Harmonics: Difference between revisions

From Hydrogenaudio Knowledgebase
No edit summary
(Category:Technical)
 
(5 intermediate revisions by one other user not shown)
Line 1: Line 1:
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. ''Bells'' are a common example of instruments with clearly perceptible harmonic overtones.  


'''Example: wavelengths of vibrating strings or overtones are proportional 1, 1/2, 1/3, 1/4, etc in a common Harmonic Series. '''
''Example: wavelengths of vibrating strings or overtones are proportional to 1, 1/2, 1/3, 1/4, etc represented mathmatically as a common Harmonic Series. ''  
<br><br>
<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} + \frac{1}{5}
\cdots + \frac{1}{h} </math>
\cdots + \frac{1}{h} </math>
[[Category:Technical]]

Latest revision as of 21:18, 15 September 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. Bells are a common example of instruments with clearly perceptible harmonic overtones.

Example: wavelengths of vibrating strings or overtones are proportional to 1, 1/2, 1/3, 1/4, etc represented mathmatically as a common Harmonic Series.