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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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