The Physics Underlying Harmony

Harmony and Harmonics

What does the Overtone Series Sound Like

Here is an audio clip of the first 13 overtones based off a starting frequency of 100 Hz, played them all consecutively at the same volume:


At the end I played all thirteen notes at once; notice how they fuse into a harsh, saw-tooth-like tone, that has a low frequency of 100 Hz.

The Harmony in the Harmonic Series

If I start with a given frequency x (like 100 Hz above), the frequency of the second harmonic is 2x, the third 3x, the forth 4x, etc.  If I play them all at the same time, I get the ratio x:2x:3x:4x:5x:6x... which becomes 1:2:3:4:5:6... Notice how inside this unending ratio I get all of the simple frequencies, in order of how consonant they are:

Also notice how right in the beginning we get 3:4:5, the major chord, right out of the harmonic series.  Also, since an octave is so consonant, when two notes are separated by an octave (that is, their frequencies are a multiple of 2 or 1/2) in a chord we treat them as if  there was only one of them, as they blend together.  Using this rule, the first 6 harmonics are just a major chord.  In this sense, each individual note that follows the harmonic series is, in a strange way, a chord unto itself.

Playing the Harmonic Series

If I attempt to play the harmonic series on a piano out, I run into a few problems; Western music doesn't have a note that corresponds to the seventh harmonic, meaning that I have to play the nearest note or play the nearest two notes at once to emulate it, Thelonious-style. I also have this problem with the 13th overtone.  Nevertheless, one of the advantages of playing the harmonic series out on an instrument is that since each note is already a harmonic series, it is easier to differentiate the harmonies between:


If I take the first 9 harmonics and I use the rule where notes that are an octave apart are effectively the same thing, I end up with what's known as the pentatonic scale, which is the most common scale in music around the world; Western music is based off a scale called the major scale, which itself is just the pentatonic scale with 2 extra notes added in:

Here, I play the first 9 harmonics moved via octaves to the same region, and then play the pentatonic scale, and then the major scale.

Now, when people started using scales and harmonies to make music, they had not a clue about how any of this works; but due to the way that sound physics work, they ended up using the harmonies and notes that are mathematically the simplest.  It is in this way that harmony itself is a derivative of the physics and mathematics.

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