"First Harmonic" .. "Second Harmonic" ?? Hmm..

[Darktrax]

I know what the fundamental is, call it Fo

When I say "third harmonic distortion", I am thinking there is more of the signal at 3*Fo than I would like.

Is not the "second harmonic" the one on the spectrum analyzer at frequency 2*Fo?

For me, there is no "first harmonic". Have I been wrong about this?

The term is used in RF, audio, music, physics, philosophy, etc. and the definitions vary. For some, me included, the first harmonic is also the fundamental. For others, it is the first one encountered after the fundamental.

Here is a definition I think is wrong-->https://stereos.about.com/od/glossaryoftermsh/g/harmonic.htm

So - is there a norm here?

 

[Jassim76]

The first harmonic is your fundemental freq.
so if f0=1000
the secound harmonic is 2000
third is 3000
4. 4000 and so on

 

[zorro]

I agree. The definition in the link is wrong, although I saw the same mistake in other places.
Sometimes, the term overtone is used with that meaning:

We saw in §3.2 and §3.5 that when a note on a stringed instrument or a wind instrument sounds at a certain pitch, say with frequency ν, sound is essentially periodic with that frequency. The theory of Fourier series shows that such a sound can be decomposed as a sum of sine waves with various phases, at integer multiples of the frequency ν, as in Bernoulli’s solution (3.2.7) to the wave equation. The component of the sound with frequency ν is called the fundamental . The component with frequency mν is called the mth harmonic, or the (m − 1)st overtone. So for example if m = 3 we obtain the third harmonic, or the second overtone.[1]

[1] I find that the numbering of overtones is confusing, and I shall not use this numbering.

Source: Music - A Mathematical Offering, by David Benson

Regards

Z


P.S.: I put a link to the source in the "Mathematics and Physics" forum:

https://www.edaboard.com/threads/311745/#post1333244

 

[ssundar.shan]

Hi
I agree with Jassim76

Regards,
Shunmuga Sundaram

 

[BradtheRad]

When talking about distortion, the even harmonics are tolerable and sometimes pleasing to the ear...
whereas the odd harmonics are grating.

The even harmonics contribute to create a triangle wave.

Odd harmonics create a square wave.

 

[Darktrax]

When talking about distortion, the even harmonics are tolerable and sometimes pleasing to the ear...
whereas the odd harmonics are grating.
The even harmonics contribute to create a triangle wave.
Odd harmonics create a square wave.

Yes ..I had noticed this. The inherent "square law" distortion produced by those old vacuum tube valve type amplifiers (Marshall et al) produced a warm pleasing sound, even if driven to max. The fact the products were even harmonic related meant the harmonic frequencies would be at a perfect chord.

The "crossover distortion" produced by the class-B push-pull amplifiers added a cubic term, and even small amounts of that kind of distortion involving 3rd, 5th, 7th terms makes a harsh unpleasant sound which I recognize when I hear square-wave.

I guess that might be why so many guitarists who have used these amplifiers say they "sounded better".

 

[zorro]

Hi again,

the even harmonics are tolerable and sometimes pleasing to the ear...
whereas the odd harmonics are grating.

Not always odd harmonics are grating. In clarinet and bassoon, for example, odd-order harmonics are dominant and are essential for giving them their characteristic sound.
Several odd-order harmonics are consonant; speaking in terms of musical intervals:

- the 3rd harmonic is an octave plus a perfect fifth above the fundamental,
- the 5th harmonic is two octaves plus a major third above the fundamental.
The 7th harmonic is dissonant.

The even harmonics contribute to create a triangle wave.

Odd harmonics create a square wave.

Triange wave has only odd-order harmonics too. Think that it can be obtained passing the square wave by an integrator, so the two waveforms have the same frequencies, but with different relative amplitudes.
Square wave is a rather extreme case, as it is too rich in odd-order dissonant harmonics (7th, 11th, 13th. etc.)

In square wave, the relative amplitudes fall off as 1/n, while in triangle wave they fall off as 1/n^2, i.e. the relative amplitudes are:

WAVE......|.fundamental...3rd...5th...7th....etc
Square....|......1........1/3...1/5...1/7....
Triangle..|......1........1/9...1/25..1/49...

This lower harmonic content makes triangular wave much softer.

Regards

Z

 

[Audioguru]

The even harmonics contribute to create a triangle wave.

I disagree.
Even harmonics produce a waveform that is not symmetrical between the positive-going and the negative-going parts.

A vacuum tube or transistor, both without any negative feedback and with a fairly high output level produce a lot of even harmonics like this:

 

[Darktrax]

Source: Music - A Mathematical Offering, by David Benson

P.S.: I put a link to the source in the "Mathematics and Physics" forum:

https://www.edaboard.com/threads/311745/#post1333244

The harmonic relationships, whether from consonance or dissonance in musical notes, or the mixture that gives the the sound of any musical instrument it's character, the contributions from harmonic distortion in amplifiers is all intensely interesting.

The the crowds of complex signals that can spread all over the microwave spectrum when the harmonic products meet themselves when encountering a non-linear situation (like a faulty PA) just get confusing, but they all have a lineage that stems from the original frequencies present.

The free e-book link is very good (thanks Zorro), though folk should be warned to just skip over the more mathematically intimidating parts, as the author does suggest.

I am amused how the original question about definition of "First Harmonic" has quickly demonstrated that the same math underpins all the diverse fields from audio tones, music, et al, right through microwave modulation and how we get blue light to mix with down-converted yellow to give us white LEDs!