Hi,
Apparently (this is all news to me) :
The clarinet being a straight pipe cannot resonate with the reed
moving at twice the note frequency, the note cancels, so the
reed has to move at 3 times the frequency to be overblown.
So overblown is the 3rd harmonic, a twelfth above normal.
This can only be true if standing waves are multiples of 1/4
wavelengths. A 1/4 wave tube resonates at the the 1st,
3rd, 5th etc, all even harmonics are nulls, out of phase.
For octave overblowing you need a 1/2 wave resonator.
It will resonate at all harmonics, all in phase.
For a given length 1/2 wave frequency is double 1/4.
Here we get to the point I can't find a good explanation.
1/4 wave is a resonant pipe essentially closed at one end.
1/2 wave is a resonant pipe essentially open at both ends.
I can't work out why a Sax supports 1/2 wave. A possibility
is the expanding design increases losses at the mouthpiece,
making it appear to be open acoustically, not closed.
I don't know enough about the details, but what has to be true,
is the clarinet models as a pipe closed at the mouthpiece and
the saxophone models as a pipe open at the mouthpiece.
rgds, sreten.
Apparently (this is all news to me) :
The clarinet being a straight pipe cannot resonate with the reed
moving at twice the note frequency, the note cancels, so the
reed has to move at 3 times the frequency to be overblown.
So overblown is the 3rd harmonic, a twelfth above normal.
This can only be true if standing waves are multiples of 1/4
wavelengths. A 1/4 wave tube resonates at the the 1st,
3rd, 5th etc, all even harmonics are nulls, out of phase.
For octave overblowing you need a 1/2 wave resonator.
It will resonate at all harmonics, all in phase.
For a given length 1/2 wave frequency is double 1/4.
Here we get to the point I can't find a good explanation.
1/4 wave is a resonant pipe essentially closed at one end.
1/2 wave is a resonant pipe essentially open at both ends.
I can't work out why a Sax supports 1/2 wave. A possibility
is the expanding design increases losses at the mouthpiece,
making it appear to be open acoustically, not closed.
I don't know enough about the details, but what has to be true,
is the clarinet models as a pipe closed at the mouthpiece and
the saxophone models as a pipe open at the mouthpiece.
rgds, sreten.
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Wiki has a lot of useful information including the acoustics:
https://en.wikipedia.org/wiki/Clarinet
The reason a clarinet overblows at a 12th appears to be its cylindrical bore.
It is mentioned that a recorder overblows at an octave because it has a tapered bore, like the saxophone.
https://en.wikipedia.org/wiki/Clarinet
The reason a clarinet overblows at a 12th appears to be its cylindrical bore.
It is mentioned that a recorder overblows at an octave because it has a tapered bore, like the saxophone.
Hi,
Except it isn't, cylindrical flutes and tin whistles do octave overblowing.
Wiki isn't always right, it is to do with how the mouth drives the tube.
rgds, sreten.
Or perhaps the mouthpiece end is the anti-node, because it is always the driven end, and, for some reason, the clarinet models as closed at the bell, whereas the sax models as open ? Why though ?Probably not right, but might lead somewhere ? Interesting !
Edit: maybe the clarinet has an abrupt change of impedance at the bell, the interface between the pipe and the outside air - whereas the saxophone progressively reduces mechanical impedance along the pipe as it tapers so that there is (almost) no change of impedance at the bell ? Transmission line like? Just a thought.
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Saxophones and clarinets appear to have very similar mouthpieces, operationally pretty identical.
The primary difference between the two would appear to be that one of them has a fairly gradual taper end-to-end, while the other does not.
So, I did something in Hornresp. This was the first set of driver parameters I came across, for a Beyma 15P1200Nd.
I scaled all lengths and cross-sectional areas accordingly.
Dark sim is the clarinet model: slight compression at the input, long, straight pipe, with a relatively large flare at the end.
Light sim is the sax model: again, slight compression at the input, long expanding pipe.
Pipe lengths were approximately the same length for both, and the "slight compression at input" was just because S1=800 is quicker to type than 855 (=SD). The difference would be neglible.
Pipe lengths are coming in around 6m for each, with the sax mouth being 12000sqcm. The clarinet mouth was more like 6000sqcm, as clarinet ends definitely aren't as big as saxophone mouths.
From the sim, we see that the pipe shape is shifting the fundamental frequency, but not the harmonics.
Chris
The primary difference between the two would appear to be that one of them has a fairly gradual taper end-to-end, while the other does not.
So, I did something in Hornresp. This was the first set of driver parameters I came across, for a Beyma 15P1200Nd.
I scaled all lengths and cross-sectional areas accordingly.
Dark sim is the clarinet model: slight compression at the input, long, straight pipe, with a relatively large flare at the end.
Light sim is the sax model: again, slight compression at the input, long expanding pipe.
Pipe lengths were approximately the same length for both, and the "slight compression at input" was just because S1=800 is quicker to type than 855 (=SD). The difference would be neglible.
An externally hosted image should be here but it was not working when we last tested it.
Pipe lengths are coming in around 6m for each, with the sax mouth being 12000sqcm. The clarinet mouth was more like 6000sqcm, as clarinet ends definitely aren't as big as saxophone mouths.
From the sim, we see that the pipe shape is shifting the fundamental frequency, but not the harmonics.
Chris
Personally I have no real idea. I posted that link because on a quick glance it appeared to show some explanation.
However when googling I stumbled across three other publications on instrument acoustics which all claimed that the phenomenon at hand is due to the taper without further explanations.
This is getting quite interesting and I would like to know the truth behind this.
The link I provided earlier itself links to this publication on saxophone acoustics which might explain a bit further under the heading 'Bore Comparisons': http://newt.phys.unsw.edu.au/jw/reprints/ChenetalAA.pdf
And a similar paper on clarinet acoustics:
http://newt.phys.unsw.edu.au/jw/reprints/AAclarinet.pdf
Hi,
The Sax has a truncated conical taper, where CSA is proportional to distance
squared from the theoretical zero point of the throat. if one dimension is
constant it looks like a flare, and must be modelled with a number of straight
line sections that approximate the flare I presume.
Only speaker with a similar flare I know of is the MLTL Metronome.
rgds, sreten.
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Maybe, when 'overblown' there can be too much air for the nearest stop hole to be at equal pressure with the outside air, so the 1/4 wavelength mode isn't supported any more ,and what happens by way of next available resonance depends somehow on the volume of air in the tube, size of stop holes, taper etc - and that is the difference between clarinet and sax supported overblown resonant modes ? Just guessing though.
Until you blow into one. Then they don't seem all that similar.
The sim was cool, thanks for that!
Sorry I missed the link which you kindly provided.
It does make me wonder about the classic non mass loaded expanding pipe speaker (voigt pipe?) which expands in one dimension and not two. Where does it fit. Does it follow the cylindrical model or the conical in terms of fundamental and harmonics?
It does make me wonder about the classic non mass loaded expanding pipe speaker (voigt pipe?) which expands in one dimension and not two. Where does it fit. Does it follow the cylindrical model or the conical in terms of fundamental and harmonics?
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