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# Harmonics and Fourier Series [Solved!]

### My question

From my knowledge gleaned from 10 years of music theory:

If cos(omega t-phi_1) is the fundamental, then wouldn't the term cos(2omegat-phi_2) be correctly designated as the FIRST harmonic?

### Relevant page

5. Harmonic Analysis

### What I've done so far

Many years of learning and using this stuff

X

From my knowledge gleaned from 10 years of music theory:

If cos(omega t-phi_1) is the fundamental, then wouldn't the term cos(2omegat-phi_2) be correctly designated as the FIRST harmonic?
Relevant page

<a href="/fourier-series/5-harmonic-analysis.php">5. Harmonic Analysis</a>

What I've done so far

Many years of learning and using this stuff

## Re: Harmonics and Fourier Series

Hi Ken

Thanks for the comment. This table comes from Wikipedia:

1f 440 Hz  fundamental      first harmonic
2f 880 Hz  first overtone   second harmonic
3f 1320 Hz second overtone  third harmonic
4f 1760 Hz third overtone   fourth harmonic


[Source: Harmonic - Wikipedia]

The fundamental is equivalent to the first harmonic, making cos(2omegat-phi_2) the second harmonic.

The article actually comments on the confusion with music conventions:

The tight relation between overtones and harmonics in music often leads to their being used synonymously in a strictly musical context, but they are counted differently leading to some possible confusion.

All the best.

X

Hi Ken

Thanks for the comment. This table comes from Wikipedia:
<pre>
1f 440 Hz  fundamental      first harmonic
2f 880 Hz  first overtone   second harmonic
3f 1320 Hz second overtone  third harmonic
4f 1760 Hz third overtone   fourth harmonic
</pre>

[Source: <a href="https://en.wikipedia.org/wiki/Harmonic">Harmonic - Wikipedia</a>]

The fundamental is equivalent to the first harmonic, making cos(2omegat-phi_2) the second harmonic.

The article actually comments on the confusion with music conventions:

<blockquote>The tight relation between overtones and harmonics in music often leads to their being used synonymously in a strictly musical context, but they are counted differently leading to some possible confusion.</blockquote>

All the best.