The musical instrument that should be considered for this competition is of (or incorporates) a turned piece that can be bashed, blown or plucked.  Below are some examples to stimulate your imagination.

Examples :

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 Hand-Held Slit Drum
The first consideration is choosing a 'sonorous' wood - most hard dense woods like Cherry are best although Paul has found an exception with Hornbeam, which despite being similarly easy to turn & shape, it can end up sounding very dead and dull.
Before the internal bore is drilled, it is best to drill the side holes & slit into a solid block rather than risking drilling after it had been bored and thus avoid splintering the resultant thin sidewall.
 Paul had prepared a cylinder from a square blank (of approximately 30cm long, 5cm square) turned between centres, had drawn a line down the side & had allowed for a chucking spigot plus length for an end-piece after hollowing. He had then marked 2 centre points on the line for 15mm drilled holes that would be equidistant from the proposed ends of the finished instrument.
 With the piece held/locked in place, Paul used an electric drill with a 15mm bit to drill down more than the intended thickness of the drum's wall. He used a small Angle Grinder (eg Proxxon) to create the 'slot'.  The spigot was then mounted in a chuck and a bore hollowed out using a Forstner Bit and Jacobs Chuck fitted into the Tail Stock. He chose a bit size about 15mm narrower than the cylinder diameter - the final thinning would be achieved at the end by turning away the outer surface to help improve a more mellow sound. Having the holes and slit drilled first also helped to self-clear the shavings during hollowing. Paul then mounted the piece that had been set aside to cover the exposed end and with a Parting tool turned a spigot to match before gluing both parts together.
 Once the glue had dried, the piece was mounted between centres in preparation for turning the wall thinner but leaving enough strength to avoid splitting. Paul used a Roughing Gouge with increased lathe speed while strictly keeping his hand movement in a straight line across the toolrest and avoiding excessive downward pressure in order to reduce the chance of the Gouge dipping into the side holes and leaving an uneven cut on either side of the Slit. When it comes to sanding any piece with holes/gaps, always use a block presented tangentially to the surface. After some touch-up fettling and sanding through sufficient grits, Paul used a Point Tool to decorate/highlight symmetrically around the ends. He then tidied both end faces with a Skew to a thin spigot before sawing off and chiselling to a smooth surface.  All that remained was to construct some sort of Mallet or Hammer to strike the Drum.

 Head Joint of a Recorder
Recorders are normally produced in 2 or 3 sections. The disadvantage of constructing it as a single section (eg as with a Tin-Whistle) is that an error in turning will require the entire instrument to be scrapped.  The Head Joint has the more complicated components (Mouth Piece, Fipple & Blade) and their construction is critical for a good sound.

 Some Recorder Sound Theory
A Fipple is the wooden plug forming a tapered windway which transforms the player's breath into a thin fast jet of air blown with steady precision onto the Blade.
The Blade splits the airflow to create sound from the resulting vortices oscillating alternatively above and below its bevelled edge (known as Vortex Shedding). This rapid periodic flipping of the air jet drives the air column inside the bore into vibration pulses that are matched to the resonant frequency of the air column inside the bore.
The longer that air column, the lower the pitch - thus the lowest note sounds with all the finger holes covered and the highest with all finger holes open.
The Timbre & Tone of the sound produced is determined by the sharpness of the Blade, the angle of its bevel and its distance from the Windway exit.
A Wind Instrument Musician aims to exploit 'Vortex Induced Vibrations' whereas an Architect of tall buildings aims to forestall them.

 Paul had a 5" length of 2x2 Boxwood blank in his wood store which is beautiful to turn but not so readily available to all. Although Box is commonly used for Recorders, Maple or other dense stable low-porous wood types are just as good. He had prepared it by turning to a cylinder, marked out the next 35-40mm for the mouthpiece and the end 25mm for the joiner to the Body section and lastly, bored a 15mm hole through the whole length and then a 20mm hole bored to about 20mm depth at the joiner end.  He had also prepared a purposed made Pin Chuck that had peg extensions that could friction drive 15mm and 20mm bores.

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 With the proposed Mouthpiece end fixed onto the 15mm peg of his Pin Chuck, the piece was mounted between centres so that all subsequent turning would remain concentric to the bore.

 He use Parting Tool & Roughing Gouge to reduce the area between his mouthpiece & joiner marks to a diameter he estimated would leave a 5mm wall around the 15mm prepared bored hole.
 As Paul planned to use a narrow chisel to create the Blade, he first drew 2 parallel pencil marks slightly larger than the chisel's width (10mm in his case) starting from the Mouthpiece end to delineate the Blade and its 'Window'. He drilled 2 small holes straight down into the bored centre, close to the Mouthpiece end and keeping within the marks - this removed the bulk of the Window and revealed exactly where the bore wall started.  He used his chisel to create sharp cut sides to the Window and a flat bevel down to the Blade. He even resorted to a scalpel to clean up any ragged thin edges as it was critical that there were no fuzzy/hairy corners or edges to spoil the clarity of sound.

 Paul had made a Tin Whistle out of American Plane but its grain at the Blade's edge was prone to leave ragged hairy edges which slightly distorted blown notes. He eventually resolved the problem by stabilising the affected areas with superglue to aid leaving a cleaner cut edge. This solution was fine for a Whistle but probably not for a Recorder.
 He finally turned some decorative beads and curved shapes making use of the 19mm collar guide on the Pin Chuck to create a 2mm wall at the end of the Mouthpiece.

 Wood for Fipples can be made from dowel but the light hardwood variety that most Builders Merchants stock should be avoided. To ensure a good fit for his own drilled bore, Paul preferred to turn one on his lathe.
 Paul had prepared an oversized 15mm diameter cylinder of Box, long enough to be spigot-gripped in his small o'Donnell jaws and extend approximately 40mm to reach through to the Window plus another 20mm to act as a rod & handle for ease of removing out of a tight fit.

 First, he used a Skew to produce a clean flat pass over the end, then reduced diameter until close-fitted the drilled bore without getting stuck.  Next, he selected a wide chisel to cut a lengthways sliver starting at the width of the Window (10mm in this case) to form a ramp slightly down towards the 40mm Mouthpiece length, from where he turned a rod & handle at the head stock end of the Fipple.  Once he had checked that the Fipple was the right fit, he parted off at the handle.
 
 While holding the handle with the Fipple end inside the Mouthpiece just short of the Window and with the Windway in line with the Blade, Paul started test blows and at the same time, progressively twisted and adjusted depth to determine the position that produced the clearest note.  Once found, he ensured it didn't move until a few drops of ultra thin superglue were directed through the window and allowed to wick before going hard aided by tilting the whole Mouthpiece downwards.

 The extension was sawn off once the glue had set.  He shaped the underside of the Mouthpiece using a Drum Sander of suitable diameter - ideally about 2 to 2½ inches. With his index finger over the window, he was able to hold the underside accurately while keeping his hand out of harm's way.

  Body Joint
This Section of the Recorder was simpler to turn although there are perils of using long drills for hollowing - select blanks with straight grain and take the first drill bit cut at reduced lathe speed.
 A 15mm bored tube of matching wood blank was mounted between the Pin Chuck used above and a Tail Centre.  A tenon was turned to match the Head Joint's socket and was guided to the correct diameter by the 20mm peg on the Pin Chuck.  Leaving allowance for decorative beads and curved shapes to match the Head Joint, the remaining thickness was reduced to the corresponding diameter.