Music Theory/The Physics of Music< Music Theory
The fundamental frequency is the frequency where the entire string vibrates backwards and forwards with two nodes at the ends where the string is tied down. To try this, hold a spring between yourself and a partner and rocking it back and forth steadily until the entire spring sways without being disrupted. This is the fundamental frequency.
In Western music, the primary reference tone is the pitch A above middle C, with a fundamental frequency of 440Hz. In twelve-tone equal temperament, all other tones are related to this pitch according to the formula:
The first overtone (also known as the second harmonic) occurs when the length of a string is halved when the tension and density of the string is unchanged. The frequency of the second harmonic is twice that of the first. The frequency of the third harmonic is three times that of the fundamental and so on.
It is not important to understand all of the physics of this, but it is important to remember that modern music is based of the harmonic series. The further something is from the fundamental on the harmonic series, the less consonant it is said to be. While typically consonant notes are the unison, octave, fifth, sixth, and third and dissonant notes the second, seventh, and tritone, as well as all augmented or diminished intervals, consonance is now considered a relative matter based on the harmonic series and context.