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Concept
Fundamental frequency
Summary
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, the fundamental frequency is the lowest frequency sinusoidal in the sum of harmonically related frequencies, or the frequency of the difference between adjacent frequencies. In some contexts, the fundamental is usually abbreviated as 0, indicating the lowest frequency counting from zero. In other contexts, it is more common to abbreviate it as 1, the first harmonic. (The second harmonic is then 2 = 2⋅1, etc. In this context, the zeroth harmonic would be 0 Hz.)
According to Benward's and Saker's Music: In Theory and Practice:
Since the fundamental is the lowest frequency and is also perceived as the loudest, the ear identifies it as the specific pitch of the musical tone [harmonic spectrum].... The individual partials are not heard separately but are blended together by the ear into a single tone.
All sinusoidal and many non-sinusoidal waveforms repeat exactly over time – they are periodic. The period of a waveform is the smallest value of for which the following is true:
Where is the value of the waveform at . This means that the waveform's values over any interval of length is all that is required to describe the waveform completely (for example, by the associated Fourier series). Since any multiple of period also satisfies this definition, the fundamental period is defined as the smallest period over which the function may be described completely. The fundamental frequency is defined as its reciprocal:
When the units of time are seconds, the frequency is in , also known as Hertz.
For a pipe of length with one end closed and the other end open the wavelength of the fundamental harmonic is , as indicated by the first two animations.
Official source
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