Harmonic Series

The harmonic series is the natural pattern of frequencies that vibrating strings (like those on the guitar or in a piano) and air columns (like in your voice or a trumpet) produce. Every sound has a fundamental frequency f, and comes with varying amounts of other higher frequencies that shape its timbre. These frequencies occur at integer multiples of the fundamental f: 2f, 3f, 4f, etc. The frequency ratios between consecutive harmonics correspond approximately to intervals in equal temperament:

• 2:1 = octave
• 3:2 = perfect fifth
• 4:3 = perfect fourth
• 5:4 = major third
• 6:5 = minor third The later an interval appears in the harmonic series the less consonant it sounds. Music theory revolves around describing how we aim to pattern consonance and dissonance intentionally.