Those of you familiar with Spongebob no doubt are familiar with the continuing trope of Squidward being a terrible clarinet player.
But what instrument does he actually play?
The most common image of Squidwards clarinet shows a black, keyless instrument with a heavily conical bore construction. Each tone hole appears to be metal, and the instrument has a two rings - one near the bell and one near the barrel.
This is a bit odd. The clarinet, keyless or not, does not have such a harshly conical bore. It cannot be a soprano saxophone due not only to lack of keys, but also to the color. It is obvious a black colored wood, or plastic, and thus we can rule out a saxophone.
What about a keyless shawm? Convincing at first, but the shawm obviously has a double-reed instead of a mouthpiece. Most representations of Squidward's clarinet show what appears to be a mouthpiece. For that reason we can rule out a shawm.
The only instrument left that could possibly cover all of these bases is a for of keyless taragato with metal tone hole inserts. Metal tone hole inserts are not unknown, as some Simple System clarinets have (for some reason) metal tone hole inserts flush with the body.
I propose the Squidward's "clarinet" is, in fact, a very early taragato.
By the 19th century, taragatos had keys, so this places the instrument between the 17th and mid-19th centuries.
The material is likely ebony with either metal or ivory rings near the barrel and bell. I would lean towards ivory due to the age of the instrument.
To explain the tone hole inserts, I believe that the since Bikini Bottom is underwater, wooden tone holes would be sensitive to water temperature changes, and would expand and contract too much for it to work well. By an aftermarket addition of metal tone hole inserts, the tone holes can be stabilized in the saltwater environment.
Although Squidward is ridiculed for his poor playing skills, it's not his fault. Remember that he is playing on a possibly 300-400 year old wooden instrument under the sea. He's just doing the best he can with an ancient family heirloom.