When does a cylinder become a cone?

[benoit trémolières]

When makers speak of 'voicing' a chanter, they are often modifying the chanter to their 'standard' reed.

Absolutely!
And all the reedmaker job consists to refind this particular way of making a reed.

And I'm pretty sure An Seanduine's method of checking the reed by means of how it crows gives to the confirmed maker a huge amount of information, probably very difficult to synthetise in an informatic progam. (many of us are able, after a few years of practising, to know if the reed is sharp or flat without even trying it in the chanter. We can deduce very precise things from this simple check.)
I think that what we need is, as previously said, a correct representation of all the parameters defining the reed head, and how they act together.
This is the first step to be achieved, and there's still a lot of work to do in this area. (I have allready written all I know on the subject, but it is a thirty page draft, in french...). The job has to be shared with as many makers as possible, to be sure the conclusions are correct.
Then the scientific part could come into action, trying to simulate things, in order to spare time in the empiric research.

But I'm inclined to believe that mere empirism could eventualy come first at the goal...

[Ted]

When a chanter is copied, I find a reed that works well in the original is best to voice the copy. That is simple enough. Many chanters have been attempted that are not copies. With hobby shop tubing available, many makers wanted to use it for staples and tried to voice and tune their efforts with a reed with this tubing. Very few have produced really good results with this approach. Some concert pitch chanters do best with a conical staple. Many flat chanters are not as particular and do well with 5/32" tubing staples. I tend toward standard head shape and use different staples to find the sweet spot for the reed.

[Tunborough]

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?

I tried using Mike Nelson's numbers to see how his reed compared to my model. I don't have enough information about the bore diameters to do a proper job. For every drone setting that produces, say, G#, the bore calculation (without the reed) should give the same susceptance. I could do that if I made some assumptions about the bore diameters from some of his diagrams, and with those assumptions I got the nice straight line my model predicts for the reed, but I'm not sure that's a fair test.

[Driftwood]

I tried using Mike Nelson's numbers to see how his reed compared to my model. I don't have enough information about the bore diameters to do a proper job. For every drone setting that produces, say, G#, the bore calculation (without the reed) should give the same susceptance. I could do that if I made some assumptions about the bore diameters from some of his diagrams, and with those assumptions I got the nice straight line my model predicts for the reed, but I'm not sure that's a fair test.

Encouraging results, I think.

[Alterius Omega]

[Thread revival. - Mod]

...So how does it suddenly switch from the 3rd harmonic to the 2nd just because the bottom end gets a bit bigger.

Turns out, it doesn't. It's a gradual change.

Thanks so much for this! I'm a flute maker (mostly shakuhachi and quena) and this question has been burning in my mind for a while but I haven't had access to modeling software or found the correct equations to make it make sense.

I always hear people talking about conical vs cylindrical in a very black or white way as if its just one or the other but that didn't make sense to me because "conical" could mean anything from barely flared to almost plate-shaped. Especially with bassoon which visually barely looks tapered at all from the outside, it seemed odd that merely tapering the bore any amount would instantly change which overtones you can play on it.

So did you find a relatively simple forumula for what taper angle is required to make a single reed instrument play in tune in both octaves for a given length?

I'm very excited to try out the WI Designer software so thank you for the recommendation!

[an seanduine]

Turns out, I found a real world example that bears on this question. I have a 19th century flageolet (a true flageolet, with a beak and upper chamber for a bit of sponge for moisture absorption) set in very close to modern key of D.) which fingers much like a concert D chanter (barring the closure of the foot). It has a back D and a tiny Eb hole at the foot. It's taper is extremely slight. I initially thought of it as fingering like an English recorder, but the more I play it the more I am struck by how it follows the pattern for a concert D chanter for the first two octaves. Because of its rather narrow bore and very slight taper, it has a characteristic sound of a whistle and not a Recorder.

Bob

[Alterius Omega]

So I hope someone can tell me if I'm on the right track. I've been reading this page and I think I'm starting to understand the nodes of conical instruments.

I've known for a long time the difference between closed-end cylindrical instruments like the pan flute and open ended ones like a normal transverse flue. I understand that the closed end ones have basically half the waveform of the open-ended ones so they are half the pitch, and I understand that they can't play even harmonics because the pressure must be atmospheric at the open end and maximum at the closed end. This means if you overblow a pan flute it will jump up an octave plus a fifth (12th)

What didn't make sense to me is how a closed-end conical instrument can play the even harmonics and my current understanding is that it actually can't. It still can only play the odd harmonics (that is, it can make the half-waveform shape of an open-end flute but only every other one). The only difference is that the taper of the bore gives a different equation for the actual wavelength/frequency produced due to the cross-sectional area increasing linearly.

What I think this means is that while a sax for example can still only produce every other hamonic waveform, the equation is different such that the actual frequencies of the pitches of those waveforms has been "squashed" closer together so instead of the 3rd harmonic producing a 12th, it actually produces an ocatve. Am I on the right track?

[Tunborough]

So did you find a relatively simple formula for what taper angle is required to make a single reed instrument play in tune in both octaves for a given length?

I didn't even try. As pointed out early in this script, much depends on the reed, so I'm not confident we can draw general conclusions.

What didn't make sense to me is how a closed-end conical instrument can play the even harmonics and my current understanding is that it actually can't. It still can only play the odd harmonics (that is, it can make the half-waveform shape of an open-end flute but only every other one). The only difference is that the taper of the bore gives a different equation for the actual wavelength/frequency produced due to the cross-sectional area increasing linearly.

What I think this means is that while a sax for example can still only produce every other hamonic waveform, the equation is different such that the actual frequencies of the pitches of those waveforms has been "squashed" closer together so instead of the 3rd harmonic producing a 12th, it actually produces an ocatve. Am I on the right track?

You're more-or-less on track, but we need to distinguish between modes of resonance, which define the resonant frequencies of a particular system, and harmonics, which are strict multiples of the fundamental resonance that may not correspond to modes. See https://newt.phys.unsw.edu.au/jw/inharm ... ances.html for more explanation.

In a flute or whistle, the resonant modes are where the tube contains a standing wave of one half cycle, two half cycles, three half cycles, .... In a cylinder, the frequencies of these resonances are pretty close to one, two, three, ... times the frequency of the lowest resonance, which are all the harmonics of the lowest resonance.

In a reed instrument, the resonant modes are where the tube contains a standing wave of 1/4, 3/4, 5/4, ... cycles. In a cylinder, the resonant frequencies are pretty close to 1, 3, 5, ... times the frequency of the lowest resonance, which are the odd harmonics of the lowest resonance. Moving to a cone, as the bottom end of the cone gets bigger, all of the resonant frequencies increase, while the ratio between those frequencies decreases. Eventually, as the cone gets wide enough (and long enough), the second mode falls at twice the frequency of the first mode, which makes it the second harmonic. (Getting the higher modes to line up with the higher harmonics can take some fancy adjustments to the bore profile.)