Which is the tragedy?

As we were prompted to think about the theme of immortality in some of Keats’s poems, I thought about the poem “Ode to a Nightingale”. I saw the theme of the immortality in the poem, but overall I saw the poem as a tragedy.
In this poem, Keats makes it very clear about his fondness for the Nightingale bird. He talks about the journeys that the Nightingale has been on, and what it has seen. On lines 13 and 14 he writes, “Tasting of Flora and the country green/Dance, and Provencal song, and sunburnt mirth!” Not only do these lines show what the Nightingale has seen, but also some of the attributes that Keats admired.
The tragedy in this poem is not that the Nightingale dies, because on line 61 Keats declares, “Thou wast not born for death, immortal bird!” The tragedy is that Keats (or mankind in general dies). The tragedy is not death itself. It’s that in dying and being mortal he can no longer hear the Nightingale sing. He can no longer just sit and watch the bird (or for that matter write any more odes to them.)
Another thing that struck me about this poem is that in lines 24-30 he implies that men just sit and waste away when there is beauty all around them to be seen and heard, and the Nightingale is just one example of what men are failing to observe and appreciate in their mortal lives.