A clarinet with a fipple is a recorder. There is some acoustical physics at work here. There is a fundamental difference between a flute (end blown, side blown or fipple) and a reed instrument. The flute is considered open at both ends. It has a velocity antinode at both ends (where the air movement varies and the pressure stays constant). A sax, oboe, or clarinet is open only at one end (the bottom). At the top it has a pressure antinode (where the air movement remains constant and the pressure varies). These do different things. A tube closed at one end has only two musically useful shapes (where harmonics are actually in tune with the fundamental--being some sort of integer multiple of that frequency). Those shapes are a cylinder and a cone. A cylinder basically only has odd harmonics in the sound, and the wave shape is square. That is why the clarinet overblows the 12th, it skips the first harmonic, the octave. A square wave sounds rather hollow.
Panpipes are another example of a tube closed at one end, which overblows the 12th, the difference to clarinet being that you blow in the open end, not the closed end. You'll notice that the sound of panpipes also sounds somehow hollow.
The other shape is a cone. This shape creates a sawtooth type wave, with all harmonics present. There is your sax and your oboe.
A tube open at both ends has only one musically useful shape, a cylinder. And in this case the cylinder also produces a sawtooth-type wave, with all harmonics present. So basically, a recorder is a clarinet with a fipple. A fipple on a cone would produce a very weak sound, and would play no recognizable overtones.
Wait a minute, you say--a recorder is an inverse cone, not a cylinder. Yes, that's true, but an inverse cone only makes a small difference, aligning the overtones to compensate for some physical facts of life at the fipple end. The old flute was also an inverse cone. It's really only a cylinder for practical purposes.
So that's the very basic story. By the way, there is a double reed instrument which is cylindrical like the clarinet. It comes from Korea and is called the pir'i. It sounds almost exactly like taking a drinking straw and flattening one end and cutting the edges off to form a double reed.