Struggling with waveform questions.

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Randy Yates
Guest

Posted: Tue Dec 14, 2004 4:40 am Post subject: Re: Struggling with waveform questions.

"Jon Harris" <goldentully@hotmail.com> writes:

Quote:

"Randy Yates" <yates@ieee.org> wrote in message news:acsh3k5j.fsf@ieee.org...
Jerry Avins <jya@ieee.org> writes:

Randy Yates wrote:

Thanks for the perspective, but in the end it's a definition game.
You use yours and I'll use mine.

And never the twain shall communicate.

Was I not communicating? I stated that I understood the usage, even
though, by the definition I choose to use (which is clearly in public
usage as well), it is semantically wrong.

What some folks here seem to want to do is control the definition I
choose to use. Sorry, they don't get to do that. If such people feel
they must show their ass to me or otherwise ostracize me for my
choice, then so be it.

Randy, do you object to the fundamental being called the first harmonic, the
numbering of the harmonics, or both? For example, for a musical signal with a
100Hz fundamental, what do you prefer to call the 200 Hz component? The first
harmonic, the second harmonic, or something else? Just want to clarify here.

Hey Jon,

Thanks for asking. In my mind, the fundamental is not a harmonic, i.e.,
the term harmonic is set apart for the tones of the form n*F, where F is the
fundamental and n > 1, n an integer. A harmonic is NEVER the fundamental
in my definition of the term. It is also never less than the fundamental
frequency.

I would call 2*F the first harmonic.

Here's partly where my issue with the engineering usage comes from:
the word "harmonic" obviously has a common root with the word
"harmony." In music, you have melody and harmony. The melody is not a
harmony. The harmony is separate from the melody. See, e.g.,

http://www.etymonline.com/index.php?search=harmony&searchmode=none

More specifically, a harmonic is a _related_ tone to the
fundamental. Thus it is set apart from the fundamental. To begin to
call the fundamental a harmonic is the beginning of obfuscation.

I believe the current engineering usage was begun many years ago by
someone who wasn't being precise. Others didn't notice the imprecision
or didn't care to make an issue of it, so here we are with it fully
entrenched. I am simply maintaining that the original usage is the
proper one, but I see the utility in using the alternate definition
for the purposes of communicating with others in our profession.

PS: There's no such thing as a "subharmonic" either! That is another
term that's been foisted on the general public.
--
% Randy Yates % "I met someone who looks alot like you,
%% Fuquay-Varina, NC % she does the things you do,
%%% 919-577-9882 % but she is an IBM."
%%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO
http://home.earthlink.net/~yatescr

glen herrmannsfeldt
Guest

Posted: Tue Dec 14, 2004 1:21 pm Post subject: Re: Struggling with waveform questions.

Richard Dobson wrote:

Quote:

Randy Yates wrote:

Here's partly where my issue with the engineering usage comes from:
the word "harmonic" obviously has a common root with the word
"harmony." In music, you have melody and harmony. The melody is not a
harmony. The harmony is separate from the melody. See, e.g.,

You are referring to a term that dates at least as far back as
Pythagoras. When the ancient Greeks referred to Harmony, they were not
referring to our modern notion based on chords (which was a deplorable
notion to them) but in fact to melody - the harmony of the notes of
which it is composed. As indeed your cited reference makes clear - the
harmony is in the junction between two ~successive~ notes.

From the ones I see on the web it seems pretty clear that
in music the first harmonic is the fundamental. Musically
the most harmonious tones are two with the same frequency.
I believe that it is also pretty clear in physics and
engineering usage.

(snip)

Quote:

This is where it gets confusing. As far as I can tell, in
music the first overtone is the frequency near, though not
exactly, the second harmonic, that is, twice the fundamental.

As far as I know from physics and engineering, especially crystal
oscillators, the third overtone is the one near the third
harmonic. For a variety of physical reasons the mode that
is near the third harmonic, the one that might be expected to
be three times the fundamental, may not be exactly three times.

In addition note that musically it is not required that the
fundamental tone exist, or if it does that it be the component
with the largest amplitude. As far as I understand it, the
sound of a tone containing, for example, the second and third
harmonics only will still sound musically (that is to the
human ear and brain) as the missing first harmonic.

