Intermodulation — why chords mush

Single notes through heavy distortion sound glorious. Full chords through the same pedal can collapse into a fighting, beating mess — “mush”. The mechanism has a name, intermodulation, and once you see it you can predict which intervals survive a given amount of dirt. The Chord Roughness chart measures it; this page explains it.

One note versus two

Distortion is a nonlinearity: output is a bent function of input. Feed a bent function one note and you get that note’s harmonics — musically related overtones, all multiples of the same frequency. That’s the pleasant kind of new content.

Feed it two notes at once and something extra happens: the bending multiplies the notes against each other, creating combination tones at the sums and differences of their frequencies (and of their harmonics’ frequencies). Play E3 (165 Hz) and G♯3 (208 Hz) — a major third — and the pedal invents tones at 43 Hz (the difference), 373 Hz (the sum), 122 Hz, 251 Hz, and on up the ladder. Almost none of those are notes in any key you’re playing. That inharmonic undergrowth is the mush.

▶ Hear this in PedalScope

Why fifths survive and thirds don’t

The intermodulation products of an interval land in tune only when the two notes’ frequencies form a simple ratio:

• A perfect fifth is 3:2. Its products (differences, sums, and their harmonics) land on multiples of a common fundamental one octave below the low note — musically, the products reinforce the chord. This is why a power chord (root + fifth) through a wall of gain sounds huge and coherent instead of dirty.

• A major third (5:4) generates products a musical third-party everywhere — near notes, but not on them, with slow beating between close neighbors. The ear reads that beating texture as roughness.

• Anything more complex (minor seconds, extended voicings) fares worse in proportion.

The practical rule every metal player discovers empirically: the dirtier the tone, the simpler your intervals want to be. Now it’s a measured rule — the app’s two-tone measurement drives your pedal with an interval and reports exactly how much energy lands outside it.

A method note falls out of the same arithmetic. When the ratio is simple, different recipes land on the same frequency — on an exact perfect fifth the third-order 2f2−f1 falls exactly on 2f1 — so a bin’s label names the lowest-order recipe that reaches it, not necessarily the one carrying the energy. That is why the app does not play the exact 3:2: the two notes are placed on an analysis lattice chosen so that no two recipes share a bin and none sits close to another, at the cost of a few cents on each note — the whole method is on How Chord IMD is analyzed. Records made before that lattice existed still carry the coincidences, and the measurement guards its second-order readings with a partner check built on the physics: pairs like f1+f2 / f2−f1 and 2f1 / 2f2 come from one shared coefficient, so their relative levels are fixed (after correcting for the tone balance). A member standing several dB above what its partner licenses is flagged and drawn faint — whether the intruder is low-frequency rumble in a difference-tone bin or a higher-order product on a coincident frequency, the bin is carrying something its second-order label doesn’t describe.

What to do with it

• Voice for the gain. At high drive, prefer roots, fifths, octaves; save thirds for lower-gain passages or higher registers (products fall further from the notes when the notes are further apart in Hz).

• Compare pedals on chords, not just leads. Two pedals with similar single-note harmonic recipes can differ sharply in two-tone behavior — that difference is the one your rhythm sound lives with.

• Hear it isolated. The Chord Roughness page’s Hear-it panel can play the products alone — the sound of everything the pedal invented — and the chord with the products removed, which is roughly what a perfectly polite pedal would do.

▶ Feed the virtual hard clipper a third vs. a fifth in Simulation mode