Obertönenreihe

Obertönenreihe, also known as the harmonic series, is a fundamental concept in acoustics and music. It refers to the sequence of frequencies that are integer multiples of a fundamental frequency. When a string or air column vibrates, it doesn't just produce a single tone; it simultaneously vibrates at its fundamental frequency and at higher frequencies called overtones or harmonics. These overtones are always at frequencies that are whole number multiples of the fundamental.

For example, if the fundamental frequency is 100 Hz, the harmonic series will consist of frequencies at 100 Hz (the fundamental), 200 Hz (the second harmonic or first overtone), 300 Hz (the third harmonic or second overtone), 400 Hz (the fourth harmonic or third overtone), and so on, theoretically infinitely. The relative loudness or amplitude of these overtones is what gives different musical instruments their unique timbres or sound colors. A violin and a flute playing the same note at the same volume will sound distinct because of the different combinations and intensities of their respective overtones.

The harmonic series is crucial for understanding phenomena such as resonance, consonance, and dissonance in music. It also plays a role in signal processing and the analysis of complex waveforms. The mathematical relationship of the harmonic series is based on the principles of vibrating strings and air columns described by physics.