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Enthalpy

Woodwind Materials

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Hello everybody!

The material used for the walls of woodwind instruments, and its real, perceived, imagined or absent influence on the sound and ease of playing, has been and is the controversial matter of recurrent discussions that I gladly reopen here. The air column is the essential vibrating element of a wind instrument, the walls are not, but this is only a first analysis.

The walls are commonly made of wood (sometimes cane, bamboo etc.), metal, or polymer aka plastic, which manufacturers call "resin" to look less cheap. Mixes exist too, with short reinforcement fibres or wood dust filling a thermoplastic or thermosetting resin ("Resotone" for instance). I'm confident that long graphite fibres were tried too, as fabric, mat or in filament winding.

The choice results from marketing, tradition, weight and manufacturing possibilities (a tenor saxophone is too big for grenadilla parts), cost - and perhaps even acoustic qualities.

==========

Plastic is a direct competitor for wood, as the possible wall thickness, manufacturing process, density, stiffness, shape possibilities, are similar. As opposed, the density of metal restricts it to thin walls made by sheet forming an assembling, but permits big parts.

Manufacturers typically use plastic for cheaper instruments and grenadilla for high-end ones - some propose cheaper wood in between, possibly with an inner lining of polymer. Musicians who own a grenadilla instrument disconsider the plastic ones; I never had the opportunity to compare wood and plastic instruments otherwise identical, so I can't tell if the materials make a difference, or if grenadilla instruments are more carefully manufactured and hand-tuned, or if it's all marketing.

Two polymers are commonly used: polypropylene for bassoons, and ABS for all others, including piccolos, flutes, clarinets, oboes. These are among the cheapest polymers, but 10€/kg more would make no difference. They absorb very little humidity, but some others too. More surprising, they are uncomfortable to machine: POM for instance would save much machining cost and (my gut feeling) easily pay for the more expensive material. But ABS and also PP absorb vibrations while others don't, which I believe is the basic reason for this choice. They limit the unwanted vibrations of the walls.

As a polymer that dampens wall vibrations, I should like to suggest polyketone
https://en.wikipedia.org/wiki/Polyketone
it's known to make gears more silent than POM and PA, its glass transition is near ambient temperature, its density and Young modulus resemble ABS, it absorbs little humidity. Still not widely used, it can become very cheap. Its creep behaviour and ease of manufacturing are unknown to me, but ABS and PP aren't brilliant neither.

Marc Schaefer, aka Enthalpy

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Here are some observations I made about wall materials for woodwinds.

==========

The most reliable experiment was with flute headjoints on a concert instrument by Miyazawa, who sent the flute to a distributor in my city for the trial.

  • Two professional flautists were invited together with me. They abandoned the trial and preferred a smalltalk after half an hour, so I could try the hardware alone for the afternoon.
  • The room was mid-small, with carpet and some furnitures, at comfortable temperature and usual humidity.
  • I was in an investigative mood, I believe without prejudice.
  • Myazawa put at disposal a flute body with perfectly adjusted keyworks, whose intonation and emission beat the new Cooper scale, and three headjoints of shape as identical as possible, of
     - silver-plated German silver
     - plain 92.5% silver
     - their PCM alloy.

All differences are small. The temperature of the headjoint is much more important than the material. Playing music wouldn't tell the differences within the test time: I provoked the known weaknesses of the Boehm flute. After 20 minutes, I could detect differences and reproduce them with confidence.

  • Plain silver is identical to silver-plated German silver, or at least the differences are uncertain. Silver might make more brilliant medium notes.
  • PCM improves over silver. The highest notes of the 3rd octave (and the traditionally unused 4th) are easier to emit pianissimo, and they sound less hard consequently. The instrument's lowest notes can be louder and their articulation is easier. I can't be positive that the medium notes are more brilliant.
  • We avoided comments during the trial. One other flautist coincided exactly with me, the other had no opinion.

So while materials do make a subtle difference, switching from German silver to silver headjoints as a flautist progresses is just superstition and marketing. Manufacturers may use silver for their better handcrafted products. I ignore if silver is easier to work and enables different shapes, but its acoustic qualities are identical to German silver, a cheap alloy of copper, nickel, zinc. The better PCM is darker than plain silver, rumoured to contain less silver and be cheaper.

I believe up to now that the wall material matters most at the tone holes, hence at the body more than at the head joint. Testing that would be uneasy, since identical shapes are more difficult at the body, and the cover pads matter more than the walls.

==========

I tried once a flute of gold, pure or little alloyed according to its colour. It was only a typical new Cooper scale, with very low 3rd G# and imperfectly stable 3rd F# - poorly made in France with very bad short C#. It didn't even have the split E mechanism, so the 3rd E was badly unstable. The lowest notes were weak, the highest hard and not quite easy. With such a thing, I couldn't concentrate on the claimed acoustic qualities of the metal and stopped the trial very quickly.

At least, they didn't squander scarce wood for that.

==========

Some piccolo flutes have grenadilla or silver headjoints, at Yamaha and elsewhere, on a grenadilla body. Wood is so much better that telling needs no frequent switches in a long experiment. The highest notes are easier to emit piano hence sound less hard. The lowest notes stay bad as on a piccolo.

Wood (and plastic) offers other manufacturing possibilities than metal sheet. Especially, undercutting the blow and tone holes is easier. This may explain a good part of the improvement.

The temperature profiles of the air column can't match between a wooden and a metal head, so "identical shapes" would be meaningless anyway, as harmonics aligned for one material would be misaligned with the other. Was the design optimized for wood and kept for metal? At least, the comparison stands for other manufacturers.

==========

I tried a modern grenadilla flute from Yamaha around 2004. I found it fabulous. While metal concert flutes don't differ so much, this instrument has by far the strongest low notes of all the flutes I've tried - a very much desired improvement - and the easiest pianissimo on the highest notes. Its sound is very mellow, what soloist seeking a "good projection" hate but saxophonists switching the instruments like.

