Cutoff frequency

[bansuri]

Can someone explain what is meant by Cutoff frequency when applied to a flute.
The term is used on a site that calculates the size and hole positions on a flute.
Tried searching google but still non the wiser

[Tunborough]

One of the primary sources would be Arthur Benade's book, Fundamentals of Musical Acoustics. In brief, when there are a lot of open toneholes, they tend to dampen the response at higher frequencies. You can see a graphical illustration of what this looks like at https://github.com/edwardkort/WWIDesign ... -frequency.

If you're up for it, there's a scientific paper by Joe Wolfe and John Smith that talks about cutoff frequencies at http://newt.phys.unsw.edu.au/jw/reprint ... gering.pdf.

[bansuri]

Thank you for your reply Tunborough, but i was hoping the reply would be something like, cutoff frequency is the highest or lowest frequency that can be played given the flutes bore and length.
Still trying to work out what "dampen the response" means.
Thank you for the references i will see if my poor brain can decipher it all.

[david_h]

Where does the term come from? What is being cut off? Is it the frequency below which a flute behaves as if it was physically cut off at the first open hole (even if that's not where the name came from) ?

[Tunborough]

When all of the toneholes are closed, the tube will have many resonances, around D4, D5, A5, D6, and on up. Presumably, the sound of D4 can include components from all of the higher resonances.

When all of the toneholes are open, the flute will have a resonance at C#5, maybe C#6, but it won't exhibit any resonances above the cutoff frequency whatever that is. The implication is that this affects the sound of C#5, that it wouldn't include components from as many higher resonances. I can't say whether this is true or not.

Personally, I wouldn't worry about a cutoff frequency from a flute calculator.

[david_h]

Ah, OK, thanks. So sawing it off at the top hole would give C# its higher frequency harmonics back?

[Tunborough]

Never thought of doing that, but it should work. Anyone have about 15 cm of tubing they could swap for their whistle body and compare what C# sounds like either way?

[paddler]

Can someone explain what is meant by Cutoff frequency when applied to a flute.
The term is used on a site that calculates the size and hole positions on a flute.
Tried searching google but still non the wiser

My understanding of the term "cutoff frequency" and the way it is used in flute modeling, is that it is a property of a tone hole lattice. Specifically, for a given flute with a set of open tone holes of given size and location along the bore (i.e. tone hole lattice), the cutoff frequency is the threshold at which sound waves with a frequency higher than that will propagate down the bore unimpeded, whereas sound waves with a frequency lower than that will not.

The intuition is that open tone holes have more of an effect on low frequency standing waves in the bore of a flute than they do on high frequency standing waves. This is especially so for small tone holes (small in relation to the bore size). This is why cross fingering works on baroque flutes, and why the first open tone hole does not, by itself, define the note played, etc.

So for a given flute specification (including tone hole sizes, locations etc) and a given definition of a pattern of open tone holes (tone hole lattice), there will be some frequency above which it makes no difference whether the tone holes in that lattice are open or closed. That frequency is called the "cutoff frequency".

[bansuri]

Thank you Paddler,
I think i understand now, but at the level that i am at in flute making and playing, i will take Tunbouough's good advice and not worry about a cutoff frequency too much.

[Flutern]

Fascinating topic, but now I'm a little confused

When all of the toneholes are open, the flute will have a resonance at C#5, maybe C#6, but it won't exhibit any resonances above the cutoff frequency whatever that is. The implication is that this affects the sound of C#5, that it wouldn't include components from as many higher resonances. I can't say whether this is true or not.

My understanding of the term "cutoff frequency" and the way it is used in flute modeling, is that it is a property of a tone hole lattice. Specifically, for a given flute with a set of open tone holes of given size and location along the bore (i.e. tone hole lattice), the cutoff frequency is the threshold at which sound waves with a frequency higher than that will propagate down the bore unimpeded, whereas sound waves with a frequency lower than that will not.

One definition seem to suggest that the open tone holes act as a kind of low-pass filter, and the other one as a high-pass filter. Or did I misunderstand something?

[stringbed]

There is only one definition. It is derived and presented in full scientific rigor in the article cited by Tunborough near the outset of this thread and summarized starting with paddler’s “Specifically, for a given [instrument] with a set of open tone holes…

[david_h]

the cutoff frequency is the threshold at which sound waves with a frequency higher than that will propagate down the bore unimpeded, whereas sound waves with a frequency lower than that will not.

