Sympathetic Resonance?

Irish Flute
1

Greenwood referred to this point the other day in the post on embouchure.

I have an acoustics question regarding alternate fingerings on simple system flutes, specifically when fingers are added below the target note. Obviously this can flatten the note, but I notice that in some cases it makes the note more resonant or helps you initiate the sound easier: XOO XOO’ for B, or OOO XXX’ for C#.

Even for the preferred fingering for the high E note, XXO OXX’, it would seem like the venting on holes 3 & 4 would make lower fingers irrelevant.

I guess the acoustic behavior of the entire flute body is important.

I can imagine that extra fingers (or holes) triggers sympathetic resonances, or maybe it cuts off or enhances higher-order harmonics.

2

I understood that that, or killing the fundamental, was what most cross-fingering was about in the second and third octave. And what we are supposed to do with the Eb key in the first octave.

3

A lot may depend on the design of particular maker’s flutes.

4

The effect of open tone holes differs depending on the frequency of the note being played. For lower frequency notes, the first open
tone hole effectively defines the end of the bore, i.e., the effective length of the bore is the length from the embouchure to
the first open tone hole, and the rest of the flute below is more or less irrelevant. However, for higher frequency notes there is
not enough time, within one cycle, for the air mass within an open tone hole to be accelerated enough to excite the outside air,
so the open tone hole does not effectively terminate the bore, and remaining part of the flute below the first open tone hole continues
to play a role. This is one reason why forked fingerings work better for higher octave notes.

The effect that these tone holes lower down the bore have on a particular note will depend on how well they align with the pressure
nodes in the vibrating air column for that note. So, it is not really about sympathetic resonance.

The following paper has some more detailed discussion of this for various types of flute (baroque, classical, Boehm etc):

https://newt.phys.unsw.edu.au/jw/reprints/crossfingering.pdf

5

Thanks Jonathon, that makes sense.

(Jonathon: The man with the most improbably clean workshop)

6

Well, yes. But unfortunately, that is mostly a sign of inactivity, due to some health setbacks I’ve had which stalled my flute making efforts a while ago.
I do aspire to a clean workshop though, but I have it on good authority (from Geoffrey Ellis) that one should never trust a man with a clean workshop! :really:

7

On one flute, all in 2nd octave
XXOOXX

Gives higher than
XXOOOO

(Actually the note between that and
XOOOOO)

And very clearly. That note is a harmonic of Eb I think, and Eb is not present in first octave, so though I agree with what you are saying Paddler, I also think that venting layout (or stopping holes) creates a “virtual” harmonic, i.e. a sympathetic resonance that starts at a vent point that does not exist. It might be understood somehow that the central OO venting has the effect of shortening the flute, or it might be that the wave frequency is set up between lower OXXO (the last O being the end) and that that sets resonance of top half of flute also . I don’t know, but I think there is more going on that just end effect differences…at least I mean that it seems the extension of end effect for higher octaves does find its own dynamic in the lower part of the flute which then effects the dynamic of main part of the flute, beyond just the straight effect an increased or decreased venting would have.

?

8

I think it is all about how the locations of the pressure nodes/antinodes for each particular frequency (note) align with the open tone holes in the part of the flute between the embouchure and the first tone hole that succeeds in terminating the bore.
If closing tone holes further down the bore has an effect on a particular range of frequencies, it is because the open holes above them did not succeed in terminating the bore for the frequencies in question. But when one of these open tone holes aligns
with the location of a pressure node for a particular frequency, it prevents the flute from resonating at that particular frequency. For an example of this, think of venting the nearest tone hole to he embouchure to cause a flute to play second octave D
rather than first. Here you are opening a hole right around the pressure node for the low octave D, and effectively turning that into a pressure antinode, cutting the wavelength in half. But that hole is not terminating the bore, because opening tone holes
further down still has an effect. By closing such a hole you reenable resonance at that frequency.

So it is not really sympathetic resonance, at least the way I understand the meaning of that term (i.e., a pre-existing resonant vibration inducing a resonant vibration in another string/body/etc that was not previously vibrating).