Did the material alone make the difference? I don't think so. At Mönnig the wooden and metal flutes played about identically.

This flute had also a new scale (holes' position and diameter) since its 3rd F# was more stable and its 3rd G# intonated almost perfectly. The mellow sound may result from the scale, as for a flute I tried in a Parisian workshop, and the stronger low notes from wood's workability like undercutting, or from a wider bore locally.

==========

Despite playing the saxophone, I was once called to try a clarinet of thin injected thermoplastic. Its covers were of injected thermoplastic too, with modified movements, and I don't remember the more important pad material.

The effect is huge, and people who claim "the material has no influence" should try that. The cheap and easy instrument offered as little blowing resistance as a soprano sax, consistently with huge losses, and couldn't play loud. The timbre suggested a clarinet, but, err.

==========

Comparative trials abound on the Internet but many ones about flutes are obviously fiddled so the hearer notices a difference. Remember on the Miyazawa, it took long to notice any difference; much was about the ease of playing, and the subtle sound differences wouldn't survive computer loudspeakers.

These shall be oboes of grenadilla versus cocobolo, both from Howarth
https://www.youtube.com/watch?v=yVouYVlDZDY
and if the construction is identical, then the material's influence is (not unexpectedly) huge on an oboe. In short, cocobolo makes bad oboes of clear and weak sound.

Grenadilla (Dalbergia melanoxylon) gets ever scarcer while cocobolo (Dalbergia retusa) is abundent, but cocobolo slashes the density by 1.4, the longitudinal Young's modulus (I'd prefer the transverse) by full 2.0 but increases damping by 1.5
https://hal.archives-ouvertes.fr/tel-00548934/document (9MB, in French, p. 117)

 

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Can a physical model justify the wall material's debated influence? I take a flute as an example because I know dimensions; a piccolo or a saxophone would be interesting too.

Most people consider a cylindrical closed tube:

WallsCyl.png.562b9c41da24529392e8bf27e523aabc.png

A usual argument is that 1Pa air overpressure in D=19mm and for instance L=30mm (a distance between tone holes) squeeze adiabatically 6*10-11m3 more air in the column, while the resulting 25Pa stress in the 0.38mm E=83GPa silver walls strain them by 0.3ppb and increase the contained volume by 5*10-15m3, or /104, so it's negligible.

Here I suggest (I'm probably not the fist) a more significant process through resonance and oval deformation.

WallsResonate.png.af8a835f92119f851401e122756aad36.png

I apply known models for flexural waves in sheet (E'=96GPa for pure silver, rho=10490kg/m3) to the cylindric wall. Its deformation is represented by a Fourier series where the fundamental is meaningless and the upper harmonics uninteresting, leaving the second, where kx covers 4pi in one geometric turn.

With 0.38mm thickness (0.45mm is common too), the oval deformation resonates at F=2342Hz, just one note above the official range of the flute. So the fundamental doesn't excite this resonance (it can't be chance) but the harmonics may.

How can such an oval mode couple with the air pressure? I exclude offhand the circle imperfection of the body, because tone holes offer a stronger coupling.

WallsOval.png.9d51a45d148a2d8110f071e53d5e7aab.png

Where the instrument has a hole, the wall doesn't receive a balanced force. It could be an open hole, if the air keeps a significant pressure at that location, or beneath a cover or a finger, which get a part of the force. As the pad or finger are much softer than the wall, they vibrate separately without transmitting the missing force to the wall.

From 1Pa overpressure, 112µN push a D=12mm hole cover instead of balancing the forces on the wall. As balanced forces have no consequence, the effect is the same as 112µN alone pushing down on the wall's top, and since the whole body can accelerate freely, the deformation is similar to 56µN pushing towards the centre at the wall's top and bottom.

The hole's chimney stiffens the body on 1/5 of the circumference and on 12mm over 30mm body length. This raises the resonances a bit, offering many proper frequencies to the sound. I neglect this stiffening for simplicity.

Taking a Fourier transform of the force distribution and solving on the cylinder for the second harmonic would have been more elegant. Instead, I model the closed cylinder as a 15mm*15mm square of same circumference, slit where the forces apply. On 30mm length, 28+28µN and 7.5mm arm length bend E'I=0.013N*m2 by 0.12µrad over 7.5mm height, so the centre moves by 0.9nm - but half without the slit, or 0.45nm. The oval deformation changes the volume little at the closed section, but at the decoupled cover it makes 5*10-14m3. That's 1200 times less than the air compressibility, without resonance.

Now, metal parts resonate, often with a big Q-factor. Take only Q=40: the volume due to the wall vibration is only 30 times less than the air compressibility. And at the resonance, the volume increases when the pressure peaks: it acts as a loss, not like extra room. This effect may be felt.

With varied hole spacing, the flute offers many different wall resonances. The computed 2342Hz is for instance the 3rd harmonic of the medium G, so it has 12 quarterwaves in the air column. For this frequency and column length, the radiation losses alone give Q=60 and the viscous and thermal losses alone Q=138, summing for Q=42 without any other loss at the pads, the angles etc. If the wall resonance adds its Q=30 at one 30mm section from 440mm air column, the combination drops from Q=42 to 38, or 10%.

Harmonics and partials change the timbre and the ease of emission. We're speaking about small effects anyway, so this increased damping of the harmonics may explain the heard and felt difference.

==========

If you tap a flute's body with a plastic rod, German silver makes "ding" while silver makes "toc", a strongly damped sound. Silver's smaller mechanical resonance would attenuate the harmonics less, providing the reported easy emission and brilliant sound (...that I didn't notice at the Miyazawa headjoint test).

