Research project on the development of new tools for musical expression at the University College Ghent

School of Arts

<Whisper>

an automated set of cavity resonators

Godfried-Willem RAES

2013

[Nederlandstalige versie]



<Whisper>

This robot was designed to be very silent. It's sound production is based on the cavity resonator, a somewhat strange device known in acoustics. In daily life people may have run into such sound generators as they are often used as a whistle on some water cookers. They find extensive applications in bird calls of different kinds and in quite a few toys (rubber ducks) and simple toy instruments. Here is a small display of bird calls from our collection, all based on the cavity resonator: All these are designed to be blown (or suck) with the mouth. From an acoustical point of view cavity resonators at first sight appear to be Helmholtz resonators: there is a cavity of air and two orifices on opposing sides of the cavity. However, the math around them developed by Herman Helmholtz around 1860 and later refined by Walter Rayleigh does not seem to apply here. Properly speaking a Helmholtz resonator ought to have a single well defined resonant frequency lacking overtones, whereas the cavity resonators under consideration here operate over a range of more than an octave and produce a manifold of non-harmonic sounds and noises, including multiphonics. The main reason for this behavior seems to be that our resonators are driven by turbulent air of very low pressure and hence the dominant sounds produced are edge tones around the orifices. It is known from organ pipes that the frequencies of these edge tones are highly dependent on applied wind pressure.

We started off by constructing a wide variety of cavity resonators. We even tried to use obsolete CD's... The orifice formed by the CD center hole is way too large for applications using very low wind pressure and flow though. It works fine with a large radial compressor. Small flat cans gave good results and had a quite wide pitch range under varying pressure conditions:The addition of a conical of even cylindrical secondary resonator increased the sound level quite a bit, although it greatly influences (and limits) the pitches obtainable. After a lot of experimentation we decided to construct these conical resonators with the large end cut under an angle of 45 degrees, this to make the resonant frequency less pronounced. These cones were made from a tin-lead alloy as used for organ pipes. The cavity resonators were glued inside the tapered end of the cones. We made stainless steel flanges to mount the resonators and their cones on the windchest.

Here is a table with sizing - from low to high- for all nine cavity resonators and the cones used in this design:

number orifice diameter inner diameter inner height material thickness calculated resonance h a b d1 d2 remarks
1 10 mm 45 mm 14 mm 0.4 mm 1103 Hz 280 mm 70 mm 210 mm 53 mm 70 mm Ilford film can
2 8.5 mm 45 mm 12 mm 0.4 mm 1095 Hz 265 mm 65 mm 200 mm 53 mm 68 mm Ilford film can
3 7 mm 38 mm 14 mm 0.35 mm 1088 Hz 230 mm 47 mm 183 mm 40 mm 63 mm perfume box
4 5 mm 33 mm 10 mm 0.4 mm 1280 Hz 180 mm 42 mm 140 mm 34 mm 47 mm Adams cork grease can
5 6.5 mm 23 mm 10 mm 1.2 mm 1945 Hz 145 mm 39 mm 106 mm 28 mm 49.5 mm brass ring underneath
6 6.5 mm 22 mm 8.4 mm 1.2 mm 2219 Hz 116 mm 38 mm 78 mm 29 mm 47 mm  
7 6.5 mm 19 mm 5.5 mm 1.2 mm 3176 Hz 114 mm 28 mm 86 mm 27.5 mm 38 mm  
8 6.5 mm 16 mm 5 mm 1.2 mm 3954 Hz 110 mm 40 mm 70 mm 27.5 mm 34 mm  
9 8 mm 70 mm 18 mm 0.5 mm 554 Hz 243 mm 77 mm 166 mm 25 mm 94 mm extra resonator mounted underneath

The calculated resonance frequency in this table was calculated using the textbook formula f = (v/ 2) SQR( r/V.L), wherein v= velocity of sound, r= surface of the orifice, V=volume of the cavity, L= lenght of the neck, or thickness of the material in this case with the endcorrection added. However, the observed frequencies (without the cones mounted) from these resonators bare very little relationship to these calculated results.