9

I understand what you are saying.

Still, first and second octave of XXOOOO both sound closely in tune, which in theory means they are both venting successfully at the first open tonehole (and basing this whole theme on first octave naturally doing so). Second octave does react more to say XXOOXO than first, because there is some venting there from overshoot of second octave pressure, possibly even a node at the extra X. However covering that tonehole lowers the second octave pitch.

To raise the relevant second octave pitch above first octave one for XXOOOO is going to need that the first O vents more than it is able to. This is not going to happen. Therefore it suggests that a distinct waveform has taken shape.

I agree that the D vent forces a low pressure node, but I cannot figure out how closed toneholes lower down are going to force up the pitch of the original 2nd octave note, unless they actually help set up a completely new waveform. I agree the remaining open toneholes contribute to that new waveform. So whether the new waveform is due to sympathetic resonance, could only really be answered by looking at if a secondary resonance sets itself up in the lower half of the flute after the initial second octave sounds and then pulls or pushes that initial second octave to conform, or if alternatively the new waveform simply forms directly from the whole layout.

It is nitpicking maybe, but actually either view does reveal or present a different detail on how the flute actually works. For example, if lower half resonance is found capable of setting/influencing 2nd octave pitch towards a new waveform , it can be built in or amplified in a way that does not only involve toneholes. If the new waveform is formed in one go, then attention to tonehole placement might be a priority.

10

Every frequency has its own waveform. The air column within the bore will resonate at the frequencies allowed by the
effective bore length, the open tone hole matrix presented to it, and the energy input. In your example, by closing a lower
tone hole you enable a resonant frequency that was not possible before because the previously open tone hole aligned the
wrong way with the pressure node locations for that frequency. Closing tone holes further down the flute can raise or lower
resonant pitches when you are considering high frequencies that are resonating in an air column that includes the lower sections
of the bore beyond the first open tone holes.

I think your reasoning based on assumptions that increasing/decreasing venting raises/lowers pitch, only applies to cases in which
the first open tone-hole effectively terminates the bore (i.e., the lower octave).

The behavior of flutes and the physics that underlies it has been well understood and documented for over a century (probably a
lot longer actually). I can provide some references to texts that cover the details if you want to do some reading about it. It might
save you a lot of time hypothesizing and trying to reinvent the wheel.

11

Yes, I second that assessment.

I tried XXOOXX in the second register on two whistles, and got the same result, a pitch higher than XXOOOO. A computer model (on a Feadog, because that was what I had on hand) shows two potential resonances for XXOOXX near that frequency: the one you expected slightly lower in frequency than XXOOOO, and another that is higher in frequency. In this case the higher one ends up masking the lower one, so you can’t actually hit the lower resonance. Next step is to measure out the tube and estimate where the pressure nodes are falling.

12

Re. Paddler

I’m not going to reinvent anything I think, because whatever mechanics are at work are what they are.


I understand well enough how the sound wave forms in a flute, and around first open tonehole is the effective end of flute in 2nd octave also, where full venting is allowed below that.


To use the D2 analogy for simplicity though, the dimensionally limited working model often used




is a little cruel maybe? Clearly though, venting of the high pressure node of D encourages the formation of an octave overtone with low pressure at that point. Similar occurs with different combinations of toneholes forming partials. There is a whole load of math to figure that out and it looks impressively time consumingly official. Is that what is occuring in reality though.

You yourself say the wave is cut in half, so my reason tells me that you agree there are two waves. One inhabits the region towards the embouchure and the other towards the lower end. The waves in each are NOT the same. You would only have to take a few measurements to understand the parameters and quality of each is very different. However, they interact, they combine, one influencing the other, to fit into, in a merged way, the overiding dimension of total bore length. Harmony.

You would notice also that placing C# vent closer to where D2 would be, changes the tone and makes it purer. This is easily understandable but also underlines the point that both waves are otherwise distinct.

