Driving Miss Digital

Grandma Moon Speaks: Harmonics

Topics Covered:

  • Harmonic
  • Fundamental Frequency
  • Harmony

I don’t know anything about music. In my line you don’t have to – Elvis Presley

You might be thinking: So far every property we’ve seen about sound is subjective. How do people get a handle on it, then? Especially a mathematical handle.

We get our ‘math fix’ with Harmonics:

A discordant note is a mixture of frequencies that don’t belong together. Somehow, it’s not pleasing to us.

But there are certain families of frequencies that gel well together to form complex tones, like those that produce the effect of timbre. One such family, expressible mathematically, is called Harmonics.

In a complex sound (a periodic waveform), there are many frequencies. The lowest of these is called the Fundamental Frequency.

A Harmonic of this wave is any frequency that is an integer multiple of the fundamental frequency. If the fundamental frequency is f Hz, then harmonics can be 2f, 3f, 4f, etc. Theoretically, there are infinite harmonics.

The cool property of harmonics is that they are always ‘in sync’ with each other, since they are just integer multiples of the fundamental frequency. Imagine square boxes in a warehouse, placed on top of each other and side by side, like a chessboard. No line is broken or out of place. They all ‘line up’.

Now what has all this got to do with anything?

Remember this first: Just because a wave has harmonic frequencies does not mean all its frequencies are harmonics.

Here’s a question to ask yourself: Why are most instruments long or wide? Guitar strings are long. Flutes are long. What’s the story?

When the oscillator (something has to oscillate for sound to appear) is long and thin, many of the frequencies are integer multiples of the fundamental frequency. Such sounds are generally considered to be musically pleasing.

Frequencies that are not integer multiples of the fundamental are inharmonic. Instruments such as cymbals, pianos, and strings plucked are inharmonic sounds. By themselves, inharmonic sounds are not musical. At best one piano note is an ambivalent thing. The same note played on a violin somehow has more depth, if nothing else.

Before you flush with indignation, remember that these are subjective feelings. A lot of this is as mysterious as the Universe itself.

Harmonics is not Harmony, even though they share the same word root. A harmonic is a frequency, a multiple of the fundamental frequency.

Harmony is the use of simultaneous pitches (tones, notes), or chords. Chords are a any harmonic sets of two or more notes that is heard as if sounding simultaneously. There is a relation between harmonics and harmony, but it’s not what it seems to be on the surface.

What history has done, via many cultures and trends, is create properties of sound that overlap each other. Not all of these properties (most of which have their base in music) are scientifically relevant, but are important in the realization of audio for practical filmmaking and audiography.


  • A Harmonic of this wave is any frequency that is an integer multiple of the fundamental frequency.
  • The lowest of the frequencies from an oscillator is called the Fundamental Frequency..
  • Harmony is the use of simultaneous pitches (tones, notes), or chords.

Links for further study:

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