Note that when applying the formula, the surfaces of both holes have to be added up in order to calculate the equivalent size for a single orifice do. If we take dg as the measured diameter of a single orifice in the resonator, then do = 2 dg / SQR(2) = dg SQR(2), or numerically: do = 1.4142 dg. The practical calculation then becomes: Sofar we have no sound explanation for the observed difference between calculated and measured resonances. We might assume turbulencies play a major role here, and maybe the velocity of sound, taken as a constant in the above calculation cannot be considered constant. As measurements on the propagation speed of sound in cavities and coupled cavities seemed to be in order, we performed some initial measurements using a pair of Bruel & Kjaer measurement microphones (type 4955) and a Tektronix TDS2024 oscilloscope set up for delay measurement between two input channels. We used an electronic metronome as pulse source, placed as close as possible behind one of the microphones.

acoustical traject (in m) medium (temperature: 22C) delay velocity of sound (precision 2%)
0.76 free air 2.17 ms 350 m/s
0.76

ribbed plastic cavity tube

d1= 27mm, d2 = 34 mm

2.32 ms 327 m/s
1.00 free air 2.85 ms 350 m/s
1.00

ribbed plastic cavity tube

d1 = 16mm, d2 = 20mm

3.03 ms 330 m/s

The differences are substantial, but apparently not large enough to thoroughly explain our mystery... However, clear multiple echo's can be observed when looking at the signals received after passing through the ribbed tubes. For the wider tube, the echo period was measured as 4.9ms, corresponding to a pitch of 204Hz and for the smaller one 7.4ms, or 135Hz. This indicates that the cavities indeed work to make the tube acoustically ca. 1/4th longer than its physical length.

 

In our design for a robot based on cavity resonators, we started from a box full of small Sunon fans used for cooling electronic components. We had assembled quite a lot of them over the years as in our designs for robotic instruments we systematically removed fans from circuits, for they make a lot of extraneous noise. These little fans work on a 12 V DC voltage but they easily can withstand 16 V as we found out. They typically produce turbulent air at very low pressure.It should be noted that this instrument works on suction wind! We have no clue as to what explains the fact that suction wind works better, given the inherent symmetry of the resonators. (In 2015 we changed all fans for more sturdy types, as found them all burned one day...)

We have been using this type of acoustic sound source in quite a few of our earlier instruments: In the 'Pneumaphone' project, Gucumatz makes use of twelve of them, Eurus and Tembo use a large single resonator. In our <Thunderwood> robot, the stormwind generator also works on this principle, though in that case on a fairly high turbulent pressure counting for the pretty high sound level obtained there.

From an electronic point of view, driving 8 small DC motors is a problem we already encountered and solved at the time when designing and building our <Sire> robot. Hence we could use the same microcontroller board in this project. The circuit using a single 18F2525 PIC microcontroller as well as four dual H-driver chips can be found on the webpage describing the <Sire> project. However, as things turned out, the firmware for that board, using only a single PIC processor, caused audible PWM based artifacts from the fan motors. In the <Sire> project, this came unnoticed as the sirens are pretty loud themselves. Thus we decided to design a new PCB from scratch. As our favorite PIC controllers have only two hardware PWM outputs on board, we used four microprocessors to steer eight fan motors. Thus is became possible to use above-audio frequencies for the PWM and getting rid of audible artifacts. The circuit -repeated four times on the PC board- came out very simple:
A second circuit board takes care of the PWM for the extra resonator, the rubbed string assembly and the lights.

The rubbed string component is based on the same sound generation principles underlying Luigi Russolo's Intonarumori. He used a crank driving a wheel over which a piece of gut string (the tension could be controlled with a hand lever) was led. The other side of the string being attached to a membrane connected to an amplifying horn, a linear cone in most of his instruments. In our design we used a metal membrane coupled to a flared cone taken from an old alarm buzzer. The crank with wheel in the Russolo design, was replaced by a small high torque Johnson motor powered by a variable DC voltage

In <Whisper> we rub the string with a small dented wheel mounted directly on the axle of the motor. Thus excitation is mostly longitudinal and passed to the center of the amplifying membrane. Acoustically one could analyse this as a series of approximate Dirac-pulses upon with the system reacts with its impulse response. The repetition rate of the pulses - a function of the rotation speed of the motor - set aside, there is no real pitch in the sound produced. It is a highly inharmonic noise. The tension on the string changes the spectrum greatly, but does not lead to 'tuning' of any kind. Friction increases of course with increasing force, eventualy leading to stalling of the motor and obvious excessive wear of the string.

The three small shakers on this robot were made from empty 35mm film cans filled with iron or lead granules. The shaking is activated by A.Laukhuff pallet lifting solenoids.