This isn't necessarily a bulk property of silver. Thin sheets dampen bending vibration also by thermal conductivity: the compressed face gets warmer, and if some heat flows to the opposite side, less force is released when the compressed face expands. For 0.38mm thickness, a typical heat diffusion time is 0.8ms, just a bit long for the body's oval resonances, so thinner silver would attenuate more the mechanical vibrations hence less the sound's harmonics, but its resonances would fall too low. 0.45mm raise the resonance frequencies but strengthen the mechanical resonances.

Again, this is consistent with the choice of silver for heat conductivity, and with the wall thickness. It's also consistent with the tried red brass for saxophones. But as PDM conducts probably less than sterling silver, it must bring other advantages.

An alloy with a big thermal expansion (but good heat conductivity) should make a damping sandwich around a conducting silver core. I didn't find practical elements (indium 32ppm/K, zinc 30ppm/K) but alloys may exist. Laminate together with silver, or weld by explosion, as usual. Total 0.4mm stay good, most being silver.

==========

Grenadilla (Dalbergia melanoxylon) is less stiff: 20GPa lengthwise hence maybe 2GPa transverse. But it's lighter hence thicker, like 1310kg/m3 and 3mm. The same resonance jumps to 14kHz. To my eyes, a good reason that high notes around 2kHz are easier. I've no data about damping at interesting frequency for transverse bending. Grenadilla gets scarce, and different wood is less stiff.

Plain polymers offer isotropic 2 or 3GPa and the same density and thickness. Damping and lengthwise stiffness may distinguish them from wood. Polyketones are known dampers, worth a try?

Polymers loaded with short graphite fibres are available industrially, notably POM and ABS. They offer 1470kg/m3 and isotropic 10GPa, very seducing. Graphite isn't very abrasive to cutting tools. Give them a try, including at bassoons and oboes?

Long graphite fibres in epoxy matrix exist for flutes (Matit). If filament winding isn't already used, it's easily tried, since small companies make tubes on request.

Marc Schaefer, aka Enthalpy

 

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In the last message, I estimated a heat diffusion time through the whole wall thickness. But after diffusing through 1/3rd of it, heat reaches already a zone where flexion compresses and heats far less the metal, so this suffices for damping. Then, the diffusion time is only 1/9th or 0.1ms, which equals a quarter period for maximum damping at 2500Hz, in the resonance range of the 0.38mm silver walls. Strong coincidence again.

==========

I've computed some figures of merit to compare alloys for damping resulting from heat diffusion. All refer to sterling (92,5%) silver, whose data comes from Doduco and Substech since mechanical engineering forgot to standardize it.

AlloyMerit.png.1312ac49fc34bec52c2430ef135cd10c.png

  • Alpha tells how thinner walls can be if a stiffer or lighter material keeps the resonance frequency.
  • Beta represents the heat diffusion distance at a given frequency.
  • Gamma shall represent the heat-to-elongation or elongation-to-heat couplings. Possibly incomplete.
  • The global figure of merit squares gamma since damping results from elongation-to-elongation, and also beta/alpha like a heat sine diffuses.

From the table, sterling silver has the best combination to dampen vibrations by heat diffusion. Brass is bad and German silver much worse.

Elemental silver's main advantage is the low heat capacity per volume unit, equivalent to a big molar volume for a metal:
https://www.webelements.com/periodicity/molar_volume/
https://www.webelements.com/periodicity/youngs_modulus/
https://www.webelements.com/periodicity/coeff_thermal_expansion/
Strong thermal expansion goes rather against stiffness for pure elements, but atypical alloys exist like Invar, so it would be worth checking. Gold, platinum, rhodium are sometimes used, but their figure of merit is worse than silver, based on incomplete data.

I've added high-copper alloys uncommon in instrument making. The last two need age hardening to conduct heat well; is it compatible with fabrication and maintenance methods? The figures of merit aren't as good as silver but far better than German silver and the alloys are cheap. Plated against corrosion, would they make better student's flutes?

The company Gévelot supplied electric igniters whose wires could be bent sharply tens of times without hardening, while electric copper would break. I ignore the alloy, but instrument makers may like it or an adaptation.

Some alloys in the table are too hard, so they could be less alloyed to improve the heat conductivity. Rolling a sheet 60mm wide uses affordable equipment, and a quick test would be to solder a tube and tap it to compare the damping with silver.

==========

A sandwich can combine a stiff alloy as the skins, ideally with a big thermal expansion, and a conductive alloy as the core. In the above table, brass can cover little alloyed copper, with thicknesses like 15%-70%-15%. Deep-rolling hot sheets can join them besides explosion welding. The sandwich dampens hopefully more than brass and is stable enough for a saxophone.

Ceramics are stiffer than metals and polymers expand more, but having both isn't obvious, and craftsmen prefer metals. A lacquer maybe, if easily removed and reapplied, and if some filler makes it stiff?

==========

Other damping processes exist in alloys. For instance a Cu-Mn is known as a damper: try it a music instruments?

Marc Schaefer, aka Enthalpy

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Here's a more formal model of the wall's elliptic deformation at the tone holes proposed on Nov 13, 2017.

I keep neglecting the stiffening by the hole's chimney in metal bodies. If it stiffened perfectly 1/5 of the circumference on the whole body length, it would raise the resonant frequency by less than (5/4)2, nearer to 5/4.

I keep the absence of pressure on the tube where the hole is, and because simplicity needs it, that the elliptic deformation is identical at the holes and between them.

The deformation equation sums the forces on an element dx of the periphery for a unit length of tube. Zeta stands for the losses; heat conduction would include some complicated function of d2Psi/dt2 too, but later I represent anyway the losses by Q, the mechanical amplification factor at the considered resonance.

WallsFourier.png.b996b5b999cbdc27874bb5263a9d2726.png

The pressure felt by the walls, and the wall movement Psi, are defined over one circumference, so a Fourier series can represent them. Less usual than from time to frequency, this Fourier goes from the circumference position to the wave vector in rad/m.

