When does a cylinder become a cone?

[an seanduine]

Benoit, the real takeaway from Patrick Murray's study is the need for more direct, real-time observations of a functioning reed. As you yourself have remarked, the behaviors of the reed observed by Murray at various frequencies appear to point toward Chladny patterns, which are a direct expression of harmonic behavior.
My intuition is that there are two linked behaviors in the reed. One is harmonic, as shown by the patterned behaviors observed by Murray, and the other, the valving action at the lips. The shape, length and symmetry of the scrape control the harmonic behavior. The stiffness and resiliency of the reed material, as well as the smoothness and regularity of their formation control the valving action of the lips. Not a simple system!!!

Bob

[benoit trémolières]

Y agree completly with this idea that what we really need, and will be really usefull, is something like filming a reed in action, with stroboscopic oblique light, in order to simply look at its very mouvements.
I'm afraid makers would do a far better use of such experiments, than with deep dark calculation devices, witch most of them are completly unable to deal with.

[Tunborough]

When we're just looking at tuning alone, and not timbre, volume, responsiveness and all the rest, I think we can get by with a fairly simple model of how a reed affects the tuning of a chanter. The model I'm working with now has only two parameters and it's given good results. Unfortunately, I can't yet get those two parameters from anything you can tell me about the reed (size, stiffness, crow, ...) until you stick it in a pipe and blow on it.

In other news, I was able to use a more conventional bell to tune the first 5 harmonics of a hypothetical double-reed instrument. WIDesigner came up with a conical bore with a modest bell on the end, rather than the highly flared trumpet-like bell I tried earlier.

[benoit trémolières]

But what Y notice more and more is that the relative tuning of the scale is deeply connected with the timber. Both are getting together.

[Driftwood]

When we're just looking at tuning alone, and not timbre, volume, responsiveness and all the rest, I think we can get by with a fairly simple model of how a reed affects the tuning of a chanter. The model I'm working with now has only two parameters and it's given good results. Unfortunately, I can't yet get those two parameters from anything you can tell me about the reed (size, stiffness, crow, ...) until you stick it in a pipe and blow on it.

What are those two parameters and what relationship do they have with a real double reed?

[Tunborough]

What are those two parameters...?

Well ... do you want the detailed answer involving impedance, admittance, and imaginary numbers? A shorter, less technical, answer would be ...

• Put a real reed and staple into a real pipe for which you know the resonances, and measure the playing frequencies.
• Calculate a difference factor (Imag(Y) or susceptance) between the resonances of the pipe and the resonances of the whole.
• It looks like, for a given reed and staple, you can model this difference with a simple linear relationship: a base value, plus a multiple of the frequency. Those are my two parameters: the base value, and the multiplier.

and what relationship do they have with a real double reed?

I know only that you can measure them with the procedure above. I can't yet relate them to anything else you can tell me about the reed.

[an seanduine]

What are those two parameters...?

Well ... do you want the detailed answer involving impedance, admittance, and imaginary numbers? A shorter, less technical, answer would be ...

• Put a real reed and staple into a real pipe for which you know the resonances, and measure the playing frequencies.
• Calculate a difference factor (Imag(Y) or susceptance) between the resonances of the pipe and the resonances of the whole.
• It looks like, for a given reed and staple, you can model this difference with a simple linear relationship: a base value, plus a multiple of the frequency. Those are my two parameters: the base value, and the multiplier.

and what relationship do they have with a real double reed?

I know only that you can measure them with the procedure above. I can't yet relate them to anything else you can tell me about the reed.

This sums up the two headed-monster of describing a reed. From the point of view of "tuning", or "resonance", the reed functions as a wave-guide. From what you've said you have a valid descriptive maths model. However, the reed is a rather complex valving system with its own resonance and feed-back system coupled to the pipe bore. . .this is the alligator in our own little swamp. . .
What's really lacking is a predictive or prescriptive model to deal with the design elements of a reed for a particular bore.
The lips have what can be described as an "aerodynamic" element. When air flows past them they "fly" or oscillate, beginning the the harmonic element of the reed. The shape and material of the scrape manifest characteristic Chladny figures which reflect and probably control the harmonic regime of the reed system.
I believe the key will be further direct observation.

Bob

[benoit trémolières]

I agree completly with that!
And, supposing such an observation will be achieved, next challenge is to get able to do it in the real world, with our primitive tools, and the mere hand to drive them!

[benoit trémolières]

Ho, and something else: I bate there will be more than one model suiting with one particular bore!

[Tunborough]

Ho, and something else: I bate there will be more than one model suiting with one particular bore!

Actually, that's where I can help you. Bob is right that the model of the reed is only descriptive. I can't tell you what you have to do to the reed to make it work in a particular chanter. But WIDesigner does have a model of the bore and toneholes that is prescriptive. If you know what the reed (or whistle head, or flute embouchure hole) does, WIDesigner can tell you what to do to the bore and toneholes to improve the tuning, including dealing with changes in the bore taper. Edward Kort has been using it for over a year to tune the NAFs that he makes.

