Profiling

[David Hornett]

Especially if you are nursing it so there is no shatter when it hits the ground. Take your time, you had to wait long enough for me to find mine.

 

Any doubts ask for a remeasure, I don't mind: I read 'em off as my son entered the date, between us there may be an inadvertent bumble here and there.

 

 

David

[Terry McGee]

OK, easy ones first. Here are the reported reed widths: (click image for full size)

 

 

Use this graph in preference (see discussion further down)

 

 

A few interesting things to note:

 

- there seem to be five available widths, perhaps surprisingly they don't simply narrow down in tiers from bass to treble. Any thoughts as to why? Anybody?

- the reeds taper fairly uniformly from heel to toe.

 

In relative terms, bass taper is about 83%; treble around 73%.

 

In absolute terms it tells a slightly different story. Reeds below about A5 are 0.55mm narrower at the tip than the heel. Reeds above that are about 0.66mm narrower, apart from the last pair which are 0.48mm narrower.

 

I should echo David's notes on the spreadsheet:

 

NOTE: REEDS EXHIBITING THE SLIGHTEST POSSIBILITY OF TUNING FILE MARKS, TIP OR ROOT WERE DISCARDED, THE INSTRUMENT WAS IN AN OLD TUNING APPROXIMATING 63 CENTS SHARP OF A440. THE INSTRUMENT WAS AN 1880 LACHENAL DUET.

 

[Note A440 + 63 cents = A456.3 - about as high as "Old Philharmonic Pitch" ever went.]

 

ALSO: SLOT WIDTHS VARIED FOR THE SAME SLOT LENGTH BY .09 ACROSS THE LENGTH OF THE SHOE, THIS WAS THE CASE WITH THE D4 AND THE C4 REEDS I MEASURED AFTER DISASSEMBLY. TO PROPERLY MEASURE WIDTH I WOULD HAVE TO DISASSEMBLE ALL THE REEDS, AND WAS NOT TO KEEN TO DO THAT. I SUSPECT DIFFERENT FLY PRESSES STAMPED SLIGHTLY DIFFERING WIDTHS.

 

What other information would we like to gather or present about reed width?

 

Terry

Edited May 23, 2014 by Terry McGee

[Chris Ghent]

OK, easy ones first. Here are the reported reed widths: (click image for full size)

 

Lachenal Duet 8816 Reed Widths.gif

 

A few interesting things to note:

 

- there seem to be five available widths, perhaps surprisingly they don't simply narrow down in tiers from bass to treble. Any thoughts as to why? Anybody?

 

They are stamped out with tapered diesets and diesets are not cheap. There has to be a system, and this one either has five diesets or the blanks are stamped from maybe a couple of diesets with limited length stock being placed under the dieset in a particular place along its length so as to create a blank of a particular width. I do this myself.

[Terry McGee]

OK, next, another easy one - Shoe Slot Lengths:

 

 

These clearly have a close relationship with the reed widths shown previously. Lower reeds are generally wider and longer as you'd expect, although I still puzzle about those shorter bass reeds such as A3 to B3. Are they second class citizens, or have we slipped up somewhere?

 

Terry

[Terry McGee]

I've also revised the reed widths graph. The line style graph is nice and clear, but gives the false impression that some reeds have widths between the actual values. I note I had also allowed it to make assumptions about reeds that David had carefully chosen to leave out. See what we make of this version instead:

 

 

Terry

Edited May 23, 2014 by Terry McGee

[Terry McGee]

OK, now down to the serious stuff - the reed thickness profile. Firstly the 3D overview:

 

 

A few explanations:

• Bass reeds are up the left hand end, treble at the right.
• The heel of the reed (the clamped bit) at the back, the vibrating tip at the front
• The thickness of the reed is shown by the scale running around the back and left hand side, with values at the right rear.
• The Legend in a column at the extreme right of image may help you locate a particular reed.

A few notes:

• They clearly worked from two stock thicknesses, around 0.82mm and 0.48mm (0.032" and 0.019"). They would have known it as 14 gauge and 18 gauge.
• As has been discussed previously, bass and midrange reeds have thinned bellies and heavier tips, while treble reeds thin all the way
• I still worry that the reeds around A3 to B3 are wrongly placed in our graph.

Terry

[Terry McGee]

Next a 2D version, focussing on the various regions of the reeds:

 

 

Some observations:

• We can follow the heels of the reeds (dark blue) and confirm there are really only two stock thicknesses.
• Following the tips (light blue), we see how they fairly uniformly reduce from full stock thickness in the bass to very little in the treble
• The first quarter (mustard) and middle of the reed (green) track pretty closely, and can be thought to comprise the belly. There might be an argument to check a few reeds scattered over the range to see if a measurement between those points yielded a similar measurement or a thinner one.
• The root (just beyond the clamped area) (red) also tracks the first quarter and middle, but a little bit thicker. Transitional between belly and heel?
• The third quarter (brown) is transitional between belly and tip?