As the deformation equation is linear, the Fourier components of the movement and pressure distributions correspond, especially the second harmonic that makes the lowest resonance with an elliptic deformation.

At a resonance, the µ*d2Psi/dt2 and E'I*d4Psi/dx4 compensate. If the mechanical amplification factor Q is not very small, the movement is Q times bigger than at low frequency where d4Psi/dx4 determines it. k4 comes from the differentiation of cos(k2x).

A spreadsheet computes the second harmonic of the pressure distribution along the circumference for a 12mm hole in a D=19mm L=30mm tube section:
WallsFourier.zip
The sine peak value is P2=-0.098 times the air overpressure.

Using:
 k2*pi*D = 4pi for the elliptic deformation, or k2=210rad/m;
 |P2|=-0.098 for 1Pa in the tube;
 E'=98GPa now for sterling silver and I=4.6*10-12m3 for 0.38mm walls;
the wall moves by peak 0.11nm at low frequency and Q times more at a resonance. This is 1/4 the value estimated previously with a square tube model, and is possibly more accurate.

==========

Mechanical Q=120 would now drop the sound's harmonics by 10% instead of Q=30. This isn't much for a metal: for instance a vibraphone bar resonates for seconds at hundreds of Hz, telling Q>1000 despite the radiation. Since we hear a tapped flute head joint of German silver resonate, a microphone and oscilloscope would tell figures.

Marc Schaefer, aka Enthalpy

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Really interesting! What are the ways to quantify how good a certain woodwind instrument sounds?

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Flexion damping by conducing heat through sheet thickness is inefficient because metal converts heat to work badly.

Pure silver serving as an example:

  • 1m*1m*1m heated by 1K stores 24kJ heat;
  • It expands freely by 19µm or pushes 1.6MN if constrained, so it transfers 15J work or 600ppm to a matched load;
  • Conversion from elastic energy to heat will be bad too and anyway <1;
  • So the strain-to-strain conversion, which gives a damping with the proper phase, is tiny.

Bad explanation of silver's damping on Nov 13 and 19, 2017. But the resonant frequencies stand.

Since music instruments are full of excellent but unexplained features, the low-alloyed coppers and the alloy sandwiches may still be worth trying.

Electrolytic deposition is an additional means to create a sandwich. Cu-Ni alloys are deposited by increasing the electrolyte's proportion of the less noble element and using enough voltage and current density
Renata_Oriakova (425ko)

  • Zr (-1.45V), Zn (-0.76V) and Cr (-0.74V) look difficult;
  • Co (-0.28V) has nealy the same standard electrode potential as Ni (-0.25V) and should work too;
  • Sn2+ (-0.13V) and Ag (+0.80V) lie closer to Cu (+0.34V) than Ni (-0.25V) is.

I'd start from a laminated core and deposit the skins, which is decently quick for 100µm.

Marc Schaefer, aka Enthalpy

On 11/27/2017 at 7:59 AM, Kurah said:

Really interesting! What are the ways to quantify how good a certain woodwind instrument sounds?

Thanks for your interest!

Quantify how good, not really... It is a matter of individual and subjective perception, and a sound can be qualified as good for a bagpipe but not for a clarinet. Or the same saxophone sound can be considered good for classical music but bad for jazz.

What's worse: we don't even know presently what physical attributes of a sound makes its quality. Helmholtz had claimed "harmonics" and everyone followed for a century and even now, but he was wrong. A few people know presently that a musical sound is, and must be, non-periodic, so its harmonics can't define it.

The perception of sound quality should, to my opinion, be investigated with a high priority. It's uncomfortable because outside harmonics and frequency response of linear systems, the toolbox of physics is quite poor - but that's what is needed. Analysing harmonics and filters have brought some interesting results for violins and wind instrument, but now it seems complete, and we know that this approach is insufficient.

So presently, our ears are the only judge.

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Keyworks for woodwind (and brass winds) are made by casting (maybe forging too) of copper alloys: cups for the covers, arms... When the covers are large, notably on the saxophone, solid parts can be heavy.

I propose to make them hollow and thin-walled hence light. Electrodeposition is a simple process for that, while catalytic deposition may be considered. It works easily with nickel, cobalt and their alloys, and more metals and alloys are possible, copper-nickel being known.

The walls of almost arbitrary shape can be deposited on shapes of cast lead alloy that is later molten away. Other materials are used, including wax covered with graphite powder. Thickness exists down to 8µm but can exceed the mm. The process is easy enough for hobbyist to make parts for model boats, so a small music instruments company can learn it.

Added layers can prevent allergies and corrosion, as is known.

A first application could be the saxophone's neck octave key, which is presently slow because it's heavy, and rebounds sometimes. The musicians can replace it by themselves, especially if the pad is in place, so a company could sell the lighter replacement for instruments of varied brands.

Marc Schaefer, aka Enthalpy

Edited by Enthalpy

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Hollow parts of thin metal let also design wider hence stiffer parts. For instance the arms that hold the biggest covers of the baritone saxophone twist easily, and some brands build two arms per cover; taller wider arms would improve and still be light. Long transmission tubes as well can be too flexible, especially on contrabasses, and wider thinner tubes would improve.

The (piston or rotary) valves and slides of brass instruments may be worth a try too. Thinner metal, electrodeposited or catalytically deposited, would make the complicated shapes lighter. The parts must be ground and run in, but could still be thinner than the present brazed tubes.

Can bells, other parts or complete walls be made by thin electrolytic or catalytic metal deposition? Complex accurate shapes are easy. But does some alloy (or sandwich of alloys, as already suggested here) make good instruments?  Ni (and supposedly Co, Sn, Ag among others) can alloy electrodeposited Cu.

