Savart violin

Almost as classic as stradivarius or stratocaster…The savart Violin is exposed in Brussel’s musical instrument museum (highly recommended).

This is one of the earliest attempt to understand the mechanics of violin and “re-engineer” the instrument with outstanding results at the time.

If you have 28 minutes to spare, check out the documentary about Dr Claudia Fritz study on stradivarius (link below) – most talented musicians don’t have millions to spend on a dream , it is time to value objectively contemporary instrument makers !


Encountering the Master

I was really fortunate this november to wander through Brussels and attend the very first concert of Stéphane Galland’s  “Mystery of Kem” on the release night of the album in Flagey. What a night ! all my family was attending and even the youngest got mesmerised by Stephane Galland mastery on drums, rising on his seat each time he felt “something was happening on the stage” …I have to say this was not drums I heard on that night, although Stephane was playing a fine vintage kit (and amazing cymbals), I heard true musical expression, with fierce, fury, emotion, openness, generosity and genuine spontaneity.


Gongs &Cymbals

I had the chance to attend a presentation by Cyril Touzé from ENSTA ParisTech, about non linear vibration of thin plates. Usually the term “Non linear” is a show stopper for most engineers, It just means that the mathematical description of a system can not or no longer be simplified using linear relations (things like : If I strike a structure with 2x more energy, I will make it vibrate 2x more, if I drive a structure with a given frequency content, I will obtain a result only in the driving frequency range…), therefore modelling the behaviour to predict sound output of a structure for example is more complex than in the “Linear world”.

For plates, as soon as the amplitude of vibration is in the order of magnitude of the thickness, non linear behaviour occurs.

For instance, even if you strike a gong with a soft mallet – injecting energy therefore “only” in low frequency, the resulting sound will be composed of much higher frequencies because the overall level of vibration will cause the gong to get in a “saturated/turbulent” state, and the more energy you will try to inject further, the higher the maximum frequency will be : energy flows from the blows of the mallet into the whole bandwidth of the structure, and “modal” behaviour is long gone.

Gong players sometimes “prime” their gongs to  raise the vibratory energy inside and therefore put the gong closer to the turbulent / saturated state and ensure the characteristic sound.

Experiment :

Mr Touzé has presented a very interesting experiment, where a 50cm gong was driven by an electrodynamic shaker exactly at one of the gong natural frequency. Then the level of injected force was slowly raised, as radiated sound and vibration fo the gong were recorded.

with very low efforts injected, the modal behavior was prevalent with vibration and sound carrying only the excitation frequency : Purely linear state.

Then as the force increased, some other modes showed up, and some “cycling” occurred between them : the structure was exchanging energy from one mode to another, and in this still “periodic” state, simple relations between the appearing modes frequencies and driving frequency were verified.

Then suddenly, as the shaker was pushing even more energy into the structure, all the tonal content disappeared in wideband energy and the whole spectrum filled up as the gong was entering its “turbulent” state radiating the shimmering full and rich characteristic sound.

gong bifurcation
in “Idiophones à plaques et coques. Deuxième partie, non-linéarité forte : cymbales, tam-tams et plaque tonnerre” by Cyril Touzé, Enseignant-chercheur, Unité de Mécanique (UME), ENSTA-ParisTech, Palaiseau ;  Olivier Thomas, Enseignant-chercheur, Laboratoire de Mécanique des Structures et Systèmes Couplés (LMSSC), CNAM, Paris

Sonagram of a Gong acceleration (frequency content vs time as level of force increases) : Three distincts states are observed : at low level of force (left side of the first dotted line) the response in only found in the driving frequency (556 Hz) and first harmonic.

Then a first bifurcation occurs and the gong enters in the quasi periodic state where it is still driven by the modal behavior : many partials are showing up, note that the sum of the frequencies of the two lower modes of higher amplitudes (around 250 and 300 Hz) are exactly equal to the driving frequency. The overall response (middle curve in blue) shows time fluctuation as modes are swapping energy between them.

Finally, second bifurcation for higher level of efforts and turbulent behavior prevails, with ultra rich frequency content, notably higher in frequency than the driving force.

What happens when you strike a structure ?

From a mallet or stick standpoint :

Depending on the “tool” selected to strike a structure, the frequency content or ability to produce high frequency will depend on the “softness” of the striking surface (assuming this one is way “softer” than the receiving cymbal or gong which is not always true) as shown in the table below.

The following table summarise the same phenomenon either seen from a time domain standpoint, or a geometrical standpoint, or a frequency content standpoint : The softer the mallet, the longer the duration of the shock and the lower the frequency content (works as inverse of shock duration).

