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Enthalpy

Intentional Losses in Wind Instruments

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Dear musicians, scientists and everyone,

here are some thoughts about the losses introduced on purpose in wind instruments.

==========

To begin with, the chambers that the oboe has at its tone holes. I claim they serve to attenuate the high harmonics that are especially unpleasant on a double reed. I haven't seen up to now that thesis in books and research papers (which I haven't read all) but I suppose it is well known from oboe manufacturers.

Chamber.png.c6477fa391ebb9693a9203d2894fffc7.png

The oboe has quite a narrow bore, some 2mm at the top, and its tone holes are even narrower to soften the sound, as opposed to a flute or saxophone. Here I take 1mm wide holes where the bore has 4mm; having no oboe at hand, I can be badly off. A finger or cover could easily tap such a hole, but oboes have chambers where the tone hole is wider. I take 3mm width for the chamber, and 4mm+4mm height - unsafe guess.

The closed tone hole builds a lossy Helmholtz resonator.

  • The D=1mm L=4mm bore makes an inductor of 6.2kH and, at 4.5kHz, 3.0Mohm due to friction losses.
  • The D=3mm L=4mm chamber makes a capacitor of 200fF and, at 4.5kHz, 15pS due to thermal losses. The finger or pad bring more losses, unaccounted here.
  • The resonance is at 4.5kHz, nice to soften the sound. There, the Helmholtz shows 3.5MOhm to the bore.
  • The wave impedance of the D=4mm bore is 34Mohm, so the lossy Helmholtz absorbs the unpleasant frequency.
  • An oboe has several chambers that can cover a frequency range. A half-tone away from the resonance, the Helmholtz still shows 3.5MOhm +-j21MOhm to the bore, or 122MOhm losses in parallel.
  • If the chambers are tuned one tone away from the other, they add the losses at mid-frequency, or 61Mohm, as compared with 34Mohm wave impedance. The set of chambers absorbs a continuous range that can span almost 2 octaves.

That is, the set of chambers is perfect in this function. It's one of the missing features in the oboes with wide tone holes that Sax, Triebert and Gautrot tried to build.

I suppose that the chambers serve also to tune the oboe. The inductance of the narrow holes lowers the pitch, but widening a D=1mm would be inaccurate, while shortening it by deepening the chamber is easy. A chamber as deep as the narrow part makes the lowest Helmholtz resonance, hence little sensitive to the chamber depth that adjusts the note's pitch.

Marc Schaefer, aka Enthalpy

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A woodwind can need stronger losses at some notes or high overtones.

Throat notes are an example, where the short air column and its small losses let a reed vibrate too strongly, deforming the sound like a saturated amplifier does. The oboe, clarinet, tárogató have smaller tone holes at the throat to increase the losses there and also to filter out the high harmonics. The saxophone keeps wider tone holes and its timbre changes stepwise at the octave jump. The bassoon, whose tone holes cover two octaves, has very long and narrow tone holes at the throat.

Cross-fingerings to play high modes can also harden the sound. On a double reed, small tone holes soften the sound at low modes, but multiple open holes for high modes that keep all harmonics tuned don't remove the strident highest ones, and their losses can be too small for the reed. The bassoon uses detuned cross-fingerings to soften the sound.

Finally, woodwinds should dampen the strident partials around 4kHz
scienceforums and two previous messages
I propose now to split some side holes in two or more.

SplitHole.png.fab4d9219fa18a07861be8e5011f1ecb.png

Several narrower holes of same length and total section increase the friction at the bigger surface.

Split holes can open the air column at several slightly different locations. This damps more strongly higher frequencies where the air circulates among the holes and acts well before the sum or difference of the lengths is lambda/2.

Split holes can combine with the previously explained chambers. A shared chamber would act on many notes in a complicated way.

==========

Split holes apply to main tone holes. Maybe Johann Heckel did it at right thumb F-emitting hole for his bassoon, but I have none to observe. The higher hole would usefully be narrower or longer.

If an instrument has special holes for cross fingerings mainly, as many systems I describe do, split holes apply to them as well.

Split holes might apply to register holes too. They could sit side-by-side, some slightly higher or lower optionally. Sitting at the same height, they spoil as efficiently the unwanted modes with a smaller total section that detunes less the extreme notes.

Numbers might follow or not. They are only weak guidelines anyway, and experiments decide at the end.

Marc Schaefer, aka Enthalpy

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Still no oboe at hand, but Nederveen reports dimensions of two oboes (without chambers) on page 105 (pdf 113/118) of his PhD thesis
Acoustical aspects of woodwind instruments
so here's an update to the chambers of Jan 28, 2018.

The tone holes are wider than I had imagined. When present, their chambers can usefully suppress the highest frequencies, say above 6kHz with banal dimensions.

Suppressing down to 5kHz, or 4.5kHz, perhaps 4kHz, would better be done by additional Helmholtz resonators independent of the tone holes. Narrow inductors keep reasonable capacitor volumes. The highest suppressed frequencies can use quarter wave resonators if desired. The added resonators act also when the tone holes are open. There can be many resonators per octave of suppressed band. They can sit at the respective pressure antinodes.