Marc Schaefer, aka Enthalpy

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Here are two records of oboes made of Pmma by a known luthier. Pmma is polymethyl methacrylate, like Plexiglas, Altuglas and more
https://en.wikipedia.org/wiki/Poly(methyl_methacrylate)

https://www.youtube.com/watch?v=NrJy8tNlBuQ
music begins at 1:26, check especially the low notes at 1:55. That same musician played other instruments on the same day with the same reed, the trials are available on the same site - so only the instrument is to blame.

https://www.youtube.com/watch?v=8AJnQk3ECYE
music begins at 0:38. The low notes are again the worst.

Two different musicians obtain the same sound, which is also how you expect a plastic to sound. It strikes even through computer loudspeakers. In short: inadequate material.

Now I believe more easily that the material makes the difference between grenadilla and cocobolo oboes (Nov 07, 2017 here). And while an oboe must be more sensitive to the walls' behaviour, I believe more easily the clarinettists' comments against plastic.

==========

Can the elliptic resonance explain it? Take E~2.5GPa and rho~1200kg/m3 for Pmma. The body widens to D~40mm at the low notes, and I take 5mm thickness, so (Nov 13, 2017 here) the first resonance for a cylinder would be around 3.3KHz, which is both our ear's maximum sensitivity and within strong harmonics of the oboe, like the 11th for low D.

Most baroque oboes had rings at the bell, where locally thicker wood stiffened the wall. Their wood was more flexible than grenadilla. This may apply to plastics too.

PC (polycarbonate) is less stiff than Pmma but it damps the resonances. Possibly a less bad material than Pmma - more factors matter.

And polyketone, known for silent gears, could be worth trying.

==========

Tárogatók are already made of boxwood (Buxus sempervirens), probably by tradition, and because wide grenadilla would be too expensive if available. Modern bassoons use even the flexible maple (with a thick moisture liner) instead of grenadilla or rosewood a century ago.

They would be prime candidates for polyketone. I've seen no formulation loaded with short graphite fibres, but maybe plastic injection companies can do it if not the suppliers. And when long graphite fibers are wound to make axisymmetric parts, they are first impregnated by some resin: is molten polyketone feasible?

Marc Schaefer, aka Enthalpy

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Being known to make more silent gears than polyamides and polyacetals, polyketones could make more silent keys for wind instruments. Pushrods at rotary valves, transmissions between keys and plain bearings at woodwinds often use polymer parts, which polyketones hopefully improve. At the bassoon and also the oboe, it would be needed.

Marc Schaefer, aka Enthalpy

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The pads that make tone hole covers airtight use archaic materials: leather, felt, cardboard, wax... Attempts with hi-tech stuff have consistently failed up to now, for excellent physical reasons.

Register keys would be better candidates. Their small size accepts a less accurate adjustment, their stronger contact pressure and humidity favour synthetic elastomers over traditional materials. For instance at the saxophone, the pad hardens quickly at the upper register key, which then rebounds.

Elastomer formulations are countless even before combining them. Perfluoroelastomers, for instance DuPont's Viton, don't rebound and resist water perfectly. Silicone rubbers rebound slightly and are less resistent. All polymers with little rebound creep over time, as far as I know and as logic tells, alas. I expect that the pads must be hard and not too thick, so adjusting their orientation must still be necessary.

Marc Schaefer, aka Enthalpy

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I suggested on Jan 01, 2018 to produce instrument parts by metal deposition, electroless or electrolytically.

Bocals (or necks) are candidates. For saxophones and low clarinets, and even more for double reed instruments like the oboe family and the basson, which are very narrow. Skilled sheet forming takes long and accuracy
is a worry. Metal deposition would make accurate parts with little human monitoring.

Bows for bassons, low clarinets, saxophones... are other candidates. Their complex curvature takes long to achieve from a metal sheet.

Metal can be deposited on complicated patterns often series-produced by casting and destroyed after the deposition. Materials for patterns include fusible metals like lead, and also insulators like wax.

Deposited metals include Ni, Cu, Co, Sn, Zn and some of their alloys, and also Ag which is praised for wind instruments.

Marc Schaefer, aka Enthalpy

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Deposited metal can make corrugated walls, at a straight tube or any shape.

Corrugated.png.b155cce174635a7528ae494a8135defd.png

The walls get stiffer against bending while keeping lightweight. Let's take a example tube of D=19mm, rho=10370kg/m3, E=85GPa, and e=0.2mm with the mean fibre corrugated to 1mm peak-to-peak. It weighs 2.1kg/m2 but is as stiff as if it were 0.67mm thick. Its first oval mode resonates at 7.1kHz instead of 2.6kHz for 0.45mm smooth walls twice as heavy.

These walls can conduct heat oscillations over much of their thickness, in case this matters. A sandwich with a core of foam, balsa or honeycomb can't.

Corrugations increase some losses, both aerothermal and by heat conduction. This is expectedly a big drawback at a flute, but an advantage for instance at

  • The bell of clarinets, especially the bass, contralto and contrabass
  • The bell of saxophones
  • The entrance of the neck of saxophones
  • The bell of adaped oboes, especially the English horn, baritone and heckelphone

Marc Schaefer, aka Enthalpy

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Here's a table of metals ordered by reduction potential, aka standard electrode potential, aka standard reduction potential, from
 CRC Handbook of Chemistry and Physics, "Electrochemical Series"

I've picked metals not very toxic and with a reduction potential not very negative: Mn can be electrowon. Nb, Cr, Zn, Ta are included despite their protective oxide layer because Zn can be electrowon, but alloys may worsen that; brass can be brazed but stainless steel is cumbersome.

Only simple ions are listed. V+++ is missing. Polyatomic ions, with less direct reductions, would offer more potentials and enable metalloids.