-- glen

Stephan M. Bernsee
Guest

Posted: Tue Dec 14, 2004 1:43 pm Post subject: Re: Struggling with waveform questions.

On 2004-12-14 09:21:06 +0100, glen herrmannsfeldt <gah@ugcs.caltech.edu> said:

Quote:

From the ones I see on the web it seems pretty clear that
in music the first harmonic is the fundamental. Musically
the most harmonious tones are two with the same frequency.

I'm not sure if two tones with the same frequency would qualify as a
"harmony", in either sense...

The concept of consonance and dissonance can get quite complicated when
it comes to the perception by a human listener. From what I know from
musicology, the notion of consonance and dissonance (ie. what is
perceived as harmonious or not) has been subject to considerable
changes throughout history (and, of course, culture!), so I believe
there is some room for discussion here :-)

Quote:

In addition note that musically it is not required that the
fundamental tone exist, or if it does that it be the component
with the largest amplitude. As far as I understand it, the
sound of a tone containing, for example, the second and third
harmonics only will still sound musically (that is to the
human ear and brain) as the missing first harmonic.

Yes exactly. I mentioned the same thing in another post here yesterday.
That's one reason why pitch estimation by picking the largest FFT bin
(which is the most obvious yet "brute-force" approach to the problem)
isn't likely to work very well with voice, for example.
--
Stephan M. Bernsee
http://www.dspdimension.com

Randy Yates
Guest

Posted: Tue Dec 14, 2004 2:04 pm Post subject: Re: Struggling with waveform questions.

Richard Dobson <richarddobson@blueyonder.co.uk> writes:

Quote:

Randy Yates wrote:

..
Here's partly where my issue with the engineering usage comes from:
the word "harmonic" obviously has a common root with the word
"harmony." In music, you have melody and harmony. The melody is not a
harmony. The harmony is separate from the melody. See, e.g.,

You are referring to a term that dates at least as far back as
Pythagoras. When the ancient Greeks referred to Harmony, they were not
referring to our modern notion based on chords (which was a deplorable
notion to them) but in fact to melody - the harmony of the notes of
which it is composed.

Got a reference?

Quote:

As indeed your cited reference makes clear - the
harmony is in the junction between two ~successive~ notes.

Don't play games with me. There is no such statement in the
reference I made. It doesn't explicity state either view,
and to assert that it clearly states your view is to lie.

Let me be clear. The two views I'm referring to here are
as follows:

View 1. "Harmony" refers to the relationship of notes within
a monotonic melody.

View 2. "Harmony" refers to the relationship of notes other than
the melody to the melody in a polyphonic progression.

The cited reference is

http://www.etymonline.com/index.php?search=harmony&searchmode=none

Quote:

http://www.etymonline.com/index.php?search=harmony&searchmode=none
More specifically, a harmonic is a _related_ tone to the
fundamental. Thus it is set apart from the fundamental. To begin to
call the fundamental a harmonic is the beginning of obfuscation.

One could equally say that your attempt to redefine it is the
beginning of obfuscation! You are using the term "harmonic" where you
should be using the term "overtone", i.e. the first overtone = 2nd
harmonic.

"Should" is a very strong word - it conveys the sentiment that you know
better than me. That's essentially a pissing contest.

Quote:

I believe the current engineering usage was begun many years ago by
someone who wasn't being precise.

The current engineering use echoes past engineering and scientific
use.

You obfuscate my meaning. When I said "current" I meant "within the
last 100 years or so."

Quote:

Why is saying "harmonics are at multiples of the fundamental
frequency" so difficult?

Why is distinguishing the fundamental from a harmonic so difficult?
--
% Randy Yates % "Maybe one day I'll feel her cold embrace,
%% Fuquay-Varina, NC % and kiss her interface,
%%% 919-577-9882 % til then, I'll leave her alone."
%%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO
http://home.earthlink.net/~yatescr

Randy Yates
Guest

Posted: Tue Dec 14, 2004 2:15 pm Post subject: Re: Struggling with waveform questions.

Jerry Avins <jya@ieee.org> writes:

Quote:

[...]
Say it as you like. I can translate.