The resonators add lumped volumes to the air column, just like tone holes do. The known parry makes the bore a bit narrower and shorter in this region.

The musician must access the narrow holes to dry and clean them.

This applies to the oboe family, and easily to the bassoon family. Saxophones and tárogatók and candidates too, possibly with a special bocal or mouthpiece.

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In the TutChamb archive here, the compiled cpp makes an exe which, fed with data from Make.txt, produces the renamed TutChamb.wav. From the artificial oboe's low B, "chambers" attenuate all components above a corner frequency, chosen here to attenuate two harmonics more per approximately 500Hz step. The programmed physical model isn't correct, but it attenuates.

TutChamb_A.7z

From the used initial spectrum, 20dB attenuation are useful but 40dB make no difference. In the 7 sounds, attenuation begins nowhere, then at 6kHz, 5kHz, 4.5kHz, 4kHz, 3.5kHz and 3kHz. 4.5kHz to 4kHz fits my taste. This is independent of the note height.

Marc Schaefer, aka Enthalpy

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Most woodwinds have tone holes. Very wide on the Boehm flute and the saxophone, less so on the clarinet, very narrow at the throat of an oboe or basoon. tone holes are inductive, so the wave doesn't reflect fully at the first open tone hole, especially high harmonics or notes, and more so at narrow long holes. This dampens and detunes the high harmonics, a useful feature for a mellow sound. tone holes are also lossy, more so if narrow, and this helps match the reed where the tube is shorter, hence the narrower tone holes at the throat of the oboe, clarinet, bassoon, tárogató (but the saxophone does it too little and its octave jump is heterogenous). I should come back some day with more quantitative reasons.

At their end, woodwinds should replicate the response of the tone holes set. Most have a flare there: it reduces the reflection of the highest harmonics by matching the impedance to free air, it detunes their resonance too, but a flare doesn't match the losses of the tone holes set, it even reduces the losses. The reed is too little damped there, it oscillates too strongly, and the sound gets readily harder, like when a guitar amplifier saturates.

At the tárogató, Stowasser added many small side holes, always open, near the end. Maybe they existed before, since many oboes and a few clarinets have one open side hole near the bell, but I'll call them "Stowasser's holes". They imitate a tone holes set by spreading the reflection over the distance and by creating losses, especially at half-wavelengths not much bigger than the distances between the holes and to the end.

At identical inductance, several narrow holes bring more losses than a wide one. Stowasser did that better, clarinets and oboes failed to copy it in a century, but you can see them in my instrument silhouettes. The heckelphone has a similar end plate.

Stowasser put holes on two ranks. Better for the wood, but it also spreads the reflection more. Here the Fourier transformation of the distribution of the reflection tells the effect on the spectrum. If expressing the distribution as a convolution of positions and amplitudes, the spectrum multiplies the transformations of the individual distributions. With two hole locations plus the end, you get the product of two frequency responses and potentially more filtering.

Here too, I should come back with more quantitative explanations, some day.

What can improve over Stowasser: more efficient filtering results from equal reflection coefficients, between the holes and the end, and also at every elementary distribution of reflections. This needs bigger holes near the end and smaller ones farther, as can be seen in my instrument silhouettes.

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The bassoon's bell has no flare: too wide and long. The French system has a narrower section in the bore, the German system has at least a wider section. Quite insufficient at my old Buffet-Crampon: the two lowest notes sound harder and need much embouchure adaptation.

At its lowest notes, the bassoon should gain much from Stowasser's holes, the contrabassoon too. Same for low clarinets and for saxophones.

StowasserHolesBassoon.png.069e1b153131c544dcfc926156b1b912.png

This would need a slightly longer bell, but the bore can have narrower sections to save length.

Marc Schaefer, aka Enthalpy

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Thanks Enthalpy.  You show very clearly, the scientific principles which ought to influence the design of musical instruments, so that they work most effectively.

Isn't it a pity that traditional instruments haven't been designed along these scientific lines.  Rather, the instruments seem to have evolved in a kind of haphazard way.

For example, we  have, nowadays, all kinds of "wind" instruments, such as the trumpet , bugle, flute, clarinet and recorder.  And stringed instruments like the banjo, violin, cello, and double bass.  Do we need all these different instruments?  Couldn't they be scientifically reduced to a single all -purpose instrument .

Just as past  key-board instruments like the clavichord and harpsichord, have been perfected into the modern piano?

 

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59 minutes ago, Charles 3781 said:

 

Isn't it a pity that traditional instruments haven't been designed along these scientific lines.  Rather, the instruments seem to have evolved in a kind of haphazard way.

Many instruments pre-date modern science, so really, trial and error is the only way for it to have happened 

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1 hour ago, Charles 3781 said:

Just as past  key-board instruments like the clavichord and harpsichord, have been perfected into the modern piano?

You know that people still play, and compose music for, harpsichords and clavichords.

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