In the space domain, the softer the mallet, the larger the contact area and the lower the highest wavelenght generated (the mallet or sticks blocks the struck surface and kills any generation of wavelength shorter than the contact area).

Shock duration.001

From a Struck structure standpoint : 

If we take for instance thin cymbals and plate and hit them with sufficient energy, those will be almost instantaneously driven into their non linear turbulent state with the characteristic crash sound. Even if a soft mallet is used with a sufficiently intense blow, the whole spectrum will be heard.

As the structure is saturated, if you continue injecting energy (such as playing a roll with increasing intensity) the energy will spread to a higher frequency.

With thicker cymbals (“un-crashable”) like some rides, bells, etc…the amplitude of vibration even with heavy hits will stay an order of magnitude under the plate thickness and the vibration thus the sound radiated will be tonally characterised with a distinctive pitch, and a quasi linear (modal) behaviour.


“…And you can have it in any colour you want as long as it’s your sound…”

Build your own sound with Repercussion patented Bessel vented snare.

  • Choose vent characteristics : we will print out spacers fitting exactly your needs to parameter the ported vent.
  • Choose top and bottom shell independently (Height, thickness, material)
  • Change the shell as easily as changing a head
  • All mechanical elements on the chassis (snare strainer and butt plate – not represented below)
  • Want to change your sound ? get some new spacers printed from us and/or change one or two shells ! Mix and match metals / woods/.. to tailor the sound colour to your exact needs –
  • Build it yourself : No drilling, No adjustment, as simple as a Swedish furniture.

Oh and of course, like all other drum makers you can have it in any colour or finishes – once you found your sound.

See samples in True sound tailored Drums

Soon issued : full drum kits !


Construction of the patented Bessel vented snare drums – heads and tension rods are not shown, they bolt into the fully threaded M12 stainless steel bolt, threaded on both sides, which holds the whole chassis together.


Shell depth , Venting & admittance

First results of numerical simulation indicates that on a dual membrane drum, the first mode of the membrane is actually more influenced by the shell depth than the tension itself. This is a direct consequence of the heavy coupling occurring in drums : the first membrane mode ((1,0) with one nodal circle being the edge of the membrane for both membranes, in phase) being volume conservative, the volume of air between the two membrane is mass-loading this mode.

The graph below illustrates how the first membrane mode shifts in frequency for standard shells (3,5 to 10″) and a purely simulated 60 inch shell.

The frequency shift follows well the square root of the depth, indicating a mass behaviour. The system is alike one mass between 2 springs representing the stiffness of the membranes.

shell depth

Then simulation of opening in the shell, corresponding to the standard venting (one single vent hole) and to the patented Repercussion radial venting system have been conducted.

The mechanical mobility – or admittance- has been computed : this quantity is the ratio of the velocity of the head for 1N applied (at its center). The greatest this quantity, the “easier” it is for the membrane to vibrate, and the more energy is likely to be transmitted to the instrument (and not reflected back into the stick).


One very significant phenomenon occurs as soon as an opening is made in the shell : a resonance “Helmhotz-like” with maximum velocities in the vent appears around 50Hz.

in practice, this phenomenon is very likely not to be heard nor felt, because of the poor radiation efficiency (small surface) of the vent and because of the very heavy damping that will be caused by air flow & turbulence.single vent maxima

Picture of the 1st “mode” maxima (the two heads are one phase opposition)

The second effect of venting is the slight raise (10%) from low frequency of the mobility : the air can now flow outside of the drum and compression added stiffness disappears.

The third major effect is, in the case of the patented Repercussion radial venting system only, the increase of the mobility at a lower frequency (the pitch drops down to the one of a 25″ shell – 4x the physical depth of the shell) and a 25% increase on the max mobility.

What does it mean for the player ?

  • A more evenly distributed sound around the shell (radial venting) with a very strong low end giving “in your chest” punch.
  • A way more present sound for the audience and musician around (the sound “flows” out of the drum very efficiently
  • A drum easier to play : more motion for the force injected : More sound, less force, less chances for injuries.

Numerical Simulation

A major step has been made in the understanding of drums acoustics thanks to the Laboratoire de Vibration et D’ Acoustique (Vibration & acoustics lab) of the National Applied Science (INSA) engineering school in Lyon.

Two students have been modelling a snare drum with the intent of :

  1. Understanding how the air loading (coupling) was influencing the  membrane behaviour in the case of 2 membranes instruments
  2. How the venting characteristics influenced the membrane vibrations
  3. Quantifying the mechanical mobility of a snare as a function of its venting system

Congratulations to INSA LVA for those progress !


True sound tailored Drums

The patent pending architecture of Repercussion “Bessel vented” drums allows for infinite combination of vent parameters, top shell and bottom shell.

