complex bore of R&R flutes?

[Casey Burns]

I have found computers great at storing and sometimes for visually processing data but I do not expect them to be of much utility at predicting the qualities of one flute design vs. another. The flutes work on a much finer scale than that. One can certainly predict pitch via certain mathematical guidelines and analogs (see Nederveen) but there is a big difference between calculating pitch and determining playability and how the flute feels to the player and how it sounds to the listener.

There is no way to get around the old Analog methods of making and testing these by hand to see what makes these flutes and other instruments tick. Like anything musical, it takes a lot of practice and experience over time, and a willingness to make several mistakes and keep going. There is No shortcut. There is No substitute.

Computers have their purpose. But using one to design a perfect flute is like asking it to grow a perfect tomato. It cannot be done.

Sorry.

[Tunborough]

I set the toneholes and embouchure hole to 4 mm deep, and reduced the effective diameter of the first foot hole. F#4 is about 35 cents flat now; as you say, the undercutting would explain a difference there, and the model doesn't handle undercutting, unless we adjust the position we assign to the tonehole. The uncompressed flute improves the flat D by still only about 10 cents.

So, no other wild effects from "decompressing"? But while it nudges the low D slightly in the right direction, it doesn't explain the flat-footed-ness.

No, I'm pretty sure the change in the bore profile alone isn't nearly enough to eliminate the flat D.

We might want to add more bore points to capture the real bore profile more accurately. Then I'll ask for more tuning information.

OK. Are you entering into new territory here, or have you already done some conical flute measurements?

The calculations for tapered bores have been around a long time, but transverse flute tuning is new territory for us. We've got lots of pitch measurements on a variety of instruments with a variety of bores, but we're in serious need of real flute pitch measurements.

[Tunborough]

One can certainly predict pitch via certain mathematical guidelines and analogs (see Nederveen) but there is a big difference between calculating pitch and determining playability and how the flute feels to the player and how it sounds to the listener.

Predicting pitch is all we're trying to do here: the effect on pitch of changes in the bore, in particular.

That said, in a separate study I'm seeing hints of the tone quality of different notes of a NAF in note spectrum plots from WIDesigner.

[paddler]

The kind of predictions that they are trying to do here (predict pitch of notes based on bore profile and tone hole size) is precisely the kind of problem that computer simulations are already very
good at solving. Computer models are already in widespread use in many disciplines and industries for this kind of purpose. It is no longer really an open question about whether it can be done,
but rather, it is just a matter of refining models and throwing more compute power at them in order to find good solutions to most problems that are governed by basic laws of physics. In the
grand scheme of things, predicting tone from flute bore models is not a grand challenge problem. Its just that is has not received a whole lot of attention to date.

Using computers to address this stage of the flute making process can certainly be a shortcut, once the models are perfected and widely available, but nobody is arguing that a "perfect" flute will
be generated automatically. The point is to improve the efficiency of the early stages of the flute making process, allowing makers to answer various hypothetical questions and to gain a better
understanding about how various parameter changes affect the outcome. Using computer models to answer these kinds of questions can ultimately free up more time to focus on the finer details
and voicing, that also have a great impact on a player's experience.

Having said that though, I think it IS important to remain clear eyed about the limitations of such models, and not to read too much into the results. As I see it, the discussion here is about the process
of improving an existing model and measuring its limitations - specifically by comparing the model's predictions with the measured performance of the actual flute. The measurements of the actual
flute are, of course, the right answers, regardless of what the model says! The point, though, is that once the difference between the predictions are the right answers gets "small enough" then the
models will become useful to practitioners. Right now, in my opinion, the difference is not yet small enough, but I have no doubt that with refinements they can eventually become accurate enough.
And just for some context here, I am a recently retired Computer Science Professor with 30 years of research experience, and I am also a flute maker that uses traditional techniques (and currently
no computer modeling) in the design and construction of my instruments.

[Casey Burns]

In casze you haven't check out Nederveen's work then if all that you are considering is pitch. He discusses the effect of different types of undercutting and other important aspects, and mathematically models these effects, etc. It may be that this computer model program you are using is basically derived from Nederveen's work and similar works published in JASA

Casey

[Terry McGee]

I set the toneholes and embouchure hole to 4 mm deep, and reduced the effective diameter of the first foot hole. F#4 is about 35 cents flat now; as you say, the undercutting would explain a difference there, and the model doesn't handle undercutting, unless we adjust the position we assign to the tonehole. The uncompressed flute improves the flat D by still only about 10 cents.

