Distortion measurements use a Sine Wave source (typically, if not always) as the base tone for measurement. Sine wave is described by the

*sin *trigonometric function over time, deviations from which are easily (if you are a mathematician, which I failed to become) detected and calculated.

Here is a Sine wave calculated and displayed in Audacity, with a fundamental tone of 128Hz

Spectrum

Integer multiples of the fundamental frequency are "harmonic" distortions.

If you blow across the top of a Beer Bottle (or in this case, a Kahlua bottle) the tone generated is

*almost *a pure sine wave. Here is a recording of that:

And Spectrum:

You can see the 128Hz fundamental, and 256Hz 2nd harmonic, and 384Hz 3rd harmonic, then it gets messy as it is recording the whoosh of my breath blowing across the bottle.

The second harmonic is about -40dB, or 1% distortion.

Great! We can easily measure distortion. Using pure tones. Which are relatively uncommon in music.

Voices are not uncommon in music, and I have one of those handy.

Here is mine, trying to make a 128Hz tone:

Ugh... Not very sine-like, though it can be decomposed into a series of sines... Hey, I hit the pitch (fundamental frequency) though. That's good on me.

Spectrum:

The second harmonic is more intense than the fundamental, so, measurement-wise, that's at least 100% distortion. And you can see the series of higher harmonics, musltiples of 128hz trailing off for a while, then it gets too messy to make more sense of.

So...

Music is distortion. Musical instruments get their "tone" from varying levels of harmonic distortion.

How to measure whether what we play is distorted is not so easily determined as the basic THD measurement.

IMD uses two sine tones.

THD + N (noise) adds calculation for sound that is not in the harmonic series.

So, make of that what you want, it's something I know.

I'll show something else in a minute.