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About Harmonics

J

Jack// ani

Jan 1, 1970
0
Hi all,

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

Thanks
 
R

Rich Grise

Jan 1, 1970
0
How is harmonics generated? Why are they integral multiple of the
fundamental frequency?

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
 
D

Don Lancaster

Jan 1, 1970
0
Jack// ani said:
Hi all,

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

Thanks

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 http://www.tinaja.com/magsn01.asp


--
Many thanks,

Don Lancaster
Synergetics 3860 West First Street Box 809 Thatcher, AZ 85552
voice: (928)428-4073 email: [email protected]

Please visit my GURU's LAIR web site at http://www.tinaja.com
 
J

Joerg

Jan 1, 1970
0
Hello Don,
Except on the paino where lateral stiffness makes the overtones
different from the harmonics.

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
 
S

Spehro Pefhany

Jan 1, 1970
0
Hi all,

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

Thanks

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


Best regards,
Spehro Pefhany
 
R

Rene Tschaggelar

Jan 1, 1970
0
Jack// ani said:
Hi all,

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

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
 
J

John Popelish

Jan 1, 1970
0
Jack// ani said:
Hi all,

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

Thanks
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.
 
D

Don Lancaster

Jan 1, 1970
0
John said:
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.

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
Synergetics 3860 West First Street Box 809 Thatcher, AZ 85552
voice: (928)428-4073 email: [email protected]

Please visit my GURU's LAIR web site at http://www.tinaja.com
 
K

Kevin Aylward

Jan 1, 1970
0
Don said:
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.

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
[email protected]
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
 
A

Anno Siegel

Jan 1, 1970
0
Joerg said:
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.

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

Anno
 
D

Don Pearce

Jan 1, 1970
0
Octaves are the *only* exact intervals in tempered tuning. The other
intervals are the "inexact" ones.

Anno

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
http://www.pearce.uk.com
 
T

Ted Edwards

Jan 1, 1970
0
Jack// ani said:
How is harmonics generated? Why are they integral multiple of the
fundamental frequency?

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
 
P

Pooh Bear

Jan 1, 1970
0
Jack// ani said:
Hi all,

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

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
 
C

Clifford Heath

Jan 1, 1970
0
Don said:
A piano isn't tuned in exact octaves... The brain is a real bugger.

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).
 
J

Jack// ani

Jan 1, 1970
0
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
 
K

Kevin Aylward

Jan 1, 1970
0
Ted said:
Fourier showed that any periodic, continuous, differentiable function

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.

http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Fourier.html

I think Euler was the first to use such series.

Kevin Aylward
[email protected]
http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.
 
P

Pooh Bear

Jan 1, 1970
0
Jack// ani said:
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.....

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.

Please tell more.

Graham
 
P

Pooh Bear

Jan 1, 1970
0
Kevin said:
I think Euler was the first to use such series.

Did he suffer from the 'oily rag syndrome' though ?

Graham
 
R

Rich Grise

Jan 1, 1970
0
Did he suffer from the 'oily rag syndrome' though ?

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