So picture one wave being sent out, what is happening really is that a lowered (because of lack of venting when only C# is lifted) C# note is formed in embouchure side. That wave then travels the lower portion of the flute and reflects, resonating between end of flute and C# tonehole, giving another distinct note. However when it reaches the C# tonehole on return, it encounters the next wave from embouchure side, and it and that merge under C#, they synchronise in spite of their differences, because the open tonehole is near enough both of their resonant nodes to allow/encourage that. The synchronised result matches total bore length by half, but, they are still two distinct waves, that resonate with different harmonics , but at a now common pitch, because the total reflected length (and so any isubdivision) is more decisive for that (obliges a set frequency) , than harmonic vent point.

By that model, tonehole size and placement matter, but should not be confused with bore characteristics on each side, which will also influence how or where the two waves meet. Clearly, the resonance in lower half effects how and where the wave in top half forms. Just move the toneholes and it sorts ? It would seem, but that is not what I am saying. Changing bore shape or diameter has as much effect. Same result and different approach ? Not if you are making a flute and choosing between a longer narrower bore or moving a tonehole north.

13

I agree with that on sympathetic resonance Turnborough as per Paddler’s definition. The definition I had in mind was the resonance of lower half of flute influencing already vibrating upper half sympathetically to a degree, in which case I would say there is some sympathetic resonance. Definitions and details etc.

What I was also wondering for the XXOOXX phenomenon, is if the partial venting of the OO had the effect of a virtual widening of the bore there. I say this because the Bb2 note sounded on a D flute with that fingering , is a partial harmonic after Eb2 for an Eb flute (if my calculation was correct) . In other words the OO venting making the flute effectively an Eb flute. That with new nodes from the OO also reinforcing the Bb2 note, and possibly the OXXO(end) length helping set frequency also to that pitch. It is just an idea.

14

This is what I think is happening with the XXOOXX fingering …

At resonance, you have a standing wave in the tube. The standing wave has pressure nodes, where the pressure isn’t changing, and air is moving back and forth. Between the pressure nodes are pressure antinodes, where the pressure change is a maximum and the air isn’t moving much. The distance between two nodes is the half-wavelength; the longer the wavelength, the lower the pitch.

Fingering XXOOXX in the second register, there are four pressure nodes: at the embouchure hole or whistle window, in the tube above hole 1, between holes 3 and 4 (possibly near hole 4), and at the open end of the tube. There is a pressure antinode in the OXX section at the bottom of the tube, possibly near the closed hole 6. At the pressure node above hole 4, the OXX bottom section presents an impedance of zero. This gives three half-wavelengths; on a D4 flute, this will sound around A5.

You can’t have a pressure antinode at an open tonehole, so when you open up holes 5 and 6, there is no longer a half wavelength standing wave in the OOO bottom section. Near hole 4, the impedance will be low, but not zero any more. This will shift that pressure node down the tube a little way. The wavelength will be a bit longer, so the sounding frequency will be lower.

15

I say this without malice, but what you write about sound waves (and acoustics) doesn’t make any sense to me. If you’re really into that sort of stuff, you might find it useful to get a better understanding of complex waveforms, standing waves and the acoustics of open tubes, instead of speculating about where this or that wave might “inhabit” in the bore of the flute. Here’s a nice introduction to the acoustics of flutes :thumbsup:

16

Oh, I think I take criticism for whatever it is worth. For example ad hominem is supposed a failure to argue rationally, or condescension might be seen as prejudiced conceit or even a form of assumed entitlement. Etc.

I don’t expect my view to be understood, and frankly I’m really not into the mathematical representation of waveforms and similar, but take a more “mechanical” approach. I will explain the difference. Mathematical models are drawn from measurements of the resulting waveform from any particular arrangement. From those a picture is deduced of how the whole has interacted at any one point in time, and the parameters that effect that whole are calculated into a reliable equation. That is fine by me, it works, and I understand the picture it represents.

My view though is based on trying to understand the detail of how a waveform is achieved based on a progressive sequence of realtime events. That is to say, I am looking at how one particular pressure wave acts as it reflects at the end of the bore, interacts with similar on its return journey, and around TH1 has the effect of interfering with an incoming wave to the extent of shifting its pitch higher, so setting up a new standing wave pattern that suits bore length, not TH1 frequency. There is no other way I can think of for D2 (TH1 lifted) to sound but by interaction from a reflected wave at bore end, a flute will just play C# at TH1 otherwise.