So, no other wild effects from "decompressing"? But while it nudges the low D slightly in the right direction, it doesn't explain the flat-footed-ness.

No, I'm pretty sure the change in the bore profile alone isn't nearly enough to eliminate the flat D.

OK, that's a valuable finding. I think it supports intuition. But it leaves a big question unanswered. Why did they think these flutes were adequately tuned?

Hmmm, remember my hypothesis that it was old man Nicholson messing with the holes on his Astor that got us into this trouble. What happens if you make the holes 6.4mm, 7.45mm, 6mm, 7.3mm, 7.3mm, 5.1mm (from the top down). It will presumably flatten the body notes. Does it get them closer to the foot notes? Feel free to shorten the cylinder below the embouchure to bring the pitch up again. Can you identify a best pitch? (I'd guess at 430Hz, but it's probably wishful thinking!)

We might want to add more bore points to capture the real bore profile more accurately. Then I'll ask for more tuning information.

OK. Are you entering into new territory here, or have you already done some conical flute measurements?

The calculations for tapered bores have been around a long time, but transverse flute tuning is new territory for us. We've got lots of pitch measurements on a variety of instruments with a variety of bores, but we're in serious need of real flute pitch measurements.

OK. This is something we should continue to work on. Perhaps on a project basis? Say I'd like to develop a flute in a different key, or Paddler wants to eradicate a particular annoying issue on his flute. Would that kind of result-focused approach work for you? Or can you articulate a better way forward?

What does the model output look like? Can we makers interpret it intuitively (e.g. can it be presented as a graph of notes vs deviation as we see with our RTTA analysers?)

[paddler]

I'm curious about the way you model the bore itself. When you say that the calculations for tapered bores have been around for a long time, are you talking about bores with a straight taper, i.e., a regular conical shape?

I think what we ultimately would need is a way to model a bore as a concatenation of short cylindrical and short tapered sections, where each section can be as short as, say, 10 mm long. I think this kind of resolution
would be enough to capture a wide range of irregularities exhibited by existing flute bores, including chambering, constriction, back reaming etc. What I'd really like to be able to do then is see the effect of introducing a
short constriction or a short chamber close to the pressure node of one note and the pressure anti-node of a different note, and then see the model predict a tone change in opposite directions for those two notes. I'm not
sure if your model can generate this kind of result just yet.

Following a similar line of thought, when you modeled the difference between the compressed and uncompressed tenon above, the results showed that all notes were flattened by uncompressing the tenon. That is not quite
what I would have expected, since the compression was fairly short and presumably fell close to the node of some notes and antinodes of others, and at neither for yet other notes. Of course, I have not mapped out the precise
location of the constriction relative to the nodes and anti-nodes of the various notes in order to say more precisely what I would have expected, but I'm surprised that the predicted effect uniform(ish) flattening across all notes.
I would have expected flattening of some notes, sharpening of others, and no effect on yet others. This makes me wonder whether the current predictions from your model are dominated by an over-simplification in the way the
bore is modeled.

I am also curious about how air temperature and humidity within the flute are taken into account, if at all. I can imagine starting out assuming some standard ambient temp and humidity. However, in reality the air inside a
flute is not going to be the same temperature and humidity as that in the surrounding room. The body of the flute may be a room temp, but the air in the head end of the bore will be warmer and more humid than that at the foot,
when the flute is being played, which of course is why we get all that condensation. Since temperature and humidity changes affect the speed at which sound waves travel, I wonder if modeling this kind of effect within the flute's
bore might help tighten up the difference between a model's predictions and measurements of reality. Just a thought.

[paddler]

OK, that's a valuable finding. I think it supports intuition. But it leaves a big question unanswered. Why did they think these flutes were adequately tuned?