I don't have any problem whatsoever with that attitude, Jerry. Likewise.
--
% Randy Yates % "Watching all the days go by...
%% Fuquay-Varina, NC % Who are you and who am I?"
%%% 919-577-9882 % 'Mission (A World Record)',
%%%% <yates@ieee.org> % *A New World Record*, ELO
http://home.earthlink.net/~yatescr

Randy Yates
Guest

Posted: Tue Dec 14, 2004 2:31 pm Post subject: Re: Struggling with waveform questions.

glen herrmannsfeldt <gah@ugcs.caltech.edu> writes:

Quote:

Richard Dobson wrote:

Randy Yates wrote:

Here's partly where my issue with the engineering usage comes from:
the word "harmonic" obviously has a common root with the word
"harmony." In music, you have melody and harmony. The melody is not a
harmony. The harmony is separate from the melody. See, e.g.,

You are referring to a term that dates at least as far back as
Pythagoras. When the ancient Greeks referred to Harmony, they were
not referring to our modern notion based on chords (which was a
deplorable notion to them) but in fact to melody - the harmony of
the notes of which it is composed. As indeed your cited reference
makes clear - the harmony is in the junction between two
~successive~ notes.

From the ones I see on the web it seems pretty clear that
in music the first harmonic is the fundamental. Musically
the most harmonious tones are two with the same frequency.

Ask any studio musician/singer to sing harmony with the melody
and see how many sing in unison.

My thoughts and opinions are formed in part from over 30 years as a
musician. I have been the lead pianist at my church for four years
now, and have served in the role of musician in other churches for the last
13 years. I've been in numerous (rock) bands as well. I think I know
something of the terminology and how it's used in music, and what
you're saying glen ain't it.
--
% Randy Yates % "...the answer lies within your soul
%% Fuquay-Varina, NC % 'cause no one knows which side
%%% 919-577-9882 % the coin will fall."
%%%% <yates@ieee.org> % 'Big Wheels', *Out of the Blue*, ELO
http://home.earthlink.net/~yatescr

Richard Dobson
Guest

Posted: Tue Dec 14, 2004 6:02 pm Post subject: Re: Struggling with waveform questions.

Randy Yates wrote:
....

Quote:

From the ones I see on the web it seems pretty clear that
in music the first harmonic is the fundamental. Musically
the most harmonious tones are two with the same frequency.

Ask any studio musician/singer to sing harmony with the melody
and see how many sing in unison.

Of course, that is the vernacular meaning; I do this myself, we all know what we

mean in that case by "singing in harmony" (usually, singing parallel thirds. Or
will they sing at the fifth, organum-style?). Harmony in this sense is more a
question of style, fashion and taste than of acoustical or mathematical rigour.

But we are surely trying to nail a scientific definition, rather than justify
every-day usage? Within music theory (both ancient and modern) the unison is
indeed defined as the "most consonant harmony between tones". In many monodic
traditions (e.g. Classical Indian raga) the "tonic" or root-note is constantly
exposed via the drone, and the moment the soloist returns to unison with that
root note is always very significant.

Quote:

My thoughts and opinions are formed in part from over 30 years as a
musician. I have been the lead pianist at my church for four years
now, and have served in the role of musician in other churches for the last
13 years. I've been in numerous (rock) bands as well. I think I know
something of the terminology and how it's used in music, and what
you're saying glen ain't it.

Usage in music is unfortunately often vague or casual, and musicians will tend
to use terms too freely from the point of view of a scientist. It is rare indeed
for music students to be taught even the basics of acoustics, a problem I
continue to battle against in muy own College. I see only one path here, that
musicians at least understand, and ideally adopt, the terminology as defined in
the scientific disciplines, and in particular in acoustics. This requires that
(at least for periodic tones) harmonics are counted from 1, where the first is
also termed the fundamental. In contrast, I own a Tibetan bowl in which,
depending on where you place the ear around the edge, you hear two different
quasi-fundamentals (for want of a better term) approximately a semitone apart.

Richard Dobson

Stan Pawlukiewicz
Guest

Posted: Tue Dec 14, 2004 7:22 pm Post subject: Re: Struggling with waveform questions.

