Only one of four coupled-oscillator modes sounds a blown-closed reed

Evidence

We can choose the reed frequency to lie above the air column frequency or below it. In each case, there are two resultant modes. That makes four candidate modes for playing the instrument. We now show that only one of these four works for making blown closed instruments sound. — Eric J. Heller, Why You Hear What You Hear- An…, 1608

Categorization

• QUESTION: Which one of the four modes works, and why do the other three fail?