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Discussion Starter · #4 ·
You might need to expand on that. To what end?
To better understand what goes on inside the saxophone when it is being played. The applications of this understanding are endless---anywhere from setting key heights to choosing the best equipment for your needs and preferences.
 

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yes
 

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That should be clear considering there's a subforum here with that exact purpose. If you're inquiring about the frequency of posts or new research, it comes down to the fact that there's no real money for research into musical instruments in the US. That much has been made clear as I've been pursuing a graduate degree in Acoustics. There are entire fields of research that don't get adequate funding. Room acoustics also suffers in this regard. Most of the best and most cited work was done decades ago and nowadays grants aren't given to dig deeper. It doesn't help that so much of the feedback from players uses pretty non-scientific language. Quantifying what the various descriptors of tone quality actually look like would be an undertaking in itself, not to mention finding methods to measure impedance for 'free-blowing' statements. It's all pretty nebulous and who is going to do the leg work without some guarantee of funding? It's hard to be a self-starting scientist when you usually need a pretty well-controlled environment.
 

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Discussion Starter · #7 ·
That should be clear considering there's a subforum here with that exact purpose. If you're inquiring about the frequency of posts or new research, it comes down to the fact that there's no real money for research into musical instruments in the US. That much has been made clear as I've been pursuing a graduate degree in Acoustics. There are entire fields of research that don't get adequate funding. Room acoustics also suffers in this regard. Most of the best and most cited work was done decades ago and nowadays grants aren't given to dig deeper. It doesn't help that so much of the feedback from players uses pretty non-scientific language. Quantifying what the various descriptors of tone quality actually look like would be an undertaking in itself, not to mention finding methods to measure impedance for 'free-blowing' statements. It's all pretty nebulous and who is going to do the leg work without some guarantee of funding? It's hard to be a self-starting scientist when you usually need a pretty well-controlled environment.
Perhaps you could help us to decipher some of the math used by Benade and others in the published studies. My personal interests at this time include calculating the length and volume of the missing cone, measuring the "effective volume" of a mouthpiece and putting the two together to try to match the science to personal experience. I am also very interested in the effect of pad porousity on the tone and response of the saxophone all else being equal, and finding the causes and possible solutions to low note warbles. As a professional repair tech I am looking for ways to improve the intonation and harmonicity of saxophones by utilizing what is known about tube dimensions and note antinodes.
 

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I am - I'm interested in the music from the past, and the future of sax in sharing music. I'm interested in the application of sax to different music from the convention. But more interested in the classic forms already established. I'm interested in the gear, the horn, designs, maintenance, collectability and performance. I'm interested in the interaction of mouthpieces, necks and horns. I'm interested in the skill and agility required to play one pleasingly, and impressively.
 

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Yes.

Regarding the missing cone and the effective volume, there is interesting stuff to read in this French blog: http://la.trompette.free.fr/Ninob/Ninob.php.

On the acoustics of conical bore instruments in general: http://la.trompette.free.fr/Ninob/Cone.pdf

Dirk, thank you for this great resource!

On the acoustics of a Conn tenor sax: http://la.trompette.free.fr/Ninob/saxophone.pdf

I don't know how well these articles will be translated by automatic translation software...
Dirk, thank you for this wonderful resource!
 

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So here's a very key passage:

"On déduit de tout cela un critère à respecter pour obtenir des octaves justes avec un instrument à anche (fig. 7) : le volume de l’embouchure doit valoir à peu près 1.5 fois le volume de la pointe du cône. Dans la pratique, le volume géométrique du bec de saxophone ou de l’air contenu dans une anche double est plus petit que cette valeur. Mais, comme on va le voir plus loin, le couplage à l’anche donne au bec du saxophone ou à l’anche double un volume effectif qui, ajouté au volume géométrique, respecte à peu près le critère (a) ci-dessus (cf tableau 3)."

"To get in-tune octave on a conical bore reed instrument, the volume of the embouchure [meant is the cavity which sits between the reed tip and the beginning of the truncated cone] has to be around 1.5 times the volume of the missing cone. In reality, the geometric volume of the mouthpiece [chamber] or the air contained within a double-reed is smaller than this value. But, as we will see later, the coupling of the reed gives the saxophone mouthpiece or double reed an effective volume which, when added to the geometric volume, respects approximately criterion (a) in table 3."

