The Common Tone · Chapter 1.8
A2 + E3
Plots measure the audio files above. Close peaks can merge at this scale.
Choose a fifth or add a major third; compare the clean and distorted sound. Changing a sound setting stops playback. Help does not.
These are generated sine tones, not a recording of a guitar or a simulation of a complete amplifier. The same combined input RMS (0.20 full scale) is used for both note sets, so each individual note is quieter when the third is added.
The model is biased soft saturation: y = tanh(drive × (x + 0.15)) − tanh(drive × 0.15). Mild uses drive 1.5; Strong uses 5. It can create both harmonics and intermodulation products. A different distortion circuit can produce a different balance.
The audio was generated at 384 kHz, filtered, and saved at 48 kHz. Clean and distorted clips are matched to steady RMS 0.10; perceived loudness may still differ. Both waveforms share the same amplitude scale.
The waveform is a fixed 40 ms excerpt at 1 second. The spectrum is a 65,536-sample Hann FFT starting at 0.75 seconds, with amplitude referenced to a full-scale sine peak (0 dBFS). Products within about 3 Hz merge here. This display cannot establish equivalence, or resolve all the differences, between equal temperament and just tuning. Coincident peaks may have several contributing causes.
Both a just fifth and a just major third have a shared harmonic basis. The comparison is an experiment, not a rule that thirds always sound bad. Register, tuning, voicing, source sound and the distortion model all matter.
Measured static figure · Audio provenance and measurements
Technical references: Amp Books: plotting intermodulation; Laguerre & Scavone, DAFx 2021. The simplified model here is original, not their amplifier model.