Inharmonicity, Strike Tones and Intermodulation Distortion
We usually think of harmonics as being pleasant things to hear. They give an instrument its timbre, they provide brightness and clarity.
Don’t know what harmonics are? Go here and read.
Usually the harmonics that our ears like to hear are mathematically related to the fundamental based on whole numbers. Whole numbers: ones and twos and threes. Octaves are a multiple of 2, 4, 8, etc., things like that. Harmonics can be even numbers, but also odd numbers, and harmonics based on 3 or 5 or 7, while they might sound a little wooly, they don’t sound plain old bad. Also, keep in mind that sometimes the math on these things isn’t perfect. It might not be a perfect multiple of 3 but something close, like 2.98, but generally this is good enough.
Inharmonicity
However, there can also be harmonics generated that don’t have any whole number relationship to the fundamental, and these harmonics are usually unpleasant to hear. This is called Inharmonicity — when the harmonics don’t make whole number sense mathematically.
Strike Tones
On many instruments, inharmonicity happens in the strike or the initial attack of the note. Bowed and reed instruments—violins and flutes, as an example, don’t have inharmonicity because they don’t have a fast transient attack. Brass instruments typically have slower attacks as well.
Fast transient attacks, on the other hand, generate a lot of “inharmonic” stuff—lots of non-whole number overtones. On a piano, the initial strike of the hammer generates a lot of inharmonicity, and that strike is basically pitch-less for a split second. It’s only once the string resonates for a moment that we get a sense of the note. The same thing is true of guitars, bells, and especially drums. That initial strike is basically out of tune, and it is the resonance after the strike that conveys a solid sense of pitch.
The faster the attack, the more inharmonicity is generated in that moment. And, by the way, the transient is typically the brightest moment of a note, because it is so rich with harmonics both good and bad.
Actually, the strike of a note is usually very out of tune! Plug a bass into a tuner and watch how the tuner behaves when you slap a note versus using a softer attack with your finger.
Bells are a great example of the inharmonicity of a strike tone. Listen to Hells Bells by AC/DC and the opening bells are out of tune until they resonate. This has to do with their strike tone. I found a great video that explains this, and while most of you won’t ever record church bells, this is fascinating stuff and it will help get the concept of inharmonicity firmly in your mind.
SO.... instruments have inharmonicity in the attack, the strike. But what about gear? Compressors? Amps? Plug-ins?
Intermodulation Distortion
The way equipment and devices, whether analog or digital, create inharmonicity is through Intermodulation Distortion.
Intermodulation distortion is overtones that are way out mathematically from the fundamental. They typically occur when multiple fundamentals mix together in ways that generate, well... non-whole number math. Harmonics are generated that don’t have whole number relationships to the fundamental. Some of these new harmonics might be undertones that happen below the fundamental, and others above. In some cases the products of intermodulation distortion sound good, but the more complex the sounds get, things get really hairy quickly.
Remember that an instrument, unless it’s like a flute or something with a very simple timbre, already has a lot of overtones to it. A human voice has an incredibly complex series of overtones, so complex that virtually every person has a unique set, which is why we can recognize someone’s voice even if they just clear their throat. So there’s this ton of harmonic activity, then there’s harmonic distortion added to it, and all of those fundamentals AND harmonics have additional harmonics added to them, and then intermodulation distortion kicks in, and ALL those fundamentals AND harmonics AND additional harmonics start negatively reacting with each other adding in yet more harmonics that have bad math going on.
This is the distortion you hear when you crank up guitar amps, or slam things through the mix bus and drive it into clipping.
Here’s a nice, non-technical video on it that makes a lot of sense. You’ll hear why intermodulation distortion can be a huge issue.
Quick Takeaways
Some things to take away from all this.
- Strike tones are out of tune and bright.
- Intermodulation Distortion gets worse and more noticeable as the sounds interacting with each other become more complex. It’s hard to get a flute to exhibit any intermodulation distortion. It’s easy to get a full mix to sound awful with even a little intermodulation distortion.