And the reed coupling volume is calculated like this:

V eff = ( A^2 / K) * Patm * gamma , where K is the "reed stiffness", A the effectively vibrating area of the reed, Patm the atmospheric pressure and gamma the adiabatic constant of air (a physical constant which you can look up).

"soit environ 2.9 cm3 pour un ténor." 2.9 cm3 for a tenor sax.

So there you have it: the mouthpiece inner volume + 2.9 cm3 for a tenor sax should be 1.5 times the volume of the missing cone.

Now, how the heck can this be a constant? Well, he translates the formula in

V eff = Patm * gamma * A * a * Pmouth, where a is the mouthpiece tip opening and Pmouth the pressure (differential, I think) in the oral cavity ... I guess this is in reality the pressure difference between oral cavity and the outside.

Anyway, the surprising bit is that Ninob states that the pressure differential Pmouth is rather constant around 50000 Pa, but that implies that a softer reed (smaller K) is used when the tip opening becomes larger. This is not always true, I'd say. There a fascinating article here: https://hal.archives-ouvertes.fr/hal-00445517/document

The really interesting bit of the first formula (V eff = ( A^2 / K) * Patm * gamma) is that a softer reed on the same mouthpiece mechanically increases Veff and not only lowers the overall tuning of the instrument, but also makes the octaves narrower. I haven't experimentally checked this myself...
 

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I'm interested, but know nothing about the topic. For instance, I'd like to know why it's often said that a horn's vibrations don't affect its sound in any way.
 

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Discussion Starter · #14 ·
Thank you Dirk for that excellent summary. That makes a great introduction to what I would like to do next. Those who care to join me, we are going to calculate both the volume and length of the "missing cone".
 

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The taper of the neck should normally be larger than the taper of the body, by the way. The missing cone is to be calculated based on the neck taper?
 

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I'm interested, but know nothing about the topic. For instance, I'd like to know why it's often said that a horn's vibrations don't affect its sound in any way.
These threads have stuff about that in them:

Does Finish/Material affect Tone?

http://www.saxontheweb.net/vbulletin...ad.php?t=62244
http://www.saxontheweb.net/vbulletin...ad.php?t=61212
http://www.saxontheweb.net/vbulletin...ad.php?t=42432
http://www.saxontheweb.net/vbulletin...ad.php?t=40249
http://www.saxontheweb.net/vbulletin...ad.php?t=96155

[edit added below:]

What the elp? I opened these in the FAQ section OK. But when I tried them here I got the dreaded 404.

Here is how I got this list above: I hit on the "Articles" option on the bar.
https://forum.saxontheweb.net/content.php?tabid=73

Then, under 'section widget' [?!] I clicked on "FAQ", which is the bottom option on my display.
https://forum.saxontheweb.net/content.php?663-faq

Usually I have to click on the "read more" option, but in this case the very first frequently asked question is about materials and finish. Having been through every one of those threads (I think), I am confident that quite a bit of the discussion is about the vibrations of a column of air in a sonorous tube as a source of sound, as opposed to the vibrations of a solid body, such as a bell or cymbal, and as opposed to the body of an instrument as a resonating chamber, such as with a violin.

In any event the whole pile is well worth reading, if that sort of thing is of interest.

The OP is particularly interested in the instant thread about the matters of missing volume of the perfect cone.

As for myself, I was long under the impression that the volume of the entire cone was of crucial importance, and could not work out how the various makers could get away with altering total cone volumes by making some bodies wider than others. I assumed that the wider the body, the shorter the tube, to maintain a constant pitch. However, it was pointed out that, to an amazing degree, the length of the tube alone determines the pitch, while the other parts of the geometry of the tube alter the timbre. In addition, however, [mostly because the sax tube is a cone, rather than a cylinder] this rule breaks down in the area of the neck and the mpc, where the volume does start to alter the pitch significantly.

There now. Should not be surprised to learn that a great deal of what I just wrote is a load of old tosh. But that is good! It can be corrected by those who know better and my understanding will be improved thereby.
 
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I am very interested!

Does anyone here know about the state of the art in acoustic modeling?
For instance, can one mock up an instrument in CAD and analyze acoustical aspects computationally (using open source software)?
 
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