Again I worry about A3 to B3 - they would seem more at home an octave up. And A4 to Bb4 would seem happier an octave up, where there is currently no data.

 

Terry

 

[Terry McGee]

Here's another view of the same data, in 2D, but this time from the point of view of each reed. Rather cluttered as you can see, but not unuseful...

 

 

Good for spotting anomalies, eg that mustard one in the root column, and an aqua one that takes an unexpected turn at the third quarter. They can be tracked down in the 3D version, where they have the same colours.

 

David also took reed shoe thickness measurements, but they would make a dull graph, all coming in at 2.1mm.

 

David, is it worth looking at the underside of a few of the reed shoes, to characterise any "undercutting" employed to enhance the reeds' responsiveness? I know a travelling microscope would be handy for measuring this; I've always said no home should be without one....

 

I think I've presented all the data David collected, but smarter people can tell us if we need to do more.

 

Terry

 

[Dana Johnson]

For some general information on profiles, if you've tuned a full range of reeds, you'll have noticed some basic patterns. Low reeds are generally thick at the tip and thin close to the root of the reed, often even weighted at the tip because the starting sheet thickness didn't add enough weight by itself at the tip. Mid range reeds are more level seeming and high reeds go from thick at the root to thin at the tip. It is quite possible to make a set of reeds that are all flat, but you end up with low reeds that are much longer and high reeds that are even shorter. Reed profiling allows you to make a set of reeds that lets you get at least a reasonable volume match between the large low reeds and the tiny high ones as well as notes that all play at similar pressures, which is crucial to a decent instrument.

When you make a reed, the pitch is determined by the length, the stiffness and the mass of the reed. you can vary all three and still get the same note. The key is understanding how they work together. At the root, mass makes very little difference because the reed moves very little there, but stiffness counts a lot because that is the place of greatest bending stress. Stiffness counts very little at the tip because it does very little bending there, but mass counts a lot because that is the point of greatest motion (and inertia ) somewhere along the length of the reed, stiffness and mass have equal and opposite effects on pitch. You can change the reed thickness here with little effect on pitch ( the balance point moves as material is removed ), but can adjust the overall stiffness of the reed in this area.

Reeds are always in my experience thinner in this neutral area than would be required for pitch because a set of reeds built on straight line profiles are much too stiff. I have a little gizmo that measures reed stiffness, and a high G with a straigh line taper from root to tip will measure around 40 (units) where a properly profiled reed will measure around 8. This is a huge difference for two reeds with the same length and width. The difference is the reduction in the neutral area and the area above and below it to spread the effect out and create a smooth bending reed.

Low reeds with straight line profiles are also too stiff, though not as much. The problem there is that they will not spread the bending evenly across the reed's length and may fail prematurely because of excessive bending at the root. In order to get a even sounding set of reeds, low reeds need to be less stiff than mid range and high reeds less stiff than both of them. Ideally, the reeds will vary evenly from bottom to top in a sort of skewed bell curve.

Low large reeds need to have their stiffness reduced to keep them from overpowering the mid range reeds as well as to feel the same when played. Low reeds that are too soft however will be much more subject to the influence of air pressure on pitch, so there is a limit to how soft they should be compared to the mid range reeds. High reeds being quite small, need to be quite light in order to play at the same pressure as the lower reeds since the reed's stiffness follows a linear slope relative to size while the pressure acting on the reed varies geometrically.. We are aided in getting enough volume out of the higher reeds by the fact that they sit in the area of our hearing that is more sensitive even while their size is so much reduced.

Mid range reeds are more nearly level in profile, and in an ideal set, you might have one reed that was dead flat, but most of them still have a reduced center section to keep the stiffness down. This doesn't mean the center will be the thinnest part, only that it will be below a straight line taper.

Reeds need to bend evenly. Part of the overall profile is directed at this end result. Rather than removing metal from one location, you balance the removal both above and below to keep a smooth bend. Low reeds should taper back to full thickness close to the root to avoid a sharp bend and high stress area. High reeds need to be thinner back from the tip so it isn't just the tip that wiggles up and down.

One thing worth keeping in mind is that whan you remove metal, stiffness is effected more quickly than mass. It takes a lot less removal of metal at the root end of the reed to lower the pitch than it takes removal of thickness at the tip to raise it back again.

A last note, reeds are the result of the preferences of the maker. some favor lighter reed sets which while more responsive, have limited dynamic range and tend to be more on / off. Heavier reeds sets take a bit more effort to play, but have greater dynamic range and maximum volume. While the

Wheatstone folks used a surface grinder to generate uniform profiles of=ver a lot of instruments, Many reeds from other makes were done by hand and show the preferences of the person who filed them. There is no right profile, only a range of profiles that work. If you are replacing a reed, you want to match the character of the profiles used so your reed blends in rather than stands apart from the rest.