That is the elephant in the room. My attempt at an explanation is that they considered the flute to be "in tune" at some quite significant slide extension, and that the tuning
slide was really there to allow the flute to be played "less in tune" at higher pitches. If we were to run with this theory for a little while, the first step would be to lengthen
the head until the flute was in tune with itself as much as possible, and then try to determine the overall pitch standard by either basing it directly on the A note produced
at that slide extension, or by basing it on a different note that was closer to the center of the flute's tuning (just in case the A was an outlier relative to the other notes).

It would not surprise me if doing the above, across several flutes that were produced over a period of decade or two, suggested that the foot and body tuning of all flutes
originated from some common ancestor whose target tuning was quite low. The idea being that head shortening (and a corresponding increasing slide extension required
to play the flute best in tune with itself) combined with tone hole enlarging after Nicholson, accounts for a lot of apparent tuning anomalies when we try to play these flutes
at A=440 hz, which I suspect will be higher than the original target tuning. I would not be surprised if Terry's informed guess that the target tuning is closer to A=430 hz
ends up being correct.

[Tunborough]

I'm curious about the way you model the bore itself. When you say that the calculations for tapered bores have been around for a long time, are you talking about bores with a straight taper, i.e., a regular conical shape?

I think what we ultimately would need is a way to model a bore as a concatenation of short cylindrical and short tapered sections, where each section can be as short as, say, 10 mm long.

That's what we're doing: a series of bore segments of varying tapers, defined by specifying the bore diameter at an arbitrary number of points along the bore. The most complex instrument I've attempted is a hautboy by Hotteterre, with 84 bore points in about 650 mm, 12 holes (6 single, two double, and two vents), and 30 notes over 2 octaves. Unfortunately, the original is in a museum in Brussels, so I have no idea how accurate the prediction was.

In case you haven't, check out Nederveen's work then if all that you are considering is pitch.

We used his work with Dalmont and Joly on flanged terminations. Our tonehole model is more recent than Nederveen's, from the work of Antoine Lefebvre. I haven't looked at Nederveen's work on undercutting yet.

What does the model output look like? Can we makers interpret it intuitively (e.g. can it be presented as a graph of notes vs deviation as we see with our RTTA analysers?)

You can see the tuning as a table or a graph, both described here. The tuning table gives target frequency, predicted frequency, and difference in cents, among other things. For a whistle, the tuning graph looks like the following. The graph for a flute would be similar.



Each sloped line is a note, which can be played over a range of frequencies depending on how hard you blow. The green, yellow, and red markers show where the target frequency lands. The blue circles show pitches that a hypothetical player would comfortably produce. (You can adjust how hard the player likes to push the notes to suit your own preferences.)

I am also curious about how air temperature and humidity within the flute are taken into account, if at all.

The temperature and humidity affect the speed of sound and some other properties of air. We assume a constant user-specified temperature (say 27 C) and humidity (typically 100%) through the whole body of the flute.

[Tunborough]

Can you identify a best pitch? (I'd guess at 430Hz, but it's probably wishful thinking!)

My attempt at an explanation is that they considered the flute to be "in tune" at some quite significant slide extension, and that the tuning slide was really there to allow the flute to be played "less in tune" at higher pitches. If we were to run with this theory for a little while, the first step would be to lengthen the head until the flute was in tune with itself as much as possible, and then try to determine the overall pitch standard by either basing it directly on the A note produced at that slide extension, or by basing it on a different note that was closer to the center of the flute's tuning (just in case the A was an outlier relative to the other notes).

There's an interesting experiment. Although WIDesigner has many ways to adjust geometry to match the pitch, adjusting the pitch standard to match the geometry isn't in its bag of tricks. Presumably though, if all of the notes are out by the same amount (in cents) at A4=440, then they would all be in tune with a different pitch standard (whatever A4 plays at).

Using this yardstick, lengthening the head wasn't enough to bring the notes on the uncompressed flute into line. Shrinking the holes as Terry suggested came closer (and A4 was close to 430), but that left the second octave relatively sharp. However, without some measurements from the real flute, I'm not sure we can rely on the model at this level of detail.

[paddler]

That's what we're doing: a series of bore segments of varying tapers, defined by specifying the bore diameter at an arbitrary number of points along the bore.

That sounds good!

The most complex instrument I've attempted is a hautboy by Hotteterre, with 84 bore points in about 650 mm, 12 holes (6 single, two double, and two vents), and 30 notes over 2 octaves. Unfortunately, the original is in a museum in Brussels, so I have no idea how accurate the prediction was.