Jerry Avins wrote:

Quote:

Stan Pawlukiewicz wrote:

...

Perhaps, but DC would be then be then be the infinite order subharmonic.
The issue of what a zeroth order harmonic is, remains.

...

Do you disagree that the nth harmonic has a frequency that is n times
the fundamental? Is it mostly true, with exceptions? If exceptions, what
justifies or requires them?

Jerry

I agree, for strings and string like systems. I think the terms
harmonic, overtone, and mode tend to be used in slightly different ways
depending on the application.

Richard Dobson
Guest

Posted: Tue Dec 14, 2004 7:57 pm Post subject: Re: Struggling with waveform questions.

Randy Yates wrote:

...

Quote:

You are referring to a term that dates at least as far back as
Pythagoras. When the ancient Greeks referred to Harmony, they were not
referring to our modern notion based on chords (which was a deplorable
notion to them) but in fact to melody - the harmony of the notes of
which it is composed.

Got a reference?

Big subject! I'll have to get back to you on that in terms of books and literal
references, but as a starting point the Harvard Dictionary of Music has a useful
article on Greek music, clearly outlining its monodic nature, centred on the
voice. Ptolemy is regarded an important source, together with scattered
descriptions in Plato, etc. It is not possible to separate descriptions of music
from their philosophical and moral principles. "logos" meant the Order of the
Universe, and also "melody". Polyphony would have been regarded as morally and
spiritually dangerous - how can there be more than one Logos?

Quote:

As indeed your cited reference makes clear - the
harmony is in the junction between two ~successive~ notes.

Don't play games with me. There is no such statement in the
reference I made. It doesn't explicity state either view,
and to assert that it clearly states your view is to lie.

Lets not get heavy here! I am referring to the etymology your reference gives,
of "harmos" as a "joint" (literally! The shoulder, etc). That is very suggestive
to me of a succession of objects joined together, hence of notes joined over
time; but I will accept that it can be read either way, especially given the
modern usage of "harmony" as distinct from "melody", that colours our reading.

But we must in any case be wary of relying on such dictionary defintions, where
we want formalised scientific definitions.

Quote:

Let me be clear. The two views I'm referring to here are
as follows:

View 1. "Harmony" refers to the relationship of notes within
a monotonic melody.

Yup; the Greek ideal; (best IMO to use the term "monody" here)

Quote:

View 2. "Harmony" refers to the relationship of notes other than
the melody to the melody in a polyphonic progression.

The modern western view - polyphony was one of the great inventions of Western
Art. In Germany in the 18th Century, "harmonie" meant in general "sounding
together" but specifically menant the wind section in the orchestra. Hence
Haydn's "harmonie-messe", which we would have to translate not as "harmony-Mass"
but "Wind-Mass". So the poetic meanings of "harmony" are very broad, and clearly
culturally mediated. If you look at the definition of Raga on that same page,
you will see it is defined as synomymous with both melody and harmony, so that
there "harmony" applies horizontally as well as vertically. I think the Raga
offers us as close an impression as is possible today of the living musical
practice of Classical Greece.

...

Quote:

One could equally say that your attempt to redefine it is the
beginning of obfuscation! You are using the term "harmonic" where you
should be using the term "overtone", i.e. the first overtone = 2nd
harmonic.

"Should" is a very strong word - it conveys the sentiment that you know
better than me. That's essentially a pissing contest.

Only if its unprovable either way :-).

These are not terms I have personally invented or defined, they are as used by
acousticians (let us say, from Helmholtz onwards). These terms have an
established meaning and usage for scientists and engineers in acoustics (and in
computer music etc). You are arguing for a different meaning; I am just arguing
for the status quo.

I have cited Benade; I could also cite Olsen, "Music, Physics and Engineering"
(1952) who provides a handy glossary:

(pp 36-37 in my copy:):

Overtone: an overtone is a component of a complex tone having a pitch higher
than the fundamental.
Fundamental frequency: The fundamental frequency is the frequency component of
the lowest frequency in a complex sound.
Harmonic: A harmonic is a partial or overtone whose frequency is an integer
multiple of the fundamental tone or fundamental frequency.
Subharmonic: A subharmonic is an integral sub-multiple of the fundamental
frequency of the sound to which it is related.

