Harmonics: Difference between revisions
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Harmonics are vibrations at frequencies that are multiples of the fundamental. They are characterized as even-order and odd-order harmonics. For instance, the "second-order harmonic" is the fundamental [[frequency]] multiplied by two, and is an even-order harmonic. Each even-order harmonic is one octave or x octaves higher than the fundamental; they are therefore musically equivalent to the fundamental frequency. Odd-order harmonics create a series of notes that are musically related to the fundamental [[frequency]]—unparallel but resonant with the fundamental, they inform musical scales and give rise to Chords. Non-integer harmonics are also called "overtones" or "partials". Overtones and partials give rise to the timbre ''(tone quality)'' of a particular instrument. | Harmonics are vibrations at frequencies that are multiples of the fundamental. They are characterized as even-order and odd-order harmonics. For instance, the "second-order harmonic" is the fundamental [[frequency]] multiplied by two, and is an even-order harmonic. Each even-order harmonic is one octave or x octaves higher than the fundamental; they are therefore musically equivalent to the fundamental frequency. Odd-order harmonics create a series of notes that are musically related to the fundamental [[frequency]]—unparallel but resonant with the fundamental, they inform musical scales and give rise to Chords. Non-integer harmonics are also called "overtones" or "partials". Overtones and partials give rise to the timbre ''(tone quality)'' of a particular instrument. | ||
'''Example: wavelengths of vibrating strings or overtones are proportional 1, 1/2, 1/3, 1/4, etc. | '''Example: wavelengths of vibrating strings or overtones are proportional 1, 1/2, 1/3, 1/4, etc in a common Harmonic Series. ''' | ||
<math>\sum_{h=1}^\inf \frac{1}{h} = | <math>\sum_{h=1}^\inf \frac{1}{h} = | ||
1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + | 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + | ||
\cdots + \frac{1}{ | \cdots + \frac{1}{h} </math> | ||
Revision as of 17:41, 18 January 2006
Harmonics are vibrations at frequencies that are multiples of the fundamental. They are characterized as even-order and odd-order harmonics. For instance, the "second-order harmonic" is the fundamental frequency multiplied by two, and is an even-order harmonic. Each even-order harmonic is one octave or x octaves higher than the fundamental; they are therefore musically equivalent to the fundamental frequency. Odd-order harmonics create a series of notes that are musically related to the fundamental frequency—unparallel but resonant with the fundamental, they inform musical scales and give rise to Chords. Non-integer harmonics are also called "overtones" or "partials". Overtones and partials give rise to the timbre (tone quality) of a particular instrument.
Example: wavelengths of vibrating strings or overtones are proportional 1, 1/2, 1/3, 1/4, etc in a common Harmonic Series.