Well, I have profiled the bores of quite a few conical bore flutes, modern and antique, usually with something like 40 to 50 data points spaced at 10 mm intervals along the bore. I also have most of the instruments in hand still, so I can pull them out and play them in the presence of a tuner. So, if you are in need of more data for other flutes to model, together with some real-world tonal measurements to compare the results of your predictions to, just let me know. I'd be happy to chip in a bit of data and some measurement and playing time.

[Casey Burns]

Bores are fairly difficult to measure on old wooden instruments due to the ravages of time. The cross grain vs. with the grain (usually the fingerholes are along this plane) are always different and not every piece of wood is exactly quartersawn along its entire length! A simple knot can cause some locally wild and significant bore deviations. And then it is a question of the tooling used to measure such as bore gauges, how far one inserts them to what degree of pressure, etc. The most acurate way to derive a bore would be to literally slice the flute serially and measure each cross section. However, this can now also be done by high resolution cat scanning services that produce digitized data that can be used for 3D printing and CNC machining.

There is a great book from Germany where some museum got tired of researchers measuring their Zinks and Serpents. So they scanned everything and posted the results in this reference that one can get for $72 on Amazon (Der Zink und der Serpent). I have a copy.

This is useful for us makers as it gives us all the data we would ever need. We could even remeasure the instruments over time and quantify how these change as they age.

But in terms of mathematically modeling the instrument even for pitch, there can be such as thing as too many data - this one has to simplify and decide what is more significant to model.

It may be interesting to some to attempt this. But in terms of doing tis to design a woodwind and actually make one, it is a worthless endeavor. I've tried it. There is no substitute for trial and error, experimentation, and the willingness to ruin a lot of perfectly fine instruments to see what would happen if I did "this".... I leave a considerable amount of wiggle rooms so that no 2 flutes are alike in any aspect and it helps me feel the way through the maze of what works and what doesn't. Much gets through that most would prefer but sometimes I have to make a decision of do I want to send this to the client who has been relentlessly passive-aggressively contacting me daily or weekly (this destroys my willingness to even work on these things and depresses me). Or do I just want to get it off the table?

Many of the flutes that leave my workshop seem to play somewhat stuffy to me. A large percentage actually. But experience has taught me that the component that I and many of my clients won't allow is the time to properly break in the flutes through most of their evolution. I do this really on a few instruments for favorite or important clients. What changes are the bore measurements and usually for te=he better. I know Pat finesses each instrument in this way. I simply do not have that luxury and my clients rarely allow it.

Casey

[Tunborough]

Well, I have profiled the bores of quite a few conical bore flutes, modern and antique, usually with something like 40 to 50 data points spaced at 10 mm intervals along the bore. I also have most of the instruments in hand still, so I can pull them out and play them in the presence of a tuner. So, if you are in need of more data for other flutes to model, together with some real-world tonal measurements to compare the results of your predictions to, just let me know. I'd be happy to chip in a bit of data and some measurement and playing time.

Your assistance would be much appreciated. I'd like to start with a keyless antique flute, if you have a bore profile for one. Keyless, so we're not trying to approximate the effect of a key pad; and antique, so we're not publicly posting measurements of a modern maker's design without their permission.

For the instrument, I'd need the measurements that Terry supplied for the Nicholson above: bore profile; position, diameter, and depth of the toneholes; dimensions and depth of the embouchure hole; outside diameter at the foot.

For tuning, I'd need the minimum and maximum frequencies for each note, as described here: https://github.com/edwardkort/WWIDesign ... tudy-Model. I'd also need the fingerings you use for any notes that wouldn't be obvious to a neophyte like me. Unlike whistle players, a flute player has a lot more control over how they blow each note. As much as possible, I'd like you to resist adapting your embouchure for each note; using as far as possible a "neutral" playing position, if such a thing exists, or at least one that varies uniformly as you go up the scale.

You could post the numbers here, or send them to me by PM or e-mail. If you want, you could download WIDesigner, and enter the data directly into WIDesigner.

Does this sound manageable?

