Harmonics

Steve Underwood wrote:


>   ... However, there are two terms, the 
> second of which seems to be falling into disuse:
> 
> 2 x fundamental == 2nd harmonic
> 2 x fundamental == 1st overtone

Let's give thanks for that. In other context, a harmonic is 
mathematically exact; an integer ratio. Real instrument overtones, such 
as a piano, rarely have exact integer ratios. Inexact harmonics are 
called overtones, and it is perplexing when the numbering system differs.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Jerry Avins wrote:

>> =D7=F2=EE =EF=EE=E4=E5=EB=E0=E5=F8=FC. =CD=E0=E4=E5=FE=F1=FC, =F2=E0=EA=
 =E1=F3=E4=E5=F2 =EF=EE=ED=FF=F2=ED=E5=E5:
>> =C8=F4 =E7=E5 =F4=F0=E8=EA=E2=E5=ED=F1=E8 =E8=E7 =FD=ED =F2=E0=E9=EC=E7=
 =EE=F4 =E7=E5 =F4=E0=ED=E4=E0=EC=E5=ED=F2=E0=EB, =E7=E5=ED =E8=F2 =E8=E7=
 =EA=EE=EB=E5=E4 =E7=E5 =FD=ED=F1=20
>> =F5=E0=F0=EC=EE=ED=E8=EA.
>>
>> Is it better that way?
>=20
>=20
> I don't know.=20

It is the same phrase in English (well, supposed to be English), but it=20
is spelled with the Russian letters. So the online translators will not=20
be able to help :-)


My father spoke Russian, but I never learned how.

When I was a kid, there used to be a popular joke:

"An optimist is learning English. A pessimist is learning Chinese. A=20
realist is learning how to use a gun".



In this
> country, my mother's mother's relatives are variously named Gorelic,=20
> Horlick, and combinations of those. Her father's relatives are Gotkin, =

> Hotkin, and (via France) Hotkine.

Oh, your ancestors are likely from Ukraine or Poland.

>=20
>>> (Matlab wasn't around when the terminology developed.)
>>
>>
>> Can you clarify that. I didn't get it.
>=20
>=20
> Matlab indices are off by one, at least off by one from the way=20
> engineers usually use them.

The Matlab probably inherited it from Fortran.
Indeed, starting the indexes of the arrays from 1 rather then from 0=20
seems more logical to me.


VLV

Vladimir Vassilevsky wrote:
> 
> 
> Jerry Avins wrote:
> 
>>> Что поделаешь. Надеюсь, так будет понятнее:
>>> Иф зе фриквенси из эн таймз оф зе фандаментал, зен ит из колед зе энс 
>>> хармоник.
>>>
>>> Is it better that way?
>>
>>
>> I don't know. 
> 
> It is the same phrase in English (well, supposed to be English), but it 
> is spelled with the Russian letters. So the online translators will not 
> be able to help :-)
> 
> 
> My father spoke Russian, but I never learned how.
> 
> When I was a kid, there used to be a popular joke:
> 
> "An optimist is learning English. A pessimist is learning Chinese. A 
> realist is learning how to use a gun".
> 
> 
> 
> In this
>> country, my mother's mother's relatives are variously named Gorelic, 
>> Horlick, and combinations of those. Her father's relatives are Gotkin, 
>> Hotkin, and (via France) Hotkine.
> 
> Oh, your ancestors are likely from Ukraine or Poland.

Poland. On my mother's side. My father's family was originally from 
Lithuania. My father's grandfather was an army surgeon and physician to 
the czar in Riga.

>>>> (Matlab wasn't around when the terminology developed.)
>>>
>>>
>>> Can you clarify that. I didn't get it.
>>
>>
>> Matlab indices are off by one, at least off by one from the way 
>> engineers usually use them.
> 
> The Matlab probably inherited it from Fortran.
> Indeed, starting the indexes of the arrays from 1 rather then from 0 
> seems more logical to me.

Sometimes, sometimes not. I like an FFT's zero bin to be DC. I want a 
choice of starting indices to match the problem. Matlab won't let us 
have that.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Jerry Avins wrote:
> Steve Underwood wrote:
>
>
> >   ... However, there are two terms, the
> > second of which seems to be falling into disuse:
> >
> > 2 x fundamental == 2nd harmonic
> > 2 x fundamental == 1st overtone

i second that.

> Let's give thanks for that. In other context, a harmonic is
> mathematically exact; an integer ratio. Real instrument overtones, such
> as a piano, rarely have exact integer ratios. Inexact harmonics are
> called overtones, and it is perplexing when the numbering system differs.

i think overtones can be harmonic or inharmonic and you start counting
the first one you see above the lowest significant frequency component
(which might be called the fundamental).  pretty much like the word
"partials".  except, i think the "fundamental" can be a partial (or the
1st harmonic) but is not an "overtone" (unless we were to call it the
"0th overtone").

when we speak of "2nd harmonic distortion" or "3rd harmonic
distortion", we mean the 2x and 3x frequencies.

r b-j

Jerry Avins wrote:
> Vladimir Vassilevsky wrote:
> >
> > Jerry Avins wrote:
> >
...
> >> Matlab indices are off by one, at least off by one from the way
> >> engineers usually use them.
> >
> > The Matlab probably inherited it from Fortran.

they inherited it from the fact that nearly any math text in "Linear
Algebra" or "Matrices and Determinants" counts elements in a matrix
from an index of 1.  it's an accident of history.

