Struggling with high-end notes

[DrPhill]

“But I don't want to go among mad people," Alice remarked.

Oh, you can't help that," said the Cat: "we're all mad here. I'm mad. You're mad."

How do you know I'm mad?" said Alice.

You must be," said the Cat, "or you wouldn't have come here.”
― Lewis Carroll

Lewis Carroll was a master of logic, logical fallacy, and disputation. Not only are his works of fiction a delight, but they are also educational if read rightly. Here we have a marvelous and witty example of a circular argument. Thanks Denny.

[benhall.1]

So if I use the term 'harmonic series' in the limited mathematical sense, and the term 'fundamental' in the sense of meaning the first term in the strictly mathematical harmonic series, then my original assertion still stands?

No! Because, and this is the point that I thought I'd made pretty clearly already, the use in its strict mathematical sense doesn't equate to the use of the term as applied to musical instruments. Which is what I meant by saying that bit about not wanting to start from here when going to Dublin.

Take set theory. Put simply, the mathematical meaning of "harmonic series" does include the meaning as applied to musical instruments. But it covers a bigger set. It includes things that don't apply to music as well as those things that do. In part of your argument, Phill, you are trying to include something that doesn't apply to music. In other words, all "harmonic series" in the musical sense will include the proportions 1:2:3 etc (as modified by string density and width, bore diameter blah blah); but not all series of numbers with the proportions 1:2:3, even as they may occur in music, are exactly equivalent to the "harmonic series" of which those proportions may form a part.

And if we use the terms 'harmonic series' and 'fundamental' in the musical sense, then my original assertion is palpably false?

Yes! And you can quote me.

Right. I'm off for a bit. Not 'cos I'm in the least fed up with this , but because I suppose I have to earn my keep at some point.

[david_h]

This is doing my head in. Can I try this ?

Go back to E5 from XXXXXO (to avoid the D issue for now). We blow the whistle in such a way that we get an E5. The jet at the fipple is flipping backwards and forwards at the frequency of E5. It is doing this because the effective length of the tube is just right to resonate at that frequency. (someone kindly put a calculator on the web so we could drill the hole in the right place)

As an alternative to MTGuru's string lets imagine the other possible resonances as pendulums. We can make a pendulum that swings a twice the frequency of E5 swing by giving it a push on every other swing (E6) , one that swings at three times that frequency by giving it a push every third swing (B6) etc. But we can't get a pendulum that is not an exact multipe of E5 swinging.

We blow a bit harder, the jet speeds up so it can't switch at E5 but it can switch at E6 which has a wavelength of halve of E5 so the tube length is OK for that as well (there is a pendulum at that frequency). But now we can't push the B6 pendulum because it doesnt swing towards us at the right time. We can only do the ones that are at twice, three times etc the frequency of E6. This is every other one of the pendulums that are available in the tube.

Blow a bit harder and the jet is going too fast to switch at E6 so it goes to the next available 'pendulum' which is B6 (and the neighbours start hammering on the wall). As well as B6 we now get every third pendulum in the sequence made available by the dimensions of the tube.

Now in each case the spectrum of the sound that comes out includes frequencies of twice, three times, four times etc the lowest one (not much for B6 but in theory it is there). What could mathematicaly be called a harmonic series.

So. We have harmonic series each of which a listener could regard as having its own fundamental and a single fundamental for that tube lenght.

However, the physics of what is happening is related to the resonances available in the original tube and which are present in E5. E5 is the fundamental note for that tube. The tube that generates E5 as its lowest note is what provides all the other frequencies that we can produce, individially and/or as part of the spectrum.

The fundamental for the tube is what matters when it comes to talking about what we can and can't get out of it.

Blow notes from XXXXXX and we get D5, D6 and A6 in the same way. The frequencies we have available are related to those in D5, the fundamental.

Blow a D6 from OXXXXX and exactly the same happens as with the one from XXXXXX except that because the open hole prevents the pendulums that swing at even multiples of D5 from working it is easier to get the jet generating the note that does not need them. The venting is different so the D6 might sound better. But once it is sounding the basic physics is exactly the same as for XXXXXX . When playing D6 using either 0XXXXX or XXXXXX the A6 note is utterly irrelevant because it can't sound - it is not mutliple of the frequency at the jet and in the case of 0XXXXX the venting stops that 'pendulum'.

(Edit for mainly for typos and grammar. And again for clarity a bit later)

[Denny]

you need to build a pendulum...

[hoopy mike]

Excellent jokes guys - brought a smile to my face.

Just call us the three stooges...

[Thomas-Hastay]

Cylindrical bore whistles are prone to shrieking in the upper notes/registers. Creating backpressure between the top tonehole and the voicing helps a great deal with this but must be done by a whistlesmith. An easy "tweak" to help with this is reducing the bore end hole diameter with putty etc. You will be required to blow harder to increase/pitch correct the lower notes but it will help reduce the windway velocity on the high notes. In effect, High notes with less breath pressure = less shrieking. A conical bore is the the most popular cure at the expence of musical range (2 usable registers).