Harmonic Series and Interval Roughness: Plomp-Levelt Consonance Lab

What is the Harmonic Series?

The harmonic series is a sequence of frequencies that are integer multiples of a fundamental frequency. When these harmonics align with specific ratios, they create consonant intervals, which are pleasing to the human ear.

For example, the ratio 2:1 (an octave) and 3:2 (a perfect fifth) are simple harmonic series ratios that produce clear and consonant sounds.

Plomp-Levelt Roughness Model

The Plomp-Levelt model quantifies the roughness of a complex tone, which is perceived as an unpleasant quality due to partial coincidences. This model helps explain why certain intervals are more consonant than others.

According to this model, roughness increases when there are many partial coincidences between two tones, leading to a perception of dissonance.

Simple Ratios and Consonance

Intervals with simple frequency ratios tend to be more consonant because they have fewer partial coincidences. For instance, the perfect fifth (3:2) has only one partial coincidence compared to a minor second (16:15), which can have up to four.

The Plomp-Levelt model predicts that intervals like the octave (2:1), perfect fifth (3:2), and major third (5:4) are consonant because they have fewer partial coincidences, leading to lower roughness.

Real-World Applications

Understanding harmonic series and Plomp-Levelt roughness is crucial for composers, musicians, and audio engineers in creating harmonious music.

This knowledge also aids in the design of musical instruments and digital sound processing systems to ensure that sounds are perceived as consonant and pleasing.

Frequently asked questions

Try it live

Everything above runs in your browser — open Harmonic Series and Interval Roughness: Plomp-Levelt Consonance Lab and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.