ReductionPotentials.png.88a782f836bd2b42b52b353d5684e066.png

The cost per kg converts Usd, Gbp, Cny, Idr to metric units as of September 2018. I took troy pounds (20% difference). Prices are for multiton amounts of pure metal at stock exchanges except Ta in kg foil by a supplier; the cheaper metals depend more on the amount.

The vertical bars extend from Ni, Cu, Ag by +-0.7V because CuNi can be electroformed - no better reason, and electrochemistry is tricky. Even CuZn (span 1.1V) can be electroformed. The oxidation number promises flexibility, but are there interactions?

To the commonly electroformed Ni and NiCo, Mo may perhaps keep the corrosion resistance and increase the hardness and stiffness, Zn Cr Ta improve the corrosion resistance but hamper the solderability, Cr increases the stiffness and In Sn Pb Bi decrease it.

In electroformed Cu alloys, Mn Zn seem difficult, but there may be tricks like polyatomic ions. Cu-Mn is a known vibration damper. Little Ni Co, preferibly together, and Ag too, harden Cu while keeping excellent conductivity. Sn alone is known to decrease abnormally the stiffness for bells while Mo Ru might increase it. Cu-Sn and Cu-Ni are usual hard alloys.

Cu looks compatible with electroformed Ag alloys. Most flutes being just 92.5% Ag 7.5% Cu, could we make body parts at once, of sterling silver or other, with protruding tone holes, bent tubes and bells, for flutes, bass clarinets and so on? That would save work time and let strict woodwind manufacturers make metal bocals, boots and bells. Miyazawa's better Pcm alloy was rumoured to contain 65% Ag with Cu Au Pd; Au is doubtful according to the table but Cu Pd would be compatible, Ru Bi Rh Ir Pt too.

==========

The table's three rightmost columns hint to relative resonance frequencies. Sound velocity looks like a plane compression wave in a wide solid. The oval frequencies are figures-of-merit relative to pure silver: sqrt(E/rho3) for bending at identical mass, sqrt(E/rho) for bending at identical thickness, having in mind the resonances of Nov 13, 2017 and followings
http://www.scienceforums.net/topic/111316-woodwind-materials/?do=findComment&comment=1023070

Among precious metals for a flute, only Rh and Ru are stiffer than Ag at identical mass. Rh resists corrosion even at brazing temperature. I ignore their other properties, especially their vibration damping.

I've added a line with Dalbergia Melanoxylon, the Grenadilla preferred for woodwinds, and taken 1/10th of the lengthwise 20GPa for want of its transverse modulus. It wouldn't be as thin as metal walls. At identical mass, grenadilla's flexural resonant frequency is 2.2 to 3.5* higher than wind instrument metals, and usually it's even thicker.

Marc Schaefer, aka Enthalpy

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I proposed on Nov 13, 2017 that the wall material can influence the sound by an elliptic vibration around the tone holes
http://www.scienceforums.net/topic/111316-woodwind-materials/?do=findComment&comment=1023070
and the effect of the toneholes' nature is consistent with my explanation.

DrawnSolderedToneHoles.png.c696a61a279bf37bea042596585b71a8.png

As explained by Miyazawa and many more, the toneholes of a flute as of some saxophones can be drawn from the body of soldered on it
http://www.miyazawa.com/media-library/educational-articles/options/drawn-vs.-soldered-toneholes/
Drawing the toneholes from the body makes them even thinner, while soldered ones are thicker.

The toneholes are the very item that stiffen the instrument against elliptic vibrations there, and the effect of soldered toneholes is said to resemble a thicker body: stronger darker sound.

I won't be more positive than "consistent with my explanation", because:

  • I never compared by myself the two hole constructions. So many sales arguments aren't justified!
  • This feature is never an option within a flute series. It characterizes series that have more differences.
  • Soldered tone holes are typically undercut, so the transition from the bore has a bigger and better controlled radius. This knowingly matters.
  • The rim shape may differ. The flow gets easily nonlinear there, and angles would change the sound.

I suggested to electroform complete flute joints, the body with the tone holes at once. With denser current or more time, including insulating masks, electroforming can produce locally thicker metal, for instance at and near the tone holes.

Marc Schaefer, aka Enthalpy

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The flexural resonances of the body explain decently the material's influence on a woodwind.

The air column's oscillating pressure creates a force on the tone hole covers, but their pads are soft and don't transmit the force to the body. This holds above the covers' resonant frequency, which is well within the playing range for a flute. Then the radial force on the tube is unbalanced where the cover doesn't transmit its fraction.

The resulting lateral force lets the body vibrate. It has many resonant frequencies within the playing range of a flute, and if the metal resonates strongly like nickel silver does (as opposed to sterling silver), then its movements versus an immobile cover create a volume oscillating in phase quadrature with the pressure - a loss.

Notice that the own movements of the covers versus the tube create losses too, better known already, which isn't my point here.

This parasitic volume is smaller than the admittance of the air column, but it contributes much to the otherwise small losses of the instrument.

Quantitative explanations should come for a Boehm flute. I expect this process to matter for all woodwinds.

Marc Schaefer, aka Enthalpy

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Flexural resonances of a woodwind body, quantitatively. Here for a Boehm flute, of 0.45mm German silver (Cu-Zn-Ni alloy), with B footjoint.

==========

I model the body by a uniform cylinder. µ=0.31kg/m, 30% more than a naked tube, to include the stiff parts of the keys. EI=183N*m2. The cylinder has proper flexural modes at 158, 435, 854, 1411, 2108, 2944, 3919, 5034 Hz and more. This is within the fundamental and low harmonics range of the flute.

BodyBending.png.34c4fd91096d51685ebf21c97a158324.png

The heavy cork could be represented by extra tube length, or better, its lumped mass included in the model. The tone holes reduce the stiffness. The joint fittings are supposedly less stiff. So the evaluated frequencies aren't accurate, but the result stands: resonances in the playing range.