Later, he makes it unambiguously clear in a diagram (p74) of a stretched string
that the fundamental is also the first harmonic, and the first overtone is the
second harmonic. This also makes explicit that all these are "modes of
vibration". So, the ratio 1/1 is just one (albeit a special one) of the set of
ratios 1/N where N is the set of integers >= 1. I am sure I have seen any
number of mathematical expositions where "an integer multiple of 1" includes 1.

Hence, "by definition", the fundamental IS a harmonic in the defined sense of a
mode of vibration; it is distinguished as the mode with the lowest frequency.

f1 = fundamental, 1st harmonic
f2 = first overtone, second harmonic
f3 = 2nd overtone, third harmonic

etc...

I have not found any texts which contradict these definitions, and all I have
read so far confirm them.

Now only one of two situations can hold:

either: all acousticians and engineers accept and use these defititions
or: they are divided, and use them in a mutually incompatible way.

I am confident the former option is true, in which case, there is a moral
imperative surely, on both of us equally, to use terms as defined by our peers
in the subject?

Richard Dobson

Ronald H. Nicholson Jr.
Guest

Posted: Tue Dec 14, 2004 8:27 pm Post subject: Re: Struggling with waveform questions.

In article <32690sF3je6scU1@individual.net>, Jerry Avins <jya@ieee.org> wrote:

Quote:

Solar time is properly determined by observation, not majority opinion.

Although something related to solar time can be determined by observation,
whether or not the thing determined has any relationship with how the
two words "Solar Time" are actually used by English-speaking humans
must be found by other means. When humans disagree on the precise
definition or usage, or observations with similar error bounds disagree,
a statistical (mean, median or *mode*, etc.) solution, or political
solution (ANSI/ISO,etc.), is sometime expedient.

IMHO. YMMV.
--
Ron Nicholson rhn AT nicholson DOT com http://www.nicholson.com/rhn/
#include <canonical.disclaimer> // only my own opinions, etc.

Randy Yates
Guest

Posted: Tue Dec 14, 2004 9:53 pm Post subject: Re: Struggling with waveform questions.

Richard Dobson <richarddobson@blueyonder.co.uk> writes:

Quote:

Randy Yates wrote:
...
From the ones I see on the web it seems pretty clear that
in music the first harmonic is the fundamental. Musically
the most harmonious tones are two with the same frequency.
Ask any studio musician/singer to sing harmony with the melody

and see how many sing in unison.

Of course, that is the vernacular meaning; I do this myself, we all
know what we mean in that case by "singing in harmony" (usually,
singing parallel thirds. Or will they sing at the fifth,
organum-style?). Harmony in this sense is more a question of style,
fashion and taste than of acoustical or mathematical rigour.

But we are surely trying to nail a scientific definition, rather than
justify every-day usage?

That is the very point - the two are at odds.

If a bunch of engineers starting calling blue red, red purple, and purple
blue, we could all make the translation from our vernacular, and if it
became entrenched we might start to think that those definitions are
the "right" ones.

I'm arguing that, while I can understand and use the scientific
definition of harmonic, it doesn't agree with the colloquial use of
the term and I would prefer that scientific usage change to match
colloquial usage since I believe the colloquial usage is more "true."
That will probably not happen, but I still maintain my position
nonetheless.

Regarding numbering, I recant my statement yesterday that I would call
2*F the first harmonic.

There is a simple solution. We can be consistent with engineering
terminology AND colloquial usage if we agree to call n*F the nth
harmonic with the exception of n = 1, in which case we call it "the
fundamental."
--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
randy.yates@sonyericsson.com, 919-472-1124

Eric Jacobsen
Guest

Posted: Tue Dec 14, 2004 10:41 pm Post subject: Re: Struggling with waveform questions.

On Mon, 13 Dec 2004 13:29:09 -0500, Jerry Avins <jya@ieee.org> wrote:

Quote:

Eric Jacobsen wrote:

...

... a theoretical system can easily have
information modulated at DC with both magnitude and phase.

???? Modulation implies change of some sort. How can unchanging voltage
carry modulation? How much time does a one-degree phase shift at DC imply?

