Fundamental tone

The fundamental frequency, often referred to simply as the fundamental, is defined as the lowest frequency of a periodic waveform. In music, the fundamental is the musical pitch of a note that is perceived as the lowest partial present. In terms of a superposition of sinusoids (e.g. Fourier series), the fundamental frequency is the lowest frequency sinusoidal in the sum. In some contexts, the fundamental is usually abbreviated as f₀ (or FF), indicating the lowest frequency counting from zero. In other contexts, it is more common to abbreviate it as f₁, the first harmonic. (The second harmonic is then f₂ = 2⋅f₁, etc. In this context, the zeroth harmonic would be 0 Hz.)

All sinusoidal and many non-sinusoidal waveforms are periodic, which is to say they repeat exactly over time. The period of a waveform is the ${\displaystyle T}$ for which the following equation is true:

Where ${\displaystyle x(t)}$ is the value of the waveform at ${\displaystyle t}$. This means that this equation and a definition of the waveforms values over any interval of length ${\displaystyle T}$ is all that is required to describe the waveform completely.

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