Definition of the Harmonic Series
The harmonic series in music theory refers to a sequence of tones produced by a vibrating source, such as a string or air column, where each subsequent tone has a frequency that is an integer multiple of the fundamental frequency. The fundamental is the lowest frequency, and the higher frequencies are called harmonics or overtones, starting from the second harmonic as the first overtone.
Key Principles and Components
The series begins with the fundamental (1st harmonic), followed by the octave (2nd harmonic), the perfect fifth above that (3rd harmonic), another octave (4th), and so on. These ratios—such as 2:1 for octaves and 3:2 for fifths—form the basis of just intonation and explain why certain intervals sound consonant. The series is infinite but diminishes in intensity with higher harmonics.
Practical Example
Consider a guitar string tuned to A (fundamental frequency 110 Hz). The second harmonic is 220 Hz (A one octave higher), the third is 330 Hz (E, a perfect fifth above), and the fourth is 440 Hz (A two octaves higher). When played open, the string naturally produces these partials, which blend to create the instrument's timbre.
Importance and Applications
The harmonic series is crucial for understanding consonance and dissonance, tuning systems like equal temperament, and instrument design. It influences chord voicings, orchestration, and why major triads align with early harmonics, providing a natural foundation for Western music harmony and acoustics.