 The Clarinet BBoard
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Author: Koo Young Chung
Date: 2008-11-20 14:00
We all know that when we play,say,F3(low),it has odd harmonic series.
1 (F3), 3 (C5), 5 (A5), 7 , 9 , 11 etc
I'd like to know when we play C5 (overblown note of the F3),
what's the harmonic series consisted of?
A.---> 3 (C5), 5 (A5), 7, 9, 11 etc
(i.e., same as low F3,except the 1(F3) missing)
OR
B.---> 1 (C5), 3 (G6), 5( E7) , 7, 9, etc
(i.e., usual odd series with C5 as fundamental)
OR
any other possibilities?
(P.S. the integer number are relative frequencies respectively.)
Thank you.
Post Edited (2008-11-20 14:05)
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Author: mrn
Date: 2008-11-20 14:39
Actually, for F3 you get:
1 (F3), 2 (F4), 3 (C5), etc...
and for C5 you get
1 (C5), 2 (C6), 3 (G6), etc...
The reed makes even harmonics and odd harmonics, it's just that the clarinet bore tends to supress the even ones, especially in the lower (chalumeau) register.
Take a look at the sound spectrum graph at the bottom of the following page:
http://www.phys.unsw.edu.au/music/clarinet/C5.html
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Author: rtmyth
Date: 2008-11-20 18:53
Complex subject that. Dominant frequencies can readily be calculated for simple geometry, but the real clarinet does not have a simple geometry. For a more accurate calculation, a set of non-linear differential equations apply, which can be solved by computer methods, but interpreting the results would be daunting. USW has done useful, excellent work; best I have seen.
richard smith
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Author: Koo Young Chung
Date: 2008-11-20 21:42
I don't think it's 1,2,3 as mrn suggested.
It's known fact that clarinet tone has no #2 partials which gives it's
distinctive tonal quality.
I know it may have a very small even overtones.
But, I'm not talking about that. I'm interested in the overtones which has
more or less comparable intensity as the lowest one.
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Author: Don Berger
Date: 2008-11-20 22:01
Tks, KYC, for this question/thread. I had often wondered when playing a "partial", 3rd or 5th, what its overtone/harmonic character might be. Trying to learn oboe playing [10 yrs] taught me that hautbois [high wood] was correctly descriptive, since there seemed to be more acoustic energy in the octave [2nd] than in its fundemental. Comments, anyone ? Don
Thanx, Mark, Don
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Author: Mark Charette
Date: 2008-11-20 23:16
Koo Young Chung wrote:
> I don't think it's 1,2,3 as mrn suggested.
>
> It's known fact that clarinet tone has no #2 partials which
> gives it's
> distinctive tonal quality.
>
> I know it may have a very small even overtones.
Depends on the note. If you look at the spectrum you'll find that the power of the 2nd & 4th on some notes is approximately equal to the 5th and 7th of the same note - not negligible in the least!
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Author: mrn
Date: 2008-11-21 02:11
Koo Young Chung wrote:
<<I don't think it's 1,2,3 as mrn suggested.>>
If that's what you think, you didn't read the graph I pointed to you (or didn't read it very carefully)--the graph I am talking about is the one at the bottom of the page on the clarinet acoustics website I posted a link to (labeled "Sound"). What I mentioned in my post is all right there in the graph.
The graph is a plot of the spectrum of the note C5 (466 Hz) played on a clarinet. The X axis is frequency (in kilohertz) the Y axis is amplitude (in decibels). You can see peaks in the graph at each harmonic. There is a peak at the fundamental frequency (466 Hz or 0.466 kHz). Then there is a peak at twice that frequency (932 Hz or 0.932 kHz)--that's the second harmonic. It's about half the height of the fundamental's peak. Then there is larger peak (about 3/4 of the fundamental's height) after that at the third harmonic frequency (1398 Hz or 1.398 kHz).
<<It's known fact that clarinet tone has no #2 partials which gives it's
distinctive tonal quality.>>
No it's not. Theoretically speaking, a perfect closed (on one end) cylindrical tube will resonate only odd harmonics, but a clarinet is neither perfectly closed nor perfectly cylindrical. Also, there is difference between the *tone* of a clarinet and the *resonance* characteristics of the bore.
<<I know it may have a very small even overtones.
But, I'm not talking about that. I'm interested in the overtones which has
more or less comparable intensity as the lowest one.>>
Well, in the graph I pointed to, the second overtone (932 Hz) is of greater intensity than the fifth overtone, so unless you think it's sufficiently accurate to model a clarinet with only a single overtone (the third one), you really can't ignore the even overtones.
As I said, the answer to your question is right there on the graph. So even if you don't want to believe what I say, I still gave you the right answer!
Post Edited (2008-11-21 03:07)
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Author: Phurster
Date: 2008-11-21 04:04
Mrn,
Thanks for that reply. The collective wisdom on the BB is sometimes amazing.
You were asked about the harmonic series of C5 and as far as I can see you gave the definitive answer, complete with graph.
Well done.
Chris.
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Author: Koo Young Chung
Date: 2008-11-21 04:58
To mrn: Thank you for the graphs,
(I didn't have chance to look at the graphs when I posted the previous one)
I can see that for C5, partials 1,3,4 have all considerable amplitude.
Even though you see a peak at 2, it is about 25 db smaller,which means it is 300 times smaller!