In the context I mentioned, an OFDM communication system, at baseband
one of the subcarriers may land centered on zero Hz (aka DC). Several
practical OFDM systems are designed exactly this way.

This means that the DC term can change. Most of us don't have a
problem with the concept that DC levels can change and still be DC,
it's just how long of an observation window are we concerned with to
consider it static enough that we're comfortable calling it DC.

For these OFDM systems a populated DC subcarrier would change at the
symbol rate, and those changes or absolute magnitudes and phases can
be recorded to recover the modulated information.

If any of the OFDM symbols were to be held static, the DC term would
remain static, while, for example, the first subcarrier would continue
to rotate at its center frequency.

Quote:

If the notion of a complex baseband signal -- we already agreed that it
can't exist on a single wire -- implies that we can assign arbitrary DC
phases, there are holes in the theory that need patching.

Jerry

I don't see why. It's still DC in the sense that it is at zero Hz and
doesn't change over the relevant observation window. In this case
the DC term has phase only because there are two wires, as you point
out, which is why I knew that this would be controversial. So it
does need a little bit of a conceptual bridge to make sense, but I
think the analogy is still relevant that the DC subcarrier in an OFDM
system can carry as much magnitude and phase information as any other
subcarrier if the system is architected to do so.

That was my only point. So from a certain perspective one could argue
that this is an example that could be seen as demonstrating that DC
can have phase.

I'm certainly not arguing it as a general concept. I'm with you that
DC does not supply an adequate phase reference by which to define the
relative phases of harmonics in a series.

Eric Jacobsen
Minister of Algorithms, Intel Corp.
My opinions may not be Intel's opinions.
http://www.ericjacobsen.org

Jon Harris
Guest

Posted: Tue Dec 14, 2004 11:00 pm Post subject: Re: Struggling with waveform questions.

"Stephan M. Bernsee" <spam@dspdimension.com> wrote in message
news:327ndvF3i6m9uU1@individual.net...

Quote:

The concept of consonance and dissonance can get quite complicated when
it comes to the perception by a human listener. From what I know from
musicology, the notion of consonance and dissonance (ie. what is
perceived as harmonious or not) has been subject to considerable
changes throughout history (and, of course, culture!), so I believe
there is some room for discussion here :-)

Yes, I've always found it interesting that Europeans several hundred years ago
considered the major third to be a dissonant interval, whereas today it is one
of the most harmonious.

Richard Dobson
Guest

Posted: Tue Dec 14, 2004 11:09 pm Post subject: Re: Struggling with waveform questions.

Randy Yates wrote:

....

Quote:

Regarding numbering, I recant my statement yesterday that I would call
2*F the first harmonic.

There is a simple solution. We can be consistent with engineering
terminology AND colloquial usage if we agree to call n*F the nth
harmonic with the exception of n = 1, in which case we call it "the
fundamental."

I guess I can settle for that; we musos do after all refer to the fundamental
most of the time! The critical thing is not to mis-number the harmonics.

Richard Dobson

Richard Dobson
Guest

Posted: Tue Dec 14, 2004 11:39 pm Post subject: Re: Struggling with waveform questions.

Jon Harris wrote:

Quote:

Yes, I've always found it interesting that Europeans several hundred years ago
considered the major third to be a dissonant interval, whereas today it is one
of the most harmonious.

This is partly because during the mediaeval period tuning was based on
Pythagorean principles. The Pythagorean third is created from four ascending
perfect fifths ((3/2)^4 --> 81/64 after octave reduction), which is a very much
wider interval than the "perfect major third" of ratio 5/4, and it is indeed
pretty out of tune. Later on just intonation took over, based on the quest for
"pure" intervals, and the major third became consonant enough to be acceptable
for a final chord. Note also the practice of "tierce de Picardie" - a minor
mode piece will end with a major third as the minor third is less consonant than
the major third. Whereas previously the fifth was preferred over the third for
the same reason, and so on.

12-note/Octave Equal Temperament (ET) is the solution to the tuning problem that
we have come (grudgingly!) to accept; here the third is not quite as wide as the
Pythagorean third, but is still the single most out of tune interval in ET.

Richard Dobson

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