Instead of sounding like a different note, it almost sounds like it just changes the tone of middle C. This is because you’re pretty much just altering how much of each of those overtones you’re getting. Because they sound so similar, we decide that it makes more sense to label them as a family of the same note.