Intermodulation Distortion
Why power chords sound great but more complex chords sound muddy through distortion
Selected interval: Power chord interval. Notice how f₂-f₁ creates a tone one octave below the root.
What is Intermodulation?
When two or more frequencies pass through a nonlinear system (like a distorted amplifier), the system generates new frequencies that were not present in the input, specifically at the sums and differences of the original frequencies. This phenomenon is called intermodulation distortion and is present in domains ranging from radio engineering to audio processing.
Input: f₁ and f₂
↓ nonlinear system ↓
Output: f₁, f₂, (f₂-f₁), (f₁+f₂), 2f₁, 2f₂, (2f₁-f₂), (2f₂-f₁), ...
The red terms are intermodulation products. They exist only because of the nonlinearity. A perfectly linear amplifier would output only f₁ and f₂.
The Math: Why Nonlinearity Creates New Frequencies
Consider two sine waves added together: sin(f₁t) + sin(f₂t). When this passes through a nonlinear function (like soft clipping), the output contains terms involving products of the input.
Using the trigonometric identity:
sin(A) × sin(B) = ½[cos(A-B) - cos(A+B)]
When nonlinearity creates terms like sin(f₁t) × sin(f₂t), you get frequencies at (f₁-f₂) and (f₁+f₂).
Higher-order nonlinearities (from stronger clipping) create higher-order products: 2f₁±f₂, 2f₂±f₁, 3f₁±f₂, etc. More gain means more prominent intermodulation tones.
Why Power Chords Sound So Heavy
A power chord consists of a root and a fifth. The frequency ratio of a perfect fifth is 3:2 (or 1.5). Let's call the root f₁.
Power Chord Intermodulation
Root: f₁ = 100 Hz (example)
Fifth: f₂ = 150 Hz (1.5 × f₁)
Difference: f₂ - f₁ = 50 Hz = one octave below root
Sum: f₁ + f₂ = 250 Hz = 2.5 × f₁ (major third above octave)
The difference tone (f₂-f₁) is exactly one octave below the root. This is a musically consonant interval that reinforces the fundamental, making it sounds thicker and more powerful. This is like having an octave pedal built into the distortion itself, which is why power chords are so effective at high gain levels!
Try it: In the simulation above, select "Perfect Fifth" and increase the gain. Watch the f₂-f₁ bar appear. This is the sub-octave that thickens the sound.
Why Full Chords Sound Muddy with Distortion
A major chord has three notes: root, major third, and fifth. The major third has a ratio of 5:4 (1.25). Now you have three frequencies generating intermodulation products with each other.
Power Chord (2 notes)
Intermodulation products:
- f₂-f₁ (octave below root) ✓
- f₁+f₂ (consonant)
- 2f₁-f₂, 2f₂-f₁ (related tones)
All products are musically related
Major Chord (3 notes)
Intermodulation products:
- f₂-f₁, f₃-f₁, f₃-f₂
- f₁+f₂, f₁+f₃, f₂+f₃
- 2f₁-f₂, 2f₁-f₃, 2f₂-f₁...
- Many more combinations
Dense cluster of dissonant frequencies
With three notes, you get intermodulation products between every pair. Many of these fall at non-harmonic frequencies that clash with the chord tones, creating a muddy, indistinct sound.
Genre Implications: Why Metal Uses Power Chords and Jazz Uses Clean Tones
High gain = power chords and single notes
Metal and hard rock guitarists use power chords specifically because they sound clear through heavy distortion. Complex chords are reserved for clean or lightly overdriven tones.
Less gain for chord clarity
Blues and classic rock players use moderate overdrive that allows for fuller chords while still adding harmonic richness.
Dissonance as an effect
Some genres intentionally use the muddy intermodulation of close intervals (like minor seconds) for aggressive, chaotic textures.
Summary
- Nonlinear systems (distortion) create new frequencies at sums and differences of input frequencies
- Power chords (root + fifth) produce intermodulation at one octave below the root, which sounds musical
- Complex chords produce many intermodulation products that clash and sound muddy
- Higher gain means more intermodulation, so heavy distortion demands simpler note choices