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# Music Theory: a Brief Overview

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In this lesson we'll go a little deeper into the physics of intervals and sound.

Any sound that is pure enough to have one fundamental frequency that it vibrates at can be called a pitch. Pitches are measured in Hertz. A Hertz is how many times per second any given pitch cycles. The lower in sound the pitch is, the lower the number of Hertz; alternately, the higher in pitch, the higher in Hertz.

Suppose you hear a pitch at 110 Hertz (the low open A string on a guitar). Then you hear a pitch at exactly double the first pitch at 220 Hertz (the A on the 12th fret of the A string). This is a ratio of 2 to 1. It is expressed like this, 2:1. Humans hear these two pitches (the second exactly twice the first) in a very special way due to the curvature of the cochlea (a part of the anatomy of our inner ear). These pitches sound very much the same to us. We call this very similar sound an octave.

We then start dividing the octave into smaller units. Finally we wind up with the most convienent and purposeful way of dividing the octave: into 12 equal parts. Guitars and pianos (and most musical instruments) are designed and built with the explicit intention of providing the player with a way of playing notes that are precise interval distances apart.

We then call these 12 equal parts "half steps". Therefore an octave is divided into 12 equal musical distances. They are labelled as such:

• 1 half step (or 1 fret) is a minor second or flat second.

• 2 half-steps (or 2 frets) is a second (sometimes called a major second).

• 3 half-steps (or 3 frets) is a minor third or flat third.

• 4 half-steps (or 4 frets) is a major third.

• 5 half-steps (or 5 frets) is a fourth.

• 6 half-steps (or 6 frets) is a sharp fourth or flat fifth.

• 7 half-steps (or 7 frets) is a fifth.

• 8 half-steps (or 8 frets) is a augmented fifth or minor sixth or flat sixth.

• 9 half-steps (or 9 frets) is a major sixth.

• 10 half-steps (or 10 frets) is a minor seventh or flat seventh.

• 11 half-steps (or 11 frets) is a major seventh.

• 12 half-steps (or 12 frets) is an octave.

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