==========

The covers move by estimated 0.1mm when the musician varies the pressing force by 0.5N (from 50gf to 100gf) so the pads are 5kN/m stiff. The covers weigh estimated 3g, so at the Eb and Ab holes they resonate around 200Hz, and above that damped resonance they behave like a mass. The other covers are pressed down by fingers that add mass and the resonance is lower.

So for all the tube resonances within the playing range, the covers transmit to the tube little of the oscillating force exerted by the air column's pressure. The covers don't balance the force exerted directly on the tube. The tube receives a net lateral force.

As well, the pads are far less stiff than the tube. A side force at a second mode's antinode bends a beam 123+123mm long which is 1.2MN/m stiff. The pads can at most limit the tube's resonance.

==========

For instance the third bending mode around 854Hz has a half-wavelength of 93+93mm so it's 2.8MN/m stiff to a force at an antinode. The flute has two covers near both antinodes of the bending mode and the air column.

In front of two D=13mm holes, 1Pa pushes 0.27mN which would move the tube by 95pm without resonance. As the covers don't follow, the tube's movement adds pulsating 2.5*10-14m3. We can compare with 0.42m air column containing 120cm3 where the 1Pa induces 4.2*10-10m3 compression as a mean over the arches.

With the resonances, the effect is significant. Just Q=20 for the metal (damped by the pads, the hands and more) produces 5*10-14m3 instead, and at the resonance it's a loss rather than a capacitance. If the other losses at the air column leave it Q=200, the tube's vibration drops it to Q=160, a significant and perceptible difference.

==========

Silver, while less stiff than German silver, damps the vibrations far better. If tapping a headjoint with a light plastic part, it sounds "poc poc" instead of "ting ting". This reduces the tube's vibrations hence steals less power from the air column's resonance.

According to this model, a silver headjoint brings some damping to a resonant main joint. But to a silver main joint, the headjoint material matters little, as I observed (here on Nov 07, 2017)
http://www.scienceforums.net/topic/111316-woodwind-materials/?do=findComment&comment=1022242

Silver keyworks damp their own resonances, which must be excited by the tube's transverse movements - but by how much?

Dalbergia melanoxylon (grenadilla) offers E=20GPa along the fibres and rho=1310kg/m3, so the tube resonates at nearly the same frequencies as German silver. Its intrinsic losses (tan=0.6%) outperform German silver but probably not sterling silver. The usual thicknesses make the tube about as stiff as with metal. But thick wood improves the oval deformation I described here on Nov 13, 2017
http://www.scienceforums.net/topic/111316-woodwind-materials/?do=findComment&comment=1023070

Dalbergia retusa (cocobolo) brings only E=11GPa for rho=950kg/m3, so it has more resonances than grenadilla, and these are stronger, as tan=0.9% can't compensate the lack of stiffness.

Buxus sempervirens (boxwood) has only E=9GPa for rho=930kg/m3 but tan=1.5% is better. It made clarinets before exotic wood became available.

Unloaded plastic has bad E=2GPa for rho=1050kg/m3. Expect 3* as many flexural resonances as with grenadilla. Only damping helps, hence the choice of ABS or PP. PMMA cumulates bad damping, as already heard at an oboe.

Stiff and damping materials give reed instruments more blowing resistance and make them louder.

All is consistent with the usual claims about woodwind materials.

Cu-Mn alloys bring high damping, are cheaper than silver but unusual and they resist corrosion less. Worth a try.

Reinforced plastics can offer 18GPa for rho=1200kg/m3 with 30% of short graphite fibres. As good as wood, and better in the transverse direction. The difficulty is to damp the vibrations, which graphite fibres don't. Aramide fibres would but they're difficult to machine. Hence my hope with polyketones, or maybe ABS.

==========

I'm convinced that some luthiers know much more about theoretical acoustics than university science does. Anyway, I haven't seen the model I propose in academic books nor papers. This explanation has been sought for a century and a half.

Now that I know an explanation, I'll surely notice the effect far better.
Marc Schaefer, aka Enthalpy

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Oops. In my last message, paragraph " With the resonances ..."
please read 5*10−13m3, sorry.

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Data about materials' internal damping is scarce, especially for the frequencies and strains common in wind instruments.

In P2Q2=E'Ik24*psi2, Q may be 50 for a damping metal, P=500Pa for a flute hence P2=50Pa for the elliptic deformation near the tone holes as computed here
scienceforums on Nov 26, 2017
and k2=210rad/m for a D=19mm tube, so E'Ik2*psi2=P2Q2/k22=0.057N*m/m, and for a 0.45mm tube, the strain is 17ppm and the stress 1.7MPa (0.25ksi).

The strain is much smaller for the resonances that bend the tube. It's stronger for a saxophone and with materials that damp less like brass or German silver, and it's much weaker for thick wood walls.

Resonances at 100Hz to 5kHz matter more to music instruments.

==========

For wood, Mankind has the already cited PhD thesis by Iris Brémaud (in French)
https://hal.archives-ouvertes.fr/tel-00548934/document
with a table of stiffness, damping, density on p117 (Pdf p141). Measurements were done by resonating a 360mm*20mm*20mm beam, hence at a meaningful frequency. I wish data existed for bending across the fibres, which determines the elliptic deformation of woodwind tubes. Tan=0.57% for Dalbergia melanoxylon isn't much, but thick wood is stiffer than metal against elliptic deformation.

==========

The Dtic 486490 document compiles many sources, reproduces curves and data for varied materials, and is openly available (thank you!)
http://www.dtic.mil/dtic/tr/fulltext/u2/486490.pdf

Copper and its alloys, including cupronickel, brass and bronze but not German silver, are on p72-76 (Pdf p98-102). Damping is very small, 10-4 to few 10-3, and its dependence on temperature and stress suggest it's even smaller for an instrument's tiny stress. The shape memory alloy Cu Al12 Ni5 Mn2 Ti1 measured in Dtic A218801 damps strongly but seems difficult to use at music instruments.

