 The Clarinet BBoard
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Author: Paul Aviles
Date: 2010-08-05 15:47
Easiest way to hear them is to listen to a ringing bell. Overtones are all the extra pitches that occur in addition to the fundamental note when any pitch on any instrument is played. Clarinet generates a square wave and its overtones (the octave, than the fifth, than the fourth.......etc) are much harder to pull out. But you can make them out better on an oboe (or string instrument for that matter, just listen in person, recordings don't help with this).
................Paul Aviles
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Author: Mark Charette
Date: 2010-08-05 15:54
Paul Aviles wrote:
> Clarinet generates a square wave and its overtones
> (the octave, than the fifth, than the fourth.......etc) are
> much harder to pull out.
????
Not close to a square wave. I think you're confusing the definition of a square wave (which contains only odd harmonics) with a clarinet (which has higher amplitude odd harmonics compared with non-cylindrical wind instruments). Even harmonics are most certainly present in the clarinet spectra.
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Author: BartHx
Date: 2010-08-05 16:30
The fundamental tone is the lowest frequency that will resonate (reflect back and forth on the basis of wavelength to reinforce the particular pitch) within a given chamber or in a given object. For a given chamber volume it can be effected by whether it is open at one end only or is open at both ends. Overtones are frequencies which are of appropriate, higher frequencies to resonate within the same chamber or object (again, effected by the chamber volume and whether it is open at one end or both) but are not reinforced (by resonance) to the same extent as the fundamental. The particular overtones which are reinforced and to what extent are what cause a particular instrument to have its characteristic sound. Without overtones, every instrument would sound like the beep you hear during a hearing test. With those beeps, they must eliminate overtones in order to identify specific frequencies with which you are having difficulty (although some very minor overtones are created as the tone resonates in the ear canal).
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Author: L. Omar Henderson
Date: 2010-08-05 17:01
Tony Pay has an interesting and informative post on clarinet acoustics and the interaction of the player and reed to form the fluctuating air column on the "Fancy Tuner" thread.
Another interesting aspect about our (human carbon forms) perception of sound is the evolutionary process of sound recognition going on in our brains. Neuroscientists have intimated from their research that our brains process even harmonic frequencies, especially high pitched ones, faster or better than an odd harmonic series of frequencies. At the same sound level (pressure) even harmonics "appear" louder than odd harmonic series.
We also tend to process certain natural sounds (e.g. rushing water, wind noise vibrating vegetation, etc.) or frequency patterns made up of both even and odd frequencies more efficiently than a series of frequencies not common in nature.
Neuroscientists go further and equate emotional responses in terms of pleasurable and disturbing with frequency patterns. Those patterns more like nature sounds are more "pleasurable". Many animal species have high pitched even harmonic alarm signals, especially young animals, that are processed even more efficiently than most even harmonics and evoke “disturbing” emotions in many animals and humans alike. These scientists also suggest certain patterns or frequency series are perceived as more "mellow" and others as "bright".
I fear that they have the same definition problems that we have in finding a universal definition of sound qualities - e.g. dark and bright.
L. Omar Henderson
www.doctorsprod.com
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Author: LesterV
Date: 2010-08-06 19:07
At the risk of confusing people let me add some additional info.
There are two ways to numerically define a continuous sound wave. The most common is to define the wave's amplitude versus time and is referred to as a time domain record. It consists of two columns of numbers - one represents time the other the amplitude at that instant in time. The column representing time can be implied by a single number representing a fixed time interval between successive amplitude samples. Sound waveforms are simply a graphical representation of these numbers
A second way, is to consider the sound as composed of a fundamental frequency and a series of harmonics or overtones, all perfect sine waves in the time domain. This is referred to as a frequency domain record and usually consists of two columns of numbers, from which both the amplitude and phase of the fundamental and each harmonic can be determined. The frequency is usually implied by position on the list rather than a third column. A graphical representation of the amplitude vs frequency of each harmonic is called the frequency spectrum.
The frequency domain record is of particular interest because it describes how we hear sounds. It is the relative amplitude of the frequency components, rather than their phase relationships that determine how something sounds to us. Consequently, radically different time domain waveforms having the same harmonic content sound the same to us. Yet, the ear easily hears the difference between the presence and absence of even a very weak overtone.
Time domain records can be converted into frequency domain records using a mathematical process called a Fourier Transform. The same process can also be used to convert frequency domain records into time domain records. Such conversions are in common use in modern digital communications to reduce the redundant information inherent in continuous time domain records.
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Author: mrn
Date: 2010-08-07 04:40
For anybody who wants to see what a clarinet waveform (time domain) and its corresponding spectrum (frequency domain) look like, I've uploaded a little example (attached to the next post).
To make these, I took about a half-second of audio of myself (excerpted from my YTSO video from a year ago) playing the Bb in the Scheherazade cadenza (which is on the A clarinet, so it's a concert G5--784 Hz) and loaded it into GNU Octave (a program for doing numerical mathematics). I then used Octave to run a Fast Fourier Transform (FFT) and to make the plots, which I fixed up a little in Visio to make the text nicer looking and to add labels to the spectral plot.
The first page is a plot of the first 12 milliseconds of the raw data--i.e., the time domain signal. As you can see, it's not a square wave--it's more like a kind of distorted sinusoid. It's almost perfectly periodic, though (owing to the fact that the clarinet produces continuous waveforms).
Now Fourier's Theorem says that any periodic waveform is composed of a sum of sinusoids, where the frequency of each sinusoid is an integer multiple of the fundamental. Since the clarinet produces a nice periodic waveform, when we run the FFT, we should see little "spikes" in the spectrum at integer multiples of the fundamental frequency--those are the overtones.
And sure enough, if you look on page 2 at the spectral plot, that's exactly what you see!