[an seanduine]

Benoit is correct when he points out that often two dissimilar reeds will be 'successful' in any particular bore. While I don't know of any comprehensive theoretical model for reeds, we do have a loose collection of empiric observations we can apply to designing and modifying reeds. . .the shape of the upper 'V' of the scrape, the area along the margins of the scrape, the thickness of the central 'spine'. . .etc, but this leads me to another question for Mr Tunborough, as well as a cautionary warning. Some reeds are at the frontier of some limits with certain bores. Examples that spring to mind are autocranning on the bell note, and 'gargling' on the back 'D'. We are almost invariably cautioned to not modify a bore to suit a reed. . .except in the earliest stages of a design development. It's fine to treat the reed as a 'black box' which will perform in a predictable manner if it is that unicorn of a 'perfect reed', or for whatever reason is very close to the 'sweet spot' for a particular bore, but can his software give us information to support this?

Bob

[benoit trémolières]

[/quote]Actually, that's where I can help you. Bob is right that the model of the reed is only descriptive. I can't tell you what you have to do to the reed to make it work in a particular chanter. But WIDesigner does have a model of the bore and toneholes that is prescriptive. If you know what the reed (or whistle head, or flute embouchure hole) does, WIDesigner can tell you what to do to the bore and toneholes to improve the tuning, including dealing with changes in the bore taper. Edward Kort has been using it for over a year to tune the NAFs that he makes.[/quote]

I did not yet envisage the things this way, and it looks really interesting.
But I'm not sure we need a program to make these tests, because checking the reed in the chanter gives us all the informations we need.
My idea is that acting on holes and bore is really much an easier job than finding what is requiered from the reed.
That is why so many makers does the job that way: because they are not able to change realy their way of making reeds (because nobody knows exactly what can be truly considered as a "parameter" in the head), they adapt the bore and holes to their reeds.
The challenge for the reedmaker is to do the opposite...

[Tunborough]

It's fine to treat the reed as a 'black box' which will perform in a predictable manner if it is that unicorn of a 'perfect reed', or for whatever reason is very close to the 'sweet spot' for a particular bore, but can his software give us information to support this?

Excellent question. The software can give some help, and maybe we can add things that will give you more help.

It can predict what the tuning will be if you put in a reed with specified tuning behaviour. You can look closer at specific notes and perhaps get an indication of trouble spots. (This post illustrates what it can do for whistles, for example.) However, I don't think we're close to being able to model your specific examples, autocranning on the bell note, and 'gargling' on the back D; I fear those may idiosyncratic reed behaviour that a simplified tuning model won't capture. Question, though: if you have a reed that tends to, say, autocrann in one chanter, is it likely to do that when you move it to other chanters? To put it another way, are there some chanters that tend to autocrann with most reeds? If it's more the chanter than the reed, maybe we can help.

WIDesigner can also tell you what tuning behaviour you need from a reed to get a specific chanter to play in tune. If we had information about the tuning behaviour of a whole lot of reeds, you would have an idea of how likely you are to find a reed with that tuning behaviour. That's a big piece of information that's missing right now.

[an seanduine]

Empiric observations allow us to design and make reeds. Clearly to get anywhere nearer a theoretical model requires more real-time observations beyond the anecdotal information we have.
My understanding of reed behavior is as individual as anyone's and probably a lot unclearer than many. However, I have several guesses based on my experience. Auto-cranning, and some difficulties with the back 'D' seem to be in that no-man's land of the relationship between a particular reed and a particular bore, not solely the fault of the bore nor the reed. (I'm setting aside the practical consideration that some reeds are so un-symmetric or poorly constructed that they barely function). This only highlights that fact there is feedback from a particular bore to a particular reed.
It's becoming more common to record the pitch of the 'crow' of a successful red in a bore, but since we don't have a calibrated manner to achieve this 'crow' we're left with information that may not exactly transfer from one reed maker to the next. "Just exactly how hard did you suck, or blow on that reed?" Crow only gets us into the neighborhood.

It can predict what the tuning will be if you put in a reed with specified tuning behaviour. You can look closer at specific notes and perhaps get an indication of trouble spots.

The difficulty with this is that individual notes produced by a reed are influenced by the gradient of the scrape: thickness/width and shape. Tuning the bore before considering the reed is, I think, ill-considered. When makers speak of 'voicing' a chanter, they are often modifying the chanter to their 'standard' reed. If the maker does have 'standard' easily reproducible reed, this fine, and doesn't lead us too far astray.
But this isn't always the case.

Bob

[Driftwood]

Put a real reed and staple into a real pipe for which you know the resonances, and measure the playing frequencies.
Calculate a difference factor (Imag(Y) or susceptance) between the resonances of the pipe and the resonances of the whole.
It looks like, for a given reed and staple, you can model this difference with a simple linear relationship: a base value, plus a multiple of the frequency. Those are my two parameters: the base value, and the multiplier.

This reminds me of some research that you can find on this website: http://www.machineconcepts.co.uk

It involved using the same drone reed and a set of drone pipes with the sliders in different positions to obtain different frequencies. The standing and sliding parts were mixed and matched to obtain all twelve semi-tone frequencies in an octave range. In each case the length of drone tube, including the reed body was compared with the "true" acoustic length (presumably based on the speed of sound as a constant). A table of ratios (i.e. x/y) was obtained from these comparisons which showed the effect the reed was having at each frequency.

Is your reed model based on something like that?