On the front of the robot, we mounted two cast bronze sleigh bells activated by a somewhat larger Laukhuff solenoid. This was designed such that on reception of a note on command, the armature holding the bells will resonate mechanically. The sound of these bells is more or less defined and corresponds to midi note 104 (G#).



Midi implementation and mapping:

<Whisper> uses midi channel 11 (counting 0-15)

Remark: The mapping of the velocity byte on the period of the note/event repeats is as follows

Velo byte period frequency MM tempo
1 1500 ms 0.66 Hz 40
126 62 ms 16 HZ 960
The mapping of the pressure value accompanying the key pressure command is the same.


Technical specifications:



Design and construction: dr.Godfried-Willem Raes (2013)

Collaborators on the construction of this robot:


Music composed for <Whisper>:

 

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Nederlands:

<Whisper>

De idee om deze robot te gaan bouwen kwam voort uit de bekommernis om een nuttige bestemming te vinden voor een vrij grote voorraad kleine ventilatoren die we hadden verzameld bij de bouw van vele eerdere robots. Om achtergrondlawaai zoveel mogelijk te onderdrukken hadden we immers steeds de ingebouwde ventilatoren in schakelende voeding, motor-kontrollers enzomeer verwijderd. Vroegere experimenten waarbij we poogden die vertilatoren te gebruiken voor het aansturen van orgelpijpen waren mislukt omdat de geleverde winddruk gewoonweg veel te gering was om resonantie op te bouwen in de pijpen. Edge-tonen konden wel worden voortgebracht. Deze observatie bracht ons op het idee klankbronnen te gebruiken die in hoofdzaak rond dergelijke edge-tonen funktioneren, met name holte-resonators zoals we die weervinden in vele vogel lokroepen gebruikt voor de jacht. We hadden deze klankbronnen al eerder gebruikt: met name in het 'Pneumafoon' projekt evenals in vroegere robots zoals <Thunderwood>, waar ze echter werden aangewend onder een vrij grote winddruk. Voor <Whisper> wilden we het subtiele van de edge-tonen maximaal uitbuiten. Het was van bij het begin van het opzet duidelijk dat dit een uiterst stille robot zou gaan worden, wat niet wegneemt dat de muzikale mogelijkheden toch vrij uitgebreid zijn. Alle negen holte-resonatoren zijn immers individueel over een groot bereik aanstuurbaar gemaakt en de robot werd bovendien nog voorzien van enkele extra klankbronnen..

Inspiratie puttend uit het werk van Luigi Russolo, bouwden we een gespannen snaar aan een kant bevestigd op een stalen membraan gekoppeld aan een korte konische hoorn. De snaar wordt longitudinaal aangewreven middels een messing tandwiel aangedreven door een DC motor.

Verder werd deze robot nog voorzien van drie kleine maracas gemaakt met twee 35mm fotoblikjes en een pillendoosje, gevuld met wat lood of ijzergranulaat. Deze maracas worden bestuurd door kleine Laukhuff kleplichtermagneten. Helemaal vooraan op de automaat monteerden we twee op een veerkrachtig beugeltje bevestigde bronzen rolbellen, bestuurd door een wat grotere Laukhuff elektromagneet.

Als extra werden nog vier bestuurbare gloeidraad lampen toegevoegd.

De besturingselektronika maakt gebruik van vijf PIC mikrokontrollers van Microchip, type 18F2525.

Omdat ons vaak wordt gevraagd hoeveel werk en tijd kruipt in, en nodig is voor, het bouwen en ontwikkelen van een muzikale robot, hebben we ook voor <Whisper> een beknopt bouwdagboek bijgehouden. Omdat we de bouw tot in de laatste details graag illustreren, kan het ook voor anderen die ons op dit pad willen volgen en/of verbeteren, van praktisch nut zijn. Dit bouwdagboek is uitsluitend in het engels beschikbaar, gelet op de grote internationale belangstelling voor onze projekten inzake muzikale robotika.


Construction Diary:

To do:


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Last update: 2017-08-05

by Godfried-Willem Raes

Further reading on this topic:

Bibliographical references:


MECHEL, F.P., "Formulas of Acoustics"

RAYLEIGH, John William Strutt "The Theory of Sound" (2 vols)

 


Technical data sheet, design calculations and maintenance instructions:

Technische gegevens, ontwerpberekeningen en instrukties voor onderhoud en demontage: