• posted

Hi all,

How is harmonics generated? Why are they integral multiple of the fundamental frequency?

Thanks

• posted

The way I understand it, the harmonics are generated by different vibration modes of the string happening simultaneously. In this case, they're called "overtones". The same thing happens with an air column in a woodwind, and so on.

Why they occur in electronic stuff like oscillators and amplifiers is because of nonlinearities that "distort" the signal, and make it be something other than a pure sine wave. If you put a pure sine wave through a speaker, it's a very boring sound, like, "oooooooo....". The overtones, or harmonics, give it tone coloring, or timbre, like "eeeeeee" or "ahhhhhh" and so on. Say "errrr" into a mic on a spectrum analyzer sometime, and I can guar-awn-tee that you will be surprised.

I can't answer "why are they ..." any more than I can answer, "why is the sky blue?". They just are. It probably has something to do with phase relationships and Laplace transforms and Fourier transforms and heavy arithmetical stuff like that. But suffice it to say, when a signal is distorted, the distortion can be seen on a spectrum analyzer as other frequencies that just plain happen to be integral multiples of the fundamental.

Maybe it's just that the ones at integral multiples don't get cancelled out with the ones that _aren't_ integral multiples, but that's just as much of a non-answer as saying "The sky is blue because it isn't red."

Hope this helps!

Cheers! Rich

• posted

Any nonlinear devicee generates harmonics. They are integral multiples because of fundamental trig identities.

Except on the paino where lateral stiffness makes the overtones different from the harmonics.

Much on harmonics at

```--
Many thanks,

Don Lancaster```
• posted

Google on zee "Fourier analysis" and/or zee "Fourier synthesis" and voilà..

Best regards, Spehro Pefhany

```--
"it\'s the network..."                          "The Journey is the reward"
speff@interlog.com             Info for manufacturers: http://www.trexon.com```
• posted

Actually, strings don't even come close. The seventh overtone of a low piano string is nearly the eighth harmonic.

Lateral stiffness completely screws up the physics with second order effects.

```--
Many thanks,

Don Lancaster```
• posted

Any time you distort a sine wave the same way each cycle, you produce continuous harmonics (multiples) of that sine wave frequency. Only multiples are produced, because they are the only frequencies that are stationary with respect to the fundamental sine wave. For example, the second harmonic produces exactly two cycles each cycle of the fundamental at some amplitude and phase shift. 2.1 times the fundamental has a different phase shift relative to the fundamental each cycle for 10 cycles of the fundamental, before it gets back to the phase it started out at. All those different phases represent different waveforms of the combination of that wave and the fundamental for each of those 10 cycles of the fundamental. Some mechanical devices do produce non harmonic frequencies, like gongs, bells and drums. Strings and organ pipes make very close approximations of harmonics, and an electrical circuit that distorts a sine wave the same way each cycle makes precise harmonics.

• posted

Hello Don,

Some of that is due to the activation of other strings and the tuning of a piano is "tempered", it usually isn't tuned in exact octaves.

Regards, Joerg

• posted

Assume a resonator, such as a windpipe. With the bottom closed, the fundamental is a halfwave enclosed. The boundary condition is now a zero on the end. This is satisfied at having 1, 2,3,4,..,N times wavelength halves. They are the harmonics.

Rene

```--
Ing.Buero R.Tschaggelar - http://www.ibrtses.com
& commercial newsgroups - http://www.talkto.net```
• posted

This is a bit misleading. The "except" is implying something that is not correct. Harmonics are by *definition* integral to the fundamental, always. The piano don't make harmonics not equal to overtones. Its an example where harmonics are not equal to overtones.

What instruments produces are "overtones". These are the natural resonant frequencies of the instrument due to its physical construction. This overtones may or may not be close to a harmonic. For strings the overtones are very close to harmonics, so the words are often used interchangeable, although their definitions are completely independent.

