# Harmonics and Fourier Series [Solved!]

**Ken** 17 Dec 2015, 04:07

### 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

**Murray** 17 Dec 2015, 15:42

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.

You need to be logged in to reply.