First harmonic
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 T for which the following equation is true:
Where x(t) is the value of the waveform at t. This means that this equation and a definition of the waveforms values over any interval of length T is all that is required to describe the waveform completely.
Every waveform may be described using any multiple of this period. There exists a smallest period over which the function may be described completely and this period is the fundamental period. The fundamental frequency is defined as its reciprocal:
Since the period is measured in units of time, then the units for frequency are 1/time. When the time units are seconds, the frequency is in , also known as Hertz.
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