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The future tense of third and fourth conjugation verbs is marked by -ē-, as in trahes and audies. The regular personal endings are added after this vowel. But in the first person singular the vowel is changed; it is traham and audiam instead of *trahem and *audiem.

Why is this? Words ending in -em are by no means forbidden in Latin, so this strikes me as very odd. What is the origin of this different vowel? Are similar changes observed elsewhere in Latin? Any help in making sense of this vowel change would be great.

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This is not exactly a sound change, but a substitution: this -am is originally that of the 1sg. subjunctive, which for some reason came to replace the expected -em of the 1sg. fut. There's actually some evidence that Old Latin had the expected ending -em; this is discussed in an article by Churchill 2000 (JSTOR link).

It's not totally obvious why this happened. The semantic change "subjunctive > future" is pretty common, and indeed the rest of the future forms in the third and fourth conjugations continue the PIE subjunctive. But in this case there was a further substitution by the new Latin subjunctive in -ā-. I don't know if there's a good theory for why this latter change was restricted to the 1sg. But compare the use of I might, which in colloquial American English can mean basically I will (e.g. I might take you up on your offer can be a polite way of saying I'm definitely going to take you up on your offer).

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