User:Em: Difference between revisions

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The mathematical formula for the harmonic series is simple: each positive-integer multiple of the fundamental frequency represents one overtone. For example, if the fundamental frequency is 100Hz, the partials, in ascending order, will be 100Hz, 200Hz, 300Hz, 400Hz, etc...

Because frequency is exponential, the linear relationship between each partial (as demonstrated in the above example) results in partials becoming increasingly dense/close together (like the frets on a guitar). An octave represents a doubling in frequency: If the fundamental is, again, 100Hz, its first octave will be at 200Hz, the second one at 400Hz, the third at 800Hz, etc. ~~The~~ number of partials will double with each consecutive octave. For more information on the exponential nature of frequency, see [[Hertz]].

Because frequency is exponential, the linear relationship between each partial (as demonstrated in the above example) results in partials becoming increasingly dense/close together (like the frets on a guitar). An octave represents a doubling in frequency: If the fundamental is, again, 100Hz, its first octave will be at 200Hz, the second one at 400Hz, the third at 800Hz, etc. With a new partial at every interval of 100Hz, the number of partials will double with each consecutive octave. For more information on the exponential nature of frequency, see [[Hertz]].

===Musical Intervals As Ratios===

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 The mathematical formula for the harmonic series is simple: each positive-integer multiple of the fundamental frequency represents one overtone. For example, if the fundamental frequency is 100Hz, the partials, in ascending order, will be 100Hz, 200Hz, 300Hz, 400Hz, etc...
-Because frequency is exponential, the linear relationship between each partial (as demonstrated in the above example) results in partials becoming increasingly dense/close together (like the frets on a guitar). An octave represents a doubling in frequency: If the fundamental is, again, 100Hz, its first octave will be at 200Hz, the second one at 400Hz, the third at 800Hz, etc. The number of partials will double with each consecutive octave. For more information on the exponential nature of frequency, see [[Hertz]].
+Because frequency is exponential, the linear relationship between each partial (as demonstrated in the above example) results in partials becoming increasingly dense/close together (like the frets on a guitar). An octave represents a doubling in frequency: If the fundamental is, again, 100Hz, its first octave will be at 200Hz, the second one at 400Hz, the third at 800Hz, etc. With a new partial at every interval of 100Hz, the number of partials will double with each consecutive octave. For more information on the exponential nature of frequency, see [[Hertz]].
 ===Musical Intervals As Ratios===