For an instrument such as a guitar, the bridge saddles of the bridge are individually adjusted to ensure that the harmonic frequency is the same as the overtone at the 12th fret. This is because the effective vibration length of the string is slightly shorter then its physical length, and progressively shorter as sting thickness goes up. That is, the string dose not start vibrating at its end point, but slightly away from the end point. Some obtuse individuals, for reasons unknown, may like to simply state "lateral stiffness" as the reason, but this is about as useful as knowing the date of the battle of Trafalgar as an explanation to the battle tactics.

Drum overtones are way off from harmonics of the fundamental. They are actually related to the roots of Bessel functions, not sine functions. The first overtone is at 2.4f.

Kevin Aylward snipped-for-privacy@anasoft.co.uk

SuperSpice, a very affordable Mixed-Mode Windows Simulator with Schematic Capture, Waveform Display, FFT's and Filter Design.

• posted

Thanks all.

• posted

Joerg wrote in sci.electronics.design:

Octaves are the *only* exact intervals in tempered tuning. The other intervals are the "inexact" ones.

Anno

• posted

A piano isn't tuned in exact octaves, but that has nothing to do with temperament. The octaves are all stretched - each higher octave is tuned a little more than double the frequency of the lower. This is because a true octave will sound flat. The brain is a real bugger.

d

Pearce Consulting

• posted

Fourier showed that any periodic, continuous, differentiable function can be expressed as a series of sinusoids whose frequencies are integral multiples of the fundamental. For hard proof, see a math book. For an intuitive reason, consider: If that wasn't so, the waveform wouldn't be periodic.

Ted

• posted

Hi Pooh,

You got it right, I'm asking in the same context. Author pretends that harmonics is a major issue and you people said it's not a big problem. How good it would be if Tomi Engdahl joins us.....

Thanks

• posted

In view of your post re: TRIACS - were you interested in power line harmonics and the problems they introduce ?

Phase control of lighting is a minor contributor to the ' harmonics problem ' btw.

Graham

• posted

err... its piecewise continuous, and I don't think Fourier actually had a rigorous proof at all. Fourier was the first to use such series for heat conduction problems, and championed their use.

I think Euler was the first to use such series.

Kevin Aylward snipped-for-privacy@anasoft.co.uk

SuperSpice, a very affordable Mixed-Mode Windows Simulator with Schematic Capture, Waveform Display, FFT's and Filter Design.

• posted

Actually what the brain is doing is completely sensible once you know the physics of string motion beyond the high-school explanations.

The harmonics of each string are sharp, due to both end effects (the stiffness of the string acting against the mounting) and aerodynamic drag. There is a choice of whether to tune to an exact multiple, making the fundamentals agree, or to favour the harmonics. Different players have their own preferences - some like their scale to be stretched more than others. At the upper limit, the scale is stretched perhaps two semitones (12%) over the 8 octaves, which puts each octave somewhere above the 2nd harmonic (which is above the 2:1 frequency ratio).

• posted

If "Euler" is pronounced, "Oyler," howcome "Euclid" isn't pronounced, "Oyclid?"

```--
Thanks!
Rich```
• posted

Different languages and pronunciation rules. But that's not I'm sure what you wanted to hear !

Even in the Uk we have alternative ( not *alternate* ) pronunciations.

A popular one is Castle. In the south it's pronounced 'carsel' ( like parcel ) . In the north it's cas-ell.

Umm - In the north they call a parcel a pas-ell. Oh well never mind.

Graham

• posted

Who's Tomi ?

I learnt about the 'harmonics issue' when the CE scheme for electrical safety and EMC was first introduced in the EC ( or EU - whatever ).

It wasn't much known about by the majority of engineers up to then I guess.

It's actually mainly about 'conduction angle' on electronic power supplies.

I could elaborate at considerable length and even get quite cross about how the IEC tried to pull a 'fast one' with IEC 1000-3-2 !

They had to eat humble pie when it became IEC 61000-3-2 and the EU had to find a bizarre way round avoiding adopting some of IEC 1000-3-2's more draconian requirements into the equivalent EN specs. As a BSI member I voted in favour of the amendment to the EN version of the IEC spec needless to say.