Post Edited (2010-08-07 04:40)
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Author: mrn
Date: 2010-08-07 04:58
Attachment: db.pdf (26k)
And here's the FFT done on a logarithmic (decibel) scale, which is more like the way we hear things with our ears. You can see more overtones (to about the 11th or 12th harmonic) on this plot than on the previous one.
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Author: CarlT
Date: 2010-08-07 14:30
This may be a dumb question, but when I look at the bottom graph of the first attachment, I see spikes for the even harmonics, as well as the odds. I didn't think the evens were supposed to show up (2nd, 4th, etc.). I must be missing something.
Thanks for showing these mrn.
CarlT
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Author: Mark Charette
Date: 2010-08-07 14:50
CarlT wrote:
> This may be a dumb question, but when I look at the bottom
> graph of the first attachment, I see spikes for the even
> harmonics, as well as the odds. I didn't think the evens were
> supposed to show up (2nd, 4th, etc.). I must be missing
> something.
It's a common misconception. Clarinets have both even and odd harmonics.
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Author: charlie clarinets
Date: 2010-08-07 20:45
Thank you all so much for your answers, they were very helpful.
Now I have another question, is it better to have more overtones or less over tones and how do you make that happen?
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Author: LesterV
Date: 2010-08-08 01:05
The vibrating reed generates both even and odd harmonics but there isn't an air column resonance for the even harmonics.
The Bb isn't using much of the bore since almost all holes are open. It would be interesting to see the spectrum of a note produced by closing all or most holes. Perhaps there would then be a significant difference between the amplitude of odds vs evens.
Thanks for the graphics - really interesting.
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Author: mrn
Date: 2010-08-09 04:04
Attachment: a440.pdf (27k)
LesterV wrote:
> The Bb isn't using much of the bore since almost all holes are
> open. It would be interesting to see the spectrum of a note
> produced by closing all or most holes. Perhaps there would
> then be a significant difference between the amplitude of odds
> vs evens.
I ran another FFT--this time on 440 Hz (written C5, so it's most of the bore)--and it does seem to show this. (see attached)
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Author: mschmidt
Date: 2010-08-09 04:24
Trangressing here from the oboe bboard--this is a subject I think a lot about, and wish I had the patience to do more research in. As someone who routinely looks at spectra obtained from Fourier transforms (NMR--nuclear magnetic resonance--spectroscopy) that last dB scale FT (for 440 Hz) looks like it has a "phase problem." I know too little about the mathematics to explain much more fully, but the second and fourth harmonics have asymmetrical peaks, going negative on one side and positive on the other. Were it an NMR spectrum, typically all the peaks would have similar character, and one would "adjust the phase" until they were more symmetrical (like the first and third harmonics). I mention this because I wonder if in fact the odd harmonics are somewhat out of phase from the even harmonics--and I wonder why, and how this affects the timbre we perceive.
I've downloaded Mac apps that do an on-the-fly FFT, but have never found them much use for investigating oboe timbre, as they (a) fluctuate a lot and (b) look roughly the same for the same note on the instrument, regardless of whether it sounds "bright," "dark," or something else. Seeing the detailed dB-scale FTs here, I am encouraged to try again with a recorded sound in an attempt to see whether better characterizations of oboe timbre are possible.
Mike
Still an Amateur, but not really middle-aged anymore
Post Edited (2010-08-09 04:28)
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Author: LesterV
Date: 2010-08-09 14:08
mrn, thanks again for the graphics.
Another bit of info - time domain waveforms with only odd harmonics will always have similar positive and negative shapes while even harmonics produce shapes that are asymmetrical about the x axis. This is easily seen in the time domain graphs of the two notes. The 440hz waveform, with its very strong third harmonic is far more symmetrical about the x axis than is the 784 Hz waveform.
As mschmidt points out, the third harmonic's negative peaks are somewhat, but not perfectly in phase with the fundamental's positive peaks.
A much different waveform would result if the positive peaks were in-phase with each other generating a far higher peak to peak waveform. These different waveforms would sound the same only if they were processed in a perfectly linear fashion. Any non-linearity generates additional harmonics not present in the original waveform which consequently, would be worse with high peak to peak waveforms. This is why high quality recording and playback equipment is highly desirable as the ear is very sensitive to harmonic content.
Post Edited (2010-08-09 23:58)
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Author: mschmidt
Date: 2010-08-11 17:46
Well, LesterV, I think you're attributing more understanding to me than I deserve! I don't fully understand your post, but tell me if I get the right idea, here: are you saying that the shape of the FT peaks is an inherent property of the nature of odd and even harmonics? That was something I didn't think of originally, but sounds plausible. I think I need to find some software to play around with to get a better sense of how FT works. I've mostly just used the results of FTs, not really gotten into how they work.
Mike
Still an Amateur, but not really middle-aged anymore
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Author: LesterV
Date: 2010-08-12 19:14
mschmidt - Any time domain waveform that contains only odd harmonics will have positive and negative waveform halves that are shaped identically - that is, if you invert the waveform it looks the same. If you made a second plot of the waveform on a clear film, flipped the top with the bottom, it would match the original plot perfectly when overlaid and properly aligned. Even harmonics destroy this property. (all this is probably totally useless information of interest only to those that enjoy math)
The FT (Fourier Transform) is a mathematical process for transforming the time domain into the frequency domain (and the reverse). The FFT or Fast Fourier Transform, which has been mentioned a few times, is simply a special case where the number of sampled points is a power of two. This happens to greatly simplify the mathematical process allowing for faster processing on a computer.
It sure would be interesting to look at the spectral differences between various players, instruments, mouthpieces, barrels, reeds, etc. The FFT's numerical data is capable of showing the tiniest differences.
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