> > Indeed, starting the indexes of the arrays from 1 rather then from 0
> > seems more logical to me.
>
> Sometimes, sometimes not.

and not for Edsger W. Dijkstra, either:

http://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD831.html

or for the hand written original:

http://www.cs.utexas.edu/users/EWD/ewd08xx/EWD831.PDF

counting from 1 is an accident of history, and from my biased and
prejudiced perspective, a sad one  (along with counting our thumbs with
fingers and canonizing base-10).

> I like an FFT's zero bin to be DC. I want a  choice of starting
> indices to match the problem. Matlab won't let us have that.

Vladimir, you weren't around here in the 90s and 2000, but i must have
typed 40000 characters to this newsgroup and comp.soft-sys.matlab to
get them to *extend* (not change and break backward compatibility) the
language to allow for other indexing bases (with a default of 1).
comp.dsp folks pretty much agreed, but at comp.soft-sys.matlab, it fell
on deaf ears.  now i'm working on Prof. John W. Eaton of Octave.org
about the same thing (i would need help, i can't crack the source code
myself, it's huge).  i hope this extension goes in and eventually
MATLAB becomes irrelevant.

r b-j

robert bristow-johnson wrote:

   ...

> when we speak of "2nd harmonic distortion" or "3rd harmonic
> distortion", we mean the 2x and 3x frequencies.

You and I mean that. We can only hope that everyone else does too.

jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Tim Wescott wrote:
> Robert A. wrote:
> > Hi guys,
>
> > If the fundamental is 110.0hz would 220.0hz be called the first or
> > second harmonic ?
>
> > Also, which are the even and odd harmonics in this series: 110.0, 220.0,
> > 330.0, 440.0 ?
>
> > I always considered 220.0 to be the first harmonic and also even but I'm
> > really not sure.
>
> > Thanks,
> > Robert A.
> I've always referred to the 2x fundamental as the 2nd harmonic.  I'll
> bet usage varies considerably here -- it'll be interesting to see what
> the rest of the group says.

For some older voices on this topic, read the thread that developed
here:

http://groups-beta.google.com/group/comp.dsp/browse_frm/thread/d3b6397b4975129b/647ca9d3b90ea8b5?&hl=de#647ca9d3b90ea8b5

Regards,
Andor

Jerry Avins wrote:

> Steve Underwood wrote:

>>   ... However, there are two terms, the second of which seems to be 
>> falling into disuse:

>> 2 x fundamental == 2nd harmonic
>> 2 x fundamental == 1st overtone

I was thinking this also, but....

> Let's give thanks for that. In other context, a harmonic is 
> mathematically exact; an integer ratio. Real instrument overtones, such 
> as a piano, rarely have exact integer ratios. Inexact harmonics are 
> called overtones, and it is perplexing when the numbering system differs.

I am trying to remember the terminology used for crystals.  I believe
it is third overtone for a crystal oscillator at approximately three
times the cut frequency.  Yes, like musical instruments crystals don't
oscillate at integer multiples of a fundamental.

I believe, though, in music it is true that the 1st overtone is
not the fundamental.  Why are crystals different?  (I should get
out my ARRL handbook (which won't fit in my hand).)

-- glen

-- glen

robert bristow-johnson wrote:

> Vladimir, you weren't around here in the 90s and 2000, but i must have
> typed 40000 characters to this newsgroup and comp.soft-sys.matlab to
> get them to *extend* (not change and break backward compatibility) the
> language to allow for other indexing bases (with a default of 1).

The "Numerical Recipes" provides for indexing of vectors and matrices 
from an arbitrary number, although most of the subroutines have the 
indexing from 1 hardcoded. The code itself is horrid, however it works.


> comp.dsp folks pretty much agreed, but at comp.soft-sys.matlab, it fell
> on deaf ears.  now i'm working on Prof. John W. Eaton of Octave.org
> about the same thing (i would need help, i can't crack the source code
> myself, it's huge).  i hope this extension goes in and eventually
> MATLAB becomes irrelevant.

I always preferred plain C/C++ as the main tool for development and 
prototyping, and considered Matlab and like as a computer games.  I 
don't believe in the open source ideas as the means of generating of the 
main profit. It can be a very good hobby though.
It would be very difficult to push the MatLab out of the way because 
they spoil the students with it in the universities.
Sorry for the pessimism, but this is how it looks to me.

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

Vladimir Vassilevsky skrev:
> robert bristow-johnson wrote:

> > comp.dsp folks pretty much agreed, but at comp.soft-sys.matlab, it fell
> > on deaf ears.  now i'm working on Prof. John W. Eaton of Octave.org
> > about the same thing (i would need help, i can't crack the source code
> > myself, it's huge).  i hope this extension goes in and eventually
> > MATLAB becomes irrelevant.
>
> I always preferred plain C/C++ as the main tool for development and
> prototyping, and considered Matlab and like as a computer games.

Matlab has a place as a tool for rapid development and prototyping.
The problems occur when it is used for application development,
which seems to be mora and more the case.

As for the index question, the 1,..,N indexing is used in linear
algebra,
which is what matlab was developed for, so it is unlikely that it will
ever change.

...
> It would be very difficult to push the MatLab out of the way because
> they spoil the students with it in the universities.
> Sorry for the pessimism, but this is how it looks to me.

Agreed. I bought my first student version of matlab 3 in -92 for
the equivalent of $50.The program was fully functional, only with
some restrictions on the size of the variables. It was a brilliant
marketing trick; these days matlab seems to have the same
impact in numerics as microsoft has in computing: What matlab
does is the definition.

In 20 years a student can just as well skip university and spend
the $$ on a matlab lisence + documentation instead. 

Rune