Either way, the wave of D2 in lower part of flute will be different from higher part, they will not be mirror of each other because pressure differences at ends are different, bore characteristics are different along each part, TH1 is situated differently to ideal node position for each half. The result will be that the wave shape (sound not length) in lower bore, will be different and influence that of the top half by interference with it - in other words it creates a new sound based on the reflection of the wave formed in the lower bore. At this point we are talking soundform, not wavelength, because the wavelength has already become harmonized to D2.


I’m ok to agree to disagree, and do not mean to complicate how others approach all of this. :thumbsup:

17

No matter how you look at it, there is no sympathetic resonance going on here. There is only one bore and only one air column.
Its just resonance! Nothing sympathetic about it. Pre-existing science explains all of this perfectly well, analytically, mathematically,
mechanically, and physically. You can even verify it practically, as many have already done.

It is not a new result or just someone else’s speculation. There is real, peer-reviewed, science on the subject. It has all been thoroughly
documented for well over a century, and is covered in most text books on musical acoustics. People build real instruments and even
computer-based simulations of instruments, on this foundation.

It may sound old fashioned, but there are real advantages, both to yourself and the community as a whole, to taking the time to read
and understand what is already there in the literature. As Isaac Newton once said, “If I have seen further, it is by standing on the shoulders
of giants”.

I have also heard people try to argue the corollary, “If I haven’t seen further, it is because giants were standing on my shoulders”. But maybe
here we can at least try not to stand on each other’s feet!

18

Greenwood, I’m not being condescending, I’m just pointing out that you have an incorrect understanding of sound waves. if you don’t expect your view to be understood, how is this supposed to lead to a constructive discussion? :confused:

19

:thumbsup:

A nice variation on this theme: “we’ll be a lot longer discovering the future if we don’t recover the past” (John Mathieson Anderson)

20

Flutern, I didn’t say you were. My reply was in the sense that you sort of implied I might take being suggested to badly, i.e. that in itself is just a tad demeaning. Clearly, people read the tone anything is written in so

“There’s a ton of info at … and that might explain something”

Is quite different from

“Why don’t you go and learn some basics before confusing everyone”

But, funnily, I’m much easier with being told than talking around in circles, just because it is that obvious. I took your suggestion as well meaning, incidentally :thumbsup:


Paddler, I’m fine with your definition, and have said so. Resonance is sympathetic, and as far as I know always. A molecule will move sympathetically to the behaviour of any neighbouring it.

For the mechanics and physics I don’t think it is fully understood. Maybe I am not up to date with the latest, but there are details that are not explained as far as I know.

For example

“As their introduction rightly says, “this involves the interaction between three different phenomena none of which are well understood”.”

http://www.ece.uvic.ca/~bctill/papers/numacoust/Coltman_1976.pdf

And sure, the paper is '76 , but the exchange is 2012 I think. There are various other details poorly defined, Benade describes several for example where he gives clear mathematical instruction but where detailed physical explanation is lacking, and understandably.


So for the example we were talking of, are you saying reflection from D1 sets edgetone and that stops C# from sounding, or would you say the waveform of D2 does not allow C# to sound for some reason, as in it shifts the pressure node somehow? I am able to play the two as a beat for a moment, where does that C# wave then go ??? If I close all toneholes below and the end of the bore the flute plays C# well, just as it does with all toneholes open. If I slowly uncover bore end it rises smoothly to D2. This seems to tell me that it is not resonance per se but impedance that is setting pitch. That is part of what I was saying re. Terry’s piccolo.

Anyway, “peace bro” (and I guess you’d have seen these, but others not)

1079×1545 319 KB



(Chlandi waves on a soap bubble in a flute, the pattern is from the film resonating and not a direct picture of pressure pattern across a flute, but I guess air might well also hold its own patterns somehow. From researchgate.net/publication/228923308_Visualization_of_sound_waves_using_regularly_spaced_soap_films )