Musical Intervals & Frequency Ratios - Interactive Visualization

What are Musical Intervals?

A musical interval is the distance between two pitches. When two notes are played together, they create a consonance or dissonance depending on their frequency ratio. Simple ratios (like 2:1, 3:2, 5:4) produce consonant, pleasant sounds, while complex ratios create more dissonant sounds.

Just Intonation vs Equal Temperament

Just intonation uses pure frequency ratios from the harmonic series (3:2, 5:4, etc.) for perfectly consonant intervals. However, this makes modulation between keys difficult. Equal temperament divides the octave into 12 equal semitones, allowing modulation but slightly compromising the purity of intervals (except the octave).

The Harmonic Series

When a note is played, it doesn't just produce its fundamental frequency. It also produces overtones at integer multiples: f, 2f, 3f, 4f, etc. These harmonics give each instrument its unique timbre and explain why certain intervals sound consonant—their harmonics align.

Real-World Applications

• Music Theory: Understanding intervals is fundamental to melody, harmony, and chord construction in all musical traditions.
• Instrument Design: Piano and fretted instrument manufacturers use equal temperament calculations to position strings and frets.
• Tuning Systems: Different cultures and historical periods use various tuning systems (just intonation, meantone, well temperament, etc.).
• Audio Engineering: Understanding harmonics helps with EQ, compression, and avoiding phase cancellation in mixing.
• Choral Singing: Professional singers often drift toward just intonation for purer harmonies, even when starting from equal temperament.

Listening Guide