[paddler]

Bore gauges do not work well for profiling antique flute bores, for the reasons Casey stated, so you need better tools.
I use a set of telescoping T-gauges with extra long handles that allow the diameter of the bore to be measured in
various orientations across the bore. Any discrepancy between the measurements at a particular location along the bore
indicates some kind of distortion, such as ovaling. This can be corrected for by taking several measurements in different
orientations and averaging them. This allows me to find a close approximation of the cross sectional area, which is what
matters acoustically.

Making an accurate map of an existing flute bore allows the construction of a reamer to replicate that bore. Of course,
there are still slight errors in the measurement, so the map is an approximation, and there are errors in the construction
of the reamer and in the effects it has when it is working the wood. But I have noticed that if you are careful, and go to great
lengths to replicate a bore accurately, warts n all, the resulting replica flute sounds very much like the original. It ends
up inheriting some of the tonal character of the original. On the other hand, if you take shortcuts and produce a reamer that
is more regular, the resulting flute sounds considerably different, and often less interesting in its tonal characteristics. This
tells me that it is possible to do the measurements, reamer construction and flute production in such a way as to get a
meaningful result. I'm not claiming that this approach is economic, or commercially viable for someone who makes their
living making flutes, but I am claiming that it is possible, based on the fact that I have actually done it.

I have not yet used any computer modeling though. I've just selected good sounding originals and then put a lot of time and energy
into replicating and subsequently tweaking the resulting flutes in order to get what I'm after. That is basically what most flute makers
seems to do, as far as I can tell, although it sounds like there may be some significant differences in how much attention to detail
different people are willing to indulge. I'm willing to indulge a lot, in part because it interests me, and in part because I do
not need to make my living by getting a large number of flutes out the door in a short time period.

But my interest in a computer modeling approach like the one discussed in this thread goes a bit further. I'd like to know
which of the bore profile irregularities really matter, for good and for bad. For each, regardless of the original maker's intent, I'd
like to be able to describe precisely what effect it has. I agree that it is going to be a while before a computer model can completely
answer such questions by itself, but I don't agree with you that this is impossible. I think it will soon be able to allow rapid virtual
prototyping that can inform the process of constructing and testing physical prototypes, and this will ultimately save time.

The modeling technology may not be at that stage yet, but I'll know when it is at that stage when a computer model can accurately
predict the tuning of flutes that I have in hand. At that stage I will know that it works well enough to be useful to me, and I will be
able to start using it with some degree of confidence, but not over-confidence.

This is basically how science works. It takes a lot of laborious hypothesizing, tool building, and testing cycles, and then you may end
up with something useful. It is not for everyone, but I still like to believe that we live in a society where those who are interested
and willing to put the work in are allowed to continue unmolested.

[paddler]

Your assistance would be much appreciated. I'd like to start with a keyless antique flute, if you have a bore profile for one. Keyless, so we're not trying to approximate the effect of a key pad; and antique, so we're not publicly posting measurements of a modern maker's design without their permission.

That is a perfectly reasonable and well-justified request, but it is a bit tricky for the following reasons. First, the keyless flute is a fairly recent
development, unless you go way back to renaissance flutes. Even baroque flutes had one key, but they are pretty hard to come by and expensive.
More recent antiques from the classical era and later had more keys. The ones we are most interested in tended to have up to 8 keys. There were
some single key flutes sold, but they tended to be mass market products for amateurs, and hence they often don't play anywhere near as well as the
multi-keyed orchestral instruments. Therefore, I haven't profiled the bore of any single key antique flutes, even though I have several in my possession.

I do have profiles for English and American made antiques with anywhere from 4-keys, to 8 keys. I also have some profiles for various modern maker's
keyless flutes, but as you say, it is not reasonable to publish such data without the maker's permission. I also have keyless flutes that I made myself, but
I have not profiled those because I already have the reamers that made them! I could profile one of my own flutes, but then I'm also not sure I want to
publish the blueprint for reproducing one, in all its details. There is a tremendous amount of work tied up in getting a flute to that level of refinement.

So, there are a range of options at my end, and I'd like to hear more details from you about what form, and in what level of detail, you would like to
be able to publish any data we use in evaluating or training the model. It's probably best to continue this kind of discussion offline. I'll send you an email
to let you know specifically what I have available.