The confusing part is that it's not obvious from this that (I think) the waves that "propagate down the bore unimpeded" do not then contribute to the sound that we hear but the lower frequency ones do. Hence my question above above sawing the tube off at the first open hole to get the higher harmonics of that note back.. I feel that to really follow the explanations I would need to be immersed in the mathematics of waveguides, impedencies, helmholtz resonators, compliances etc.

Or to put it another way if all the holes of a D flute are open then the waves that propagate down the bore as if the holes were closed don't contribute to the sound of a C# in the same way they don't do when all the holes really are closed. Except I think we are talking about resonances - potential sound waves.

[Flutern]

Thanks David, that was the source of my confusion .
This page also has some nice explanations that I found quite helpful, especially with respect to cross-fingering .

[paddler]

These are good questions/observations. At the risk of introducing further confusion, I'll try to address them in a way that reconciles.

Fascinating topic, but now I'm a little confused

When all of the toneholes are open, the flute will have a resonance at C#5, maybe C#6, but it won't exhibit any resonances above the cutoff frequency whatever that is. The implication is that this affects the sound of C#5, that it wouldn't include components from as many higher resonances. I can't say whether this is true or not.

My understanding of the term "cutoff frequency" and the way it is used in flute modeling, is that it is a property of a tone hole lattice. Specifically, for a given flute with a set of open tone holes of given size and location along the bore (i.e. tone hole lattice), the cutoff frequency is the threshold at which sound waves with a frequency higher than that will propagate down the bore unimpeded, whereas sound waves with a frequency lower than that will not.

One definition seem to suggest that the open tone holes act as a kind of low-pass filter, and the other one as a high-pass filter. Or did I misunderstand something?

The open tone hole lattice acts as a high-pass filter. This means that low frequencies do not get past it. These low frequency waves bounce back up the bore. As far as they are concerned, it is as if the bore was cut off somewhere close to the first hole. In essence, the effective length of the bore for these lower frequencies is roughly the distance from the embouchure to that first tone hole. This distance, together with the speed of sound, will determine the frequencies at which resonances can occur. The resonances are what we hear.

Higher frequencies do not perceive the tone hole to be open and hence continue down the bore. They will eventually reach a point, perhaps at the very end of the bore, where they too bounce back. The distance from that point back to the embouchure is longer and not necessarily a multiple of the effective length of bore experienced by the lower frequencies. This longer length will also have the potential to resonate at some frequencies, but frequencies lower than the cut-off frequency for the open tone hole lattice will not be able to contribute to this resonance. Hence there will be no lower frequency resonances for this longer bore length with the tone holes open. Because of this, the low frequency resonances of the flute (lower than the cut-off frequency) are determined by the first open tone hole, but the high frequency resonances are not. The high frequency resonances are influenced by the overall length of the bore.

the cutoff frequency is the threshold at which sound waves with a frequency higher than that will propagate down the bore unimpeded, whereas sound waves with a frequency lower than that will not.

The confusing part is that it's not obvious from this that (I think) the waves that "propagate down the bore unimpeded" do not then contribute to the sound that we hear but the lower frequency ones do. Hence my question above above sawing the tube off at the first open hole to get the higher harmonics of that note back.. I feel that to really follow the explanations I would need to be immersed in the mathematics of waveguides, impedencies, helmholtz resonators, compliances etc.

Or to put it another way if all the holes of a D flute are open then the waves that propagate down the bore as if the holes were closed don't contribute to the sound of a C# in the same way they don't do when all the holes really are closed. Except I think we are talking about resonances - potential sound waves.

The sound that we hear from a flute is determined by the strongest resonances. When a high frequency wave propagates past the open tone holes it does not contribute to the resonances of that upper part of the bore (between embouchure hole and first open hole), so it does not contribute to the sound that we hear if that upper bore resonance is the dominant one, as would be the case in the first register, say. When we play in higher registers, we may get different resonances that occupy lower parts of the bore beyond the open tone holes. This is what happens when you employ cross fingering in third octave notes, say. So what we hear is determined by the dominant resonances, and those are determined by the flute design, open tone hole lattice, and the way we blow.

I hope this helps to clear the confusion.

By the way, I don't think that any of what I have said contradicts Tunborough's statements. For a D flute, say, any high frequency sound waves that propagate further down the bore and reaches the far end will not contribute to a resonance at the frequency of C# simply because the flute's bore length is such that it will only resonate at the frequency of D. So I would expect the open tone hole lattice to effectively filter out the higher frequency components of C#. By chopping off the flute near the C# hole, we would allow higher frequency resonances for C# because the actual bore length would now match that required for C# rather than D.

[Flutern]

Thanks, Paddler, for this thorough and clear explanation. I now understand how your original explanation and Turnborough's fit together