[Mister Underhill]

In his Poetics, Aristotle offers these ideas (somewhat condensed, for your convenience) of what makes a tragedy:

A perfect tragedy should [...] imitate actions which excite pity and fear, this being the distinctive mark of tragic imitation. It follows plainly, in the first place, that the change of fortune presented must not be the spectacle of a virtuous man brought from prosperity to adversity: for this moves neither pity nor fear; it merely shocks us. Nor, again, that of a bad man passing from adversity to prosperity: for nothing can be more alien to the spirit of Tragedy; it possesses no single tragic quality; it neither satisfies the moral sense nor calls forth pity or fear. Nor, again, should the downfall of the utter villain be exhibited. A plot of this kind would, doubtless, satisfy the moral sense, but it would inspire neither pity nor fear; for pity is aroused by unmerited misfortune, fear by the misfortune of a man like ourselves. Such an event, therefore, will be neither pitiful nor terrible. There remains, then, the character between these two extremes- that of a man who is not eminently good and just, yet whose misfortune is brought about not by vice or depravity, but by some error or frailty.

[...]

Fear and pity may be aroused by spectacular means; but they may also result from the inner structure of the piece, which is the better way, and indicates a superior poet. For the plot ought to be so constructed that, even without the aid of the eye, he who hears the tale told will thrill with horror and melt to pity at what takes Place.

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Let us then determine what are the circumstances which strike us as terrible or pitiful. Actions capable of this effect must happen between persons who are either friends or enemies or indifferent to one another. If an enemy kills an enemy, there is nothing to excite pity either in the act or the intention - except so far as the suffering in itself is pitiful. So again with indifferent persons. But when the tragic incident occurs between those who are near or dear to one another- if, for example, a brother kills, or intends to kill, a brother, a son his father, a mother her son, a son his mother, or any other deed of the kind is done- these are the situations to be looked for by the poet.

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The action may be done consciously and with knowledge of the persons [...]. Or, again, the deed of horror may be done, but done in ignorance, and the tie of kinship or friendship be discovered afterwards. [...] Again, there is a third case - to be about to act with knowledge of the persons and then not to act. The fourth case is when someone is about to do an irreparable deed through ignorance, and makes the discovery before it is done. These are the only possible ways. For the deed must either be done or not done - and that wittingly or unwittingly. But of all these ways, to be about to act knowing the persons, and then not to act, is the worst. It is shocking without being tragic, for no disaster follows. It is, therefore, never, or very rarely, found in poetry. [...] The next and better way is that the deed should be perpetrated. Still better, that it should be perpetrated in ignorance, and the discovery made afterwards. There is then nothing to shock us, while the discovery produces a startling effect. The last case is the best…

Under this set of criteria, Túrin’s tale is probably the most classically tragic.