We will engineer air gap, profiles, material, heights, thicknesses to sound tailor your drum…oh and yes, you can choose the colours too…

So far we have issued prototypes with thick or thin maple / brass / steel combination resulting in awesome sonic richness.


Proud to innovate !

Repercussion is devoted to innovation in the field of musical instruments, linking acoustics and structural dynamics developments with musical instrument crafting in order to propose innovative concepts to performers.

Today, a major step has been done as Repercussion filed a patent for the “Bessel vented drum system” after month of lab research and feedback from users.

Sound tailoring of drums is now a reality thanks to patented Repercussion technology.

More for your eyes and for your ears soon !





Building the HeloCaster

No drums building today – A great way to spend valuable time with my daughter : found a DIY Stratocaster for Heloise, my 13 years old birthday…leading to questions like : why are there 3 pickups ? and how do they work anyway ? why would they sound different ? Great times ahead !

Lots of good time and fun, even though the body painting process was tedious, the result is amazing ! Helocaster rocks !

History of acoustics

Bart Van Der Zee had me in his “drum history podcast” to talk about the history of drums and the history of acoustics.

Interestingly acoustics phenomenon have been observed for millennials but acoustics engineering is about 50 to 60 years old, drums was one of the first musical instrument but its physical understanding just starts to be explored.


“…And you can have it in any colour you want as long as it’s your sound…”

Build your own sound with Repercussion patented Bessel vented snare.

  • Choose vent characteristics : we will find spacers fitting exactly your needs to parameter the ported vent.
  • Choose top and bottom shell independently (Height, thickness, material)
  • Change the shell as easily as changing a head
  • All mechanical elements on the chassis (snare strainer and butt plate – not represented below)
  • Want to change your sound ? get some new spacers from us and/or change one or two shells ! Mix and match metals / woods/.. to tailor the sound colour to your exact needs –
  • Build it yourself : No drilling, No adjustment.

Oh and of course, like all other drum makers you can have it in any colour or finishes – once you found your sound.

See samples in True sound tailored Drums

Soon issued : full drum kits !

Construction of the patented Bessel vented snare drums

First modes on snare drums

This post will be about summarising the understanding so far about snare drums mechanical behaviour, build parameters and sound characteristics.


On all “classically vented” drums, the first mode is hard to spot because of its heavy damping – numerical simulation showed for a 14×6,5″ drum a first mode at 50Hz – in this case both membrane are in phase opposition, compressing the volume of air which results in important flow and therefore energy loss in the vent. This mode is not heard nor seen on acoustical measurement probably because of its very damping and very small radiation surface (even though the heads are moving, most of the velocity is in the vent)

This second mode corresponds to the lowest tone perceived on a drum, and explains why deeper drums sound lower in tone : a common misconception is that it is linked to lower “cavity mode” of a larger volume – rather, in this case and IF the drum is vented (suppressing all pressure rise within the shell), the volume of air is mass loading the drum (see Shell depth , Venting & admittance) and the depth of the shell ends up having more importance for this mode than the tension of the heads. The venting suppresses some of the air stiffness but not all of it : the larger the opened surface, the lower the mode.


This is an attempt to explain observed peaks on the acoustical measurements, disappearing as soon as the vent section was modified – this partial is more related to a “Helmhotz” like resonator as the position of the vent in the shell (altitude) and width showed some clear effect on this behaviour. However this did not show up in the numerical simulation – For sure, the larger opened area leads to lower velocity and the profile of the vent cleans up the airflow : probably less damping of this mode. For sure the larger area and spatial distribution causes  better radiation coefficient from the vent.

This is indeed observed on the acoustical measurement for repercussion snares only, and is unaffected by the snare effect.


On REPERCUSSION snares, the second mode is both lowered in frequency, and heard. In that case because of both the larger opened surface and the evenly distributed vent with respect to this membrane mode. see The snare was killing batter head sound ! for further explanations on snare effect : in essence the top head is now better decoupled from the snare head and able to vibrate longer. Soundwise this makes drums with increased presence and projection – remember we are talking about wavelength of about 2 meters, so the feeling for the audience around the drum is really different.

Also this eases lower mechanical impedance on the batter head saving your wrists (see Shell depth , Venting & admittance)



Intuitively when opening  a shell, one could think that the effect would be mostly on the high frequencies, as there would be less shell wall to block those. This is true but the major effect is first found on the lowest components of the sound as a consequence of modifying the coupling. There is a subtle balance between opening up and letting more high frequencies escaping, and enabling too much of the lowest partials to take over. Repercussion snares sounds louder and with more presence because of the enhanced low end, better sound diffusion, and effects of the port acting as a magnifying glass for very high frequencies components – It acts as a “loudness” filter on your stereo.