We’ve had much discussion over the years about the relative merits of flutes that are “well tuned” – i.e. just blow them and you get the notes you need, vs the “old-style flutes” which tend to have very flat low end notes. The enthusiasts for these old-style flutes (either actually old flutes or in the form of modern replicas) maintain they get better results by having to deal with the tuning by special blowing. So far no-one has managed to support this claim in terms of physics. I’ve been putting in a lot of work (almost to the point of detriment of health and fortune!) on flute acoustics over the last few months and now believe I have an angle on it. Whether I can spell it out well enough to make sense to others is still to be determined. We need to start with a short flute physics refresher…
When we softly play low D (D4) on a “well-tuned flute”, a pressure wavefront runs down the flute from one end to the other, reflects at the first open hole and returns to kick the jet out of the embouchure hole. The turnaround time is precisely what is needed to generate D4.
When we push a bit harder, some of the energy goes only halfway down the flute, before turning back. Because it takes only half as long to get back, the frequency and therefore the pitch is double – we’ve added some 2nd harmonic content, D5.
Push a bit harder and some of the energy goes only 1/3rd of the way down the flute, we’ve added some third harmonic, known also as A5.
It doesn’t stop there – there will be harmonics up to about 5KHz. But we’ll stop there – it’s enough for our story to consider the first three.
Because this is a “well-tuned flute”, the three energy waves arrive back at the embouchure at the same time, reinforcing each other as they kick the jet back out of the embouchure hole. The now harmonically-enriched D4 sounds focussed, crisp and hard-edged. A Fast Fourier Transform (FFT) of the resultant sound would show the three harmonics. The D4 note is easy to play.
When we blow softly in a “old-style flute”, D4 comes back flat, probably between 20 and 60 cents flat. But when its skilful player starts pushing into the note, the perceived pitch rises as the note becomes harder, as the harmonic content rises. We’ve assumed in the past that the skilful player is “lipping up” the note, closer to the D4 we want. I now believe that is not what is happening.
(Aside: In the real world we can expect a range of things to happen, and lipping might be part of it. But not, in this submission, the main part.)
Instead, I believe the skillful player is getting the D4 in tune by eliminating it from the mix of harmonics. Or, at least, by minimising the proportion of D4 in the mix. Let’s see how that would work.
The skilful player introduces significant offset between jet and edge, typically by blowing downwards towards the centre of the flute. Fletcher has shown in both experiment and theory that this offset reduces the fundamental content(D4 in our example) and increases the 2nd and 3rd harmonic content (D5 and A5 in our example).
The mix of wave energy returning to kick the jet out of the embouchure hole no longer has appreciable amounts of D4 in it. So the timing of the resonance is no longer dependant upon it, but on the timing of the remaining mix of upper harmonics. In the old style flute, second octave notes tend to be reasonably well tuned, so that’s got to help.
The ear still hears the missing D4, as the brain assigns pitch based on the distance between harmonics, not just the pitch of the lowest harmonic. This can be readily demonstrated by filtering the fundamental out of a triangular wave – the listener can readily appreciate the change in timbre but will not hear it jump an octave.
So our skilful player has taken an old-style flute with a very flat D4 and, by dint of selective blowing, made the flute sound more in tune, not by lipping up the defective note, but by minimising the contribution of the defective note. Further, the tone has been enhanced by two different and equally important mechanisms. Firstly, the combination of harmonics gives a hard-edged sound that pleases the traditional player. Secondly, eliminating or minimising the discordant contributor improves the focus of the sound, as the remaining in-tune harmonics reinforce at the jet. The flute will be more resonant and more in tune than if the flat D4 were permitted to remain in the mix.
This would explain why it took about 100 years to eliminate the flute’s flat low end - there was not a great need to do so. This seems more likely than the alternative explanations, such as “they liked it flat” (why?) or “they didn’t realise it was flat” (I bet the piano player did!) or “they couldn’t find a solution” (and yet they made such lovely flutes in all the other respects).
It’s often felt by skilful players that the “old-style flute” is better than the “well-tuned flute” as it permits the harder toned low notes. Nothing in the theory above supports that view – the “well-tuned flute” should be capable of being played in the same way, producing the same results. It’s just less necessary. Rephrasing slightly, we can say ‘it is only possible to play the “old-style flute” in tune if we use a selective blowing method that reduces the impact of the discordant fundamental’. It may be that the greater, indeed absolute need to push the “old-style flute” provides more incentive to the skilful player, subsequently providing great satisfaction when achieved.
A few other things become evident:
We are not all skilful players – not everyone will be able to achieve satisfactory results on an “old-style flute”.
If new makers want to make “old-style flutes” they need to advise their customers that they will need to use a selective blowing technique.
New “old style flutes” really should be marked so that 2nd-hand purchasers know what they are getting.
Those makers wishing to build “well-tuned flutes” need to consider the relationship of their harmonics to ensure that a range of tonal colours can be educed without unwanted apparent pitch changes. A combination of this new understanding and real-time measurement techniques (RTTA) should be able to deliver flutes that are capable of great results across a wide range of blowing approaches.
The usual wisdom of placing the stopper at around 19mm will need to be reconsidered. Soft blowers may find better results at greater stopper distances; selective (hard-edged) blowers may benefit from reduced stopper distances, even in the 15 to 17mm range. This weakens the fundamentals (who cares, if you are trying to kill them off anyway!) but improves the tuning and focus of the harmonics, where such blowers are intent upon placing their energy.
It would be good to hear from selective blowers as to what works best for them. Interestingly, players using Rudall & Rose’s Patent Head are probably already there. This supports my view that the 19th century English tonal ideal is not dissimilar to the 21st century Irish ideal.
There are quite a few more ramifications of this new understanding, but they’ll have to wait their turn.
(Exhausted, he slumped back. Foolishly, he allowed himself to lapse into a deep sleep before donning his flak jacket…)
Terry
.) So in my universe the harmonics travel the full distance but do it twice/thrice as fast. But then there would be that pesky instant where the positive pulse on the way down meets the negative pulse on the way back. Hmmm..
) But using this model I can see where putting more (different?) energy into the embouchure would favor the harmonics over the root.