You said the 2nd peak is about half the height of the 1st peak ,but please note that the vertical scale is not linear,it is logarithmic scale,which makes the 2nd peak 300 times weaker than 1st peak and 10 times weaker than 3rd peak.
Even though it is a local peak,we may say it doesn't have 2nd peak for all practical purposes.
*** Here, the meaningful measurement is not the (absolute) height of the peak from the bottom(X) axis,but the DIFFERENCE btw the 1st peak and the nth peak. ***
But for F4,it is obvious that 2,4,6 are missing.
I think you misread the exact location of the Y axis.
The spacing btw 1st and 2nd peak is twice as wide as the spacing btw Y axis and 1st peak.
Even though it appears that the width btw each peaks are equal ,they are not.
The spacing btw Y axis and 1st peak is mapped too wide.
Please look at the graphs very carefully.
10 db --> 10 times ratio
20 db --> 100 times
30 db --> 1000 times etc
http://www.phys.unsw.edu.au/jw/dB.html
To MC: What I wrote was ,of course ,over simplification.
I mainly talk about the harmonics of the lower tones.
Thank for pointing out.
Post Edited (2008-11-21 07:10)
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Author: mrn
Date: 2008-11-21 15:22
Koo Young Chung wrote:
> I think you misread the exact location of the Y axis.
No, I didn't. Look, my undergraduate degree was in engineering (computer/electrical). I've also done graduate-level work in signal processing. I know that decibels are a logarithmic measure. That's why I said "half the height" to help you identify the peak I was referring to, and not "half the value."
But as it turns out, we actually hear differences in volume on a logarithmic scale. A normal conversation between people 1m apart, for instance, will range between 40-60 dB above the auditory threshold (a 20 dB difference). The human ear is much more sensitive than you think it is. The whole reason we measure sound intensity in decibels is because the human ear works logartihmically. (and also because otherwise we'd be dealing with mind-bogglingly huge numbers)
> The spacing btw 1st and 2nd peak is twice as wide as the
> spacing btw Y axis and 1st peak.
> Even though it appears that the width btw each peaks are equal
> ,they are not.
> The spacing btw Y axis and 1st peak is mapped too wide.
>
> Please look at the graphs very carefully.
You need to take your own advice. If you look more carefully, the "Y-axis" in the graph is drawn a little ways to the left of "X=0." So you can't just glance at the graph and tell me it's wrong. You have to actually read the numbers off the X-axis to interpret this graph.
Post Edited (2008-11-21 19:12)
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Author: Koo Young Chung
Date: 2008-11-21 17:28
To mrn
If you look at the F3 graph and cannot recognize they are odd series,
there are no reason to discuss any more.
Post Edited (2008-11-21 23:11)
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Author: mrn
Date: 2008-11-21 21:08
Koo--
I want to apologize for getting a little heated in my previous post. I have since edited it to make it a little nicer. I was frustrated by some of your responses to my attempt to answer your question, but it was wrong for me to take it out on you like that. I'm sorry.
You correctly note that in the F3 spectrum from the UNSW website, the 2nd harmonic is not visible (it IS visible in James Pyne's spectral graph, which Mark posted a link to). As I said in my original post, the clarinet bore does tend to suppress or weaken even harmonics, especially in the lower register.
In the UNSW F3 graph, the 2nd harmonic is weakened to the point that it is exceeded by the level of "pink noise" in the recording. (By "pink noise," I mean noise with an intensity that is inversely proportional to the frequency) That still doesn't necessarily mean that there is no 2nd harmonic produced at all, however, even at a pp dynamic. In fact, it might actually be possible to filter out the noise (using an "adaptive filter"--I wrote software to do this once) and make the 2nd harmonic visible in the graph. You can actually see the 2nd harmonic peak exceed the noise floor on UNSW's F3 graphs for louder dynamics.
Since the UNSW website suggests that the pink noise we see there is actually part of the clarinet sound (due to reed hiss)--and I don't have any reason to doubt this--it may be that Pyne used such a filter and that's why we can see the 2nd harmonic more clearly on their site. On the other hand, it's also possible that they just used a less noisy recording (either because the player had a less airy sound or because the pink noise was in fact more attributable to the electronic equipment at UNSW than they may have thought [since all electronic equipment produces pink noise or "flicker noise" to some degree or another]).
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Author: Koo Young Chung
Date: 2008-11-21 23:00
mrn:
I'm looking forward to more constructive discussions about clarinet (or any other) acoustics in the future.
Thanks again for the link.
Koo Young
Post Edited (2008-11-21 23:11)
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Author: Mark Charette
Date: 2008-11-21 23:14
mrn wrote:
> Since the UNSW website suggests that the pink noise we see
> there is actually part of the clarinet sound (due to reed
> hiss)--and I don't have any reason to doubt this--it may be
> that Pyne used such a filter and that's why we can see the 2nd
> harmonic more clearly on their site. On the other hand, it's
> also possible that they just used a less noisy recording
> (either because the player had a less airy sound or because the
> pink noise was in fact more attributable to the electronic
> equipment at UNSW than they may have thought [since all
> electronic equipment produces pink noise or "flicker noise" to
> some degree or another]).
I've visited Jim Pyne's studio, examined the equipment, and built that web site 9 years back No pre or post processing was used for those graphs other than placing markers at the peaks; the recording was done on (at that time) state of the art digital recording equipment with a calibrated microphone and preamp (the chain of calibration was known and validated). I unfortunately can't remember the specifics from way back then, and I can't seem to find them in any emails ...
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