A last , last note, Side Tapered reeds are effectively partially profiled in width. They add stiffness near the base sideways rather than in thickness and can bend smoothly with less attention to the thickness profile. They allow slightly larger high reeds than parallel reeds, and side tapered reeds usually vary from nearly parallel low reeds to quite tapered high reeds, allowing a flatter thickness profile overall.

Edited May 23, 2014 by Dana Johnson

[Wolf Molkentin]

Thanks much for the insight Dana, this is very interesting stuff for a concertina player who very occasionally does little filing but loves to learn about how the tone generation is working...

 

Best wishes -Wolf

[Terry McGee]

Thanks, Dana, lots of interesting stuff there.

 

One thing worth keeping in mind is that whan you remove metal, stiffness is effected more quickly than mass. It takes a lot less removal of metal at the root end of the reed to lower the pitch than it takes removal of thickness at the tip to raise it back again.

A last , last note, Side Tapered reeds are effectively partially profiled in width. They add stiffness near the base sideways rather than in thickness and can bend smoothly with less attention to the thickness profile. They allow slightly larger high reeds than parallel reeds, and side tapered reeds usually vary from nearly parallel low reeds to quite tapered high reeds, allowing a flatter thickness profile overall.

 

These observations make sense when we remember that the stiffness of a beam is proportional to its width, and to the square of its thickness. So halve the width of a beam and you halve its stiffness. But halve the thickness and you quarter the stiffness (in the same plane). But you only halve the weight.

 

Terry

Edited May 24, 2014 by Terry McGee

[Terry McGee]

Now that we have some point of comparison, I'd be interested in hearing from those who have delved into such things how these measurements compare with other makers', eg Wheatstone and Jeffries for a start. And whether we see much variability between models by each maker? Can we say, for instance, that Anglo reeds are always <insert descriptor here> than English reeds?

 

(Happy to manipulate any available data into a similar form, or, if there are suggestions on how better to present this data, carry out those changes.)

 

Terry

Edited May 24, 2014 by Terry McGee

[alex_holden]

Very useful insights Dana, thanks a lot.

[Chris Ghent]

Lovely to see you posting here again Dana, you were missed...

[Terry McGee]

You'll notice above that I wasn't convinced about the location of some of these reeds.....

 

Next a 2D version, focussing on the various regions of the reeds:

 

 

Again I worry about A3 to B3 - they would seem more at home an octave up. And A4 to Bb4 would seem happier an octave up, where there is currently no data.

 

 

So, I thought I'd play with relocating them as I'd talked about. I'd suggest they are more at home an octave up...

 

 

Still not sure about the pair of F3 notes - they still appear to be out of order, but it's not so clear where they belong. Is it possible that they are badly stamped and are not really Fs at all?

 

Terry

Edited May 26, 2014 by Terry McGee

[David Hornett]

Terry,

 

I have emailed you the re measurements you asked for without consulting the original table. (This time I took every reed out of its shoe, rewashed it, and used two tuners just in case I getting lies from one)

 

Dana, thank you for you comments: they are born out precisely in what I found when I was measuring the reeds.

 

And Terry thanks for all the tabulation -- and to think, I began all this by simply asking what profiling was, as having fiddled with accordion, harmonica and bandoneon reeds for years, other than tip weighting, I had never come across it.

 

Terry wrote this: And A4 to Bb4 would seem happier an octave up, where there is currently no data.

 

There is no data here because there was evidence these reeds had been tuned (judged by the different direction and pressure of the scratch marks and glossy appearance on the tip, unlike all the others, in fact one was brass and the other German silver, so they were discarded as being too unreliable).

 

David

[Terry McGee]

OK, David and I have been back and forthing behind your backs, and I think we now have a more coherent tale to tell. Let's start with the reed lengths:

 

 

We can see, depending on how you interpret a few intermediate lengths, that there are about 10 reed lengths employed, although most of the reeds fall into 7 categories. I've put in a trend line (thin blue) to illustrate the general slope followed.

 

I've also illustrated what the slope (thin orange trend line) would be if the reeds followed the theoretical lengths, i.e. doubling in length each time you go down an octave. As you can see, the bass reeds would be much longer (and therefore harder to fit into the instrument) and the treble reeds much shorter (and therefore quieter and less responsive). This illustrates points Dana makes above.

 

But having stepped away from theoretical scaling, the laws of physics demand we make adjustments elsewhere. We should keep a lookout for where these compensations are made as we go through the other parameters of the reeds.

 

Thanks to David Hornett for all the measurements.

 

Terry

[Terry McGee]

Now we move on to reed widths.

 

 

The blue columns indicate the reed width at their tips; the orange at the base.

 

Once again, we find they are not incrementally scaled, but in about 5 tiers, for practical reasons. Note that over half the reeds are in the middle tier. Reed width is not something that needs to be scaled, but some tweaking is clearly called for at the two ends of the range.

 

Terry