Silver, pure and alloyed with Cd, In, Sn but not Cu was measured in
 "Internal Friction and Grain Boundary Viscosity of Silver and Binary Silver Solid Solutions"
 by  S. Pearson and  L. Rotherham
the already cited Dtic 486490 reproduces the curves on p102-103 (Pdf p128-129), where damping is very small at these very low frequencies. Obviously "sterling silver" differs to sound poc-poc at flutes. Whether the usual copper makes the magic, or something else?

The high-damping Mn-Cu alloys, especially the M2052 Mn Cu20 Ni5 Fe2, was measured against amplitude and frequency, there
https://www.jstage.jst.go.jp/article/matertrans/42/3/42_3_385/_pdf/-char/en
Fig.4 tells tan=3,7%-2,2% at 200Hz-5kHz and 20ppm. Excellent, but the alloy corrodes, and annealing can't restore all the damping after >5% cold deformation.

Many Co alloys like 20Fe, 23Ni, 28Ni or 35Ni show high damping on p69-72 (Pdf p95-98) of the already cited Dtic 486490, but this demands a strong strain of 10-4. Worth a try, especially at saxophones? Co-Ni is easily electroformed to intricate net shapes, annealing should achieve the shown properties. Mo should be easy to co-deposit, Fe too, see here
scienceforums on Sep 29, 2018 2:24 pm
a magnetic field <40kA/m (<500 Oersted) ruins the damping, and wide thin parts concentrate the 30A/m geomagnetic field. This isn't extremely critical, and maybe some alloy has a low permeability, or if a layer of Co-Ni is deposited on a core, it can be interrupted at short intervals, and a pattern like zigzag still give stiffness. Some thin layer, usually Ag, can protect against contact allergies.

Sharp grooves perpendicular to the strain, like from rough sanding, would concentrate the stress and increase the damping. Cheap to try at least.

==========

I tried to reproduce by software the ting and poc I heard long ago when tapping flute headjoints with a small plastic part. Here
TingPoc.zip

  • TingPoc_A_GermanSilver.wav plays an exponential decay of 100ms, 80ms, 60ms at 3100Hz. I feel 80ms reproduce the German silver sound, telling Q=800 and 1/Q=0.13%. This includes damping by sound radiation and by viscosity.
  • TingPoc_B_SterlingSilver.wav decays with 50ms, 20ms, 10ms, 5ms, 2ms at 2300Hz. With 20ms I still perceive a duration, so sterling silver must decay with 10ms at most - I didn't even hear a height, so it may have been much shorter. Viscosity and radiation are identical, so sterling silver itself brings Q<=70 and 1/Q>=1.4%.

The softer shock on silver didn't prevent ringing, I believe. The ratio of yield strength, 120MPa vs 500MPa, is too small, and the plastic clapper was soft.

It would be interesting to try with the Pcm alloy.

Marc Schaefer, aka Enthalpy

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The rare alto and tenor tárogatók have a curved metal bocal that fits in a mouthpiece with wider end bore like the saxophones do, instead of fitting outside a mouthpiece with narrower end like the clarinets do. As opposed to the soprano tárogató that uses clarinet (-like) mouthpiece and reed, they must even use bocals, mouthpieces and reeds from alto and tenor saxophones, leaving even a chamber in the mouthpiece. One tenor can be seen and heard there:
pn6X4vvbbz8 on youtube at 12min
Logically, the alto and tenor don't sound like the soprano tárogató, but very much like saxophones, hence are little useful.

Already Stowasser used saxophone-like alto and tenor bocals:
TarogatoFamily.gif.b84f7ebfcc586af1b8e66ddcbd36a034.gif

I suggest instead that the alto and tenor tárogatók receive bocals that fit on the mouthpieces of alto and bass clarinets, and use corresponding reeds, to achieve the distinctive sound.

==========

All low wooden clarinets and tárogatók, beginning with the altos, have their curved parts made of metal. Though, a wooden bell is claimed to give the bass clarinet a "more powerful and centred sound":
wMbK_zhcmOk on youtube at 2min16
so graphite composite may improve the bells and bocals of clarinets and tárogatók.

While injection needs a costly mould, filament winding companies would easily produce a bocal shape. A U-turn and a bell may need several parts. I suppose a low-melting alloy can make the mandrel, cast for each part and molten away. Paraffin loaded with talc makes great mandrels for glass web, but may be too weak for graphite winding.

Graphite fibres don't, so the matrix must dampen the vibrations. Epoxy doesn't. Whether ABS, PP or polyketone can impregnate the filament?

Marc Schaefer, aka Enthalpy

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This is how filament winding can make a bell, bocal or other part, at least in my imagination. Illustrated here with a bell of axial symmetry, for which turning is possible, but it applies to asymmetric shapes too.

WoundBell.png.c3b59eefbc1000e941a20b1dcf21abf5.png

The preimpregnated filament is wound on a mandrel, usually by CNC, then polymerised. Bells are concave along the axis but convex along the azimuth, so some winding angle puts the filament on a convex path, where the mechanical tension presses the filament on the mandrel, as usual too.

The filaments can't end at the flare's rim because they would slip on the mandrel, so a bigger part is wound that converges at its end. The excess portion is cut away: turned or ground or somehow.

Here with axial symmetry, the scrap part can be cut at it maximum diameter too and removed to reuse the mandrel. More complicated shapes, like bocals or bass clarinet bells, need to melt the mandrel away, which can be of low-melting alloy, maybe of talcum-loaded paraffin, and is cast for each bell.

The rim can get a protective or aesthetic part, and the fitting is typically turned, milled or ground.

Marc Schaefer, aka Enthalpy

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